Manual Cedrus5

Manual Starting from program version 1.19 Copyright Cubus AG, Zürich www.cubus.ch

Table of Contents

Part ABase Module . . . . . . . . . . . . . . . . . . . . . . . . A−1 A 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−1

A 1.1 Changes since CEDRUS4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−1

A 2 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−3

A 2.1 Element Model and Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−3

A 2.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.1 Geometry of the Plan Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.2 Slab Thickness and Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isotropic Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drilling%Soft Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthotropic Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Downstanding Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.3 Area%Supported Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.4 Columns / Point Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Point Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Area Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.5 Walls / Line Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.6 Lines of Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.7 Hinges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.8 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.2.9 The FE Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−4 A−4 A−5 A−5 A−5 A−5 A−6 A−7 A−7 A−7 A−7 A−8 A−9 A−10 A−10 A−11

A 2.3 Actions and Limit State Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.3.1 Basic Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.3.2 Overview of the Limit State Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.3.3 Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Definition of the term ’Action’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . How actions are formed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Dialog with the List of Actions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Properties of an Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Action Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Automatically−generated Action Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.3.4 Limit Values of nonlinearly−determined Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.3.5 Limit State Specifications with Action Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.3.6 Automatic Generation of Action Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−12 A−12 A−12 A−13 A−13 A−13 A−14 A−14 A−14 A−16 A−16 A−17 A−17

A 2.4 Load Transfer from Floor to Floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Realization in CEDRUS%5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.4.2 Load Export . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Automatically generated Export Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manually created Export Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calculating the Export Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.4.3 Load Import . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.4.4 Checklist for the Load Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−20 A−20 A−20 A−20 A−21 A−21 A−22 A−22 A−24 A−25

A 2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.5.1 Raw Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.5.2 The Structuring of the Output of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The quantities for load cases and load case combinations . . . . . . . . . . . . . . . . . . . . . . Quantities for limit state specifications (envelope values) . . . . . . . . . . . . . . . . . . . . . .

A−26 A−26 A−26 A−26 A−27

CEDRUS–5

Table of Contents

1

Table of Contents

Required reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Forms of Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−28 A−29

A 2.6 Punching Shear Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.6.1 The Punching Shear Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Strengthened slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Required bending resistances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notation for the tabular summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SIA 162 − Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SIA262 (Swisscodes) − Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EC2 − Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E%DIN 1045%1 − Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DIN 1045 − Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . OeNorm B4700 − Specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.6.2 The Punching Shear Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 2.6.3 The Punching Shear Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−31 A−31 A−32 A−32 A−33 A−34 A−35 A−36 A−36 A−37 A−37 A−38 A−38

A 3 Working with CEDRUS5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−40

A 3.1 Presentation Conventions for the Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−40

A 3.2 Starting the Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−41

A 3.3 Opening a Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−41

A 3.4 The Control Tab Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 3.4.1 The Tab Sheet /Structure/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plan Outline, Openings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . On the Input of Geometrical Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Undo / Redo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Selection of Objects and the Right Mouse Button . . . . . . . . . . . . . . . . . . . . . . . . . Printed Documentation of the Structure Input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The CubusViewer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 3.4.2 The Tab Sheet /Loads/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Dialog ’Actions’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Dialog ’Load Import’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 3.4.3 The Tab Sheet /FE Mesh/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 3.4.4 The Tab Sheet /Calculation/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 3.4.5 The Tab Sheet /Results/ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Properties of Output Zones and Downstanding Beams . . . . . . . . . . . . . . . . . . . . . . . . 3D Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−43 A−44 A−44 A−45 A−45 A−48 A−48 A−50 A−52 A−52 A−53 A−55 A−55 A−56 A−57 A−58 A−59 A−59

A 3.5 The Layer Switches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Layer Group DUser" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Layer Group DResults" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−60 A−60 A−60

A 3.6 The Documentation of a Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A−61

Part BThe Graphics Editor . . . . . . . . . . . . . . . . . B−1 B 1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−1

B 2 Interaction of Application with Graphics Editor . . . . . . . . . . . . . . . . . . . . . . . . .

B−2

B 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−2

2

Table of Contents

CEDRUS–5

Table of Contents

B 2.2 The application window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 2.2.1 The control of the application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 2.2.2 The application status line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 2.2.3 The window of the Graphics Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 2.2.4 Toolbar of the Graphics Editor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 2.2.5 The layer buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−2 B−2 B−2 B−2 B−3 B−3

B 3 Screen Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−4

B 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−4

B 3.2 Toolbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.2.1 Graphics objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.2.2 Selection mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.2.3 Zoom functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.2.4 Undo / Redo functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.2.5 Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.2.6 Working planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.2.7 Projection control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Parallel perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Point perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eccentric perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The buttons for projection control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−4 B−4 B−5 B−6 B−6 B−6 B−6 B−9 B−9 B−10 B−10 B−11

B 3.3 Layer buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.3.2 Layer groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Close . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Size adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . All layers visible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . All layers invisible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . New layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Labels visible/ invisible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.3.3 The layer group ’User’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Active . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Delete contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Delete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.3.4 Layer buttons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Visible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grabbable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selectability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Labels visible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exclusively visible . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exclusively selectable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Select . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Deselect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sublayer visibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sublayer selectability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−13 B−13 B−13 B−13 B−13 B−14 B−14 B−14 B−14 B−14 B−14 B−15 B−15 B−15 B−15 B−15 B−15 B−15 B−15 B−16 B−16 B−16 B−16 B−16

B 3.4 Coordinate fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−17 B−17

B 3.5 Context menus of the graphics area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−18

B 3.6 The Input context menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.6.1 Input graphics objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.6.2 Activating the labelling layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−18 B−18 B−19

CEDRUS–5

Table of Contents

3

Table of Contents

B 3.6.3 Paste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Changing graphics object types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.6.4 Export . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.6.5 Select all . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.6.6 Grabbing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.6.7 Input options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.6.8 Coordinates, distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−19 B−19 B−19 B−20 B−20 B−20 B−21 B−21

B 3.7 The Modify context menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.1 Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.2 Move . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.3 Moving labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.4 Rotating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.5 Mirroring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.6 Stretching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.7 Duplicate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Duplicating in the Move tabsheet: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Duplicate in the Rotate tabsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Duplicate in the Fill tabsheet: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.8 To the front / to the back . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.9 Cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.10 Delete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.11 Copy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.12 Deselect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 3.7.13 Modify selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−22 B−22 B−22 B−23 B−23 B−24 B−24 B−25 B−25 B−25 B−26 B−26 B−27 B−27 B−27 B−27 B−27

B 3.8 The Point Input context menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−28

B 4 Input of Graphics Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−29

B 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−29

B 4.2 Point input methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.2 Point input method ’Free’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.3 Point input method ’Absolute’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of point input ’Absolute’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.4 Point input method ’Relative’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of point input ’Relative’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.5 Point input method ’Polar’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Reference point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example of point input ’Polar’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.6 Point input method ’Middle’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.7 Point input method ’Intersection’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.8 Point input method ’Normal’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.9 Point input method X−direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−30 B−30 B−30 B−31 B−31 B−31 B−31 B−32 B−32 B−32 B−33 B−33 B−33 B−33 B−33 B−33 B−34 B−34 B−35 B−35 B−35 B−35 B−35

4

Table of Contents

CEDRUS–5

Table of Contents

See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.10 Point input method Y−Direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.2.11 Point input on a Help Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−36 B−36 B−36 B−36

B 4.3 Graphics objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.3.2 Construction points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.3.3 Handles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . When moving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . When inputting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−36 B−37 B−37 B−37 B−37 B−38

B 4.4 Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.4.1 Start input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.4.2 Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.4.3 Completion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . See also: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−38 B−38 B−38 B−38 B−38

B 4.5 Circles and circular arcs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.5.2 Circular arc defined by 3 points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.5.3 Circular arc defined by 2 points and centre of circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 4.5.4 Circular arcs defined by centre of circle and a point on the circumference . . . . . . . . . .

B−38 B−38 B−39 B−39 B−40

B 4.6 Dimension lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−41

B 4.7 Labels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−41

B 5 Modifying Graphics Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−42

B 5.1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−42

B 5.2 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Exclusive selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additive selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.2 Select individual graphics objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.3 Select using a Window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Window from left to right . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Window from right to left . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.4 Select with a polygon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.5 Select with the context menus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.6 Select with the keyboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.7 Seleting by means of search criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.8 Modify selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.2.9 Cancel selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−42 B−42 B−42 B−43 B−43 B−43 B−43 B−43 B−43 B−43 B−44 B−44 B−44 B−44 B−44 B−44

B 5.3 Working with attributes dialogues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.2 Contents and position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.3 Opening the attributes dialogues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.4 Closing the attributes dialogues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.5 Inspect attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.6 Different attribute values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.7 Change attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.8 Paste new graphics objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.9 Dialogue default values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−45 B−45 B−45 B−45 B−45 B−46 B−46 B−47 B−47 B−48

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Table of Contents

5

Table of Contents

B 5.3.10 Range of values of input fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.11 Invalid input values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 5.3.12 Selection using search criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−48 B−48 B−49

B 6 The Help System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−50

B 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−50

B 6.2 Viewing help documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−50

B 6.3 Navigating in document collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 6.3.1 Hypertext links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B−50 B 6.3.2 Accessing documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 6.3.3 Full text search in document collections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accessing Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B−51

B−50 B−50

B 6.4 Help on WorldView . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−51

B 7 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−52

B 7.1 Input options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.1.2 The tabsheet ’Coordinates’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Origin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Save . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coordinate axes and rulers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.1.3 The tabsheet ’Grabbing’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grab modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Grab radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.1.4 The tabsheet ’Preselect’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preselected graphics objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preselect hint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−52 B−52 B−52 B−52 B−53 B−53 B−53 B−53 B−54 B−54 B−54 B−55 B−55 B−56 B−56 B−56

B 7.2 Colours and line types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.2.2 Tabsheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.2.3 Style attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.2.4 Copying a style table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 7.2.5 Importing default values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−57 B−57 B−57 B−57 B−57 B−58

B 7.3

Automatic save . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−58

B 8 Importing DXFData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−59

B 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−59

B 8.2 Use of imported graphics objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 8.2.1 As input help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 8.2.2 Converting DXF elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−59 B−59 B−59

B 8.3 Large DXF files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−59

B 8.4 The import dialogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 8.4.1 Button bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 8.4.2 List of DXF layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−60 B−60 B−61

6

Table of Contents

B−51 B−51

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B 8.4.3 Dimensions of the visible layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 8.4.4 Circular arc subdivision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 8.4.5 Tolerance value for short lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B 8.4.6 Coordinate transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−61 B−61 B−61 B−61

B 9 Key Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B−63

Part CThe CubusViewer . . . . . . . . . . . . . . . . . . . C−1 C 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−1

C 2 Creating a report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−1

C 3 Preview of the report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−1

C 4 Document styles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−2

C 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−2

C 4.2 Choosing a document style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−3

C 4.3 Modify or create a document style . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C 4.3.1 Paper format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C 4.3.2 Page borders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C 4.3.3 Header and footer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−3 C−3 C−4 C−4

C 5 Modify the report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−6

C 6 Printing a report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C−7

Part DReinforcement and Ultimate Load Analysis . . . . . . . . . . . . . . D−1 D 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−1

D 1.1 Reinforcement Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−1

D 1.2 Ultimate Load Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−2

D 2 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−3

D 2.1 Material Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 2.1.1 Moment%Curvature Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 2.1.2 Plasticity Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 2.1.3 Yield Condition and Flow Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kinematic hardening model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−3 D−3 D−3 D−4 D−5

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7

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D 2.1.4 Plastic Moment of Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−6

D 2.2 Reinforcement Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 2.2.1 Reinforcement Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 2.2.2 Slab and Downstanding Beam Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Downstanding beam reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 2.2.3 Sloping Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−7 D−7 D−7 D−8 D−8

D 2.3 Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 2.3.1 Nonlinear Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Incremental, iterative calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Influence of the initial state and load history . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−9 D−9 D−10 D−10

D 3 Reinforcement Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−11

D 3.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.1.1 Dimensioning for Ultimate Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.1.2 Elastic Design as an Optimization Task . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.1.3 Optimum Plastic Dimensioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.1.4 Dimensioning for Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−11 D−11 D−12 D−13 D−14

D 3.2 Dimensioning Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Introductory example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.2.1 Input of the Reinforcement and Elastic Dimensioning . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.2.2 Preparation of the Output Zones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.2.3 Creating a Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.2.4 Input of Reinforcement Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bottom reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Duplicating in another direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Construction based on elastic reinforcement requirement . . . . . . . . . . . . . . . . . . . . . . Additional reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Settings for the display of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Top reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additional reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Positioning of the field label . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.2.5 Elastic Dimensioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.2.6 Optimum Dimensioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design Monitor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.2.7 Interpretation of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 3.2.8 Production of the Reinforcement Drawings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−16 D−16 D−16 D−17 D−17 D−17 D−17 D−19 D−19 D−20 D−21 D−21 D−21 D−22 D−22 D−23 D−23 D−24 D−25

D 4 Ultimate Load Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−29

D 4.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear Calculation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 4.1.1 Calculation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear Moment%Curvature Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Load History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Partial Safety Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 4.1.2 Termination Criteria for Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D 4.1.3 Calculation Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D−29 D−29 D−29 D−30 D−30 D−30 D−30 D−31 D−33

Part EPrestressing Module . . . . . . . . . . . . . . . . . E−1 E 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−1

E 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−1

8

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CEDRUS–5

Table of Contents

E 1.2 Tendons and Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−1

E 1.3 Input Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−1

E 2 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−3

E 2.1 Tendon Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 2.1.1 Geometrical description in the plan view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 2.1.2 Geometrical description in the side view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Support and point attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of generated tendon profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−3 E−3 E−3 E−4 E−4

E 2.2 Force Variation along Tendon and Friction Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−8

E 2.3 Deviation Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−8

E 2.4 Dimensioning of the Non−Prestressed Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 2.4.1 Prestressing as an external action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 2.4.2 Prestressing as self%equilibrating stress state . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The dimensioning conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dimensioning as beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross sectional resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Constraint moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Direction of the tendons and of the associated beam sections . . . . . . . . . . . . . . . . . . E 2.4.3 Use of program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input in the tabsheet ’Calculation’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input in the Tabsheet ’Results’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Remarks on the Results Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−9 E−9 E−9 E−9 E−10 E−10 E−12 E−12 E−13 E−13 E−14 E−15

E 3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−17

E 3.1 Flat Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.1.1 Description of problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.1.2 Tabsheet ’Structure’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.1.3 Tabsheet ’Loads’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.1.4 Tabsheet ’Prestressing’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Input of tendons and supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.1.5 Tabsheet ’Calculation’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.1.6 Tabsheet ’Results’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.1.7 Checklist . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−17 E−17 E−17 E−17 E−18 E−19 E−21 E−24 E−25 E−25

E 3.2 Two Span Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.2.1 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E−27 E−27 E−28

E 3.3 Tips and Tricks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.3.1 Duplication of groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.3.2 Generating possibilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.3.3 Checks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.3.4 Detecting tendons lying on top of each other . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 3.3.5 Reference height of supports with different slab thicknesses . . . . . . . . . . . . . . . . . . . . .

E−31 E−31 E−31 E−31 E−31 E−31

Part FDynamic Analysis . . . . . . . . . . . . . . . . . . . . F−1 F 1 Natural Vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

F−1

F 1.1 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

F−1

CEDRUS–5

Table of Contents

9

Table of Contents

F 1.2 Mass Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

F−1

F 1.3 Input parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

F−2

F 1.4 Output of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

F−2

Part GWalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G−1 G 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−1

G 2 Basic Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−1

G 2.1 Element Model and Solution Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−1

G 2.2 Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 2.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 2.2.2 Thickness and Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Isotropic Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orthotropiv Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 2.2.3 Point Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 2.2.4 Line Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 2.2.5 Lines of Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 2.2.6 Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−2 G−2 G−2 G−3 G−3 G−4 G−4 G−4 G−5

G 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 2.3.1 Raw Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G 2.3.2 The Structuring of the Output of Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The quantities for load cases and load case combinations . . . . . . . . . . . . . . . . . . . . . . Quantities for limit state specifications (envelope values) . . . . . . . . . . . . . . . . . . . . . . Required reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Forms of Presentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−5 G−5 G−6 G−6 G−7 G−7 G−8

G 3 Slab with Normal Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−9

G 3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−9

G 3.2 Changing the Structural Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−10

G 3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

G−10

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CEDRUS–5

Part ABase Module A 1 Introduction CEDRUS5 is a Finite Element program for the linear elastic, static and dynamic analysis of plate structures (both for bending and in−plane actions). It is especially conceived, however, for reinforced concrete slabs and provides the corresponding reinforcement for limit states as well as the reinforcement contents. Besides the basic module for plates the following modules are available as options: S Plates subjected to in−plane actions (plane stress states) S Ultimate load capacity for slabs S Optimum design (with possible plastic redistribution) of the slab reinforcement S Dynamics S Prestressing The handbook available in printed form comprises Chapter 2 .Basic Theory" with a de scription of the general principles and scope of CEDRUS5, without treating matters of program handling, and Chapter 3 .Working with CEDRUS5", which with the help of an example gives an introduction to the use of the program. .

It is highly recommended that each user for getting started with CEDRUS-5 works through these two short chapters completely, before venturing on a serious calculation. Besides these two printed chapters there is also the Help System of CEDRUS5, which during program execution provides contextsensitive help on all aspects of program handling. It is also equipped with search functions for any technical terms and thanks to the many hyperlinks (navigation aids to further information) one can obtain the re quired information quickly. Some information is also given in Chapter 3 on the use of the Help System. CEDRUS5 is suitable for the solution of complex problems. But this means that there are various sources of error, from the static modelling to data input, numerical problems, interpretation of results and finally possible programming errors, which for such exten sive software cannot unfortunately be eliminated despite all care taken in the develop ment work. Thus the main requirements for the successful application of CEDRUS5 are an adequate theoretical background and checking the results by means of rough cal culations and plausibility considerations. CEDRUS5 is continually being improved by the Cubus corporation. Therefore, criti cisms, suggestions and special wishes from the side of engineering practice are always welcome. Our clients will, of course, be informed of any major changes or develop ments. We reserve the right of small deviations of the program from the printed description in the sense of selfevident changes in the dialogue.

A 1.1 Changes since CEDRUS-4 The goal of CEDRUS5 was a better integration of the national codes (namely Eurocode and Swisscode) in the fields of materials, dimensioning procedures and load combina

CEDRUS–5

A–1

Part A Base Module

A 1 Introduction

tion generation. Besides these aspects a lot of productivity tools and functions have been implemented. The most important changes are listed here: User Interface S

Functionality was added to the graphics editor: Objects can now also be stretched, rotated, searched for properties, selected with polygons, renumbered, labelled with the point coordinates (and the labels easily displaced via context menu). Dialogs do automatically shrink when objects are constructed. The structure can be rendered. Shortcuts / for ’Calculate’ and ’Create print entry’ and help documenta tion in pdf−format are now available. A ’direct conversion’ (from clipboard) function was introduced (e.g. making DXF−import even easier than before).

S

Automatic generation of a net box (default).

Model S

Introduction of ’project materials’ and the corresponding material manager (Menu Settings>Materials). Project materials are containers for all material specific values (material class according to the code, mass, Poisson ratio, temperature deviation co efficient etc.).

S

Stiffness factor for zones (material boxes, downstanding beams).

S

Analysis parameter sets (Menu Settings>Analysis parameters).

S

Support for Swisscode.

Loads, Actions, Limit State Specifications S

Actions and Limit State Specifications were reorganized, automatic generation ex tended to Swisscode/Eurocode.

S

Load cases have now text Ids.

S

Load case ’Dead load’ is autom. generated. The self weight is defined via acceleration loads (and the mass from the project material).

S

Loads for differential temperature.

S

Detailed legend of load objects with netto sum.

S

Improved load transfer from floor to floor. (dialog ’Load export’ in the tabsheet ’Loading’).

Results, Output

A–2

S

Envelop values for area supports.

S

Report generator.

S

Result combinations of nonlinear calculations.

S

Dimensioning according to Swisscode.

S

Punching according to Swisscode.

S

Improved numerical output.

S

Output of edge stresses.

CEDRUS–5

Part A Base Module

A 2 Basic Theory

A 2 Basic Theory A 2.1 Element Model and Solution Method CEDRUS5 is a Finite Element (FE) program primarily for the calculation and design of reinforced concrete slabs. The linearelastic FE calculation also permits supports in capable to resisting tensile forces. The element models used are hybrid triangular and quadrilateral elements of arbitrary shape with the three displacement degrees of free dom vz (bending), rx, ry (rotations about the axes x,y) in the corner nodes. vz

Z Y X

ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ

ry

ÎÎÎÎÎ ÎÎÎÎÎ ÎÎÎÎÎ ÎÎÎÎÎ ÎÎÎÎÎ ÎÎÎÎÎ rx

Bending actions are considered, but not membrane forces. The most important element properties are: S

Quadratic functions for moments within elements.

S

Cubic functions for displacements at element boundaries.

S

Section forces in corner nodes as well as at the centre of an element.

S

Possibility of area supports (if desired without tensile fixture).

The elements are among the best available today for this area of application. They were first proposed by Pian and are to be found in numerous programs. For a detailed study of this element model refer to the following: S

J.P. Wolf: .Generalized Stress Models for Finite Element Analysis", Institute of Struc tural Engineering, ETH Zurich, Report Nr. 52, 1974 Birkhäuser, Basle.

S

U. Walder: .Beitrag zur Berechnung von Flächentragwerken nach der Methode der Finiten Elemente", Institute of Structural Engineering, ETH Zurich, Report Nr. 77, 1977 Birkhäuser, Basle.

The FE method in CEDRUS5 essentially involves the following steps: 1. Determination of the element matrices for the hybrid method. 2. Determination of the load vectors (right hand sides of the system of equations). 3. Summation of the element stiffness matrices to form the global stiffness matrix. 4. Solution of the resulting system of equations for the unknown nodal displacement parameters (possibly iteratively in the case of supports that do not take tension). 5. Calculation of the section forces in the elements for the now known nodal displace ment parameters. One should observe that the FE method is an approximate numerical method. The numerical solution, however, converges for an ever finer element mesh, within the limits of numerical accuracy, to the exact theoretical solution of Kirchhoff’s plate bending theory.

CEDRUS–5

A–3

Part A Base Module

A 2 Basic Theory

A 2.2 Modelling A 2.2.1 Geometry of the Plan Outline The geometry of the plan outline is basically fixed by the following conditions: S

Outline: An arbitrary closed polygon.

S

Recesses and openings: Arbitrary closed polygons.

S

Downstanding beams: Wall−like lines or polygons of specified width and arbi trarily directed closure lines. Downstanding beams may intersect, but at most two at any one place.

S

Walls: Wall−like lines or polygons of specified width and arbitrarily directed closure lines. Walls are modelled as line supports. The position of the support axis can be chosen anywhere within the wall (centrical, eccentrical). The wall outline has a vis ual function and is irrelevant to the calculation model.

S

Columns: Rectangles or parallelograms to model columns. The user has the choice between point or area support.

S

Material separators: Lines or polygons which divide up the slab into several zones with different material attributes.

S

Hinges: Lines, along which and normal to the direction of the line only shear forces and no moments are transmitted.

S

Lines of symmetry: Along these lines the slab may bend but normal to them it may not rotate. Thus one has a special type of linear support, which may only lie on the slab boundary.

ÏÏ ÏÏ

ÏÏ ÏÏ

Hinge

ÏÏ ÏÏ

ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ Ï ÏÏÏÏÏÏÏÏÏÏÏÏ Ï ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏ

Down standing beams

ÏÏ ÏÏ

Columns

Wall

Opening

Material separators

Outline

ÏÏ ÏÏ

The distance between the corner or end points of the outline elements as well as the distance of these points to lines of the outline elements may not be less than a minimum permissible length. In the case of walls only the wall axis is relevant in this respect. This minimum length depends on the FE method and is preselected by the program. It can, if necessary, be changed by the user, provided appropriate attention is given to numeri cal effects. Material properties and the slab thickness are constant within each zone. For later pro gram versions a linear variation within a zone is planned. Note, on this question one can get help within the program itself.

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A 2 Basic Theory

A 2.2.2 Slab Thickness and Material A slab can be subdivided into different zones by material separators. Downstanding beams automatically create their own material zones and also act as material separators. In the case of columns one has the choice of giving them their own material properties or using the material of the zone in which they lie. In the first case the boundary of the column also acts as a material separator. CEDRUS5 recognizes the following material models: isotropic, orthotropic, drilling% soft and downstanding beam which are described in detail in the following sections. Downstanding beams have implicitly a downstanding beams material, while columns with their own material are isotropic. Any of the material models listed above can be assigned to the other zones. In the description of the material models the following notation is used: mx , my ,mxy : kx , ky , kxy : E,n : d

slab moments 2 (Ë xy + 2 ē w  , w + bendingdeflection) slab curvatures ēxēy elastic modulus and Poisson’s ratio thickness of the slab

Isotropic Material Isotropic material is directionally independent and is completely described by two elas tic constants, i.e. the modulus of elasticity (or Young’s modulus) E and Poisson’s ratio n as in Kirchhoff’s plate theory. The relationship between plate curvatures and plate mo ments is governed by the following elasticity matrix (i.e. a matrix containing the elastic constants):

NJNj Ëx Ëy Ë xy

ȱ ȧ Ȳ

NJNj

ȳ mm ȧm ȴ

0 1 *n 12 0 * n 1 + fEEd 3 0 0 2(1 ) n)

x y

xy

whereby d = thickness of the element, fE = factor of the stiffness (deafult=1.0)

Drilling-Soft Material If the third diagonal coefficient of the elasticity matrix for isotropic material is chosen to be very large, then the slab is very soft in drilling action with respect to selectable directions (x,y) and therefore no drilling moment mxy can be resisted. In special cases this can be useful, e.g. if one wants to have no drilling reinforcement thereby accepting larger values of mx and my. It should be noted, however, that in certain cases without drilling moments equilibrium is not possible.

Orthotropic Material Orthotropic material exhibits different properties in the two directions x and y normal to one another. It is described by the following elasticity matrix:

NJNj Ëx Ëy Ë xy

NJNj

ȱdd dd 00 ȳ mm +ȧ ȧ Ȳ0 0 d ȴ m 11

12

21

22

33

x y

(d 12 + d21 x 0)

xy

Here the condition d11 *d22 > d12 *d21 must be fulfilled. The xdirection (material direc tion) is selectable.

CEDRUS–5

A–5

Part A Base Module

A 2 Basic Theory

Downstanding Beams x

Downstanding beams (just called beams in the following) are treated in CEDRUS5 as orthotropic elements using the following elasticity matrix:

d

y

NJNj Ëx Ëy Ë xy

ȱ 12 Eh ȧ 1 + ȧ 0 f ȧ Ȳ0

3

E

ȳ m ȧ 0 ȧ m m 24 ȧ Ed ȴ 0

0 12 Ed3 0

NJNj x y

xy

3

h = fictitious height of underbeam d = thickness of neighbouring element (=input value) fE = factor of the stiffness (deafult=1.0)

whereby Illustration

Thus the beam elements have the full stiffness in the longitudinal direction (on h see below), whereas for the transverse and drilling stiffness the thickness of the neighbour ing slab is used. To determine the fictitious beam height h model 4 described below is used. It lies be tween the extreme cases represented by models 2 and 3. d

B

Model 1: Tsection with effective width B

h

n

This model corresponds best with reality. It cannot, however, be applied, since CE DRUS5 does not take membrane effects (i.e. membrane strains) into account. b

e

n

Model 2: Beam eccentric

h

Since the neutral axis in slabs lies in the middle, the stiffness here is too high. I n * I nslab + bh ) bhe2(I nslab + IpartofslabofwidthB * b) 12 3

Model 3: Beam centric

h

n

The stiffness of this model is too small, since the eccentricity is neglected. I n * I nslab + bh 12

3

Model 4: Lies between model 2 and model 3 = CEDRUS5 model

h

h

n

3

ǒ

3 3 I n * I nslab + bh + 1 bh ) bhe 2 ) bh 12 12 2 12

Ǔ

;

3 h+Ǹ h 3 ) 6e 2h

For intersecting beams, in the zone of intersection an orthotropic material is used which exhibits in the direction of the higher underbeam, if present, the bending stiffness, while normal to it as well as for drilling action that of the other beam. More than two beams may not intersect at a point. If an beam connects laterally to another one, it shold inter sect this one (and not just touch) in order to permit a correct introduction of its shear force.

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Part A Base Module

A 2 Basic Theory

A 2.2.3 Area-Supported Elements Areasupported slab zones exhibit a uniformly distributed reaction pressure for each finite element and the average settlement is determined on the basis of the given modu lus of subgrade reaction and the support pressure. If the modulus of subgrade reaction ks has a very high value, an element may theoretically be free to bend and rotate, but on average it cannot exhibit settlement. With an areasupported element alone or even several acting on one line, therefore, a stable support of the slab is not guaranteed. A good visual model for the areasupported element is the liquid filled cushion: Element Subgrade reaction ks:

ÏÏÏÏ

liquid filled cushion stiff plate elastic support

ks =

support pressure settlement

[kN/m3]

A use of areasupported elements is the supports of columns. The support elements are described in the next section. Another use of areasupported elements is the Modulus of Subgrade Reaction Method. Areasupported elements can be employed with or without tension capabil ities. In the latter the program reaches the correct solution by means of iteration.

A 2.2.4 Columns / Point Supports The column object of the CEDRUS5 Input Module offers the following modelling possi bilities. Special columns, which cannot be modelled in this way, must be modelled with other support types. For each column the settlement sdz (or the modulus of subgrade reaction ks for areasup ports) and rotational stiffnesses srx, sry can be specified. If one provides reasonable va lues of elasticity modulus and column height, then the stiffnesses can be calculated automatically by the program using the following formulas: s dz + EA ; h E: A: Ix ,Iy : h:

s rx +

4EIx ; h

s ry +

4EIy h

elasticity modulus of the column sectional area of column = area of input column object second moments of area of column section column height

There are two support models for columns: area supports and point supports.

Point Supports Since point supports, because of the moment singularities resulting from plate theory, involve rather problematic modelling, they should mainly be used only when an area support is difficult to include in the input. Whereas for an area support the sides of the column quadrilateral represent fixed lines for the FE mesh, with point supports it is only a question of a point. With point supports the column dimensions are used for punching shear verification and to determine the stiffnesses of the column.

Area Supports In the FE model area supports are modelled with areasupported elements. By means of an arbitrarily directed parallelogram a limited areasupported zone is input together

CEDRUS–5

A–7

Part A Base Module

ÏÏ ÏÏ

1)

column section supported area

ÏÏ ÏÏ 2)

Support area subdivided into several elements b

A 2 Basic Theory

with the effective column cross section, which can either be a rectangle or a circular section. In the following cases it is better if the supported zone is not identical with the column section: 1) Columns of circular section of rather small diameters cannot be modelled with a rea sonable FE mesh. 2) For small diameter columns one chooses with advantage the support zone to be somewhat larger than the column section, in order to obtain a more homogeneous FE mesh and also more realistic column moments. The user has to decide whether an area support should be with a single finite element or with subdivision into several elements. Area supports with one element are necessary if a column should not resist moments. If in spite of this a bending stiffness is specified, then this is distributed by the programm automatically in the form of bending stiffnesses to the four corner nodes. Area supports distributed over several elements are unavoidable if their sides are divided up by other geometrical input objects like material separators. They may be de sirable if one wants a finer FE mesh over a column. Distribution over several elements, however, means that such a column always exhibits a certain bending stiffness, since each element acts like an independent support spring. With the value of ks for the modu lus of subgrade reaction of the supported elements the bending stiffness for a rectangu lar column section resulting from the area support (see figure alongside) is given ap proximately by: s r + ab k s 12 If one determines ks from the settlement of the column (see following figure), then as suming that the supported zone is identical with the rectangular column section ks=E/h and thus

a

3

s r + Eab . 12h If the column section deviates from the shape of the support zone, then these consider ations about stiffness can be adapted accordingly. 3

ÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏ ks

A column of the same dimensions fixed at its base (column extreme right in figure), on the other hand, exhibits a bending stiffness four times higher: s r + Eab 3h

3

b

1

1

h

1

a

M + 1 @ sr

M + 1 @ sr

N + Eab h

ÏÏÏ ÏÏÏ ÏÏÏ ÏÏÏ

ks + N + E ab h

ÏÏÏ ÏÏÏ ÏÏÏ ÏÏÏ

Since it is not allowed to fall below the stiffness sr , this value represents a minimum for the input. Higher stiffnesses, as for a column with one element, are modelled by a rotational stiffness uniformly distributed over all column nodes.

A 2.2.5 Walls / Line Supports Line supports are input in CEDRUS5 basically as wall objects. Wall objects are polygons of selectable width with information about modulus of elasticity and wall height.

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The computational model, however, is a line support, whose axis can be feely chosen within the inputted wall. These support axes are fixed lines in the FE mesh and thus are subject to the conditions of minimum distance between each other and to other structure objects. The wall outline only serves a visual purpose and is not bound to any geometrical consistency condition. The settlement stiffness sdz and the bending stiffnesses srx and sry of the walls are de fined per unit length of wall and can be freely input or determined by the program on the basis of wall thickness and height and elasticity modulus. They are defined as fol lows: sdz : srx : sry :

force per unit settlement; moment for a unit rotation about support axis; moment for a unit rotation normal to support axis

sdz = Et/h srx = Et3/3h

The program does not calculate any stiffness for sry. This stiffness component is difficult to model, but is only of secondary importance and usually is either set to .blocked" or .free".

A 2.2.6 Lines of Symmetry Lines of symmetry are special line supports, along which the slab is free to bend, about whose axis, however, it cannot rotate. Symmetry conditions are really only meaningful at slab boundaries, which is why lines of symmetry are only allowed to lie on the plan outline.

Lines of symmetry

Lines of symmetry are used to demarcate parts of the slab in the model, be it a genuine line of symmetry or if by means of a symmetry condition one obtains the most favour able boundary condition. Note, that with symmetry conditions the loads too always act symmetrically. An example of genuine symmetry is given by the circular slab − even if with the condi tion of a symmetrically acting load it is rather academic. Here the input of a sector with the corresponding symmetry conditions along the radial boundaries suffices. Lines of symmetry on walls are not allowed. If a wall, however, has to act as a line of symmetry then the rotation about its support axis is blocked. But the user is respon sible for reducing the settlement stiffness by 50%. Point supports on lines of symmetry are permitted. Their xdirection, however, has to coincide with the direction of the lines of symmetry. The program then blocks the rotation about the xaxis, but does not reduce any stiffnesses due to symmetry. The user has to supply the corresponding values. A simple possibility is to halve the elasticity modulus of the column. Point supports at the intersection of two lines of symmetry are also allowed. If these form an angle of 180 degrees, then one has the same case as if the line of symmetry would run right through (previous section). Otherwise the input direction of the column is unimportant and the program blocks both rotations. The user is again responsible for the correct input of the settlement stiffness.

CEDRUS–5

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Part A Base Module

A 2 Basic Theory

A 2.2.7 Hinges Normal to hinges only shear forces and no moments are transmitted. Hinges are preset (i.e. fixed) lines in the FE mesh and thus are subject to the conditions of minimum distance between each other and to other structure objects. Several hinges in a chain are allowed but no branching. The hinge lines are implemented in the program as double nodes with the correspon ding nodal connections.

A 2.2.8 Loads CEDRUS5 permits the following types of load: 1) Area loads (i.e. loads per unit area) Rectangular or arbitrary polygons for: − body force (e.g. dead or selfweight) − uniformly distributed force − differential temperature loading 2) Line loads Constant or trapezium distributed − forces − moments (about loading line) 3) Point loads − forces − moments about x or ydirection 4) Displacements of point supports (the corresponding displacement parameters of the support nodes have to be blocked) − settlements − rotations in x or ydirection 5) Influence fields for − moments mx, my, mxy in the global coordinate directions − bearing pressure of areasupported elements By introducing a unit point load or a unit support displacement one can also obtain influence fields for point displacements and point reaction forces, respectively. The load types 1) to 3) are independent of the FE mesh, so that they can be arbitrarily arranged geometrically. Loads are combined to individual load cases, which can be combined or superimposed in any way for the calculation of the results. The load cases can be assigned to particular action types, like dead weight loads, surcharge loads, imposed loads etc., whereby in standard cases a load superposition automatically carried out by the program to deter mine the design section quantities is possible (see Chapter 2.3). The influence field load cases are a special case. Each influence field requires a load case, which cannot be combined with other load cases. It should be noted that in the region of the influence point a very fine FE mesh is needed to obtain sufficiently accu rate results.

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Part A Base Module

A 2 Basic Theory

A 2.2.9 The FE Mesh An important part of modelling in an FE calculation is to have a suitable mesh subdivi sion, so that accurate results can be obtained with acceptable input, calculation and data storage expenditure. There is no simple recipe. One factor is element quality (see Ch. 2.1). Further, in an FE calculation it is always important to know which results are of primary interest. To want to obtain all results exact in every detail according to plate theory is uneconomic and also not necessarily desirable (e.g. infinitely large moments at point supports and in recessed corners). In CEDRUS5 the FE mesh is automatically created within zones if certain parameters are provided. The zone boundaries are automatically defined by polygon line chains (mesh separators), which themselves represent mesh lines and thus fulfil the conditions regarding the distance of separation between structure objects. Automatic mesh gener ation can also be suppressed in individual zones. In these zones the mesh is input man ually. The following parameters influence automatic mesh generation within a mesh zone: S

Maximum element side length: This important parameter defines the fineness of the mesh.

S

Minimum element side length: The minimum element side length is usually gov erned by the structure’s geometry. If in regions without geometrical restrictions of the structure one does not want, if possible, to go below a certain element side length, then with this optional parameter one can specify a corresponding value. But only values in the range 0.1 to at most 0.5 of the given maximum element side length are meaningful.

S

Direction of the mesh lines. The mesh is created by two families of lines in the given directions, whereby all input structure objects have to be taken into account and ad justed to. It is recommended, if possible, to choose these directions orthogonal to one another.

The program considers area supports to be separate mesh zones, which are automati cally treated taking into account the input column attributes.

CEDRUS–5

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Part A Base Module

A 2 Basic Theory

A 2.3 Actions and Limit State Specifications

A 2.3.1 Basic Considerations The aim of all structural analysis is ultimately the dimensioning of a structure. This is based on limit states, which requires among other things the selection of design situ% ations with the associated load cases. Each load case is characterised by a leading action and a simultaneously acting accom panying action and thus consists of a weighted combination of actions. An experienced engineer can − at least for preliminary dimensioning − often limit the consideration to a few points and also without much effort can recognize the critical load cases for the investigated design situations. The strength of a program however lies in the systematic treatment of numerous sections or points. For many dimensioning tasks it is best to work with limit values of section forces, reactions or displacements. These are determined by the Cubus programs on the basis of limit state specifications, which uniquely describe the combination rules for the individual loading. How these limit state specifications are arrived at is described below.

A 2.3.2 Overview of the Limit State Specifications A simple limit state specification at the highest level looks as follows in the programs:

The considered actions are dealt with in the left half of the dialogue, and in the right half the investigated combinations of these actions with the corresponding combination factors. How these combinations were obtained is clearly seen here: the permanent ac tions ’Dead Load’ and ’Surcharge/Live Loads’ are investigated with the factors γsup (here 1.35) und γinf (0.8). In addition there are the variable actions, of which on the one hand the snow loads as leading action (γQ=1.5) and the wind load as accompanying action (ψ0=0.6) and on the other hand the wind loads as leading (γQ=1.5) and the snow loads as accompanying (ψ0=0.88) actions are considered. The load and accompanying action factors depend on

A–12

S

the code

S

the actions

S

the design situation

S

the limit state under consideration

CEDRUS–5

Part A Base Module

A 2 Basic Theory

The design situation and the limit state are specified on creating a new limit state specifi cation by the user . The list of actions in the left part of the dialogue is created automatically on the basis of the input loads, each of which is assigned to an action. The right part of the action combinations can be automatically generated, but also be arbitrarily defined by adding to, deleting or modifying columns. Regarding automatic generation see Chapter A 2.3.6. The programs CEDRUS5 and STATIK5 automatically create a limit state specification for the limit state (Type 2) of the ultimate limit state (structural safety) for the standard design situation. The actions, which have not yet been discussed in detail, will be treated in the next chapter.

A 2.3.3 Actions Each individual load case is strictly speaking an action. But as is evident from the previ ous chapter, the term ’Action’ is defined more narrowly here. Before it is defined pre cisely, the following terms are once again clearly defined: Loads: As loads all elementary load elements are meant, which are available in a pro gram as actions on a structure (see also above in A 2.3.1). Examples: concentrated loads, line loads, etc. Loads are always summed up together in loadings (see below). Load Cases are a type of container for individual loads. On the load side they represent the basic unit for which results can be calculated, and also from which actions are formed.

Definition of the term ’Action’ Actions are load cases grouped to form individual categories like dead loads, live loads, wind loads, snow loads, etc., which then finally are combined to form design situations in the limit state specification.

How actions are formed During input new load cases are always assigned to an action. Thereby the most used actions available in the codes for the chosen structural type can be selected, whereby the user can also define his/her own actions. For the creation of limit state specifications all load cases assigned to the same action are treaded as one. A user is still free to choose how the loadings interact to form an action, i.e. whether e.g. they can all act together or are mutually exclusive (e.g. action truck load: each position of the truck is a load case that is mutually exclusive). The corre sponding specification is called an action specification and is explained in detail later.

CEDRUS–5

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Part A Base Module

A 2 Basic Theory

The Dialog with the List of Actions In order that on the one hand one has an overview of the actions that can arise in an analysis with their properties and on the other hand to be able to define ones own ac tions, the programs have been provided with a special dialog: Load factors and combination factors

Code prescribed action categories (cannot be changed)

Actions created by user

The Properties of an Action Action type For an action type there are the following selection possibilities: ’permanent’, ’variable’, ’prestressing’, ’accidental’ or ’undefined’. The type influences the way in which action combinations are formed in the limit state specification. Load Factors and Combination Factors To each action category there belong load factors and, depending on the type, combina tion factors. In the case of the actions prescribed in the codes these values cannot be modified in the dialog. If this is necessary a user−defined action must be defined. Action Sets and Action Groups Several actions can together form an action set (e.g. several load models for a bridge). Such actions are not considered separately in forming the action combination, but the set appears as a whole in an action combination (e.g. as leading or accompanying ac tion). The codes speak in this connection of action groups. This term is also supported in a general sense in the Cubus programs. By it is understood the combinations, in which the actions of a set have to be differentiated. Example: The vertical and the horizontal live loads of a road bridge should be able to occur as follows: 1) vertical loads full, without horizontal loads, 2) vertical loads * 0.75, horizontal loads full. Solution: The loads are defined by two actions, which together form a set. The set ap pears in two so called action groups with the following combination factors,: (1,0) and (0.75,1). Which combinations should together form a set is specified in the above action dia logue. All actions which have the same names in the Set column form together an action set.

The Action Specification To the full definition of an action there belongs the combination specification for the participating loadings. Whereas permanent actions often consist of just one loading, for

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A 2 Basic Theory

variable actions a complicated superposition may be necessaray. Take for example as an action the live loads acting on a multispan beam, for which loads have to be con sidered in an unfavourable position in the individual spans and in addition with a ve hicle load in different positions. One can imagine as a simple combination scheme − denoted here by E1 − the compari son of all possible loading combinations. This may be represented in a loading scheme sequence as follows: Loading combination

Action =

( E1 )

or

where Loading combination

Loading ( * factor )

=

( E1 )

Example: Spans with unfavourably applied live load for a three span beam A

B

C

3 loadings A, B and C are introduced for the individual spans. The specification of the action Live Load according to the scheme E1is: A or B or C or AB or AC or BC or ABC In the case of a five span beam one would already have 31 load case combinations to compare one with another. If two spans and perhaps a vehicle load in n possible posi tions were added, then the user would find it rather challenging in terms of combina torial analysis and soon lose track of the number of loading combinations. According on the other hand to the extended superposition scheme − denoted here by E2 − a compact and clear definition of all possible loadings is possible. This is best illustrated in a loading scheme sequence: permanent optional

Action =

( E2 )

plus

wobei: Loading step

Loading step

=

Loading combination or

Loading combination

=

Loading ( * factor )

The scheme is based on an unconditional (permanent) or optional superposition of loading steps. In contrast to the scheme E1, no complete loading combinations are de scribed, but instead there is an instruction on how the results have to be superimposed in forming the limit values and how the limit values are formed. From optional loading steps the value of the result for an extreme value in a point is only considered if it is decisive, that is the extreme value is increasedby the correspon ding amount. Thus a positive value increases a maximum value and a negative one de creases a minimum value. A loading step consists in the simple case of a single loading or of a loading combina tion. It can however also consist of a series of loadings or loading combinations, of which only one can occur at any one time (e.g. different vehicle positions). In this case, in the evaluation of the loading step there is in each point a minimum and a maximum value of the considered result quantity. The specification for the above example for scheme E2 is:

CEDRUS–5

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Part A Base Module

A 2 Basic Theory

A plus B plus C In the case of a five span beam with loading in the spans A,B,C,D,E and an additional vehicle in 9 positions (a,b,c,..,i) the specification is: A plus B plus C plus D plus E plus a or b or c or d or e or f or g or h or i The user can specify an arbitrary number of actions following the superposition scheme E2. .

The scheme E1 is contained in E2 as a special case (without ’PERMANENT’ and ’PLUS’).

Automatically–generated Action Specifications The programs automatically create for each action (exception: prestressing actions) an action specification according to the folowing rules: Permanent actions: all associated loadings are added up. Such an action consists therefore of a fixed loading combination. Variable actions: Each loading that is assigned to a variable action is also given during input the superposition attribute, ’additive’ or ’exclusive’. Additive loadings (a1,a2,...) can occur simultaneously, exclusive (e1,e2,...) are mutually exclusive (e.g. vehicle in different positions). These actions are formed corresponding to the superposition scheme E2 described above as follows: a1 plus a2 plus a3 plus . . . plus e1 or e2 or e3 or ... In cases, which are not covered by this simple rule, the specification must be done man ually. In the programs these specifications are performed in a dialogue, which looks as follows and is self−explanatory:

A 2.3.4 Limit Values of nonlinearly–determined Results When using loading combinations or the specification ’plus’ in the above schemes the programs superimpose results that were obtained for the participating loadings. Such

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superpositions however are not permitted in nonlinear analyses as well as those ob tained by second order theory. In order nevertheless to obtain useful limit values for such cases, one has to consider the following points: S

One has to limit oneself to a single action, so that in the limit state specification no action combinations result,

S

In the specification of the single action one may only use the superposition scheme E1, that is only B1 OR B2 OR B3 ... , whereby the B1 may only be single loadings. In order nevertheless to be able to work with the input loadings, the programs pro vide the combination loadings. Here the loadings are combined before the analysis with the necessary factors to form a new loading, which is then equivalent to a nor mal loading.

A 2.3.5 Limit State Specifications with Action Sets Working with action sets is necessary or recommendable when all loading configur ations of an action cannot be obtained or only with a lot of effort using the superposition scheme described above for action specifications. This case is certainly necessary for the following example:

Excerpt from the dia logue ’Actions’

The automatically generated action combina tions each consider the action set with the two defined groups (lower dialogue)

In the case of a multi−span bridge, the action Road Traffic Loading with the condition that it must be considered in the two above groups, could scarcely be specified without dividing it into two separate sub−actions. This way of handling the problem also gives a better overview, as one can follow more easily what has actually been done.

A 2.3.6 Automatic Generation of Action Combinations Depending on the design situation and the limit state, for which a limit state specifica tion is foreseen, the action combinations can be automatically generated.

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They are formed according to the following scheme (code−dependent), whereby it is assumed that an action is always defined in the same way as a leading action, as also an accompanying action. The correctness of the hazard scenarios formed in this way has always to be checked in each case by the engineer and if necessary adapted to the actual requirements. Eurocode/E%DIN: Basic combination (without accidental loading): Sd +

ȍg

G,j

ƪ

@ G k,j ) gQ,1 Q k,1 )

ȍy

0,i

ƫ

@ Qk,i () g p @ Pk)

iu1

Accidental action combination: S d,A +

ȍG

k,j

) A d ) y1,1 @ Q k,1 )

ȍy

2,i

@ Q k,i() g p @ P k)

iu1

Gk : char. values of the permanent loads (actions dead load, surcharges) Qk,1 ,Qk,i : char. value of the first or further varaiable actions Pk : prestressing Ad : design value of the accidental action g G : partial factors for permanent actions (1.35 and 1.0) g Q : partial factors for varaible actions g P : partial factors for actions due to prestressing y 0, y1, y 2 : combinationvalues for occasional, frequent and quasi−perm. actions.

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SIA 260: Standard design situation E d + E(gGG k, gPP k , g Q1 Q kl , y0i Qki) g G : Gk : g P : Pk : g Q : Qk : y 0 :

(4.4.3.4)

load factor for permanent actions characteristic value of the permanent action load factor for prestressing actions characteristic value of the prestressing action load factors for variable actions characteristic value of a variable action reduction factors for variable actions

Note: For a variable accompanying action y 0i Qki (the decisive one) is considered. Accidental design situation E d + E(G k, P k , A d, y2i Q ki) Ad : y 2i :

CEDRUS–5

(4.4.3.5)

design value of the accidental action load factor for the accompanying action i

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A 2.4 Load Transfer from Floor to Floor A 2.4.1 Overview

Problem

floor i with wall ans column supports:

The transfer of the vertical loads is a central problem in the dimensioning of buildings. It deals with the dimensioning of vertical elements, foundations and floor slabs. The problem is very complex and it is not easy to find a good model with a reasonable effort. Here rae a fews points that should be noted: S

Reaktionen:

Why not just build a finite element model of the hole building, introduce loads everywhere, press a button and print out the results? This approach is not unrealistic and has been implemented a long time ago (with little success in practice however). It has advantages and disadvantages: + You have a simple model: Equilibrum is always garanteed and you could even con sider soil−structure interaction and the influence of horizontal forces. − Such a model does only seem to deliver high accuracy and the results are exremly sensible to stiffness assumptions (especially with high rising structures, see notes below). It does in no way take into account the nonlinear behaviour of the structure (cracking of concrete, long term behaviour) and construction stages. Therefor it can not give more accurate results than the much simpler model, which analyses isolated parts (i.e. floors) of the structure and then transfers the loads from one floor to the next below.

Loads on floor i−1:

S

Both models, the hole structure model and the from−by−floor model, have to deal with the problem of stiffness assumptions. If the vertical elements, supporting a slab, are irregularly distributed, it can lead to stress concentrations in the slab. These stresses and the corresponding reactions do not match the reality, because due to the nonlinear behaviour of the slab (i.e. cracking, creep etc.) stress redistribution (and with it also reaction redistribution) takes place. In order to overcome this prob lem one must choose a reasonably high stiffness for the vertical elements.

S

The distribution of the reactions of a slab are known to be rather ’wild’ on the supporting walls. For the floor below these reactions should be intoduced as loads with a much simpler distribution, ’flatened’trough the walls.

S

The selfweight of a wall is usually modeled as a constant line load. The engineer has to decide, if this model is realistic for his concrete problem.

S

In order to model the load transfer for most buildings it is sufficient to have, besides the dead load, a single load distribution for all the variable loads. It’s up to the engineer to decide, if this simplification is accurate enough or if a series of loading patterns have to be investigated and propagated to the underlying floors.

S

According to the national codes the loads effective for the dimensioning of the structure usually consist of several different actions with different partial safety factors (e.g. snow load, live load cathegories like office space, storage space etc.). For the dimensioning of the individual floors it can be usefull, to model all of them accordingly. For a hole structure (i.e. by load transfer from floor to floor) however one could end up with hunderets of load combinations to investigate at the bottom floor, leading to ’strange’ results. A single variable load transferred from floor to floor is a better approach.

S

National codes allow for reduced partial safety factors when transferring live load from floor to floor (e.g. if more than two floors share the same live load cathegory).

Realization in CEDRUS-5 For a slab calculation CEDRUS5 models pure bending action only, i.e. the vertical load transfer can only be realized with importing the reactions from the floor(s) above as

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loads and exporting the reactions of the walls and columns as loads to the floor below. In previous versions of CEDRUS this scheme was also supported, but it was not as tightly integrated into the application, since the user had to do all the steps by hand. This is no longer the case. In CEDRUS5 the calculation of a hole building, i.e. the load transfer from the top to the bottom floor, is very straightforward: How the load transfer is implemented and how easy it is to actually do it, is explained in the following two sections. Import load cases =

Export combinations of the selected floors directely standing on top of the actual

Permanent loads marked for export (incl. coresp. import loads)

Live loads marked for export (incl. corresp. import loads)

Prestress loads marked for export (incl. corresp. import loads)

Export combination G

Export combination Q

Export combination P

actual slab (floor)

Solver (result generation) Dead load of walls and columns

Reactions of Export comb. G

Export load G Action ’Dead load’

Reactions of Export comb. Q Export load Q Action ’Live load − general’

Reactions of Export comb. P Export load P Action ’Prestressing’

The floor below can import the export loads G,Q and P as import load cases

A 2.4.2 Load Export The load export, i.e. the transfer of the reaction forces at wall and column supports as well as the dead load of these elements to the underlying floor, is realized over so−called export combinations. These are special load case combinations, that are automatically solved and make the ’loads to be exported’ ready for import in the underlying floor. Which load cases are combined to what export combination can be controlled by the user. Since load cases usually have different action cathegories and you may want to analyse them individually, one export combination would be needed for each of the actions. Although this is possible to do (and can be done by hand), this leads to a system too complex. Therefore CEDRUS does automatically generate three export combinations only: one for all the permanent loads, one for all the variable loads and one for prestressing. .

For the treatement of the dead load of the vertical elements (i.e. walls and columns) see the section ’Calculating the Export Calculations’.

Automatically generated Export Combinations CEDRUS−5 provides the follwing export combinations:

CEDRUS–5

S

’!Exp−G’ for permanent loads (action type=’Dead load’).

S

’!Exp−Q’ for variable loads (action type=’Live load−general’).

S

’!Exp−P’ for prestressing loads (action type=’Prestressing’).

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For each load case the user can specify with a check box in the dialog, if it should be included in the corresponding export combination (e.g. a variable load case goes into ’!Exp−Q’) and what factor should be used for it (see next section).

Newly created load cases and import load cases are automatically activated for export. All the export combinations are inculded in the list of load cases. Reduction factor for load export Some national codes allow for a reduced load transfer to the underlying floor, if a number of floors share the same type of action (e.g. ’Live load − office space’). By specifying a value < 1.0 this reduction can be taken into account. The reduction factor is used for the generation of the automatic export combinations only. .

Automatically generated export combinations are only supported for the structure type ’Building’.

Manually created Export Combinations The user can define his own export combination by creating a load case of type ’Export combination’. The specification does not differ from a normal load combination. Manually created export combinations are treated just like the automatically generated.

Calculating the Export Combinations For the current floor export combinations are normal load combinations. However, besides the load elements that are actually exported and shown in the tabsheet ’loads’, the user cannot get any results for these combinations. The self weight of the walls and columns is automatically added to the export combination ’!Exp−G’ if 1. 2.

a load case ’dead load’ with an acceleration load for the hole slab is specified and the self weight is activated for the walls and columns.

For a newly created calculation the first condition is always fullfilled, since CEDRUS automatically generates the load case ’dead load’. For the second condition however, the user must make sure that the shown interface elements in the dialogs of walls and columns are set accordingly:

The calculated reactions along a wall can vary a lot form node to node (see figure below). The direct transfer of these reactions to the underlying floor is not a realistic

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model, because the force distribution is ’flattened’ in some way by the wall. CEDRUS does automatically equalize the reactions by calculating an uniformely distributed force per section. finite element nodes Reactions (raw):

Reactions (flattened for export) Length of section = ca. height of wall (at least 1 section per input wall)

Nonlinear Export Combinations In the load case dialog you could activate an export combination, like any ther load case, to be solved nonlinearly, in order to avoid tension in the suporting walls and columns. Although this is possible it seldom makes sense, since the tension part of the reactions is usually eliminated by the procedure described above. Transfer of the Exported Reactions After changes on the structure or loading the load export is automatically started whenever the system is solved, i.e. when the user requests an result output in the tabsheet ’Result’ or he presses the ’flash’ button in the tabsheet ’Calculation’. The calculated reactions from the export combinations are then ready to be imported by the underlying floor. .

CEDRUS–5

Changes in a floor effect all floors below that do import loads. Therefore you must recalculate all the dependent floors in the right order.

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A 2.4.3 Load Import As discussed in the last section, by default no steps must be taken for export of the reac tions of a slab. However, in order to import these reactions in the floor below, there you must define the source, i.e. the floor above it. This is done in the dialog ’Load Im port’ that opens when you click on the corresponding button in the tabsheet /Loads/. Since more than one source is possible (e.g. departement complex with several houses as sources for the underlying slab of the parking garage), here you can specify a number of slabs as sources. Every export combination of the specified slabs will become an (read only) import load case listed in the dialog. The actual import is performed by pressing on the ’Update’ button, what you should do everytime changes where made in the upper floors.

The imported load cases have take their action types form the export combination and will be treaded accordingly. .

A–24

The exported loads are imported in their original coordinate system. If the origin of the upper floor does not match the actual, you can specify the offset dX and dY, which are added to the (imported) coordinates X and Y upon import.

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A 2.4.4 Checklist for the Load Transfer The checklist applies to the use of the automatically created export combinations. For the floor exporting its reactions (load export) 1) Use the List of loadings (tabsheet ’Loads’) for the check if all the necessery loadings are marked for the automatic load export (column ’AutoExport’/’On’) and if they are related to the correct actions. Note concerning the selfweight of walls and columns: They are exported toge ther with the loading that contains the dead load (given as dead load on whole struc ture). The weights of the walls are defined as force/m2 in the walls dialogue and the weights of the columns as force/m in the columns dialogue. The List of loadings must also the following two export combinations S !Exp−G for permanent loads S !Exp−Q for live loads If you want to exclude negative reactions you can mark the export combinations in the column ’NL’ for a nonlinear calculation. The properties for all supports with non negative reactions must be set accordingly. Have you imported loads from the floor above the following two import loadings should also be listed:: S !Imp−G for permanent loads S !Imp−Q for live loads 2) The system must be solved in order to create the load export files. This is done automatically if you request any result in the ’Results’ tabsheet or if you press the ’Start calculation’ button in the ’Calculation’ tabsheet. Don’t forget to resolve the system after relevant changes. 3) If the system is solved you can check the loads of the export combinations. For a numeric check use the ’Legends of loading data’ in the ’Loads’ tabsheet. For a graphical representation switch on the layer button of the corresponding export loading (right margin of the CEDRUS5window).

For the floor receceiving loads (load import) 1) Call the ’Load import’ dialogue (Loads tabsheet). 2) Define the load import (if it doesn’t exist yet) It normally consists of one link to one other floor (plate) from which loads are to be imported (one line in the upper list of the dialogue). In the lower list of the dialo gue all export combinations found in the linked plate are shown. Note that they can only be found, if the system of that plate is solved. If you need to import from more than one plate, it is possible to define more than one link. 3) If all the settings are correct press the button [Update] in order to copy the specified export files into the actual project. This [Update] has to be done again manually after relevant changes in the lin% ked plates. 4) The imported loadings can immedialtely be checked − graphically by selecting the desired loading from the combobox of all loadings and numerically through the le gends of the loading data. The load sums however are displayed only after solving the system.

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A 2.5 Results

A 2.5.1 Raw Results The solution algorithms of CEDRUS5 produce raw results for each load case input: S

The nodal displacements

S

Reactions of the support nodes and elements

S

Section forces at the element centres in global coordinate directions

S

Section forces at the element corners in global coordinate directions, which are then immediately and zonewise converted to averaged nodal values and are not given as separate values

These calculated and binary stored raw results serve as a basis for determining the re sults types described below in the desired form of presentation.

A 2.5.2 The Structuring of the Output of Results Output results are not created unless the user specifically demands them. Firstly, it is defined for what the results are required (e.g. load case number), then comes the choice of the quantities (e.g. section forces), a possible component (e.g. mx) and finally the presentation form (e.g. isolines), which can still be influenced by certain parameters. From a list one first chooses for what the results are wanted. The list contains S

All input load cases

S

Any defined load case combinations

S

All automatically or manually produced limit state specifications

S

Required reinforcement

Load case combinations are fixed combinations of load cases provided with arbitrary factors, of which the user can define as many as desired. In the output of results they are treated in exactly the same way as individual load cases.

The quantities for load cases and load case combinations Deformations: With the deformations it is a question of settlement as well as the rotations about the x and yaxes, respectively, in each node of the FE mesh. The rotations of nodes not acting as supports are output in the global coordinate system. For point and line sup ports the xdirection of the input object is adopted and the ydirection normal to it. The xaxis of line supports shows the support direction. Section forces: The slab section forces consist of the moments mx , my , mxy and the shear forces vx , vy . The following figure shows the forces acting on an infinitesimal slab element: The output of the slab section force is carried out in zonewise definable output direc tions. The transformation formulas are as follows (Mohr’s circle for the moments and vector transformation for the shear forces): Depending on the form of output the principal moments or the maximum shear forces are output.

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y

A 2 Basic Theory

mxy

y

my

y

z

my

mxy

vy

vy vx

vx

vy

mxy

mx mxy

mxy

vx mx my

vy

mxy

mxy

mx

vx

f

x

x

my

mx

x

mxy

m x + mx cos 2 f ) m y sin 2 f ) 2m xy sin f cos f m y + mx sin 2 f ) m y cos 2 f * 2m xy sin f cos f m xy + * (m x * m y) sin f cos f ) m xy(cos2 f * sin 2 f)

v x + v x cos f ) v y sin f v y + * v x sin f ) v y cos f

v max + Ǹv x 2 ) v y 2

Reactions: The reactions, arranged node− and elementwise, are output according to the individual supports. In the graphical output of the line supports the possibility exists, of combining the nodal reactions in sections, provided the section length is given. For nodes with prescribed support movement, for the corresponding load cases no reac tions can be output. Storage of reactions: The reactions can also be stored and introduced as loading on an underlying floor.

Quantities for limit state specifications (envelope values) Deformations: One can obtain the envelope values of bending deflection with the associated rotations. Reactions: All kind of reactions results are available as envelope values, except the combined nu mericalgraphical output, . Reinforcement moments: The slab section forces are combined to reinforcement moments according to the com bination rules specified in the limit state specifications. The reinforcement moments at a point are the four moments required to determine the slab reinforcement in two orthogonal directions. Their calculation is based on the well known linearised plasticity conditions (cf. e.g. SIA 162 (1989) Art. 3 25 23): mbx+ mbx− mby+ mby−

= Max ( mx +mxy , mx −mxy ) = Min ( mx +mxy , mx −mxy ) = Max ( my +mxy , my −mxy ) .= Min ( my +mxy , my −mxy )

where: mbx+: positive reinforcement moment in xdirection (bottom reinforcement )

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mbx− : negative reinforcement moment in xdirection (top reinforcement ) mby+: positive reinforcement moment in ydirection (bottom reinforcement ) mby− : negative reinforcement moment in ydirection (top reinforcement ) The output directions are defined for each zone. Maximum shear forces: The maximum shear forces for a load case are calculated from v max + Ǹv x 2 ) v y 2 and cannot be directly combined to envelope values, since a particular direction, which can be different for each load case, is associated with this maximum value. Nevertheless, in order to obtain reasonable results for such limit states, CEDRUS5 uses the following method: vmax is not determined for each load case, but the shear force in all eight directions shown left. 22.5° In each of these eight directions the maximum value (all positive values) and the mini

mum value (all negative values) are evaluated in building the limit state values and at the end from the sixteen values carried through the evaluation the maximum absolute value is output as the envelope value. In this way the combination of envelope values is possible and one obtains a value which is normally sufficiently accurate. The associated directions are also part of the numerical output, in addition to the envelope values.

Required reinforcement The required top and bottom reinforcement of the slab in two orthogonal directions (axt and ayt for the top, axb and ayb for the bottom) is determined on the basis of design limit values of the reinforcement moments described above. For the dimensioning of the reinforcement in slab zones the following points are relevant: S

Dimensioning is based on the chosen limit state specification, i.e. envelop values in the from of reinforcement moments (see above).

S

Each limit state specification has an associated analysis parameter set, which is specified in the limit state specification dialog. The analysis parameter set (denoted APxx) is a series of criteria for the design of a reinforced cross section. Generally two different concepts for the dimensioning of the longitudinal reinforcement are sup ported: Strain limits for concrete in compression and reinforcement in tension: This cri terion is activated in the analysis parameter set ’AP2: ULS verification’. The AP2 is assigned by default to the limit state specification ’!Ultimate limit state’. Tensile stress limit for the reinforcement: This criterion, providing a minimum reinforcement ratio for crack control, is activated in the analysis parameter set ’AP1: SLS verification’. The AP1 is assigned by default to the limit state specification ’!Ser viceability’. The tensile stress limit is a parameter of AP1 and must be set by the user. Besides the two criteria the user can specify a number of other parameters in the sets APx, e.g. the partial safety factors for the materials and the strain−stress relation for concrete and reinforcement steel.

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S

The dimensioning according to the specified code and the selected analysis para meter set is based on pure bending action of a rectangular cross section. The result is the required reinforcement area per unit width, if necessary acting in tension and compression (Therefore it could result in a bottom reinforcement at a column sup port, without a positive reinforcement moment!).

S

The dimensioning for punching shear is realized independent of the bending design in the punching verification (see A 2.6).

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1 top concrete cover

reinforcement moment

bottom concrete cover

S .

The vertical position of the reinforcement is defined via the reinforcement cover, specified in the dialogs of the material zones and downstanding beams.

Note: the reinforcement cover is the vertical distance from the edge of the concrete body to the center of gravity of the reinforcement layer. S

In the same dialogs the material properties for concrete and reinforcement and the reinforcement direction are specified.

For the dimensioning of beam sections all the points mentioned above also apply. The following addition points, however must be noted: S

The dimensioning is based on a beam section cut off from the slab. The extension of this beam is defined by the userdefined width of the section: width of the section top concrete cover reinforcement moment integrated over the cross section

bottom concrete cover

In a beam section, like in any rectangular cross section, there is just one reinforce ment layer to be dimensioned at the top and one at the bottom. If, due to different material zones, the upper or lower edges are not constant (like in the figure above), the zone with the most eccentric edge is used for dimensioning. Note that the dimen sioning is based on pure bending only, i.e. not taking shear into account. S

Downstanding beams are treated just like ordinary beam sections, with the effective slab width determining the width of the section.

S

In all beam sections the reinforcement direction is automatically taken from the direction of the section.

S

The reinforcement moments to dimension for are calculated by integrating the calcu lated slab moments over the width of the section.

Forms of Presentation The following table provides information about the possible forms of presentation for the different derived quantities: *) Sections: These are simple sections through the corresponding contour plot. In the case of design limit values and reinforcement these section results can only be deter mined in zones, whose output direction coincides with that of the section direction or the normal to it, respectively. **) Beam%sections: These are sections with a selectable width, which cuts out therefore a .beam" from the slab. They may be obtained for those quantities, which are defined per unit length, e.g. section forces, reinforcement moments and reinforcement cross sec

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/

reactions columns/walls reactions area support zones

/

/

/

/

/

/

/

/

/ /

stored reactions

Limit state values:

section forces

/

displacements

/

/

/

/

/

/

reinforcement moments

/

maximum shear forces

/

/

/

/

/

/

/

/

/

/

/ /

punching shear verifications reinforcement sections

/

/

reactions columns

Reinforcement:

Load case file

/

Beamsections **)

Sections *)

displacements

Axonometrical

Load cases and load case combina tions:

Table

Contour plot

Results and their form of presentation:

Numericalgraphical

A 2 Basic Theory

Principal value graph.

Part A Base Module

/

/

/

tions. The value of the result in a point of the beam is given by the integral of the quan tities. On the other hand, in the case of reinforcement not the required reinforcement contents are integrated but the cross section of the cut out beam (e.g. a T−section in the case of an underbeam) dimensioned for the integrated action.

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A 2.6 Punching Shear Verification With the punching shear verification the aim is to confirm that no punching of columns or other concentrated forces through the slab is possible. The verification is considered to be proven if the following condition is fulfilled: V d v VRd Vd V Rd

design value of punching shear load design value of punching shear resistance

The punching shear verification in CEDRUS5 proceeds in four steps: 1. CEDRUS5 requires socalled punching shear objects for the punching shear verifica tion. Columns are a priori punching shear objects whereas for other actions of a punching shear nature (wall ends, concentrated loads) such objects have to be input in the form of polygons to define the areas to which load is applied. Each punching shear object contains all necessary parameters and the critical circumference (see below) in the form of a polygon, which normally is generated automatically. 2. In this way the punching shear resistances are determined and output in table form together with all the parameters used. 3. Finally, on the basis of a chosen load combination CEDRUS5 can also calculate the punching shear loads and these are compared in a punching shear verification table with the resistances. In the following it is explained how the design values of punching shear resistances and loads are calculated.

A 2.6.1 The Punching Shear Resistance In most codes the punching shear resistance is given by the total shear resistance along a socalled critical circumference u around the punching shear load. Thus the size of the punching shear resistance depends basically on the circumference length, the slab thickness and an "admissible" shear stress and, on the basis the concrete quality and the geometry, can be determined at the stage of structure input. V Rd + f (u, t, dm) 1) DS1

ÏÏÏ ÏÏÏ

u t dm

length of critical round section (=critical circumference according to SIA) nominal value of limiting shear strength effective static height (average)

In order to treat and be able to document the punching shear resistances in CEDRUS5, for each action with potential punching shear (wall end, concentrated load) a punch% ing shear object is introduced. This is an attribute box, to which belong a load applica tion area and a punching shear polygon to determine the critical round section.

2)

3)

1) Punching shear obje (Attributebox) 2) Load area (column section or polygon) 3) Punching shear polygon

The load area for a column in CEDRUS5 is identical to the column section. For other punching shear loads the load area is input in the form of a closed polygon. The punching shear polygon is automatically created on initialising a punching shear object according to the code rules and the geometry, whereby the slab boundaries are taken into account and portions of a polygon lying outside the slab are set to inactive. Circular arcs are approximated by polygon sections of constant side length. In principle, the punching shear polygon is closed. But it may consist of any number of active and inactive parts, where only the active parts contribute to the decisive circum ference u. The inactive parts are displayed graphically in a weaker style. The program tries to recognize whether it is an internal, edge or corner column. If at a certain distance from the column boundary no boundaries or recesses are encoun

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inactive polygon part

ÏÏ ÏÏ ÏÏ

ÏÏÏ ÏÏÏ ÏÏÏ

slab boundary

inactive part

active polygon part

active part

tered, then the column is treated as an internal column. Otherwise, the angle subtended by the punching shear polygon between the slab entry and exit points is a criterion to differentiate between boundary and corner columns. The maximum length of u is li mited depending on the code. It is compared with the length of a standard boundary or corner column and, if necessary, supported brought back from the boundary. Important restriction: The program is not always able to suggest a reasonable punch ing shear polygon (complicated geometry of slab boundary, zones of different thick nesses, etc.). Downstanding beams are also not considered, i.e. the proposed solution therefore has to be checked in each case and if necessary corrected using the Graphics Editor or manually.

Strengthened slabs If the existing resistance is inadequate, one can resort to shear reinforcement. The punching shear resistance with shear reinforcement depends on the code and the prod uct and is determined with the information provided by the supplier. The corresponding value (designated by VRd’) is input in the program. The increase of punching shear resistance due to shear reinforcement is limited and is again codedependent: SIA:

V R,max + 1.5VR

EC2:

V Rd2 + 1.6VRd1

(1.6 = countryspecific value)

With strengthening in the form of steel constructions (mushroom or collar construc tion) there are no such upper limits. Here too the the resistances VRd’, which have to be supplied by the producer, are input in the program.

Required bending resistances In order to achieve the maximum punching shear resistance, the bending resistances also have to fulfil certain requirements. In all codes supported by CEDRUS5 the re quired bending resistance mRd is made dependent on the existing punching shear load Vd: m Rd w hVd m Rd h

minimum required design value of bending resistance, so that the required shear capacity can properly adjust itself moment factor, dependent on column type (internal column, edge column, corner column η = 0.125 .. 0.5)

In CEDRUS5 this condition is reformulated, so that from the reinforcement content ρ prescribed by the user firstly a bending resistance and then from it the design value of a maximum punching shear load Vd,max is calculated: m V d,max + hRd The bending resistance mRd is estimated assuming a rectangular concrete compression distribution as follows:

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Reinforcement area:

A s + òbh

(b: width of slab strip, h: slab thickness)

Thickness of the compression zone: A sfy x+ (rectangular compressive stress distribution) bfc m Rd + 1g (dm * x )A sf y (g: resistance value for steel, d m: average effective static height) 2 In the case of scew boundaries and/or for rotated output directions the plastic resis tances are transformed into the corresponding directions parallel and normal to the boundary.

Notation for the tabular summary Together with the other stucture input data the program produces a table listing all the factors described above. In order to be able to name and compare the different inter mediate results, the notation has to be taken from the EC2 code, even in the use of the SIA code in some places, according to the summary given below: Case a: Slab without punching shear reinforcement: V Rd1

Design value of shear capacity (according to SIA: V Rd1 + VRńg)

Case b: Slab with punching shear reinforcement: V RdȀ

Design value of the total resistance, input by user.

V Rd2

Maximum design value of the punching shear resistance for a slab with punching shear reinforcement (according to SIA 162: V Rd2 + VR,maxńg )

Condition resulting from bending resistance: V d,max

Maximum attainable design value of the punching shear resistance due to the existing bending resistance (with or without punching shear reinforcement)

Case c: Total resistance supplied by user:

V RdȀ

When using steel constructions or in other cases where support for the de1 termination of the resistance is not given by the program, the total resistance has to be input by the user: Design value of the total resistance, input by the user.

Additional resistance: V Rd)

CEDRUS–5

A value input here is added in each case to the design value of the punching shear resistance, and thus to any input total resistance as well. The value may also be negative. One possible application of this could be the resistance correction for prestressing cables. If, however, the prestressing load case with the deviation forces arises in the load specification for the punching shear verification, the influence on the punching shear load is taken into ac1 count and no correction is required here.

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The critical value for the punching shear verification is given the name VRd (without further indices) in CEDRUS5 and, depending on the case, is obtained as follows: Case a: Case b: Case c:

V Rd + min(VRd1, V d,max) () V Rd)) V Rd + min(VRdȀ, V Rd2, Vd,max) () V Rd)) V Rd + VRdȀ () V Rd))

where V RdȀ w VRd1

SIA 162 – Specifics The punching shear resistance without shear reinforcement (without normal force) ac cording to the code SIA 162 is: V R + 1.8 @ t c,red @ u @ dm u g @ Vd t c,red u

dm

Nominal value of the limit shear stress according to Art. 3 25 403 and Table 2 (depends on concrete quality and slab thickness) Decisive circumference at a distance of 0.5 dm from the column boundary; Limits for u: internal column=16 dm, edge column = 8 dm , corner column = 4 dm Average effective static height of the slab in both directions

If the existing resistances do not suffice, then the value VR can be increased with shear reinforcement by at most 1.5 times: V R,max + 1.5VR + 2.7 @ t c,red @ u @ d m whereby according to Art. 3 25 414 the total punching shear load has to be resisted with punching shear reinforcement. The corresponding calculation is usually carried out with a productspecific design program. The tabular listing within the structure data looks as follows for a slab without punching shear reinforcement: PUNCHING SHEAR RESISTANCES (according to SIA Code 162 Section 3 25 4) Values for slabs without additional punching shear reinforcement (Concrete: B35/25, Steel: S500) Id Typ β ρx ρy τc,red h dm utotal urecess [%] [%] [N/mm2] [m] [m] [m] [m] DS1 E 1.00 0.80 0.80 0.900 0.25 0.21 0.76 0. DS2 R 1.00 0.80 0.80 0.900 0.25 0.21 1.23 0. DS3 I 1.00 0.80 0.80 0.900 0.25 0.21 1.86 0.

ucrit [m] 0.76 1.23 1.86

VR [kN] 260.23 418.401 632.682

Limitation of punching shear resistances due to existing bending resistances (of ρx, ρy and dm) αr mxR myR mLBordR m//BordR Vd,max VRd1 Id Typ αa [°] [°] [kN] [kN] [kN] [kN] [kN] [kN] DS1 E 166.750 166.750 277.917 216.859 DS2 R 9.0 180.0 166.750 166.750 166.750 166.750 555.833 348.667 DS3 I 166.750 166.750 1111.667 527.235

VRd [kN] 216.859 348.667 527.235

For cases b and c (see above) as well as for the input of additional resistances the follow ing table is also output (and then the last two columns are not shown in the above table): Summary and critical values (including taking account of punching shear strengthening) Vd,max VRd2 VRd’ Id VRd1 [kN] [kN] [kN] [kN] DS1 216.859 277.917 325.288 300.000 DS2 348.667 555.833 523.001 500.000 DS3 527.235 1111.667 790.852

A–34

VRd+ [kN] 0. 0. 0.

VRd [kN] 277.917 500.000 527.235

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A 2 Basic Theory

Finally the following legend is printed out: Type β ρ τc,red h dm u αa mxR/.. VR VRd1 Vd,max

: : : : : : : : : : : :

VRd2 VRd’ VRd+ VRd

: : : :

Column type I=internal column, R=edge column, E=corner column (italics = automatically created) Factor to consider a non−uniform distribution of the shear force according to Art. 3 25 404 Reinforcement for longitudinal reinforcement (ρx, ρy = tensile reinforcement in x− and y−direction) Nominal value of limit shear stress according to Table 2 Slab thickness Average effective static height Length of critical round section ucrit = utotal − urecess Output direction (=x−direction of reinforcement), αr : direction of slab boundary Bending resistances in x− and y−direction, as well as normal and parallel to slab boundary Punching shear resistance Art. 3 25 403 VR = 1.8 τc u dm Design value of punching shear resistance VRd1 = VR/1.20 Limit on punching shear resistance due to existing bending resistance: Vsd = mR / (η γ ) Moment factor η depending on column type I: η = 0.125, R: η// = 0.25, R: ηL = 0.125, E: η = 0.5 Maximum punching shear resistance with additional shear reinforcement VRd2 = VRd1 * 1.50 Total punching shear resistance specified by user Correction of resistance due to prestressing Critical value for the the punching shear verification (**** =not checked)

SIA262 (Swisscodes) – Specifics The basic relation in eq. (51) is very simular to all the other EC based codes: v Rd + kr·t cd·d The major difference consists in the calculation of the parameter k r, which cannot be calculated by hand with a reasonable effort anymore. k r depends on the provi ded reinforcement and the geometry of the system. In order to get k r the following values must be determined (width v Rd calculated by iterating width eq. (51)): k r + kr(h, d x, dy, l x, l y, ò x, ò y, v Rd) The first three geometrc values (slab thickness, effective heigth) are taken from the material box of the zone (calculated from slab thickness and concrete cover). y

x f

x

The two values for the spans (l x, l y) and the geometric reinforcement content (ò x, ò y) must be provided by the user (In future versions CEDRUS will alternatively deter mine these values for a given punching force). If the output direction was rotated, the values for d x, dy, l x, l y, ò x, ò y are determined in the new orientation. The Swisscode differentiates between clamped and simply supported configuration. The program does take this information from the support condition of the column object. For a simply supported configuration both rotational degrees of freedom must not be blocked.

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Edge column simply supported Case A

1.5·d clamped support border of the slab

u−calculated witdh A nom

d

ÏÏ ÏÏ ÏÏ

active portion of the polygon inctive portion of the polygon

A nom

Case B

d In order to check the assumptions made a series of intermediate results is given in a table (e.g. m Rd and r y ). In the help menu of the program a number of examples with all the different column types can be found (see Help>Examples). This is the resulting output table within the legend of the structural data: PUNCHING Table 1: Summary ρx ρy Id Typ ke DS1 +E DS2 +R DS3 +I

1.00 1.00 1.00

τc,red

h

d

ly

uBrutto

[%]

[N/mm2]

lx

[%]

[m]

[m]

[m]

[m]

[m]

0.635 0.635 0.635

0.635 0.635 0.635

0.90 0.90 0.90

0.200 0.200 0.200

0.155 0.155 0.155

5.700 5.700 5.700

5.700 5.700 5.700

0.587 1.012 2.087

uAussp umassg [m]

[m]

0 0 0

0.587 1.012 2.087

EC2 – Specifics The punching shear resistance without shear reinforcement (without normal force) ac cording to the code EC2 (or Version SIA−ENV1992−1−1 and GRN−91): V Rd1 + u @ t Rd @ k @ (1.2 ) 40ò 1) @ d m u b @ V Sd V Rd1 t RD u dm ò1 k b V Sd

Design value of the shear capacity without shear reinforcement Basic value of design shear strength according to Tab. 4.8 Length of the critical round section Average effective static height Average reinforcement content Factor, dependent on dm: k = (1.6− dm) ≥ 1.0, dm in [m] Factor to consider the effect of eccentric load Internal column b=1.15, edge column b=1.4, corner b=1.5 Design value of the total shear force to be resisted

With shear reinforcement this value can be increased by up to 1.6 times: V Rd2 + 1.6 @ V Rd1

E-DIN 1045-1 – Specifics 1

V Rd1 + u @ 0.14 @ Ë @ (100ò 1fck) 3 @ d m u b @ VSd

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Ë +1)

Ǹ200d v 2.0

( d in [mm])

Length of the considered round section Characteristic cylinder compressive strength Average effective static height Factor to consider the effect of eccentric loading: internal column β=1.05, edge column β=1.4, corner column β=1.5 Design value of the total shear force to be resisted

u f ck dm b V Sd

DIN 1045 – Specifics With the "old" DIN Standard 1045 the punching shear load depends on the column di mensions, the effective height of the slab and an admissible shear stress, not however on u. This procedure is not supported by CEDRUS5 but instead the above described formula from 10451 is used. The strengths of the old materials are then approximately determined according to the following formula: fck=βR/α (α=permanent condition factor according to EC2, α= 0.85) Comparison for ρ = 0.005: Quality after E1DIN 104511

C12/15

C20/25

C30/37

C35/45

DIN 1045

B15

B25

B35

B45

α fck

10.2

17

25.5

29.8

10.5

17.5

23

27

1.82

2.15

2.47

2.60

1.83

2.18

2.38

2.51

βR

[N/mm2]

[N/mm2]

(100 ρ

fck)1/3

(100 ρ βR /

α)1/3

OeNorm B4700 – Specifics The punching shear resistance without shear reinforcement (without normal force) ac cording to the Austrian Code OeNorm B4700: V Rdc + 1.2 @ t d @ Ë c @ (1.2 ) 2000 @ d @ ò) @ u @ dm u b @ V Sd l V Rdc td l Ëc dm ò u b V Sd

Maximum column force without punching shear reinforcement Nominal value of shear stress according to Table 4 Adjacent column width (in CEDRUS15 probably fixed for slab, e.g. l = 8m) Factor, dependent on dm: k = (1.6− dm) ≥ 1.0, dm in [m] Average effective static height Average reinforcement content ò + Ǹò x @ ò y v 0.015 Length of the critical round section Factor to consider effect of eccentric loading of internal column β=1.15, edge column β=1.4, corner column β=1.5 Design value of the total shear force to be resisted

The determination of an "adjacent" column width is fairly difficult to implement for a generalpurpose program. Since in practice it is hardly likely that one will meet with slabs, which are more slender than d/l = 1/35, the corresponding term has been simpli fied. Therefore. for the determination of VRdc in CEDRUS5 the following formula is used: V Rdc + 1.2 @ t c @ (1.2 ) 57 @ ò 1) @ u @ dm

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A 2.6.2 The Punching Shear Load The design values of punching shear loads are determined by the program if a punching shear verification is demanded on the basis of the chosen limit state specification and is listed in the verification table. Since with the punching shear verification it is a question of an ultimate load verifica tion, the starting point is a limit state specification for ultimate load verification. To deter mine the critical punching shear loads the program carries out its own limit state calcula tion, which determines for each punching shear object the maximum (and minimum) sum of all reaction forces and loads, which act within the critical load area. The sign of the largest absolute value must be in agreement with the punching shear type speci fied in the punching shear object (column=positive or concentrated load=negative). As critical load area a polygon is assumed, which encloses the loaded area at a dis tance of one half the average effective static height. In the SIA code this polygon usually coincides with the punching shear polygon. In EC2 and other codes the critical round section, however, is at a greater distance from the loaded area and it would not be per missible, e.g. for prestressing cables in the column region, to deduct the deviation forces in the complete region within the punching shear polygon. For this reason it was de cided not to consider the punching shear polygon also for the definition of the critical load area. If prestressing load cases are included in the limit state specification, the effect of the deviation forces are likewise considered within the punching shear polygon.

A 2.6.3 The Punching Shear Verification For a punching shear verification the following steps are necessary: 1. Introduce punching shear objects or input the corresponding attributes for all en dangering actions. 2. There must exist a suitable limit state specification for the ultimate load, which takes account of the important loading positions. 3. This limit state specification has to be chosen in the Results Register of CEDRUS5 and a punching shear verification has to be demanded. As result the following table is created:

PUNCHING SHEAR VERIFICATION Id DS1 DS2 DP1 DP2 Dtype VReac VLoad β Vd Vd ’ VRd

A–38

Dtype Column Column Load Load

VReac [kN] 123.45 142.50 0.00 45.90

VLoad [kN] −4.23 −88.43 −80.66 −204.22

β 1.00 1.25 1.00 1.00

Vd [kN] 119.22 67.59 −80.66 −158.32

Vd ’ [kN] − −15.40 − −

VRd [kN] 138.76 120.75 −105.20 −145.38

Verif. ok ok ok Vd>VRd

Column: main punching shear load positive; Load: main punching shear load negative Reaction part of Vd Load part of Vd Load factor to consider a non−uniform distribution of shear force Design value of punching shear load corr. Dtype: Vd = β*(VReac + VLoad) Is proved, if the other extreme of punching shear load has a different sign to Vd Design value of the punching shear resistance

CEDRUS–5

Part A Base Module

CEDRUS–5

A 2 Basic Theory

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A 3 Working with CEDRUS-5

A 3 Working with CEDRUS-5 This chapter will help one to become acquainted with the main features in CEDRUS−5 − by concentrating on the most important steps of a complete calculation. To prevent one from losing the thread, we dispense with the treatment of many details that are fully described elsewhere. The most important source of information is the Help System of CEDRUS%5, whose intensive use we strongly recommend. It can be called in various ways: S

By clicking on the menu .Help" in the program’s menu bar. A list with corresponding hyperlinks of all available help documents appears. One of these is called .How to use the help system". It provides instructions on the use of the Help System.

S

By pressing the key one obtains specific help on the current action (e.g. point input) or on the input element that the mouse pointer currently highlights.

S

Many of the dialogue windows which appear during input have their own Help Sym bol

for information on the corresponding dialogue.

It is assumed that one has an adequate basic knowledge of the use of the Microsoft Win dows operating system. This includes the handling of windows (move, zoom), together with the Start Menu, Task Bar, Clipboard and the Windows Explorer. .

As in Windows, in general one always works with the left mouse button. Clicking or selecting a symbol on the screen means: move the mouse pointer onto the symbol and then press briefly the left mouse button. The right mouse button is only to bring up a context menu to the screen (see later) in a particular situation. A detailed description of the Graphics Editor as well as of the CubusViewer is given in Parts D and C of this manual.

A 3.1 Presentation Conventions for the Examples For all application examples the following presentation conventions hold: S

All actions to be carried out are indented and marked as follows: " Description of action

A–40

S

All bold print in the description of an action has to be typed exactly with the follow ing exceptions.

S

Special keys enclosed in (e.g. =, , , etc.)

S

The mouse buttons are abbreviated with and (left and right)

S

Buttons on the screen are shown in square brackets (e.g. [Cancel])

S

Words in italics like Click, Select, ... are clearly predefined user actions

S

An entry to be chosen in a menu is given within apostrophes, separated for multi− selection by ’>’ (e.g. ’Options’ > ’Language’ > ’German’)

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Part A Base Module

A 3 Working with CEDRUS-5

A 3.2 Starting the Program CEDRUS−5 can be started in two ways: 1) By executing the program file CEDRUS5.EXE, e.g. via the Start Menu of Windows (for standard installation: [Start] > Programs > Cubus > CEDRUS5). CEDRUS5 re sponds with an empty window and the following menu bar:

This method of starting is recommended above all if one wants to continue with one of the last calculations worked on (these are listed in the File menu). 2) Via the CubusExplorer. The CubusExplorer is an independent program for managing calculations with different Cubus programs and is also called using the Start menu of Windows. For our example we use Start Method 2). The procedure is described in the next chapter.

A 3.3 Opening a Calculation " Start the CubusExplorer via the Windows Start menu. If you are doing this for the first time, the following display on the left could appear. Click on the ’+’ beside ’My Computer’ and one obtains the display on the right.

The CubusExplorer is very similar to the Windows Explorer. The main difference is that in the window on the left only those directories are displayed which one wants and these are usually those which contain calculation data from Cubus programs. For a de tailed description of the CubusExplorer see the Help menu. For our example we want to create on a harddisk (here C:) a folder (directory) named .CD5Data", in which we then store our first calculation. Basically one has complete free dom with the directory structure for managing the projects. One can reorganize it at any time and rename or move folders.

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" First click on the symbol of the desired harddisk and then on the symbol on the left to create folders or make them visible.

The window then displayed shows the directory structure of the selected harddisk. One can now select one of the shown folders or subfolders and using the symbol [Choose] introduce it into the CubusExplorer to display it. We want to create a new folder,. " First select for this purpose the object (Harddisk or Folder), where the new folder should reside 1 in our case the harddisk D:. " To create a new folder click on

upper right.

Then a new folder appears on the chosen directory level. " We now rename it to ECD5Data" and then introduce it with the button[Choose] into the CubusExplorer. " lSelect the newly created folder and click on this button to create a new calculation Below this button a list of all installed Cubus applications pops up:

" Choose the symbol for CEDRUS5, whereupon in the middle window of the CubusExplorer a new calculation entry with the standard name .CD5Calculation" appears. Rename it .Example1" by clicking again on the chosen name or by pressing the right mouse button and using the command Rename. Thus, one has created the desired calculation folder. " Start CEDRUS15 with the button [Modify] bottom right in the CubusExplorer.

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Now the following dialog pops up. Here you can define the basic properties of your calculation including the texts in ’Description’, which will be printed shown on the out put:

" Leave the input fields like they are and close the dialog with [OK]. .

The user can, with the exception of the ’Structure type’, change all the properties in the dialog at any time.

.

After opening a new calculation there is the possibility of importing input data from an older CEDRUS calculation or a DXF file. Use for this purpose “Import” in the File menu shown above.

A 3.4 The Control Tab Sheet After a new calculation has been opened, there appears at the top of the CEDRUS5 win dow the Main menu of the program in the form of a sheet:

The tab sheets are arranged from left to right as used in a normal calculation. They are activated by clicking their tabs. Each sheet page possesses a number of functions which can be called using the corresponding symbols. These symbols are also arranged from left to right, as usually required in the course of a calculation. The first thing to do with a new slab is define its structure. The corresponding tab sheet, therefore, is already selected.

CEDRUS–5

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A 3.4.1 The Tab Sheet /Structure/

Status indicator

Selectability switch:

all on all off

Symbols to input and check the individual structure objects

The structure relevant to the FE calculation consists of a series of objects, like outline, openings, etc.. For each of these object types there is a corresponding symbol, with which new objects of the corresponding type can be input.

Plan Outline, Openings We begin with the input of the plan outline: " Click on this button in order to start the construction of the outline. Now on the left the drawing tools of the Graphics Editor become active. With these the outline or parts of it can be created. " Input the outline shown below with the polygon tool, by clicking on it and then type, in correct sequence, the five coordinate pairs of the corner points (x + , y + , etc.). One closes the polygon by clicking on the first point again. The direction, i.e. clockwise or anti1 clockwise, is unimportant. (0,13)

(10,13)

(16,8) 3

3

2

(0,0)

4 (16,0)

The slab outline can consist of many pieces (lines, polygons, circular arcs), so that at the end the desired outline polygon without any gaps is to be seen on the screen. " Click on this button in the tools list to zoom all (see for help). .

A slab may only have one outline.

.

The Graphics Editor offers several possibilities for inputting new points, which can greatly simplify the work, depending on the situation. To obtain this information use the Help key on inputting a point. Openings are input in the same way as the outline. " Click on this button and Edraw" the opening shown here with the available tools. The quickest way, of course, is to

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use the rectangle tool for which one only has to input two points directly opposite. .

An opening may not cut or touch the outline or any openings. An “opening” right on the boundary of a slab, i.e. a recess, has to be included in the outline.

On the Input of Geometrical Objects Here some important remarks are necessary, which not only concern the input of an outline or openings, but all geometrical structure objects. The geometrical definition of a slab structure consists essentially of points and lines. Higher objects, like rectangles, polygons, wall−like objects etc. consist of several lines. Since the FE mesh has to take into account all these points and lines, the following con ditions apply: S

All points must have a distance of separation of at least dmin. The value of dmin can be inspected in the menu Settings>Tolerances and in special cases can also be changed.

S

The distance of a point from a line also has to be at least dmin.

S

If two points are at the same place (e.g. two lines, which converge to a point), then, depending on the method of inputting these points, it may be that because of round ing errors they do not have exactly the same coordinates. For this purpose CEDRUS5 possesses a tolerance value dtol. If two points are closer that dtol, then they will be merged by the program. The value of dtol can be inspected in the menu Settings>Tol erances and in special cases can also be changed.

Summarizing: If the distance between two points or between a point and a line is greater than dtol but smaller than dmin the program rejects this during checking and issues an error message.

Material Properties

ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ Ä ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÔÔÔÔÔÔÔÔÔÔÔ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ ÓÓÓÓÓÓÓÓÓÓÓÓÓÓÓ Ä Ä Ä

The material and thickness properties of our example slab are specified as follows: Concrete C25/30 Reinf. steel B500B isotropic material Columns 40x40 cm

d=35cm

6m

Downstanding Section A−A:

60cm

A

d=25cm

40cm

A

8m

Using the first 3 symbols the material properties (material model, thickness, concrete and reinforcement material...) of the slab are defined. Firstly, any existing lines of sepa ration (so−called separators) for different materials are input. Downstanding beams are separate objects and their outlines always act as separators.

CEDRUS–5

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" In our example we have input two separators, which de1 marcate the zone of 35 cm thickness. Click on the symbol for material separators shown on the left and draw the two lines. :

Astuce: The simplest way of inputting these lines is to: Click on the Line Tool of the Graphics Editor. For the starting point of the horizontal separator click on the bottom right point of the opening. Then press the key (= line in Xdirection) and click on the extreme right on the outline line. One continues in the same way with the vertical separator, by drawing a line in the Y−direction upwards from the upper right corner point of the opening. With these separators one has divided up the slab into two material zones. In each mate rial zone an attributes box with the corresponding material properties is now required. " Click on the symbol shown, whereupon the dialogue window for material attributes appears. Set the following val1 ues:

Here all the materials form the material list are selectable (Menu Settings>Ma terials, for more details press the help button of this dialog).

" Click on the symbol [Create] and place an attribute box by clicking with the left mouse button in the upper right zone of the slab. These material properties apply now at the position of the material box up to the zone boundary through the edge of the slab or material separators. .

If the dialogue window for placing the box is in the way, move it by clicking on its header and dragging it to a different place. " In the dialogue window, which is still on the screen, change the thickness to 0.25 and in the same way using [Introduce] also place the attribute box for the second material zone. For further explanations on material properties click on the Help symbol of the dialogue window. " To input the downstanding beam at the bottom boundary of the slab click on the symbol shown. Here also a dia1 logue window appears to set the desired attributes of the

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downstanding beam:

Choice of input axis and width of downstanding beam. MRight" means that the input axis runs along the right side of the downstand ing beam. Upper surface of downstanding

Upper surface of the adjoining slab

Slab thickness

Total height

" Apply settings according to above sketch of outline. Then choose [Create] and define the downstanding beam line by clicking on the lower left and lower right corners of the outline. Since the input for the downstanding beam is performed using the polygon tool, the polygon, which here only con1 sists of one segment, must still be closed. This is accom1 plished by clicking again on the end point. .

If by mistake one inputs a point incorrectly with polygon input using the -key one can go back one point at a time. For further explanations on downstanding beams press on the Help symbol of the dia logue window. " After inputting all material objects one can check these with the program using the symbol shown on the left. This, however, is not absolutely necessary and is only meaningful for complex conditions, since this check is carried out automatically before solution by the program.

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Undo / Redo We want to draw attention here to a very useful function of the Graphics Editor. If one has made an incorrect input or even several in a row this is not a problem with CE DRUS5: With the Undo Function (on left side of window) one can reverse stepwise (provided the symbol is active) as many changes to graphics objects as desired. Key combination: Ctrl+Z With the Redo Function one can reverse stepwise changes made using the Undo Func tion. Key combination: Ctrl+Y

Supports Our example slab is supported as follows:

Storey height=3 m Wall t=24 cm freely supported

ÄÄ ÄÄ

6m

S1

4 columns 40x40 cm freely rotational

Ä

S2

ÄÄ S3

8m

ÄÄ S4

For slab supports the five object types shown on the left are available. The first two serve to define area support zones and function with respect to input regarding attribute boxes and separator lines as for the material zones described above. They find applica tion with foundation slabs using the method of the coefficient of subgrade reaction or with special column and wall supports, which cannot be satisfactorily modelled with the other objects. For details refer to the Help System.

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The last of the five symbols permits the input of lines of symmetry along slab bound aries. The remaining two types − columns and walls − occur in our example. " Click on the column symbol. A dialogue window for col1 umns appears, in which one makes the following set1 tings:

One can differentiate between the effec tive column section and the supported zone for the FE model. For the determination of the column stiff nesses and the punching shear verifica tions the effective column dimensions are required. In the FE model there are two reasons why one wants to model the supported zone differently from the column sec tion: 1) It is very difficult to introduce a corre sponding support zone for a circular column of small diameter. 2) The choice of a somewhat larger sup ported zone leads, for slender columns, to better FE meshes and more realistic column moments. The underlying idea is a cone−shaped spreading out of the support area from the top of the column to about the middle of the slab, e.g. at 45 degrees. In our example we dispense with a sep arate input of the column section and the supported area.

To introduce the different columns first select the suitable anchor point in the graphics shown (within the Column dialogue window), then select the symbol [Create]. By input ting a new point or by clicking on an existing point one inputs a new column. The input point corresponds to the chosen anchor point. " For column S1 in our example choose the anchor point in the middle, click on [Create] and input a new point at the position (8.0,6.0). " For column S2 choose the anchor point bottom left, click on [Create] and click on the outline point bottom left. " For column S3 choose the anchor point lower middle, click on [Create] and input a new point at (8.0,0.0). " For column S4 proceed as for S2. .

If by mistake one inputs a point incorrectly, remember the Undo Function! For the column model there are a number of variants and attributes. Regarding these read the corresponding chapter of the Basic Theory and consult the Help System of the Column dialogue window.

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" Besides the columns there is also in our example a wall. Click on the Wall symbol, whereupon again the corre1 sponding dialogue window appears.

Although they have to be input as gen uine walls with a certain width, in the FE model walls are modelled as line supports. The line support is introduced on the input axis, unless one inputs a distance from the support line (from the input axis). Positive val ues signify a position looking right in the input direction. The input axis can lie on the left, in the middle or on the right of the wall (in the input direction). .

Although in reality the wall axis does not lie on the slab boundary, in practice it is often simpler and acceptable from the modelling point of view, to input the wall in this way. Otherwise, since the FE mesh has to take account of the support line, very small elements between the boundary and the support line would result. The width, height and EModulus of the wall are used by the program to determine the stiffness and dead load but are otherwise not of importance. " Set all input fields according to the preset values of our example and then click on [Introduce]. The simplest way of inputting the polygon points is as follows: 1) To produce the first point of the wall polygon click on the upper right opening point. 2) The second point lies on a horizontal line through the first. Press therefore the − key and click on the left slab boundary. 3)

The remaining four points can be clicked directly.

For detailed information on the Wall dialogue window click on its Help symbol.

The Selection of Objects and the Right Mouse Button These remarks highlight very important properties of CEDRUS5, which it is indispens able to understand. Whereas, before now, to input new structure objects one has worked with menus (e.g. Column symbol to input a column), this way of working is not very suitable for modifying existing objects, as can be seen in the following exam ple: We want to move the opening as well as the adjacent end of the separator line shown bottom right by 50 cm to the left. One does this in the following steps: 1) If a Structure object symbol is still active, click on it to switch it off. Thereby all Struc ture objects are now selectable (if a symbol is active, then only the objects of that type are selectable). 2) Now one has to select those objects, which have to be subsequently moved. First of all, the most important points on selecting objects are explained: S Objects are normally selected by clicking with the left mouse button or by means of a window. If the window is opened by drawing from left to right, only those

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objects which lie completely within the window are selected, whereas on draw1 ing from right to left also the cut objects are selected. S Selected objects are presented in red (colour can be set). S When selecting by clicking or by means of a window any objects already or still selected are automatically deselected beforehand by the program. If one wants to suppress this action, during selection one presses the key. With a pressed key objects already selected can be deselected. S Geometrical objects normally consist of lines, rectangles or polygons. If one wants to select the end or corner points of such an object, one first has to select the object. In the selected state its points are visible and can then be selected in the usual way. For our example one has to select the left end point of the horizontal material separa/ tor as well as the opening. For the reasons given above we proceed as follows: a) Click on the material separator and then on the left end point of the line. On select/ ing the point the selection of the line is lost, which also corresponds to our intentions. b) In addition to the selected point the opening should now be selected. With pressed key click on the opening. 3) Now press the right mouse button, and the menu shown below appears, which lists the modifying possibilities for the selected objects. This menu is called a context menu. If nothing is selected, the context menu appears in the graphics area. 4) Click on .Move" in the context menu. 5) The text at the mouse pointer tells one that one should choose the move point. Click on a corner point of the opening. As a result of the movement or the new position of this selected move point one fixes the new position of the selected object. 6) The point now to be input defines the new posi tion of the move point. In our case there is no tar get point to grab, so we input it. This is simplest with the method Relative Input. Press the key . The relative point, marked by a small red triangle, must be placed on the move point. If it is not there click on this point. As con firmation the Triangle symbol to mark a point is moved to this point. Now type in the relative coordinates (−0.5 ↵,0↵). Successful? In any case reverse the changes with the Undo function.

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.

The described procedure (select objects, then call the context menu with the right mouse button) is called object–oriented working. The more different the selected objects are, the smaller the number of active functions in the context menu, since it comprises the number of all applicable methods for these objects . CEDRUS-5 works strictly according to this principle.

.

On the different techniques for selecting objects see the corresponding chapter in the Help Document of the Graphics Editor. Important hints are also to be found in the following section.

.

Modifying object attributes is a very important function, which is also carried out using the right mouse button. The row “Attributes” in the context menu is only active, if a single object or several identical objects are selected. Important information on this topic can also be found in the Help Document of the Graphics Editor under “Working with Attribute Dialogues”as well as in the next section.

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Printed Documentation of the Structure Input The structure input is now complete, but we still want to produce a printed documenta tion of the input. For this there are two possibilities. The first provides a tabular documentation and is performed using the symbol on the left in the Structure Tab Sheet. Click on it and the information appears in a separate win dow. If one wants to print the document, there are two symbols for this purpose in the header part of the document window. The first prints the document immediately, while the second stores it in an output list to be printed later. Regarding this see the comments below. A graphical documentation of the Structure Input is obtained by clicking on a Print sym bol upper left in the CEDRUS5 Window. Here too the upper symbol causes direct print ing, whereas the lower one creates an entry in the output list. Always that is printed, which is seen in the working area or, more precisely, in the current visible layer. One can switch on and off individual layers at will. For this purpose use the layer switch on the right side of the working area. The symbols to print the graphics working area can be used at any time. Before printing or entry in the output list a dialogue window always appears, which serves the following purposes: S

Possible choice of figure detail

S

Preselected scale

S

Modification of or addition to the preset figure title

S

Modification of the short title for entry in the output list

For further details on this dialogue window use its Help symbol.

The CubusViewer The CubusViewer serves to preview and print all previously made entries in the output list. In the left part of the CubusViewer is the list of all entry titles and in the right the print preview. The CubusViewer offers the following possibilities (the details may be consulted in the Help menu):

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S

Activation/deactivation of individual entries

S

Move entries (order of printing)

S

Change scale of individual entries

S

Insert page break

S

Choice of page layout / paper format

S

Definition of ones own page layout

S

Choice of printer

S

Zoom in the print preview

S

Deactivating print preview for a quicker handling of the entry list

S

Choice of print output in colour, black/white or with grey shades

S

Print the active entries

S

...

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A 3.4.2 The Tab Sheet /Loads/

In this sheet all the load cases and the corresponding loads can be input and modified. " Click on the tab and one obtains the following tab sheet: load case handling

input of load objects

legend of load data

Load import List of actions active load case

select active load case

check/reset loads

switch to next/pervious load case

scaling factor for 3D view

We want to introduce the following load cases for our example: S

Dead load, consisting of the selfweight of the slab and a uniformly distributed load of 0.6 kN/m2 for the surfacing

S

Live load of 2 kN/m2 (Category A) field−wise unfavorable on four fields.

The first load case with the selfweight is automatically generated by the program and set as the active load case. For the load case, the self−weight is realized with a accelera tion load for the mass of the slab, with the mass calculated form the volume of the slabs and the mass per unit volume of the concrete material (see menu: Settings>Materials). All we have to do is add the surface load: " Use for this the symbol for uniformly distributed loads and set the value of the load in the dialogue to −0.6.

.

Due to the global coordinate system, in which the Z-axis points upwards, the downwards acting loads, inclusive of the value for the body force, have to be input with a negative sign. " Click on the button [hole structure] and place the box somewhere inside the outline of the slab. Now the input of the live load. These, analogous to the case of dead weight, can be defined individually or more easily, as shown below, using an so called ’generator load case’. Proceed as follows: " Click on the symbol to create a new load case. The fol

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lowing dialogue window appears: load case type (cannot be chan ged later) short id description

A correct input of the action cate gory and subcategory allows a pro per automatic generation of limit state specifications Note: The avaiable actions depend on the structure type

" Set the input fields according to the dialog shown. Now the newly created load case is active for input. The symbols for inputting load ob jects are also now active in the tab sheet. " Click on the symbol for area loads and set the load value to −2.0 kN/m2. " Now draw with the rectangle tool of the Graphics Editor the four load rectangles, which together cover the whole slab. If you click on the button twice, the rectangle tool will stay active and you can input multiple rectangles easily. To quit this mode press the ESC key. 4 load rectangles

From the Generator load case just defined, which for the subsequent solution is auto matically marked as inactive, the program generates as many individual load cases as were defined, in our case 4, named after the generator GU in the form of GU%Fx. .

If afterwards one wants to modify the generated load cases, one always has to make the corrections in Generated Load Case. CEDRUS-5 regenerates the corresponding load cases on leaving Generated Load Case each time.

.

To simplify matters, the input load cases can be drawn without any difficulty over openings and also across the slab boundaries. The program only considers the load on the effective slab area. " Click on the symbol EList of load cases" and one can see a list of the previously defined and generated load cases. The Inactive symbol with the Generator is switched on.

.

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Besides the generator ’unfavorable pattern’ a second named ’moving load’ is supported by CEDRUS. In that case you input a series of load objetcs (e.g. the load pattern of a truck) and a nubmer of positions, where this load objects should be placed. CEDRUS will automatically generate a load case for each position and make proper (i.e. exclusive) superposition of these load cases in the limit state specification.

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The Dialog ’Actions’ " Click on this button in the tabsheet to open the list of ac tions.:

The dialog shows all actions, that have been assigned to load cases. If you want to use actions, that are not available for selection in the load case dialog, you can define them here. The actions and their partial safety factors are used for the automatic generation of limit state specifications. For details see Chapter A 2.3 as well as the online help. of this dialog. If you check all the actions in the dialog you will notice, that the action ’Live load gen eral’ you didn’t specify so far is listed. This action was automatically introduced for the socalled ’load transfer’ mechanism, i.e. export of the reaction forces to the floor below where you can import them. All load cases with the property ’export automatically’ turned on (=default) are combined to socalled ’export combinations’ and exported for the next floor. So by default you don’t have to do anything to export your reactions. If you want the self−weight of the columns and walls to be included in the exported loads, make sure you activated the checkbox ’Consider weight of ..’ in the property dia logs of the walls and columns! For more details check the chapter A 2.4 of this manual.

The Dialog ’Load Import’ As discussed in the last section, by default no steps must be taken for export of the reac tions of a slab. However, in order to import these reactions in the floor below, there you must define the floor that resides above yours. This is done in the dialog ’Load Im port’: " Close the dialog ’Actions’ and press this button.:

After specifying the floor (or floors) that do transfer load to your slab you actually per form the load import by pressing the [Update] button (see chapter A 2.4).

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A 3.4.3 The Tab Sheet /FE Mesh/

The FE mesh required for the computational method is automatically generated by the program. One only has to supply certain parameters, usually only the maximum element side length. This is done, as for the material properties, by placing an attributes box for FE mesh zones. The mesh parameters may vary from zone to zone. In this case the corresponding zone separator lines are required and per zone one attributes box. .

by default the program automatically places an attribute box inside the outline including default parameters for the control of the mesh generation. So there is no need to place a box yourself. However it is always up to the user to make sure, that the generated mesh is appropriate for your analysis, since the program cannot do this. You can inspect the mesh by making it visible with this layer button. " In our example we want to work with an element mesh length of max. 0.8m. If a box is generated make sure the value is set to 0.8. If no box is present, click on the symbol for attributes boxes and in the dialogue window that appears set the maximum side length to 0.8. Click on [Create] place the box anywhere on the slab. With the symbol shown left one can now cause the mesh to be generated. This, how ever, is not really necessary. The mesh generation is in any case carried out automatically by the program when needed. In special cases one can also define zones with a manually created mesh. Regarding this and also the other mesh parameters one can find more information in the Help function for the dialogue window of the attributes boxes.

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.

General information on FE meshes can also be found in the chapter Basic Theory, Section 2.2.9.

.

A modification of an automatically generated mesh is not possible in CEDRUS-5. If one feels that the generated mesh is not really suitable, try a finer mesh, try changing the other mesh parameters or try using more mesh zones.

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A 3.4.4 The Tab Sheet /Calculation/ This tab sheet contains the following briefly described symbols. If one does not have any input to make here, one can change directly to the Results Tab Sheet. The standard solution procedure is automatically carried out by the program when results are re quested. Results for all input and active load cases are located in the Results Tab Sheet and can be inspected at any time. But if one wants combination of other results (with arbitrary factors), then one has to define these combinations using the symbol shown on the left. The details can be obtained with the Help function of the dialogue window that ap pears. This is the symbol for the input of limit state specifications. In standard cases, as in our example, the limit state specifications are automatically created on the basis of the as signment of the load cases to particular actions and given the name .!Serviceability SLS" and .!UltimateLoad ULS". These unmodified specifications can be seen by clicking on the symbol and for printing they can be entered into the output list. The details can be obtained with the Help function of the dialogue window that appears. " Click on this button and check the generated limit state specifications. With this button you can open the dialog for the definition of a dynamic analysis (op tional). With this button you can start the system solver, which will calculate the raw results and update the export loads. As mentioned above, this is never necessary and is done auto matically whenever a result is being asked for (see next section).

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A 3.4.5 The Tab Sheet /Results/

1

2

3

4

With the .Lightning" symbol far left one starts the calculation and the display of a result corresponding to the settings in the tab sheet. In the different parts of the tab sheet set the following (the contents of each zone de pend on the settings shown to the left of it): This zone contains a list with all input load cases, load case combinations, limit state specifications and reinforcement for each limit state specification. Click on the small symbol with the arrow in the text field and choose the desired entry in the list that ap pears.

1

Depending on the settings in the region (1) other output quantities are also available here. Choose the desired quantity from the list, if there is more than one to choose from.

2

Choose the form of presentation here. The available choice depends on the selected output quantity. If one points the mouse to a symbol an explanatory text appears. The six symbols shown in the above tab sheet (for section force results) signify, from left to right: isolines, principal value plots, numerically labelled mesh, tabular output, nor mal sections and beam sections (sections for which the results quantities are integrated over a certain width).

3

If an output quantity has different components, then these can be individually chosen.

4

Finally, there are the following two symbols: With this symbol sections are defined. These have to exist before the section results can be obtained as mentioned above under (3). A dialogue window appears in which cer tain parameters are specified, before one [Introduces] the sections. Details can be ob tained from the Help function of the dialogue window. Here just a few possibilities for the settings are mentioned:

.

S

Sections can be provided with a certain width. Such sections may be used for the creation of the results both for beam sections and for normal sections. The section type is always fixed in the region (3) of the Results Tab Sheet.

S

Each section is assigned to a section group (Preset to Group 1). Section groups are sublayers of the section layer and so can be switched individually to visible or invis ible. This improves clarity when one has many sections.

S

Also note the settings in the Tab Sheet /Options/ in particular the possibility of mak ing the variation of the slab’s top and bottom surfaces visible. This is less important in regard to results but much more as a check on the variation of slab thickness.

Downstanding beams are in effect beam sections and just like other sections can be selected for beam section output. The section width corresponds as default value to the width of the downstanding beam. One can change it, however, by selecting a downstanding beam (in the Results Tab Sheet) and adjusting it in its attributes dialogue to the “effective structural width”. In some types of presentation one can specify additional parameters, like equidistance for isolines or the exaggeration factor in the case of sections. For this purpose the dia logue window of the symbol shown on the left is available.

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Properties of Output Zones and Downstanding Beams The material zones defined in the Structure Tab Sheet also contain some output properties. If one selects the corresponding attribute box (for the active Results Tab Sheet) and request its at tributes, the dialogue window on the right ap pears. If the boxes are not visible, one can acti vate them with the corresponding layer switch on the right side of the window. Regarding specifiable attributes it is a question mainly of the output direction for section forces and re inforcement as well as the concrete surface cover for the reinforcement. It is possible for certain outputs to make zones inactive. Downstanding beams also have a similar attributes dialogue in the Results Tab Sheet, whereby there the effective structural width is available as an input field. . b The effective struc tural width = the width of the beam section automatically generated for the re sults output

In the case of downstanding beams the symbol “Active for the Output of Results” is by default switched off. This means that in the downstanding beams for area outputs (isolines, principal value plots, numerical graphics) no results are displayed. This is because otherwise the isolines in the downstanding beams would be very close together and in the other zones hardly any others would be seen. For beam section output the downstanding beams are of course always active.

3D Presentation Certain methods of presenting the results are intended for a 3D view. In this case the program automatically switches to the 3D mode (parallel projection), in which the pro jection direction can be freely chosen. This takes place in the self−explanatory dialogue, which in the 3D view is always visible on the screen, or it can be performed more quickly with the mouse: Keep the keys and pressed and move the mouse with the left button pressed. A horizontal mouse movement rotates the projection direction about a vertical axis and a vertical movement rotates the projection direction about a horizontal axis (one which is normal to the current projection direction). In order to check the thickness of the slab and the donwstanding beam, try out the ren dering functionality (=press the camera−button). With this button on the left side of the window one can switch back and forth between 2D and 3D presentations.

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A 3.5 The Layer Switches The graphics shown here on the left contains all layer switches. By clicking on the sym bol of a layer its visibility is switched on and off. This is important above all in the Results Tab Sheet. In the input (e.g. in the Structure Tab Sheet) the layers are automatically set correctly by the program. Click with the right mouse button on a layer switch and the context menu shown right is opened, which can vary slightly depending on the layer type. The menu items should be self−explanatory (get Help if necessary using the key ). This refers to the layer that was clicked.

Certain layers contain a series of sublay ers, whose visibility one may also some times want to switch on and off individu ally. Click in the context menu on the menu row .Sublayer visibility" and the dialogue shown left appears, in which the symbols of the corresponding sub layer can be set as desired. This is of interest, e.g., for the following layers: S .FE Mesh": One can switch on the node and/or element numbers. S In the case of the figures for numericalgraphical results the values at the nodes and element centers can be labelled. Since these are in their own sublayer, they can be switched on and off individually. As may be seen from the adjacent figure, the layers are subdivided into certain groups. The blue head of each layer group also has a small self−explanatory context menu (click with the right mouse button). Some layer groups still need further explanation:

The Layer Group “User” If the figures to be printed should be complemented with further information like di mension lines or additional labelling the layer group .User" has been provided, in which the symbol for a first User layer has been preset. If one wants to spread the added infor mation over several layers, then in the context menu at the top of the group .User" one can create as many additional User−Layers as desired. In order to be able to draw within a User layer, this must first be made the active layer (note, this is not the same as making it visible). Click with the right mouse button on the symbol of the desired UserLayer and then in the context menu on the row .active" or use the corresponding menu entry in the context menu of the graphics area (this ap pears when nothing has been selected and one clicks with the right mouse button any where on the working surface). Now one can use all the active drawing tools of the Graphics Editor.

The Layer Group “Results” The last 6 results figures created remain, provided the calculation is not closed, in inter mediate storage and are made available here with continuously numbered symbols. Above all, the following possible application was in mind:

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1) One can place several results figures .on top of each other", by switching on the corresponding results layer. For this purpose one has to keep the key pressed, since otherwise the results layers already switched on will be switched off again. 2) One can switch quickly between the last couple of results. 3) The storing of results figures can also be useful in the structure or load input. In the input of critical vehicle loading positions one can, e.g., show previously calculated influence fields. On this some further remarks: S

The limitation to six figures is deliberately, since the figures can take up a lot of stor age space. This number cannot be changed by the user.

S

When storing the results buffer is always deleted. This is also done because of stor age economy and while otherwise loading a calculation can last a long time.

S

By entering in the output list any number of figures can be stored and inspected again at any time (see below).

A 3.6 The Documentation of a Calculation

Print entry

As mentioned earlier, all printable data, whether in text or graphics form, can be sent to the printer at the corresponding places in the program directly or be entered in an output list for printing later.

Print preview (CubusViewer)

If you press one of these buttons a dialog pops up, where you can perform the following task:

Print directely

S

Choose a viewport

S

Define a scale (can be changed later in the CubusViewer ).

S

Edit the short title and the legend of the figure (printed out).

For the complete documentation of a calculation one works with print entries, since before printing one wants to see a preview of the whole .Report" and still be able to make corrections regarding sequence, scales, page breaks, page numbers, etc.. The following list highlights all points in the program, where print entries are possible in a typical sequence that one would require for a report: Structure S

For documenting the structure input in the Structure Tab Sheet one would preferably enter at least one figure showing the slab. Make sure that all desired layers are active. If one is dealing with a big slab with many structure objects, it is perhaps advisable to enter several figures with different layer switches or extra figure sections. Also remember that for objects with labelling boxes the amount of labelling can be influenced for most objects in their attributes dialogue in the Tab Sheet /Options/. Further, do not forget the possibility of dimensioning the figures with a view to an optimal documentation and to amplify them with drawing detail. This is done in layers of the group EUser".

S

The tabular listing of structure objects, which can be created with the symbol shown (extreme right in the Tab Sheet /Structure/), serves as legend for the figures of the structure.

FE mesh S

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For documenting an FE calculation one also needs the FE mesh. Activate the FE mesh layer with the layer switch shown on the left and make the print entry.

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If one uses tabulated results it may be necessary to include a figure with the node and element numbers. These can be added by clicking with the right mouse button on the FE mesh layer switch and activating the desired sublayer in the menu Description...’). Page number

PAGE_NUMBER

Page number

Author

PRO_FIRMA

Company name

Object

PRO_ZEILE1

Name of project

Structural element

PRO_ZEILE2

description of structural element

Engineer

PRO_INITIALS

Name of responsable engineer

Tabelle A–1

Layout objects of a document style

The coordinates of the layout objects (see Fig. A−1) are values in [mm] followed by one of the letters ’L’, ’R’, ’T’, ’B’ indicating the origin of the coordinate system (i.e. border at L=left, R=right, T=top and B=bottom).

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C 4 Document styles

list of specified layout objects new objects can be added via the contect menu

properties of layout objects

Fig. A–1 Editing header and footer

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Part C The CubusViewer

C 5 Modify the report

C 5 Modify the report In this section the most important functions to edit the generated report are explained. Most of them can be reached via the menu and via the context menu. The menus are activated if you have selected a number of items in the list or in the preview and click on the right mouse button. Fig. A–2 List of print entries You can resize the list by mooving the splitter control separating the list and the preview area

selected print entry activate/deactivate entries

C–6

S

Selecting entries: Select an entry in the list by clicking on it, use shift for multiple selection and B to select all. The preview allows the selection of a single entry highlighting it with a blue frame.

S

Activate/deactivate entries: Only the activated entries will be printed. Change the activation of an entry with its associated check box (see Fig. A−2).

S

Order of appearance: Drag&Drop to change the order of appearance.

S

Delete entries: Select a series of entries and press the ’Del’ button.

S

Changing the scale: Select a series of entries and change the scale via the context menu.

S

Insert page break: Select the first entry on the new page and call the ’Insert new page’ function in the context menu.

S

Insert additional text: You can insert any additional text in the entry list if you select a text in a WindowsBApplikation, copy it to the clipboard (B) and paste it into to print entry list of the CubusViewer (B). This will add a new entry at the bottom of the list that can be moved via Drag&Drop to the correct postion in the report. Note that the text must be either in ASCII− or RTF−format.

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Part C The CubusViewer

C 6 Printing a report

C 6 Printing a report Only the activated entries in the list are printed (see C 3 and Fig. A−2). After printing, the list remains untouched i.e. you have to delete or deactivate the items you don’t want to print again. If you print a report for the first time, you have to make the following steps:

CEDRUS–5

S

Choose printer: If there is more than one printer installed, you can choose one in the menu ’File / Printer’.

S

Setup page: Choose a document style in the menu ’File / Setp page’ (see C 4).

S

Page numbers: The page number of the first printed page, shown in the header/footer (see C 4), is taken from the current settings in ’Options / page header information’. If you do not change this value it is incremented each time a page is printed. Setting the page number to 0 will not print it at all.

S

Choose colors/line types: Depending on the capabilities of your printer you should choose the color/line type scheme and the fillmode: The colors and linetypes are defined in the Cubus application that created the report (menu ’Options / Colors−line types’).

S

Print the report: By clicking on this symbol the report is sent to the printer.

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Part C The CubusViewer

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C 6 Printing a report

CEDRUS–5

Part DReinforcement and Ultimate Load Analysis D 1 Introduction The optional modules Reinforcement and Ultimate Load Analysis represent an exten sion of the Basic Module of CEDRUS5 and are completely integrated in its environment. Using the Reinforcement Module the arrangement of the reinforcement in the form of bar and mat (steel mesh) positions can be designed and dimensioned. The Ultimate Load Module allows one to realistically estimate the strength reserves of a reinforced concrete slab. The calculation method used in the Reinforcement and Ultimate Load Modules corre sponds largely to most modern building codes. They are in fact compatible with the following codes: S

SC

(Swisscode SIA 260/262, Ausgabe 2003)

S

SIA

(SIA 162, Edition 1989)

S

EC2

(Eurocode 2, ENV 1992−1−1)

S

DIN

(E DIN 10451, 1998)

In the following sections it is shown why it is advantageous to design the reinforcement using CEDRUS5, and how a realistic ultimate load calculation is possible without great modelling effort.

D 1.1 Reinforcement Module Depending on the plan outline, the purely elastic determination of the reinforcement content, as provided by the Basic Module of CEDRUS5, requires a great amount of de sign calculation before it can be translated into an actual reinforcement arrangement. This depends to a large extent on the high concentrations at columns , wall ends or corner recesses. With the beam sections one does have an aid to smooth out stress peaks. But they involve extra work and can only solve the problem partially. What is still missing is the treatment of sloping reinforcement and above all an automatic final check on whether a reinforcement layout is satisfactory from all points of view. The Re inforcement Module can overcome these problems and substantially help to reduce the procedure of going from the FE results to the reinforcement plan. An additional increase in efficiency can be achieved especially with the reinforcement interfaces supported by CEDRUS5, whereby the reinforcement arrangement can be directly transferred to a CAD System to produce plans. The reinforcement module provides the following properties:

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consistent and statically ’clean’ solution (equilibrium)

S

support of multiple load combinations

S

much freedom in placing the reinforcement (>introduces engineering experience)

S

rational working procedure through CAD integration

S

sloping reinforcement arrangement

S

small amounts of reinforcement

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D 1 Introduction

compatible with modern codes (e.g. SC,SIA,EC2,DIN)

The underlying theory and properties of the Reinforcement Module and its use for practical design problems are explained in more detail in Chapters D 2 and D 3.

D 1.2 Ultimate Load Module More and more engineers are confronted with the task of determining the load bearing capacity of existing structures, and this is rarely successful using an elastic solution. Using the Ultimate Load Module of CEDRUS5 the inelastic material behaviour of rein forced concrete can be taken into account, enabling structural strength reserves to be estimated more realistically. Starting with an initial reinforcement layout the elastic and plastic structural behaviour can be analysed for a given loading arrangement. In contrast to the yield line theory of plastic hinges, which can only provide upper bound limits on the bearing capacity, this module provides realistic values even for complex struc tures. The Ultimate Load Module is characterised by the following properties: S

realistic estimate of the structural strength reserves

S

simple use

S

interactive following of the structural behaviour

S

estimate of the required deformation capacity

S

sloping reinforcement arrangement

The underlying theory and properties of the Ultimate Load Module and its use for practi cal design problems are explained in more detail in Chapters D 2 and D 4. .

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For an introduction to the Reinforcement and Ultimate Load Modules it is highly recommended that every user works through the following chapters completely. Before this one should not attempt a serious calculation.

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Part D Reinforcement and

D 2 Basic Theory

D 2 Basic Theory In this chapter the models and solution methods are explained which are used both for the Reinforcement and Ultimate Load Modules of CEDRUS−5.

D 2.1 Material Model The nonlinear structural behaviour of reinforced concrete slabs is considered both in the Reinforcement and the Ultimate Load modules. With the realistic assumption that the deformations remain small also in the plastic state and second order effects are negli gible, this nonlinearity derives entirely from elastoplastic material behaviour. By limiting the reinforcement contents to values which prevent brittle behaviour, it is possible to describe the material law of a slab subjected to bending by an elastoplastic moment−cur vature relationship in a cross section of unit width.

D 2.1.1 Moment-Curvature Diagram As the following figure shows, for each of the two calculation modules a special idealisa tion of the actual material behaviour is employed: Reinforcement module (Design)

m

m

m

mu

my

Ult. load module (Analysis)

m pl R

m pl d

1ńmEI II mr x a) from tests

EI I 1 b) elastoplastic

x

1

EI II 1

x xu

c) elastoplastic with hardening

Diagrams (b) and (c) both exhibit initially a linear characteristic, which after reaching the yield limit m pl changes to a well−defined plateau. Modelling as a linear elastic rigid plastic material (b) with initial uncracked stiffness (State I) represents for a reinforce ment design a sufficiently accurate material model, which permits the application of the limit state bounds of plastic theory (see D 2.1.2). In order to estimate the required plastic deformation, an additional model (c) is used for the ultimate load analysis with cracked stiffness (State II) and hardening. With this idealisation it is possible to model quite accu rately the real behaviour (a). A further refinement of the model hardly improves the accuracy despite much greater modelling and computation times, since there are many uncertainties in the model parameters (material parameters, creep and shrinkage effects, load history etc.). The calculation of the characteristic values of diagrams (b) and (c) is described more fully in Chapters D 3 and D 4 of this manual. It should be noted that long−term effects are not considered.

D 2.1.2 Plasticity Theory Plasticity theory attempts to idealize the mechanical material behaviour by means of sim plified nonlinear material laws, which establish relationships between force and de

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formation quantities, whereby as a special case a general nonlinear theory can be con sidered. It demands adequate deformation capacity (see section D 3.1.3 and Chapter D 4). Its applicability to reinforced concrete slabs has been verified by numerous tests and its successful use in practice over the last few decades (e.g. the strip method). In modern codes of practice it is expressly permitted for the calculation of reinforced con crete slabs. In the case of plastic material models (see e.g. diagram (b) in D 2.1.1) the deformation increases at first proportionally under increasing load up to a limiting value (=yield limit). Afterwards deformations increase without additional load increase, which is called plastic flow. By simplifying the actual behaviour one restricts oneself to those quantities, which basically determine the ultimate load, whereby simple design rules can be obtained. Among other things plasticity theory postulates the following two the orems: S

Static (or lower) bound theorem: Each loading, to which an arbitrary equilibrium state S can be assigned, which no where exceeds the elastic limit R, is not greater than the ultimate load.

SvR Under equilibrium state is understood a stress state, which everywhere fulfils equi librium and the statical boundary conditions. The elastic stress state S el represents e.g. an equilibrium state. If several load cases have to be investigated, then the above inequality can be formulated with the corresponding limit values:

S GW v R S

Equilibrium theorem (according to MelanBleich): Given limit values of the loading intensity lie within the deformation capacity of a structure, if the limit values of the elastic stresses S GW of each possible loading, super el imposed with any equilibrium stress state S 0, nowhere exceed the yield limit R.

S GW ) S0 v R el An equilibrium (or residual) stress state S 0 is one which is in equilibrium with itself (i.e. without external loads). An example of S 0 is a stress state due to temperature effects. The application of this theorem to practical dimensioning tasks is described in detail in Chapter D 3.

D 2.1.3 Yield Condition and Flow Rule The stress state of a slab subjected to bending action (Kirchhoff theory) is described by the three components m x, m y, m xy, which are associated with the three components x x, x y, xxy of the strain state. For the orthogonal xy coordinate system used it is a ques tion of the local system of the point considered within the slab. This is defined in CE DRUS5 by the outut direction of the corresponding material zone (=angle in the anti− clockwise direction from the global xaxis) . With the well known plasticity conditions for reinforced concrete slabs (see e.g. EC2 A 2.8) the yield limit can be given (see moment−curvature diagrams D 2.1.1) in each point of the slab using two cross sections each with two positive plastic resistance mo ments m pl :

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S

cross section in xdirection, bottom reinforcement:

S

cross section in ydirection, bottom reinforcement:

m udx + m x " m xy v m plx m udy + m y " m xy v m ply

S

cross section in xdirection, upper reinforcement:

mȀ udx + * m x " m xy v mȀplx S

cross section in ydirection, upper reinforcement:

mȀ udy + * m y " m xy v mȀply Geometrically considered the above yield conditions form a body enclosed by a convex bounding surface F (=yield surface) (=elastic region) in the three dimensional space of the moment m + ǀm x, m y,m xyǁ:

my . x pl + f dF dm

mȀ plx

m ply

yield surfaceF

m plx

m

mx

mȀ ply m xy When the load increases reaching a point on the yield surface, plastic curvatures . . . . x pl + (x x, xy, x xy) result which are normal to F, according to the associated flow rule. Therefore, in an ultimate load analysis the intensity and direction of the plastic curva tures can be calculated (see Chapter D 4).

Kinematic hardening model In tests it is observed that the yield surface changes after plastic deformations occur. Thus e.g. cross sections in which plastic flow occurs resist greater moments as the plastic curvatures increase (see diagram (c) in D 2.1.1). This behaviour is called hardening. In the three dimensional stress space one can show that the elastic region(=size of F) often does not increase. This so−called Bauschinger effect is modelled in the ultimate load module by kinematic hardening, which corresponds to a displacement of F in the mo ment space m (see sketch below).

my

mx

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D 2.1.4 Plastic Moment of Resistance The plastic moment of resistance m pl of a cross section can be determined from the thickness of the slab h, concrete quality, steel quality and vertical position of the bend ing reinforcement (see following figure). Thereby the stress−strain diagrams for con crete and reinforcing steel are used that are given in the codes. Due to the different prob lems considered, for the two calculation modules slightly different methods are adopted. As explained in Chapter D 3, for dimensioning a linear dependence between plastic mo ment of resistance and the unknown reinforcement areas a si is necessary. By assuming an average lever arm z independent of a si it is possible to formulate a model (1), which provides sufficient accuracy. This simplified formulation assumes that the reinforcement only acts for tension and plastic flow is exhibited in all areas.

Model 1: Reinforcement Module Analysis with average lever arm

Model 2: Ultimate Load Module Analysis with strain planes

D concrete compression zone

h

z a s2 a s3

c2 c1

Z+

ȍ as

i

f yi

reinforcement position

Z å mpl + Z z

åc å s3 strain plane

å s2 å s1 å mpl + f (å)

In an ultimate load analysis, however, the reinforcement areas are known and the plastic moment of resistance can be calculated iteratively by varying the strain planes. Thereby the stresses in the concrete and the steel can be determined by means of the strains and the plastic moment by integration (Model 2).

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D 2.2 Reinforcement Model Besides the structure and load data of the basic module both the reinforcing module and the ultimate load module are based on additional data described by the bending reinforcement.

D 2.2.1 Reinforcement Fields

material zone with output direc# tion Z1

The top and bottom reinforcement is specified separately in the form of reinforcement fields, which correspond to individual round reinforcing bars and steel mesh reinforce ment. These fields exhibit a constant resistance and cover an area of the structure, which corresponds to its statically active zone (i.e. without anchorages). They are defined as arbitrary polygons or parallelograms in the slab plane, with a free reinforcement direc tion and they may overlap each other. Their vertical position can be given in two ways:

Y X

a

round re# inforcing 1. By inputting four parameters bars By inputting attributes of the concrete body enclosing them (top surface ok, slab thickness h and concrete cover top cȀ and bottom c) the vertical position of a field is specified (see also following figure). 2. By assigning a material zone

reinforcement field with statically active zone

ok

Since each material zone (=output zone) describes a concrete body including top and bottom cover, the vertical position of a reinforcement field is uniquely specified by assigning a zone. The angle a between the bar direction of the field and the out put direction of the material zone decides whether the concrete cover has the same output direction (for |a| v 45° ) or is normal to it (see CEDRUS5 Handbook Chapter 3: Register Page /Results/).

cȀ The second method requires less effort in the input of the the reinforcement and offers in particular the advantage in dimensioning tasks, that after project changes (e.g. slab thickness) the reinforcement fields are automatically repositioned.

h c

The used steel is by default automatically taken form the material zone as well. However, the user can specify a special steel for each reinforcement field (see tabsheet Options>Steel of the field dialog). .

The values of concrete cover c correspond to the distance of the centre of gravity of a reinforcing bar from the corresponding concrete surface, whereby for an assigned material zone for the top and bottom positions the bottom cover distance is decisive.

D 2.2.2 Slab and Downstanding Beam Reinforcement In the design of the bending reinforcement for calculating the plastic moments of resis tance m pl only those bar positions are considered which lie within the so−called dimen sioning range B (see following figure). Each slab zone has four of these boundary re gions (in x and y directions at top and bottom), whose height b corresponds to twice the cover c of the zone or 10% of the slab thickness if c + 0 . Bars which lie outside

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this zone are inactive, so that this does not apply for the ultimate load analysis, where all bar positions are always included. slab zones Z1

X

cȀ x

downstanding beam

Y

cȀ y

ok u

ok

cȀ x cȀ y

cx

U1

Y

cy

cy

B dimensioning regions

X

hp hu

h

bx

ok p

inactive bars

cx

The above figure shows a slab zone Z1 (top ok, thickness h) and an downstanding beam U1 (top ok u, thickness h u) with neighbouring slabs (top ok p, thickness h p) and the corresponding concrete covers c x, c y, cȀ x, cȀ y.

Downstanding beam reinforcement In CEDRUS5 the downstanding beams are modelled as orthotropic slab zones (see CE DRUS5 Handbook Chapter 3.3.1 Material Properties). These form their own material zone with given output direction, corresponding to the downstanding beam axes. They exhibit an increased stiffness longitudinally and act like the adjoining slab normal to the axis. The dimensioning of downstanding beams is analogous: The reinforcement is dimensioned longitudinally in the downstanding beam cross section and normal to it in the slab cross section. Just like the slab zones the downstanding beams are also dimensioned only for bending reinforcement, i.e. the stirrup reinforcement and the corresponding spacing for the longitudinal reinforcement has to be subsequently deter mined by hand calculation. :

Astuce: If the top and bottom slab reinforcement is layed through the downstanding beam, then for the downstanding beam only a longitudinal reinforcement has to be de fined. A prerequisite for this is that the details for the neighbouring slab in the down standing beam dialogue box agree with those of the adjoining zones. In the same way this applies also for downstanding beams in which only the longitudinal reinforcement has to be specified.

D 2.2.3 Sloping Reinforcement In the yield condition (D 2.1.3) it is assumed that in the point considered an orthogonal reinforcement is placed in the direction of the local coordinate system and the moments of resistance can be determined according to (D 2.1.4). This applies to most practical cases, provided the user is certain that the local coordinate system (i.e. output direction of the material zone) corresponds with the reinforcement direction. However, if the re inforcement arrangement is not orthogonal, then the yield condition has to be ex tended. This is achieved by a refined analysis of the plastic moments. By means of equilibrium conditions, from all existing reinforcement positions six moments of resistance can be determined in function of their deviation b i with respect to the local xaxis, whereby each bottom and top reinforcement field exhibits a moment of resistance m pl or mȀ pl , i i respectively:

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ȍ mpl cos b2i m plY + ȍ m pl sin b 2i m plXY + ȍ m pl sin b i cos bi m plX +

i

i

i

ȍ mȀpl cos b2i mȀ plY + ȍ mȀ pl sin b 2i mȀ plXY + ȍ mȀ pl sin b i cos bi mȀ plX +

i

i

i

Subsequently the equivalent moments of resistance can be found and substituted in the yield conditions (D 2.1.3).

m plx + m plX " m plXY

m ply + m plY " m plXY

mȀ plx + mȀ plX " mȀplXY

mȀ ply + mȀ plY " mȀplXY

This resistance transformation enables the consideration of arbitrarily oriented rein forcement fields. However, it should be noted that the results are not invariant with re spect to direction, i.e. they depend on the orientation of the local xy coordinate system. The ultimate load resistance of sloping reinforcement fields cannot be additionally ex poited very much, which is why sloping reinforcement should be avoided if possible. For a more detailed derivation of this method refer to: S .

R. Wolfensberger: HTraglast und optimale Bemessung von Platten", Institute of Struc tural Engineering, ETH Zurich, Dissertation Nr. 3451, 1964.

In order to obtain good results one should note that the directions of orthogonal reinforcement must coincide with the coordinate system and for non–orthogonal reinforcement positions an axis of the coordinate system has to coincide with the main reinforcement direction, in order that the corresponding position can be fully exploited.

D 2.3 Solution Method The computational methods used in the Reinforcement and Ultimate Load Modules are based on the FE model (element subdivision, nodes, degrees of freedom, support conditions) of the Basic Module, whereby instead of the hybrid element model (see CE DRUS5 Handbook Chapter 2: Fundamentals) a kinematic model is used following the so−called FreeFormulation theory. For an in−depth study of this model refer to the fol lowing literature: S

P. G. Bergan, M.K. Nygard: HFinite Elements with Increased Freedom in Choosing Shape Functions", Int. Journal for Num. Meth. in Eng., Vol. 20,1985.

In most FE programs the material law is formulated for the stresses in the so−called in tegration points of all elements. In contrast, the material behaviour in the Reinforcement and Ultimate Load Modules of CEDRUS5 is described for each element in terms of the element nodal forces in space, which has big advantages, especially for reinforcement dimensioning. For an in−depth study of this formulation refer to the following literature: S

P.N. Steffen: HElastoplastische Dimensionierung von Stahlbetonplatten mittels Fi niter Bemessungselemente und Linearer Optimierung", Institut für Baustatik und Konstruktion, ETH Zürich, Bericht Nr. 220, 1996 Birkhäuser Verlag Basel.

S

E. Anderheggen, G. Glanzer, P.N. Steffen: HYield Surfaces in the Element Nodal Force Space", Computers & Structures, 1999.

D 2.3.1 Nonlinear Analysis In the Ultimate Load Module the elastic and plastic behaviour of a slab can be analysed with a known reinforcement arrangement under a given loading.

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Incremental, iterative calculation The ultimate load calculation is carried out by means of the incremental, interative New tonRaphson method. Starting from a given state (i.e. stress and strain states, initial stif fness) the loading is successively increased in increments. Thereby the moments in the slab are investigated and plastic curvatures are induced in zones when the plastic resis tance is reached (see D 2.1.3). Schematic Load#Deformation Curve Load Factorl

l MAX Dl

equilibrium iterations

Deformation w

In order to determine the associated point on the load−deformation curve, within a load increment Dl equilibrium iterations are necessary (see above figure). If this is not poss ible, then the applied load lies above the ultimate load and Dl has to be reduced. This incremental, iterative process is terminated as soon as the load increment becomes very small, whereby the ultimate load factor l MAX is reached. At this moment the reinforced concrete slab loses its stability and a collapse mechanism is formed, which finally causes the structure to collapse. A mechanism, however, can only form if the model assump tions (see D 2.1) apply. In order to guarantee the fulfilment of these assumptions after every load increment an additional so−called termination criterion is checked (see D 4.1.3), in order to be able to abort the calculation.

Influence of the initial state and load history The ultimate load of a slab (neglecting hardening effects and assuming an adequate de formational capacity) depends theoretically only on the sum of all applied loads. Since the rotational capacity of reinforced concrete slabs is limited, in an ultimate load calcula tion the deformations must also be determined for the purpose of limiting the rotations (see D 4.1.3 Rotational Capacity). However, these depend strongly on the initial stress and strain states and the intensity and order of the different actions (=load history). The initial state of a reinforced concrete slab, however, cannot be described accurately, since it depends on many unknown factors (e.g. concrete quality, cracking, environ mental influences, shrinkage etc.). In an ultimate load analysis, however, not the actual effective deformations are of interest, but only maximum values to check the deforma tional capacity. A useful estimate for this limiting value is obtained, if as a starting point an undeformed, stress−free configuration with an initial stiffness corresponding to the cracked state is assumed (see D 2.1.1).

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D 3 Reinforcement Module The reinforcement module is a comprehensive tool for dimensioning and detailing the reinforcement in a slab. In this chapter firstly the basic concepts of the module are ex plained and then the reinforcement dimensioning is illustrated by means of an actual example.

D 3.1 Basic Concepts

D 3.1.1 Dimensioning for Ultimate Load According to modern codes the load carrying capacity of a section is deemed to be veri fied, if

Sd v Rd whereby by S d is understood the design value of the section quantity and by R d the corresponding design values of the resistance. Design values for resistances For reinforced concrete slabs subjected to pure bending R d corresponds to the plastic moment of resistance m pl d (see figure in D 2.1.1), which is determined from the char acteristic material values ( f ck, f yk for concrete and reinforcing steel) with reduced partial safety factors ( g c , g s for concrete and reinforcing steel). CEDRUS5 uses for this purpose always the partial safety factors of the analysis parameter set ’AP2: Ultimate limit state (ULS)’ (s. main menu: Settings>Analysis parameter). The characteristic material values are taken from the material box of the zone (s. D 2.2.1), with the exception of the steel quality, which can be specified individually for each reinforcement field.

R d + m pl d + g1

s

ȍ as fyk z i

i

Corresponding to D 2.1.4 the moment of resistance m pl d is determined from the rein forcement areas a si and strengths f yk of all reinforcement layers. The inner lever arm i

is assumed within each finite element top and bottom in the x und y directions to be approximately z + 0.9 (h * c) (see figures in D 2.1.4 and D 2.2.2), whereby for c the distance to the edge of the corresponding output zone is used. For sloping reinforce ment the formulas in D 2.2.3 are used. Design values for the sectional quantities The codes require that as design values for section quantities the design limit values S GW of all investigated design situations are used, which can be automatically gener ated with the Basic Module (see CEDRUS5 Handbook: Chapter 2.3.):

S d + GW(g i Si) + S GW With the reinforcement module the section quantities can be calculated linearelastically (=elastic) or according to plasticity theory (=plastic). Both methods have in common that the distribution of the section forces represents an equilibrium solution, i.e. they are in equilibrium with the applied load and fulfil the statical boundary conditions. .

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According to SC, EC2 and DIN the determination of the section quantities can be performed linear-elastically, using plasticity theory or by means of nonlinear methods. CEDRUS-5 (with

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the Reinforcement and Ultimate Load Modules) can determine the section quantities by all three methods. Dimensioning the reinforcement by means of the extremely computationally expensive nonlinear methods, however, is not suitable for practical problems, since the reinforcement has to be known before a nonlinear analysis and each load combination has to be analysed individually..

D 3.1.2 Elastic Design as an Optimization Task With the FE model of the CEDRUS5 Basic Module the elastic design limit values S GW el can be calculated directly on the basis of a given limit value specification (see CEDRUS5 Handbook: Chapter 2.3.3.). If the user has placed reinforcement fields everywhere in the slab according to D 2.2 with still undefined reinforcement areas a si, the design task can be formulated as follows:

S GW + S GW v Rd el

å SGW v g1

el S

ȍ as fyk z i

i

This inequality has as unknown only the reinforcement areas a si. Since the reinforce ment fields may overlap each other the choice of a si represents a linear optimization problem, which is solved in the Reinforcement Module for minimum weight of rein forcement. The so−called objective function of the optimization G, which is minimized, corresponds to the total weight of the placed reinforcement and may be calculated from the reinforcement areas (still to be calculated) a si ,the areas of the individual reinforce ment fields F i and the unit weight of steel ò :

G+ò

ȍ as Fi ³ Minimum i

After the user has prepared the structural model including loading using the Basic Mod ule of CEDRUS5, chosen a limit state specification and defined the reinforcement fields, the Reinforcement Module determines with the press of a button the optimum values for the reinforcement areas a si. These are automatically converted to diameter and spac ing or mesh type, respectively, whereby a complete and structurally safe reinforcement results, which finally can be printed in the form of reinforcement drawings or for the purpose of preparing a reinforcement plan can be transferred to a CAD system (see Chapter 5). .

The dimensioning algorithm can only peform a consistent dimensioning if reinforcement fields have been defined in all stressed zones. Prescribed minimum reinforcement content In large areas of a slab, e.g. to fulfil serviceability requirements (see Section D 3.1.4), a minimum reinforcement has to be placed. These requirements can be taken into ac count directly in the optimization procedure described above, in that for each reinforce ment field a minimum reinforcement content is specified, such that in the optimum choice of the reinforcement areas one never goes below this value. Limits of the elastic dimensioning A purely elastic dimensioning of the slab reinforcement results in reinforcement areas that are in many cases much too high. This is due, on the one hand, to the unrealistic concentrations over supports, at ends of walls or recessed corners, which arise from elastic plate theory (singularities). On the other hand, a minimum amount of reinforce ment has to be prescribed in many places, which cannot be exploited in the statics. In order to avoid unreasonable reinforcement arrangements, engineers often do not de sign the reinforcement to cover the peak moments and as a compensation place some what more reinforcing steel in neighbouring areas. This method requires intuition and a considerable amount of extra work. In principle, such a solution is not compatible

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with the codes, since one can hardly speak of elastic determination of section forces any more. What is more serious, however, is the fact that this ’manual redistribution’ has to be considered to be theoretically questionable, since a state of equilibrium can no longer be guaranteed.

D 3.1.3 Optimum Plastic Dimensioning The problem of high reinforcement concentrations (see D 3.1.2) can be alleviated, by considering the inelastic behaviour of reinforced concrete slabs, which characterizes this material, in the determination of the section quantities. The Reinforcement Module allows the reduction of the high bending moment peaks by introducing controlled section force redistribution. In contrast to the above mentioned often problematical ’manual redistribution’ this is carried out on a firm theoretical basis: According to the lower bound theorem of plasticity theory (see D 2.1.2) the following holds:

S GW ) S0 v Rd el

å SGW ) S 0 v g1

el S

ȍ as fyk z i

i

The above dimensioning inequality corresponds, except for a dead load residual stress state S 0 (see D 2.1.2), to the elastic dimensioning of the last section, whereby S 0 causes a redistribution of the section quantities. With a suitable choice of S 0 it is possible to optimize the elastic dimensioning, by redistributing the peak moments. CEDRUS5 gen erates this residual stress state S 0 from a series of several residual stress states S 0 , j

whereby the optimum plastic dimensioning can be formulated as a linear optimization problem with two types of unknowns:

S0 +

ȍ S0

å SGW ) el

j

ȍ S0 v g1S ȍ as fyk z j

i

i

Starting from an elastic dimensioning (D 3.1.2) the choice of the reinforcement contents can be optimized by an automatic procedure, whereby, stepwise, residual stress states S 0 are generated and superimposed. The program user can follow on the screen, how j

the moments are redistributed, whereby it is possible to stop the optimization procedure at any time. Efficiency parameters The design optimization is numerically an expensive incremental method, which es pecially for large systems necessitates very high computational times to determine the optimum solution. Thanks to the refined methods offered by CEDRUS5, however, it is possible to find a sub−optimum solution within a short time, which is already quite close to the absolute optimum (e.g. 90%) and consequently, in spite of long calculation times, can only be little improved upon. Thus the program user can stop the calculation as soon as he is satisfied with the solution obtained. The variation of the so−called effi ciency parameter helps one to estimate whether a further calculation is worthwhile. This scalar parameter is defined by the ratio of the static and constructionally required rein forcement volume V req to the volume of the reinforcement placed V act.

as

2 min

ÏÏÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏÏÏ Ä ÏÏÏÏÏÏÏÏÏÏÏÏÏÏ Ä ÏÏÏÏÏÏÏÏÏÏÏÏÏÏ ÏÏÏÏÏÏÏÏÏÏÏÏÏÏ

a s1 a s2

As shown in the figure beloe, for a uniformly loaded beam with two reinforcement layers, V req (hatched area) corresponds to the constructional minimum and what is re

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quired in addition to this. If the efficiency parameter is close to 100%,the reinforcement is optimally exploited. Adjustment of the structural action to the reinforcement arrangement Although the dimensioning process is largely automatic, the engineer determines to a considerable extent the quality of the resulting reinforcement arrangement. The op timization process tries to utilize the resistance of the introduced reinforcement fields optimally, by adjusting as far as possible the supporting action of the slab by redistribu tion of the moments of the given reinforcement arrangement. Thus, e.g. the resistance of the reinforcement fields is mobilized in zones only lightly stressed according to the elastic calculation, which because of the serviceability requirements, however, have a minimum content. This gives the engineer much freedom in the placement of the rein forcement: in the input of the reinforcement fields one does not have to proceed exactly according to the elastically determined reinforcement contents, but one can take ac count of constructional aspects and choose a simpler reinforcement arrangement. Since the detailing of the reinforcement has a big influence on the subsequent structural be haviour (see next section) and the execution costs, in this way economic solutions can be obtained. Limitations of plastic design One can show that plastic deformations occur before the ultimate load is reached for all statically indeterminate structures, even if these were dimensioned according to elas tic theory. Therefore all statically ultilized reinforced concrete slabs require a certain de formation capacity (=ductility). The rotational capacity depends thereby to a large ex tent on the detailing of the reinforcement. The engineer has to guarantee this irrespective of the way the section forces are determined by fixing the reinforcement fields accordingly: This means that no cross section is over− or under−reinforced and the reinforcement is well distributed everywhere (i.e. appropriate to the slab thickness, relatively small bar diameters and fine spacing) and likewise anchored. A careful detail ing of the reinforcement is especially necessary for optimum plastic dimensioning, since this makes full use of plastic rotations. Fortunately, the rotational capacity of two−way spanning reinforced concrete slabs (in contrast to frame structures) is generally much greater than normally assumed. In modern codes there are corresponding rules to guarantee the cross sectional ductility (e.g. prescribed steel quality, maximum amount of reinforcement) and restriction of sec tion force redistribution, which should be taken into consideration in the input of the reinforcement fields. In particular, according to the new DIN code it may be necessary in some cases to verify the rotational capacity. This task can be carried out using the Ultimate Load Module, which is explained in detail in Chapter D 4.

D 3.1.4 Dimensioning for Serviceability Besides checking the structural safety modern codes also require verification of the ser viceability, which must be carried out at different level of applied stress. For this purpose usually a calculation with the uncracked elastic stiffnes, as is available in the Basic Mod ule of CEDRUS5, for example to determine the bending deflection (with a correspon dingly adjusted Young’s modulus E) or to check maximum steel stresses for the purpose of safety against cracking. In connection with the effect of redistribution of moments due to a plastic dimensioning on structural safety, however, it must be ensured that inadmissibly large deformations and crack widths are prevented for the serviceability limit state. This is achieved on the one hand by good detailing of the reinforcement (see e.g. the last section ’Limitations of plastic design’) and, on the other, by preveneting a big redistribution of moments under working loads. Prescribed minimum reinforcement for ulimate load design The second requirement can be fulfilled directly using the Reinforcement Module while dimensioning for the ultimate load, in that, before the optimum plastic dimensioning

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for the reinforcement fields, minimum reinforcement contents are defined, which result from an elastic dimensioning for working loads. Thereby it might be reasonable after inputting a reinforcement arrangement to determine in a first step the contents of the reinforcement fields for working loads elastically. These reinforcement contents can subsequently (possibly limited to critical fields) be prescribed as minimum contents. Af terwards this reinforcement arrangement can be dimensioned for ultimate load using optimum plastic dimensioning, whereby it is often seen that only a small amount of additional reinforcement is necessary.

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D 3.2 Dimensioning Process In this section the dimensioning process using the Reinforcement Module is illustrated by means of an example. In order to make this introduction clear and understandable many details will be left out. For a description of all functions one should refer to the detailed Help System of CEDRUS#5, which is available at any time via the Main Menu HHelp" or context−sensitively by pressing the key or the button [?]. .

For this section it is assumed that one is acquainted with the Basic Module of CEDRUS-5 and thus one knows already the functionality of the Control Registers, the Dialogue Windows and the Graphics Editor. If this is not the case we recommend that beforehand one works through Chapter 3 ’Working with CEDRUS-5’ of the CEDRUS-5 Handbook.

Introductory example The introductory example consists of a rectangular slab of constant thickness h sup ported on three sides by walls, which in addition to dead load is loaded by a uniformly distributed imposed load q. The slab’s reinforcement is dimensioned acccording to the SC code (SIA Swisscode) using concrete of quality class C20/25 and a steel of class B500B:

5m 7m

q + 5 kN2 m

z y

h + 22 cm

x fixed

simply supported

In order to input the structure and load data, firstly one opens a new calculation and chooses as code ’Swisscode’. Then one opens the materials dialog (menu: Settings>Materials) and makes sure that the ’concrete’ is of class ’C20/25’ (E−Modu lus=3e7 kNńm2 , n=0.17) and the ’reinf. steel’ of class B500B. Afterwards in the Register/ Structure/ one inputs the plan outline (rectangle tool, absolute coordinates 0,07,5) and one places a material box (Dialogue: isotropic, thickness=0.22[m], Stiffness factor fE=1). Next one defines the supports (walls of width=0.2[m], height=3[m], E modulus=2.1e7 [ kNńm2 ]) by inputting a wall with free support rotation (Dialogue: displacement=wall stiffness) on the left boundary and a corner wall of general support type (Dialogue: dis placement=wall stiffness, rotation X=blocked, rotation Y=free) at the bottom and right boundaries. In the Register/Loads/ one now adds (to the automatically generated self−weight) a second load case of action ’Live Load − general’ with an area load box (Dialogue: −5 [ kNńm2 ], [Whole slab]). Finally, in the Register/FE mesh/ one makes sure, that the property ’Maximum Side Length’ is set to 0.5[m] in the attribute dialog of the automatically generated mesh box. Without starting the calculation one can from here change directly to the Register/Reinforcement/.

D 3.2.1 Input of the Reinforcement and Elastic Dimensioning In a dimensioning task the program user must, in a first step, place reinforcement fields everywhere in the slab in the form of bar and mesh layers with as yet undefined rein forcement areas a s.

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D 3.2.2 Preparation of the Output Zones The vertical position of a reinforcement field is most easily defined by assignment to an output zone (=material zone) (see Chapter D 2.2). In order to facilitate this method the output direction and the concrete cover of the material zones have to be correctly specified. This can be done in the Register/Structure/ (possibly already in the structure input) in the dialogue window of the material zone (Register/Output Zones/). For the example slab only one zone, for which one specifies the output direction 0 (=corre sponds to Xaxis) and the concrete cover each to 3[cm] have to be specified. .

As was explained in detail in D 2.2.3,the output direction should, if possible, coincide with the main reinforcement direction. Therefore, with complicated geometries it is necessary to input several material zones with different output directions, although the whole slab has the same material properties (i.e. height of top surface, thickness, E modulus etc.).

D 3.2.3 Creating a Layout The input of the reinforcement is done in the Register/Reinforcement/. In order to allow the comparison of variant solutions, the reinforcement in a slab is managed in indepen dent layouts.

layout management

display control specification of current reinforcement direc# tion and position

In order to create a new layout one clicks on the button shown , whereby a dialogue window appears:

Here one can give the layout a name and specify the bar diameters and con crete cover used in the dimensioning. For the dimensioning example delete the smallest bar spacing (7.5.[cm]) from the default values. If one wants to work with a reinforcement mesh one can choose here the steel mesh pro gram (=list of mesh types).

After closing the dialogue with [OK] for the layout, the new layer ’1’ in the layer group ’Reinforcement’ is created and made visible. In addition, the new layout is set to active in the register (see register figure above, Layout Management).

D 3.2.4 Input of Reinforcement Fields

Bottom reinforcement The input of the reinforcement fields can now begin, which as mentioned above is done separately for the top and bottom reinforcement. By clicking on the button shown left for the input first choose the bottom reinforcement.

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In view of the slab geometry in both directions a continuous bottom reinforcement is placed. In order to start the reinforcement in the Xdirection, ensure that the Xreinforce ment is activated (button on left). Thus everything is ready for the reinforcement in the Xdirection. .

The X-direction chosen here (or Y-direction) thereby corresponds to the current coordinate axis, which is defined in the dialogue ’Input Options’ (button

on left boundary). Since

the X- and Y-axes may be arbitrarily oriented, the input of sloping reinforcement is also possible. Click on the button ’Input Reinforcement Field’. The following dialogue window ap pears:

vertical position

choice of bar and mesh posi# tions preview

properties bar position bar and laying direction (only active if fields selected)

anchoring conditions (no influence on calculation; serve only as additional informa# tion for preparing a reinforce# ment plan)

This dialogue shows all attributes of a reinforcement field. For the example slab no steel meshes should be used. One chooses therefore the setting Bar Field. Before construct ing the geometrical extent in der plane of the slab first define the vertical position by assigning to Zone 1: for zone selection with mouse

For constructional reasons a minimum reinforcement often has to be placed. This can be done directly in the input of the reinforcement fields, by specifying a minimum content in the Register/Design/. For the example choose a geo metrical reinforcement content of 0.15%(according to SIA code), which corresponds to a minimum reinforcement area of 3.3[ cm 2ńm]. Each reinforcement field can have a different steel quality, which can be specified in the Register/Options/. In most

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cases, however, one uses the same steel as chosen already in the project settings (shown here in light grey). On opening the dialogue the drawing tools shown on the left are activated, enabling one to construct rectangular and polygonal fields. The bottom reinforcement in the X direction can be input as a rectangular field, by pressing either the button [Introduce] and then on the left lower and right upper corner of the dialogue or on the button of the plan outline. The reinforcement field just constructed is now shown on the screen as a broken−lined rectangle (=effective static zone) with a labelled continuous rein forcement bar. The labelling is positioned on the bar, is in its direction and shows the current reinforcement area. Since dimensioning has not yet been carried out, it corre sponds at the moment to the prescribed minimum content. .

The labelling, beside the current reinforcement area, shows other attributes of a field as well, e.g., by means of an underlined text, that a minimum content was prescribed. For further explanations on this topic see Chapter D 3.2.8 In order to input the same Yreinforcement, without closing the dialogue, press on the register button shown on the left. Thereby the preview graphics and the values for the directions in the dialogue can be adjusted, while the other settings remain unchanged. Analogous to the Xreinforcement construct now the reinforcement field in the Ydirec tion by pressing on the button [Introduce] and then click on two opposite plan outline corners.

Duplicating in another direction For the frequent case of having the same fields in both reinforcement directions, instead of the above de scribed input method one can use the convenient duplicating function: In order to use this here, firstly undo the input of the second reinforcement field (CTRLZ=Undo). Then select the field in the Xdirection (click left mouse button). In the Object Menu (click right mouse button) then choose ’Duplicate in another direc tion’. Thereby a field is created in the Ydirection with the same attributes. .

The function ’Duplicate in another direction’ can be applied simultaneously to several reinforcement fields, as long as only rectangular (or parallelogram, respectively) fields are selected. Hereby, one should note that newly created fields are only different from the original in the swapped bar and laying directions and thus have no effect on the current setting of input directions.

Construction based on elastic reinforcement requirement Up to now the reinforcement fields were defined without considering the stresses, but purely on the basis of geometrical and detailing considerations. In order to be able to detail based on the elastically required reinforcement contents, first the critical action must be specified, whereby all previously specified limit state specifications are avail able.

calculate reinforcement requirements

Choose the specification ’!Ultimate (ULS)’, which was automatically created by CE DRUS5. Then click on the button ’Calculate reinforcement requirements’, whereby (if not already done) the FE mesh is generated, the load cases solved and the elastic limit

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state values of reinforcement requirement are calculated.

On the screen the statically required reinforcement areas are displayed graphically ele mentwise as blue lines in the output directions, whereby the thickness of the line in creases with increasing area. In order to see the numerical values, move the mouse pointer over the coloured figures and CEDRUS5 shows the reinforcement areas for the corresponding mouse pointer position in the status line (bottom of window). With the buttons on the left one can also display the requirements for top reinforcement (see above). As expected one needs from the elastic calculation reinforcement above all at the top for the fixed support and below along the free boundary. Now change to the bottom reinforcement again. To have a better overview, the simula taneous display of the fields and the results for both reinforcement direc tions can be suppressed. Above the register button on the right set the cur rent reinforcement direction to X and the display to ’Show fields in reinforce ment direction’. Thereby only the field in the Xdirection is visible and the re quired reinforcement areas in this direction are now shown as coloured graphics.

Additional reinforcement Now the question arises whether and where extra reinforcement has to be introduced. This is certainly useful in those areas where the required content is much greater than the minimum reinforcement. Such areas can be displayed by CEDRUS5, provided fields with minimal reinforcement have already been input. For this purpose press first on the button ’Elastic Design’ , whereupon the following dialogue appears:

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Since no top reinforcement was input, at this stage no elastic dimensioning is possible. The presentation of the re quired reinforcement contents, how ever, is adjusted, whereby only those zones are highlighted using colours, whose value of bending moment ex ceeds the resistance of the minimum prescribed reinforcement.

.

D 3 Reinforcement Module

2m

0.5 m

1.5 m

As soon as the button for ’Elastic Design’ is pressed, in the display of the results only those zones are visible whose values exceed the minimum reinforcement. As explained in the following box, this behaviour can be configured using the Dialogue ’Display Settings’.

Settings for the display of results The dialogue for changing the display of re sults and reinforcement fields can be opened using the button on the left. As a default value in the Register/Results/ the current rein forcement content (required and present) is selected. In addition the button ’Without fixed and minimum content’ is activated, whereby the fixed prescribed and minimum contents are deducted before display.

On the basis of this presentation and conctructional considerations additional reinforce ment should be specified along the free boundary. Place, therefore, a new reinforce ment field, by first deactivating in the Dialogue Reinforcement Field (Register/Design/) the minimum content, press the button [Create] and then construct as shown the addi tional reinforcement field shown top right.

Top reinforcement For constructional reasons a top continuous minimum reinforcement should also be specified. One can do this in the same way as for the bottom reinforcement, in that in both directions one provides a reinforcement field with prescribed minimum content. The same can be done more quickly and more easily by first making all fields of the bottom layer visible using the button , selecting both big reinforcement fields (left mouse button:click on the first bar and with SHIFT click on the second bar) and copy this to storage (via Object Menu or CTRL−C). Afterwards change to the top reinforce ment and introduce both fields (via Object Menu ’Paste into active layer’ or CTRL−V).

Additional reinforcement In order to be able to detail the additional reinforcement press again on the button

.

Since everywhere in the slab a minimum reinforcement was specified, which exhibits

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a variable reinforcement content, this time elastic design is possible. On the screen be sides the required (blue) also the placed reinforcement based on elastic dimensioning (grey) is displayed:

The result obtained of over 94 kgńm3 (see figure top left), however, is purely theoretical, since in the top reinforcement no gradation was input. For detailing the additional rein forcement in the Xdirection set the visibility according to the buttons on the left and also press the register button ,which draws the bottom reinforcement in a light grey colour (see figure top right). Thereby one can then construct an additional top reinforce ment (without minimum content!) on the bottom one, by pressing in the Dialogue [Create] and then clicking on the bottom right corner of that additional reinforcement and on the top right corner of the plan outline. Analogously define a second reinforce ment field directly next to it. In the Ydirection input only an additional reinforcement field, which, with a width of make first the approx. 1.5 m, runs along the complete fixed boundary. Then with Ydirection the reinforcement direction, press in the Dialogue [Create] and construct this field with the Graphics Editor (e.g. with absolute coordinates 0,0−7,1.5).

Positioning of the field label In the construction of a reinforcement field the reinforcing bar and the labelling are automatically positioned. As in the present example (with the additional reinforcement in the Ydirection) this can lead to two bars lying exactly over each other. Since the posi tion of the labelling and thus also of the shown reinforcing bar corresponds to a point (=labelling point), one can move the labelling. This is done as follows: S

Select the last created additional reinforcement. Thereby the field will be shown red.

S

Right−click the mouse, select the menu ’move label’ and move it to a new position.

D 3.2.5 Elastic Dimensioning Thereby the input of the reinforcement is complete and the elastic dimensioning can be restarted using the button . This time a realistic reinforcement weight of approx. 62 kgńm3 results from the statically required reinforcement areas (see figure below). These are subsequently converted into bar positions with diameter and spacing (see Chapter D 3.2.8), whereby the total weight increases somewhat. Thereby, one should note that in this calculation the anchorage lengths, splices and edge bars are not yet included, which by experience can further increase the weight by approx. 10−15%.

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If all fields are made visible using and first the bottom (left) then the top reinforce ment is activated, the above displays are presented. These show that the minimum rein forcement placed can covers a large part of the elastically required reinforcement and the resistance of the extra reinforcement is not exploited in an optimum way. By means of a finer subdivision of the additional layers the total weight of reinforcement could be reduced. This small saving, however, would be ruined by the increased numer of the reinforcement positions and anchorages. .

If one does not want to carry out an optimum plastic dimensioning one can skip over the next section and go directly to the production of reinforcement drawings.

D 3.2.6 Optimum Dimensioning By means of optimum plastic dimensioning one can, for what is really an unproblematic example slab, obtain an improved solution:

Design Monitor In order to start the optimization process press the register button

, whereby the

Dialogue ’Monitor’ appears. Click there on the adjacent button , which starts the auto matic dimensioning optimization. One can follow the calculation on the screen, whereby after each step the figures of the reinforcement contents are redrawn.

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In the Monitor the progress of the di mensioning optimization is docum ented by two parameters, which are plotted as a function of the optimiz ation steps: The first parameter shows the required reinforcement content, while the second illustrates the effi ciency of the optimization (see D 3.1.3). Already after a short time both curves become very flat. This is a sign that the algorithm has brought one close to the optimum and further calculations of the weight of reinforce ment can no longer be decisively re duced. Therefore one could stop the calculation by pressing on the adjacent button and close the Monitor Dialogue. The resulting solution exhibits a reinforcement content of ap prox. 54 kgńm3 , which is about 86% of the elastic requirement:

D 3.2.7 Interpretation of the Results From the above presentation it is clear that of all specified additional reinforcement layers only those are necessary which run along the free boundary. In comparison to the elastic solution, where the distribution of force is continuous over the whole slab, the optimized solution exhibits there a predominant structural support direction. This method of support is even more evident, if one only shows the Xdirection and clicks on the button (at left edge of window) to switch to a 3Ddisplay:

The above figures show the reinforcement required in addition to the minimum rein forcement in the form of a column representation. Easily recognized are the moments at the column support (right) and the field moment (left). The resulting method of struc tural support of the slab may be interpreted more or less as follows:

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Between the zone at the free boundary and the rest of the slab a clear ’Load separation’ stands out. Due to the arrangement of the rein forcement fields, the method of support resembles in the boundary zone a simple beam, which is sim ply supported on one side and fixed on the other. The remainder of the load is partly transmitted through a cantilever beam along the long fixed edge and partly through a beam in the longitudinal direc tion. Thus the optimization algo rithm has chosen a load distribution such that the minimum reinfor cemnet suffices. .

This method of support reminds one of solution by the strip method. This is no coincidence, since it is also based on the same theoretical considerations. In contrast to the strip method, however, the calculation here is for a continuum, wherby strain compatibility is implicitly fulfilled. In addition CEDRUS-5 works with limit values and chooses the optimum force distribution by itself on the basis of specified reinforcement fields. These considerations clearly show that the choice of the reinforcement layers decisively influences the structural behaviour, since the optimization algorithm tries to adjust the structural action to the given reinforcement arrangement. From the point of view of economy, besides the low total weight, the simplicity of the reinforcement arrangement also contributes to the economy of the optimized solution.

D 3.2.8 Production of the Reinforcement Drawings The last step in the dimensioning process is the construction of the individual bar layers and the production of the reinforcement drawings. Change again to the 2D presentation and ensure that both directions of the bottom rein forcement are shown. Since the presentation of the results is no longer necessary, one can switch it off, by deactivating the results layer using the adjacent button in the layer group Reinforcement and then causing the figure to be redrawn (F2). Diameters and distributions should now be assigned to the reinforcement fields. Select in addition both large fields, open the reinforcement field dialogue (e.g. ’Attributes’ in the Context Menu) and change to the Register/Design/. The input fields diameter Ĭ and subdivision a are not yet active, but contain a default value (light grey), which one can adopt by clicking on both the buttons: required area existing area

As additional information for the production of the reinforcement plan one can specify in the Register/Attributes/ one tick each and an anchorage length. Now press the button [Apply], whereby both fields are fixed and the effective existing reinforcement area be sides that statically required are shown (see above). Now select the additional reinforce ment layer and choose a spacing of 15 cm (by clicking on the button a with subsequent input of 15) and activate the default diameter 8 mm. Here one should choose at both ends an anchorage length and press [Apply] again. Now change to the top reinforcement and proceed with the large fields analogously to the bottom layers ( Ĭ8mm every 15 cm). Then select the additional top reinforcement,

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choose a spacing of 15 cm and activate the default diameter of 14 mm. Also choose here an anchorage length for both ends and press [Apply]. The remaining statically unuseable fields can now be selected and deleted with the DELkey. Thus the reinforcement ar rangement is constructed and one can close the reinforcement dialogue. In order to provide the display with more de tail open the Dialogue ’Display Settings’ with the adjacent button and change to the Regis ter/Reinforcement/. Choose there detailed field labelling and specify for the view 1:100 a text height of 3 mm. Press also ’Renumber Fields’, whereby the input fields are provided with an increasing position number, begin ning with the bottom layers. Afterwards close the dialogue again. A reinforcement sketch now appears on the screen, which is similar to a plan diagram. Prepare this by moving the labelling points optically somewhat higher (see above, box ’Positioning the Field Labels’). Thus the dimensioning is complete and one can print the drawings (see figure below).

If one has a CAD system that can exchange reinforcement data with CEDRUS5, one now has the possibility of exporting the reinforcement arrangement. Thereby all reinforce ment layers with their attributes (diameter, spacing, anchorage condition etc.) are written to a file, which can then be read into the CAD system, in order to finish detailing the reinforcement there (i.e. constructional additions, splices etc.) and to produce the reinforcement plan. To do this open with the adjacent register button the dialogue ’Layout Settings’. Click there on the button ’Export’ and then specify the name of the target file, on which one wants to store the complete reinforcement data. The default value is a file named after the layout in the ’User’ directory of the project.

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CEDRUS-5 supports several reinforcement formats, which one can specify using the Main Menu ’’Options>CAD Interfaces>Export Reinforcement”. Basically one has the choice between CEDRUS’s own ECB format, a series of special formats (part of module CAD interfaces) and the industry standard DXF, which, however, only permits the transfer of a reinforcement drawing in the form of lines and text and thus is only of limited usefulness. CEDRUS-5 also supports several proprietary formats of CAD vendors, which one can acquire by purchasing the option ’CAD Interfaces’.

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D 4 Ultimate Load Module

D 4 Ultimate Load Module The Ultimate Load Module permits the nonlinear calculation of a reinforced concrete slab with a given reinforcement arrangement. In this chapter the basic concepts of the calculation are explained in detail and the procedure for an ultimate load calculation is demonstrated by means of an example.

D 4.1 Basic Concepts Modern codes permit the use of nonlinear calculation methods to verify the limit states for serviceability and ultimate load. The Ultimate Load Module of CEDRUS5 is restricted to calculations of the structural safety, i.e. ultimate load, and can provide, therefore, no information on crack widths and bending deflections under working loads. Since the reinforcement has to be known before the calculation starts and only one load combina tion can be investigated simultaneously (i.e. no process of critical action combination for limit states is possible), it is not suitable for dimensioning tasks. With the Ultimate Load Module, however, strength reserves of existing structures can be determined or the rotational requirement can be estimated at the end of plastic dimensioning.

Nonlinear Calculation Method By nonlinear methods are meant FE calculations, which take into account and exploit the nonlinear properties of the construction materials. Beginning with an initial stress and deformation state the behaviour of the structure is analysed with specified rein forcement and a stepwise increase of the loading (see D 2.3.1). Up to now these ex tremely computationally intensive calculation methods, however, have been little used in practice, although they have already been employed in research for a long time. One of the main reasons for this is the nature of nonlinear calculations, in which even small variation in the input parameters can cause big differences in the results. In view of the poorly understood properties of reinforced concrete structures (initial stress/strain state, material parameters, support conditions, loading etc.) these methods demand from the user much experience in problem modelling and interpreting the results. This difficulty grows with the complexity of the models employed, which is why in the Ultimate Load Module of CEDRUS5 a simple material model with few parameters is used (see D 2.1.1), which essentially determines the ultimate load. In combination with the simple calcula tion control (see D 4.1.3) and the vivid graphical output the simplicity of the model makes the interpretation of the results easier. With the Ultimate Load Module of CE DRUS5 the required user input is limited to the reinforcement arrangement and the loading. There is no specification of a material model. Thus ultimate load calculations are also amenable to practicing engineers, who do not possess specialist knowledge in the field of nonlinear FE methods.

D 4.1.1 Calculation Model Calculations with the Ultimate Load Module (see D 2.3) are based on the FE model of the Basic Module and the reinforcement model (see D 2.2), which are automatically generated from the user input of structure geometry and reinforcement arrangement. Thereby the following basic assumptions are made:

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S

small strains (also in the plastic state)

S

no second order effects

S

ductile behaviour (see D 4.1.3 Rotational Capacity)

S

adequate shear resistance (see D 4.1.3 Punching Shear)

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S

D 4 Ultimate Load Module

constant or linear support conditions

In this way the nonlinear modelling is restricted to the nonlinear material law.

Nonlinear Moment-Curvature Relationship As described in Chapter D 2.1, the nonlinear behaviour of a slab subjected to bending actions can be described by an elastoplastic moment−curvature relationship. The dia gram for a section of unit width used in the Ultimate Load Module is shown in D 2.1.1 c) and is defined by four characteristic values: The cracked stiffness of the cross section EI II, the plastic moment m pl R, the hardening parameter m and the limiting curvature

x u. CEDRUS5 determines the values for EI II, m pl R and x u automatically on the basis of the concrete cross section and the actual reinforcement (see D 2.1.4). The calculation is performed following the method of the variation strain plane (see e.g. Handbook Cross Section Program FAGUS). Thereby the nonlinear stress−strain diagrams for con crete (see e.g. EC2 Figure 4.1) and reinforcing steel (see e.g. EC2 Figure 4.5) as well as the safety factors for the materials are taken form the analysis parameter set ’AP3: Nonlinear analysis’ (see main menu: Settings>Analysis parameter). The characteristic material values (i.e. f ck, f yk for conrete and reinf. steel) are taken form the material zone and the reinforcement field (see D 2.2.1).

Hardening The hardening behaviour of reinforced concrete sections prevents, among other things, the localization of the deformations after the start of plastification. This allows the plasti fied zones in the slab to spread (i.e. the hinge region will get wider), which reduces correspondingly the required curvatures. As a welcome side effect material models with hardening increase the stability of numerical calculations. The positive hardening para meter m is the only calculation parameter, which has to be provided by the user. It is defined in the bilinear material properties diagram (see D 2.1.1 c) as the ratio of the stif fness after plastification of the cross section and the initial stiffness EI II and is constant over the slab. Hardening behaviour is implemented as kinematic hardening (see D 2.1.3), whereby the behaviour in the plastic region can be accurately modelled for loading and unloading.

Load History In CEDRUS5 the user has to specify the load history as a series of different load steps, which are successively applied to the slab and correspond each time to an arbitrary com bination of load cases. As soon as the given load level of a load step has been reached, the next one is applied, whereby the load factor for the last step is increased as far as possible. For ultimate load calculations on actual structures one is often not interested in a global ultimate load factor for all applied loads, but wants to calculate a safety factor, e.g. for a certain loading arrangement acting in addition to the permanent loads. This problem can be solved using different load steps.

Partial Safety Factors The safety concept of modern building codes is based on probabilistic assumpitions, resulting in partial safety factors for actions and material properties. The safety factors for loads are always to be considered in the load history. In order to account for the safety factors of the materials the user has the choice of two modes: S

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Reduction of the material properties If the material safety factors g c and g s for concrete and reinf. steel are > 1.0 in the used analysis parameter set (i.e. ’AP3: Nonlinear analysis’), then the calculated plastic

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resistance of the cross sections is reduced. As a result the load−deformation curve is pretty far from reality (i.e. yielding of the steel layers occurs far too early). In this case the user does not have to account for the material safety factors in the load his troy, in order to achieve the safety level required in the code. S

Scaling of the applied loads If the material safety factors g c and g s for concrete and reinf. steel in the used analysis parameter set are all equal to 1.0, then a more realistic load−deformation curve is found. In order to achieve the safety level required in the code, however the user must account for all safety factors (i.e. for loads and materials) in the load history. Unfortunately this is only possible, if g c and g s do not differ (like in the older codes SIA 1xx and DIN). Otherwise one has to use the method described above.

The ultimate load module does not automatically account for these factors (as the base and reinforcement moduls of CEDRUS5 do). But the safety factors for actions and ma terials, prescribed by the building codes, are easily introduced in the load history specifi cation (see figure below).

.

Example for SIA 1xx (’Scaling of applied loads’): if you want to investigate the structural safety of an existing slab, loaded by self-weight, an applied surface load and a imposed load, you can combine the first two actions into a single load step using the partial safety factor for dead loads (e.g. 1.3 accordingto SIA) times the partial safety factor of the materials (e.g. 1.2 accordingto SIA). The imposed load is introduced into a second load step using the partial safety factor for imposed loads (e.g. 1.5 accordingto SIA) times the factor for the materials. In this way, the dead load is applied first up to the specified level. Then the imposed load is added and increased until the ultimate load is reached. If the resulting load level (=load factor of the second load step) is bigger than 1.0, according to the building codes the structure is safe against collapse.

D 4.1.2 Termination Criteria for Calculation As mentioned in Chapter D 2.3.1, with an incremental, iterative calculation besides the criteria of system stability there are additional termination criteria. This is necessary to ensure that the model assumptions made (see above) are complied with. In CEDRUS5, after each load increment four scalar parameters are calculated, which clearly describe the current state of the system. Each of these quantities is automatically checked, so that the calculation can be terminated if given limit values are exceeded. In order always to give the user an overview of the whole system behaviour, the variation of these system parameters is plotted. In addition, the user has the possibility to deactivate the control of these parameters and to configure individual limit values. The four state parameters are briefly described in the following: .

CEDRUS–5

Since the computational ultimate load for a calculation with the hardening parameter m u 0 can theoretically become infinitely large without an additional termination criterion, all control parameters may never be deactivated. As a rule it is advisable to leave all controls active (default).

D–31

Part D Reinforcement and

D 4 Ultimate Load Module

Bending deflection With further increase of the loading the load−deformation curve (see D 2.3.1) becomes ’flatter’ and the bending deflections increase enormously in the neighbourhood of the ultimate load. In order not to ignore the limits of the computational model (see D 4.1.1), one must ensure that the deformations do not become too large. For this reason CE DRUS5 compares the value of the maximum bending deflection w max with a value w u prescribed by the user. If this is exceeded, the calculation is terminated.

w u w w max Here one should note that as a rule the calculated bending deflection corresponds to an upper limit of the expected value (neglecting long−term effects), (see D 2.3.1 ’Influ ence of Initial State and Load History’). System stiffness The system stiffness K s is a measure of the current remaining stiffness of the system. After each load increment Dl (see D 2.3.1) it is determined using the following formula:

Ks +

W(0) u0 W(l)

mit W(l) +

W Dl Dl2

Here W Dl signifies the work of the last load increment and W(0) the normalized work of the initial load increment. At the start of the calculation K s + 100%. If the structure becomes ’softer’ or ’stiffer’ under increasing load, then K s t 100% or K s u 100%, respectively. On reaching the ultimate load K s becomes zero. The region between the beginning of and the completely formed mechanism is often very fluid and the latter is numerically somewhat unpredictable. In order to obtain a conservative value for the ultimate load, the low value of K s points to the exhaustion of the ultimate load resis tance. Therefore CEDRUS5 terminates the calculation as soon as the system stiffness falls below one percent or the value of the hardening parameter is reached. Rotational requirement As explained in D 4.1.1, the calculation model assumes that the structure behaves in a ductile manner. In contrast to frame structures, as a rule this assumption applies to rein forced concrete slabs fixed along two axes, since these are usually lightly reinforced and exhibit a multidimensional load transmission. The rotational capacity required to redis tribute the moments is in general much smaller than the existing rotational capacity. However, at the end of plastic dimensioning of the reinforcement (see D 3.1.3) determi nation of the rotational requirement can be useful, since much use is made of moment redistribution. In order to carry out a rotational capacity verification the deformations have to be known. As explained in D 2.3.1 (see ’Influence of Initial State and Load History’), these can only be roughly estimated, so that an exact calculation of the rotational requirement is impossible. Using the calculation model of CEDRUS5, however, a reasonable esti mate can be obtained: The required rotations are checked after each load increment, by comparing in all cross sections the limiting curvature x u (see D 4.1.1) with the aver age curvature x m:

x u w x m + xel ) x pl The average cross section curvature x m is calculated from the sum of the elastic x el and plastic parts x pl (see D 2.1.3), which are determined from the average element curva tures in the reinforcement directions. In order to express the current deformation capac ity of the system as a scalar quantity, the rotational requirement K r is defined as the maximum value of all cross sections:

x K r + MAX( xm) u

D–32

CEDRUS–5

Part D Reinforcement and

D 4 Ultimate Load Module

For K r t 100% the slab has an adequate rotational capacity. If K r u 100%, the rota tional capacity is not guaranteed. Punching shear If the shearing resistance of the slab is exceeded brittle failure results, a condition that cannot be predicted by the calculation model (see D 4.1.1). Since the shear stresses are also determined from the deformations, their exact determination is not possible. The greatest danger of shear failure, however, is at the supports (columns, wall ends etc.) and concentrated loads, for which punching shear can be verified during dimensioning (see CEDRUS5 Handbook Chapter 2.6.). This problem is handled in CEDRUS5 by checking, after each load increment, the punching shear objects generated by the user beforehand. The check is restricted to those punching shear objects which are con nected with supports. Here one should note that the calculated support reactions can exhibit big differences for a particular loading between an elastic solution (Basic Mod ule) and a nonlinear solution (Ultimate Load Module). In order to express the current danger of shear failure with a scalar parameter, the punching shear parameter K p is de fined as the maximum of the ratio between the current punching shear load V and the corresponding resistance V Rd of all punching shear objects:

K p + MAX( V ) V Rd The slab possesses an adequate punching shear resistance if K p t 100%. If K p u 100% there is a danger of brittle failure. :

Astuce: Punching shear objects for concentrated loads, which are not checked by the Ultimate Load Module, can be checked directly without a nonlinear calculation on the basis of the total applied load.

D 4.1.3 Calculation Control A nonlinear analysis is more demanding for the engineer in terms of modelling, calcula tion control and interpretation of results than a linear elastic analysis. As shown in Sec tion D 4.1.1, the additional modelling work (after an elastic calculation) with CEDRUS5 is limited to the input of the reinforcement, the loading and a hardening parameter. In order to simplify the nonlinear analysis for the program user as much as possible, an automatic calculation control has been implemented, which requires no user input. In this way the engineer can concentrate on the interpretation and verification of the cal culation, for which CEDRUS5 provides him the following support: The user can ob serve the structural behaviour during the calculation directly on the screen. After each load increment the stucture’s deformations and the plastified zones (including crack concentrations) are displayed graphically and the control parameters are plotted (see above). Thus the current system state and the general stuctural behaviour can be easily inspected. The calculation can be terminated at any time, e.g. if the engineer feels that the system’s behaviour is not realistic or the calculation is lasting a very long time. The required computational expenditure for an incremental, iterative analysis is much greater than for an elastic analysis. Depending on the available hardware, the problem investigated (system size, reinforcement arrangement, loading etc.) and the FE model used (mesh size), the computational time for calculating the ultimate load can be very large. :

CEDRUS–5

Astuce: The maximum size of the FE model depends only on the available computer memory. However, since the required computational time increases greatly with the in creasing number of nodes and elements, it is advisable to avoid a very fine element mesh subdivision.

D–33

Part D Reinforcement and

D–34

D 4 Ultimate Load Module

CEDRUS–5

Part E Prestressing Module

E 1 Introduction

Part EPrestressing Module E 1 Introduction E 1.1 Overview With the Prestressing Module (PT) of CEDRUS−5 the effect of prestressing can be treated either as an external load or as a resistance within the context of design and dimension$ ing. The program is intended to aid the search for a suitable prestressing arrangement and provides all calculated data for further planning and design. Thanks to its data ex$ change capabilities CEDRUS−5 allows the export of diagrams, tables and graphs into other applications for post−processing, e.g. CAD systems, spreadsheets and word pro$ cessors.

S4 S3 S2 S1

Fig. A–1 Diagrammatic illustration of prestressing

E 1.2 Tendons and Supports The term ’tendon’ is used in the following as a generic term for every kind of prestress element (cables with bundles of wires, strands, bars). In contrast to most other graphical 3D objects the geometrical input of the prestressing is done separately for the horizontal and vertical directions. With the aid of the Graphics Editor the horizontal direction is drawn in the plan view as a straight line or as a polygon. In the case of curved tendons the individual polygon points serve as discrete points of the continuously curved tendon. By moving these dis$ crete points, the introduction of intermediate points or changes in the tangents, the changing shape of the curve can be influenced by the user. The vertical variation of the tendon is also defined in the plan view along the straight line with height attributes at so−called 2supports". Just like on the construction site the supports serve to support the tendons at the points of intersection, whereby the follow$ ing attributes can be assigned: S z−coordinate (different input possibilities regarding slab geometry) S slope of tendon S rules regarding minimum radius and inflexion points

E 1.3 Input Procedure Normally one attempts to compensate the permanent loads in the slab by means of the deviation forces from the prestressing. In the case of a vertically directed tendon, with

CEDRUS–5

E–1

Part E Prestressing Module

E 1 Introduction

second order parabolas, in the ideal case without friction losses straight constant devi$ ation forces are produced. With the standard cases described in E 2 many useful tendon profiles can be described in a simple manner. The basic steps of the interactive input comprise: S

Input of the tendons in plan view

S

Input of the supports for fixing the vertical profile

S

Definition of the stressing program

S

Assignment of the tendon groups to CEDRUS load cases

The choice of the arrangement of the tendons is governed both by statical and construc$ tional considerations. Basically, the prestressed elements can be placed in one or two directions. Regarding the subdivision into field and column strips (sometimes referred to as ’support strips’) running along the grid over columns there are different recommen$ dations (e.g. 50 % of the tendons in the field and the other 50 % in these concentrated column strips). In addition to compensating the dead load, with regard to punching shear behaviour as well one wants to profit from as many of the favourable effects of prestressing as possible. To obtain an initial estimate of the required prestressing force for the input of the ten$ dons a small program is available, with which a 2pre−dimensioning" sheet with all char$ acteristic values can be printed out. For a better overview of the input several tendons can be grouped together. Each group corresponds to a layer in the Graphics Editor. One can switch between the individual groups. 2Inactive" tendon groups can, if necessary, be graphically superimposed. A standard subdivision could look like the following: S

Group 1: Tendons in x−direction, supports in y−direction

S

Group 2: Tendons in y−direction, supports in x−direction

For further treatment in CEDRUS the tendon groups are put together to form one or more CEDRUS load cases. For control purposes, at any time during the input the following diagrams can be in$ cluded: S

3D view with arbitrarily selectable viewing direction

S

Longitudinal view of a selected tendon

S

Presentation of the force variation along the tendon itself based on the selected stres$ sing procedure

S

Presentation of the deviation forces in the section

S

Presentation of the deviation forces in plan or in 3D view

The amount of graphical information produced can be controlled using various options (presentation in the prestressing direction, tendon attributes etc.) and the diagrams can also be output on a printer or plotter to any desired scale. General stressing procedures can be defined by specifying the anchorage forces or the anchorage movements, whereby arbitrary stressing (tensioning, overtensioning) and re$ lease of tension (wedge draw−in during lock off, anchorage slip) is possible. The vari$ ation of the prestressing force calculated by the program takes into account all friction losses.

E–2

CEDRUS–5

Part E Prestressing Module

E 2 Basics

E 2 Basics E 2.1 Tendon Geometry As already mentioned in the introduction, the tendon profile is first drawn in plan view with the Graphics Editor and then brought into the desired vertical position using the supports. It is also possible to assign height attributes directly at every input point. For all internal calculations (e.g. of friction losses) the three dimensional profile of the ten$ don is used.

E 2.1.1 Geometrical description in the plan view y

Plan view

If the tendon was defined in plan by just two input points, a straight line profile is as$ sumed. Curved tendons are produced by inputting several points, whereby the curved variation between two points is assumed to be a polynomial of third order. The slope of the tangent at a particular point is given by the slope of the two neighbouring stretches (i.e. the bisector). This default value can be overridden by the user. straight and curved ten dons

x

E 2.1.2 Geometrical description in the side view z

The definition of the tendon’s vertical profile is given by the supports or by specifying height attributes at the tendon input points. The so−called folded view in the vertical section, which is permitted by the program, corresponds, as may be seen in the follow$ ing pages of the manual, to the development of a curved surface in vertical section x’ through the respective tendon. Therefore, the abscissa designated by x’ represents the projection of the tendon onto the plan view.

Section View

z’ z y

Plan View

x’

tendon sup port

sup port

In view of the deviation forces one often wants to work with special generating el$ ements (e.g. 2straight line−parabola", 2parabola−parabola"). By means of the following example it is shown how in most cases met with in practice the support attributes can be controlled.

x A tendon can be given the attribute 2Standard elements" or Polynomial segment

of 3rd order". Normally one works with standard elements (described below). The program tries in this case to describe the profile of the tendons between the support points with (quadratic) parabolic sections and straight lines, based on the attributes specified at the supports or at the intermediate points. The advantage of (quadratic) par$ abolas lies in the practically constant deviation forces: 8f u [ P
2 l

f P

P u

with:

l

u = deviation force per unit length P = prestressing force, f = parabolic height (sag), l = span

CEDRUS–5

E–3

Part E Prestressing Module

E 2 Basics

Support and point attributes The following support and point attributes can be input:

Fixed point: Height z:

Explicit height information or with reference to the boundary of the slab (highest and lowest points). The z−axis points upwards. Slope z’:

The slope input is optional. For the highest or lowest point input z’=0, otherwise (without explicit informa$ tion) z’ is determined by the program: z’=slope of the bisecting angle. Minimum radius conditions:

Par.min Kr.fix

free : no special condition parabola :condition is that tendon at support or at the indicated polygon point should exhibit the minimum radius (prerequisite: 2standard elements"). circ. arc : instruction that here a circular arc with the minimum radius and half chord length l k should be introduced.

Point of inflexion: This attribute is used to fix the position of the point of inflexion of two adjoining parabolas (left and right curve).

Examples of generated tendon profiles In the following some standard cases are put together to show how they are created by the program on the basis of the attributes in the section (support and polygon points, respectively). As mentioned already in the introduction, the tendon profile is first drawn in the plan view using the Graphics Editor and then brought into the desired vertical position by inputting the supports. It is also possible to assign height attributes directly to the support points. In all internal calculations (e.g. of friction losses) the 3 D profile of the tendon is used. It could happen that some conditions in a certain section are in conflict with each other or that the input values do not allow reasonable results to be obtained (e.g. chord lengths that are too long for circular arcs). In this case the program may have to ignore some conditions to still be able to draw a curve. All input height attributes (height z), however, are always used! In the vicinity of a support one should not assign height at$ tributes to the polygon points, to avoid defining them twice. At the ends of the tendons a height input is always required by the program otherwise the start and end points are specified in a standard way at the middle axis of the slab (reason: avoiding tolerance problems with the calculation of the points of intersection between the tendons and the supports). The required user input is demonstrated by means of the two span beam shown in Fig. A−2 .

E–4

CEDRUS–5

Part E Prestressing Module

E 2 Basics

Polygon points: A, E = start and end points (elevation z defined by default in middle axis of slab, can be changed) Supports: H,T = highest and lowest points Par.min = extra condition: parabola with minimum radius at vertex A T H, T Par.min

E

W

W Par Par Par Par Par’ G . Calculated sections: G = straight line, Par = parabola, Par’ = parabola with minimum radius at the vertex G

Fig. A–2 User input for a prestressed two span beam

Further examples of single sections: z

z( z’)

straight line

z, z’

parabola (2nd order)

z (z’)

straight line

deviation forces u+

To avoid the start and end sections being geo metrically redundant, at the anchorages only the height is specified. Then, optionally, at the end of the first section also the slope of the tangent z’ can be specified.

polynomial of 3rd order deviation forces u+

If, in addition to the height at the start, the slope is specified, the program uses at the end of the in itial straight line a polynomial of 3rd order.

Fig. A–3 Geometry at start of tendon: straight line – parabola

z ( z’)

parabola (2nd order) deviation forces u−

Point of inflex ion w

z ( z’)

parabola (2nd order) deviation forces u+

If, in the section under consideration, a point of inflexion is introduced between the highest and lowest points, then this defines the subdivision of the two parabolic sections. If no extra information is supplied the point of inflexion is placed in the middle of the section.

z ( z’)

v

Points of inflex ion w w

str. line deviation forces u−

z ( z’)

parabola (2.ord.)

deviation forces u+

If there are two inflexion points, then the part in between is a straight line. Further inflexion points lying in between do not influence the shape of the curve, i.e. only the two outermost inflexion points are effective.

Fig. A–4 Geometry in a middle section

CEDRUS–5

E–5

Part E Prestressing Module

E 2 Basics

z, Par.min

z

lp1

z, Par.min

z, Par.min

parabola (2. order)

parabola (2. order) parabola (2. order)

parabola (2. ord.) straight line

u–

u–

u+ u+

If a point of inflexion is moved closer to an end point, the radius of the shorter parabola section is always smaller. In the extreme, just permissible, case the minimum radius at the vertex of the curve is reached. This corresponds to the condi tion Par.min (parabola with minimum radius at vertex), which can be input as a support attribute, i.e. in this case the corresponding length of the parabola lp1 is determined by the program.

If, in the highest and lowest points, the condition Pmin is input, a trapezium can be produced.

Fig. A–5 Parabolas with minimum radius at vertex

z, Cir.min

lk

z

z

lk circular arc circle Bezier curve (approximated by pol. of 3.ord)

polynomial of 3rd order u–

z, Cir.min

u+

In contrast to the condition Par.min (see above) for which the minimum radius is just reached at the vertex, with the condition Cir.min a circular arc segment of half chord length lk is produced. Purely geometrically therefore, at a given dis tance lk the steepest variation (max. shear forces due to prestressing !!) is enforced. The program of course takes no account of constructional con straints (stiffness of the duct, etc.). If the length lk is too short, the point of inflexion of the connect ing 3rd order polynomial may not occur at the de sired position.

u– u+

With a higher value of lk the second section is ap proximated by several polynomials of 3rd order, in order to produce as smooth a curve as possible (approximation with Bezier curve).

Fig. A–6 Circle instead of parabola at vertex

E–6

CEDRUS–5

Part E Prestressing Module

E 2 Basics

z, Cir.min

z, Cir.min

z, Cir.min (lk=large)

lk

lk

circle u–

lk

lk

circle

3rd order poly nomial circle u+

Section with circular arc conditions at both ends. For smaller values of lk the transition is with a polynomial of 3rd order.

z

str.l .

circle

straight line

u– u+

Circular arc section with very large value of lk . In the extreme case the curve passes directly from one circle to another.

Fig. A–7 Further possibilities with circular arcs at vertex

z, z’

z, z’

3rd order poly nomial

3rd order poly nomial

u– u+ For +Non−Standard" input of tendons the pro gram uses cubic polynomials. If the tangent slope is not explicitly given, it is calculated from the two adjoining polygon sides (bisector). This input possibility is needed above all to re calculate existing objects, by inputting sequen tially the tendon heights measured from the plan.

Fig. A–8 Cubic polynomials

CEDRUS–5

E–7

Part E Prestressing Module

E 2 Basics

E 2.2 Force Variation along Tendon and Friction Losses P(x)

ÄÄÄÄÄÄ ÄÄÄÄÄÄ ÄÄÄÄÄÄ

Po

The prestressing force along the tendon (after the initial stressing) is calculated using the following formula:

P(x) + P o·
e *m
(a)Da
x) x P(x)

x Po m a

Da

: : : : : :

prestressing force at distance x from the stressing end tendon length measured along curve prestressing force at stressing point friction coefficient (typical values in range: 0.1 .. 0.3) sum of all angular displacements (absolute values, radians) over distance x unintentional angular displacements (wobble) per unit length values in range: 0.004 .. 0.01 /m

The associated contraction due to strain is proportional to the area under the curve P(x) and amounts to (not taking into account the concrete compression): L

DL +

ŕ P(x) dx EA 0

Other prestressing operations (overtensioning, tension release etc) are possible after$ wards. The corresponding instructions have to be input via the tendon attributes. .

In contrast to CEDRUS–3 the formula for friction losses had to be adjusted to comply with the standard that is usually applied today. The earlier CEDRUS–3 definition was: P(x) + Po·
e *(ma)kx)

m a k

: friction coefficient : sum of all deviation angles (in radians) at distance x : friction coefficient for unintentional angular displacements(/m) (CEDRUS–3 default value: 0.0008 /m’)

E 2.3 Deviation Forces As a result of prestressing the following loading elements are generated:

.

E–8

S

Deviation forces These continuously distributed forces are proportional to the curvatures of the ten$ don (determined in the vertical section) and to the prestressing force. By not taking into account the friction losses the deviation forces would be constant for each sec$ tion (2nd order polygon) or linear (3rd order polygon)

S

Friction forces In sloping tendon sections, due to friction a small vertical component is produced, which has to be considered for vertical equilibrium to be fulfilled.

S

Anchorage forces Due to the anchorage forces vertical point loads and correspondingly directed end moments are introduced. To guarantee consistency such concentrated forces are also introduced at abrupt changes in the slab thickness.

The loading elements generated by the the Prestressing Module can be checked individually in the Tabsheet ’Loads’ as with ’conventional’ loads.

CEDRUS–5

Part E Prestressing Module

E 2 Basics

E 2.4 Dimensioning of the Non–Prestressed Reinforcement Basically prestressing can be treated in two different ways in the dimensioning of non− prestressed reinforcing steel. Either as an external action on the structure, i.e. only on the loading side, or as a dead load case with the tendons as part of the system. In the second case the tendons are included in the determination of the resistance.

E 2.4.1 Prestressing as an external action The prestressing load cases, as they are generated in the Prestressing Module, comprise all actions of the tendons on the slab. Therefore, using the standard procedures of CE$ DRUS the reinforcing steel is dimensioned for ultimate load conditions (i.e. failure). It should be noted that here the load factors for the prestressing case are specified accord$ ing to the codes. What cannot (without the possibilities described in this chapter) be considered by CEDRUS as a program specifically for slabs, however, are the axial forces in the slab.

E 2.4.2 Prestressing as self-equilibrating stress state In many publications it is implied that prestressing should be considered as self$equili$ brating stress state (due to constrained deformations) and thus the tendons can be con$ sidered in the determination of the cross sectional resistances. While this is obvious in the case of beams and there is no problem, in the case of slabs several difficulties have to be overcome. How this is solved in the CEDRUS in dimensioning for prestressing, is described below.

The dimensioning conditions The actions on the slab consist of the components

Sd

: Design limits of the sectional forces due to external actions

Sz

: Sectional forces due to constrained deformations during prestressing (constrained sectional forces)

The action effects are determined by means of a linear elastic analysis using the FE method. The verification of the ultimate load bearing capacity is carried out at certain points or over sections as follows:

S d ) z
S z v gR

R

z

R gR

: Constraint factor: The constrained moments represent a load−free stress state and can be taken into account according to plasticity theory using an arbitrary factor z. Practi cal values of z are in the range 0 to 1. : Cross sectional resistance taking into account the tendons. : Resistance factor.

Since the bending action at a point in a slab does not comprise one value only ( M x, M y, M xy), the above formula cannot be applied directly, but in a appropriate form for the slab. In CEDRUS the linearized yield conditions are:

M xB) v Rx)ńg R M xB* w Rx*ńg R M yB) v Ry)ńg R M yB* w Ry*ńg R

CEDRUS–5

M xB) : Max
(M x) )ø M xy ø) M xB* : Min
(M x* *ø M xy ø) M yB) : Max
(M y) )ø M xy ø) M yB* : Min
(M y* *ø M xy ø)

E–9

Part E Prestressing Module

E 2 Basics

These conditions apply for two orthogonal reinforcement directions x,y. They cannot be applied for non−orthogonal reinforcement.

Dimensioning as beams The dimensioning in CEDRUS generally follows at particular points according to the above yield conditions. While, in the determination of the necessary resistance, the rein$ forcing steel can be considered to be ’smeared’ (cm2/m), this is difficult for individual tendons. Thus the question arises of the width of influence of a tendon in determining the resistance at a point. A point−wise consideration is hardly possible any more.

Longitudi nal− section with width

ÄÄÄ ÄÄÄ

The dimensioning program, therefore, uses for the prestressing a type of strip method. The user defines these strips in the form of longitudinal sections of a certain width (beam sections of CEDRUS$5). Such a longitudinal section cuts a beam out of a slab, which is considered as such for the dimensioning.

b

The action effects in such a beam are supplied by the beam sectional results of the basic CEDRUS module, which summarizes the results of the FE calculation for the beam width.

Cross sectional resistance The determination of the cross sectional resistance is carried out according to the usual design rules for bending and axial force (equilibrium, plane sections remain plane etc.). The following information describes the default settings made by the program. With the aid of the cross section program FAGUS−5 it is possible, to change these for special in$ vestigations. By default a maximum concrete compression of −3.5 o/oo and on the tensile side a maximum strain of the reinforcing steel of 5 o/oo are assumed. This limit also applies to the additional strain of the prestressing steel, if this is also in the extreme fibre posi$ tion. Each tendon is treated with it correct position and initial strain, corresponding to the geometrical input. The concrete is assumed to be cracked in tension. concrete com pression zone

åc å s1

D

As −

Md

z

prestressing force As +

Z 5
ońoo

couple and inner lever arm

å p + åp o ) Då p å s2

strain plane

beam section forces

Fig. A–9 Determination of cross sectional resistance

The initial strain å p o is calculated in every section according to the stressing programme and the friction losses for each tendon individually. In a section at a distance x from the start of the tendon this is:

å po +

P(x) EA p

The effective contribution of the tendon then depends on whether it is bonded to the surrounding concrete. For unbonded tendons Då p=0 and therefore the prestressing force depends on the actual strain plane.

E–10

CEDRUS–5

Part E Prestressing Module

E 2 Basics

For the resistance of the beam all tendons within the beam are considered. Through the choice of the beam width b, therefore, the user also determines the influence width of the tendons. For the cover of the reinforcing steel the values input for the zone attributes are used. If the dimensioning cross section includes several zones of different thickness and con$ crete cover, the reinforcement used in dimensioning is placed in the extreme positions (represented by a circle symbol in the diagram on the left). If necessary, compression reinforcement is introduced. b

Zone 1 Zone 2 Zone 3

Serviceablility limit state (SLS): By default the design criterium is the stress limit for the mild reinforcement in tension. The limiting stress (depending on bar diameter, spacing etc.) must be specified by the user (see menu Settings>Analysis parameter>SLS).

CEDRUS–5

E–11

Part E Prestressing Module

E 2 Basics

Constraint moments The constraint moments caused by stressing a group of tendons may be calculated as follows:

ÄÄÄÄÄÄÄÄ ÄÄÄ ÄÄÄÄÄ ÄÄÄÄÄ Variation M z

+

b Tendon 1.. i

M P + M P@e ) M z MP M P@e Mz

³
Mz + M P * MP@e

: moment in beam due to prestressing as external action, i.e. calculated from the load case deviation forces + anchorage forces. : * P @ e (negative portion of sectional force in the tendon) : constraint moment (in CEDRUS this constraint moment can be changed using a factor z )

This means that in zones where there are no tendons we have directly the constraint moments. In the other zones the question of the influence width arises when introduc$ ing the portion of the sectional force in the tendon. The user also solves this problem by choosing the beam width. All tendons lying within the beam give their portion of the sectional force to the beam. .

Consistent with other actions the moment M p here too is formed and correctly superimposed by M px "ø M pxy ø

Direction of the tendons and of the associated beam sections The above dimensioning conditions apply to reinforcement in the orthogonal directions x,y. In order to include tendons here, they must also lie in these directions. Small devi$ ations α are permitted, whereby the program multiplies the corresponding steel sections by cos2α. Tendons with α > 10_ are not considered for the resistance. In the case of buildings this condition is usually fulfilled, but rarely for skew bridge deck slabs. The directions of the beam sections have to agree with the directions of the reinforce$ ment, and the complete dimensioning within a slab zone must always be carried out in these directions. If, for example, in one place only two skew beam sections are con$ sidered, the yield conditions would not be fulfilled! In zones with no tendons the normal dimensioning results of CEDRUS can be used. These are also supplied in the 2tendon strips", but there they are not relevant in the ten$ don direction.

E–12

CEDRUS–5

Part E Prestressing Module

E 2 Basics

E 2.4.3 Use of program The calculation method described in the previous section is available only for beam sec$ tions for the reasons mentioned. In order to obtain the corresponding results, the input described below is necessary:

Input in the tabsheet ’Calculation’

With the aid of the above dialogue, first of all a special specification has to be made. For each calculation run up to 5 different dimensioning criteria may be decisive. In the above case, e.g., first of all dimensioning is carried out for 2failure" with the actions de$ fined under ’!Ultimate load state’ and then for ’!Serviceability state’. Both sets of results are output in tabular form, as also the As limit values from both calculations. Basically, all automatically or self−defined limit state specifications in dimensioning for prestressing can be used, whereby the action ’!Prestress load’ in the design situations should normally appear with the factor 1.00. Values which differ from this influence the prestressing force and the initial strain in the prestressing steel, but not the tendon ge$ ometry. With a factor = 0.85, e.g., the prestressing losses due to creep and shrinkage can be considered. Constraint factor z: In dimensioning for the ultimate state the constraints of the prestressing load cases are taken into account using an arbitrary factor. This constraint factor z has to be input in the corresponding field on the right hand side, where, as a rule, reasonable values are in the range 0.00 to 1.00. It is recommended when calculating a floor slab to use the same value everywhere! Without bonding: With the instruction ’Not bonded’ the property input as tendon attribute for this calcula$

CEDRUS–5

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Part E Prestressing Module

E 2 Basics

tion run is deactivated (e.g. assessment of construction states, if the bonding is pro$ duced later).

Input in the Tabsheet ’Results’ The ’Prestressing Beam Section Dimensioning’ designated as ’As: Prestressing = Resis$ tance’ is available in the selection list shown on the left below. As Output Type for such results only beam sections are available.

Axial force due to prestressing For two reasons it may happen that the total prestressing force of all tendons in the beam under consideration are transferred to the concrete cross section of the beam. S

In the case of column strips over the columns the axial force distributes itself more or less uniformly at a certain distance from the anchorage over the whole slab. The cut−out beam therefore only resists a part of it. In general, this part can be estimated quite well.

S

The slab supports themselves can also impede the transmission of the prestressing force into the beam. This effect, if present, is difficult to estimate.

In the input field ’Portion of Axial Force: Factor’ the user can define the expected portion of axial force in the beam using a factor. With the factor = 0.0 there is none, with 1.0 the whole of the axial force is transmitted to the beam. .

Since this factor is constant for the whole of the beam section it may be necessary to introduce several sections one after another. But due to the uncertainty of the factor too much time expenditure is not justifiable. 4spreading out of axial force" support

ÎÎ ÎÎ

b = width of beam section

Fig. A–10 Prestressed slab beam

E–14

CEDRUS–5

Part E Prestressing Module

E 2 Basics

unimpeded axial force due to prestressing

zero or reduced axial force in the slab due to pres tressing

Fig. A–11 Plan view of floor slab

.

Tip: It is not always simple to decide how large is the existing axial force in a certain region due to prestressing. This, admittedly, places certain demands on the user. The advantage of a pure slab calculation, however, is that thereby in the calculation assumptions one is forced to adopt simple and clear models. In contrast to apparently more exact calculations (plane stress states, shells) there is the danger of false interpretations (uncertain assumptions regarding stiffness of supports etc.).

Remarks on the Results Tables The additional reinforcing steel can be shown for each beam section both in a graphical form and in a numerical form. In the following the relevant numerical outputs are shown, whereby these, depending on the program version, can differ slightly from the form presented. Limit state specification The table with the limit state specifications gives information on the loading, as well as the verification type: With the limit state ’Ultimate Load’ the calculations are carried out at the dimensioning level. The material strengths are reduced according to the partial safety factors input with the calculation settings. In contrast, the dimensioning for serviceability is normally carried out at the working stress level. The cross section is dimensioned for ’Admissible Stresses’. The correspon$ ding load factors can be adjusted, but in this case for the material behaviour no partial safety factors are used. LIMIT STATE SPECIFICATION ACCORDING TO SIA: !Ultimate (ULS) Limit state: Ultimate (ULS) Actions Design situations –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– Nr Name 1 2 0 !Dead load 1.3 0.8 1 !Imposed load 1.5 1.5 2 !Prestressing force 1 1

CEDRUS–5

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Part E Prestressing Module

E 2 Basics

As–Table The As−Table for the additional reinforcing steel looks as follows: Beam section: A (0.00,1.50 – 23.60,1.50) Beam width 3.00 Limit state specification: !Ultimate (ULS) As–design ultimate state:B35/25, S500, γc=1.20, γs=1.20 Portion of axial force due to prestressing = 1.00 PT treated as resistance, constraint factor= 1.00 Distance Md_min Md_max Mp_min Mp_max –P*e As–top As+bottom [m] [kNm] [kNm] [kNm] [kNm] [kNm] [mm2] [mm2] ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 0.00 1.23 3.32 0.05 0.05 0.00 0.00 0.00 0.48 41.50 111.91 –15.45 –15.45 18.06 0.00 2.00 0.97 81.28 219.17 –30.90 –30.90 36.05 0.00 5.00 [1] [1] [2] [2] [3] [4] [5] Explanations: [1] Limit state moments due to external loading (without prestressing): [2] Limit state moments due to prestressing (anchorage and deviation forces) [3] Moments due to –P*e (only for tendons in corresponding section) [4] Dimensioned top reinforcing steel [5] Dimensioned bottom reinforcing steel

The distance between two neighbouring dimensioning sections along the beam is chosen by the program itself and cannot be changed.

Prestressing record For a check on the tendons within each dimensioning section the following table is out$ put: PT– and cross section record: Dimensioning calculation performed with PT treated as resistance Beam section: A (0.00,1.50 – 23.60,1.50) Dist Id

zs hmax Width co cu P Ap Eps zp e –P*e Angle Bonded [kN] [cm2] [o/oo] [cm] [cm] [mkN] [rad] –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 0. –17.50 35.00 300.00 3.00 3.00 1.4 P1670 500.59 4.00 5.9594 –17.50 0. 0. 0.0 m.V. 1.5 P1670 125.15 1.00 5.9594 –17.50 0. 0. 0.0 m.V. 1.6 P1670 125.15 1.00 5.9594 –17.50 0. 0. 0.0 m.V. 1.8 P1670 125.15 1.00 5.9594 –17.50 0. 0. 0.0 m.V. 1.7 P1670 125.15 1.00 5.9594 –17.50 0. 0. 0.0 m.V. Sum P.restressing forces: –P 1001.17 [kN] –P*e 0. [mkN] Steel

Legend: Dist : zs : hmax : width : co,cu : Id. : steel : P : Ap : Eps : zp : e : angle

E–16

Distance from start of section Coordinate of centroid of dimensioning cross section Max. cross section height Beam width of dimensioning cross section Concrete cover of reinforcing steel (top,bottom) Tendon identification Name of PT steel Tendon force Total cross section of prestressing steel Strain in prestressing steel due to chosen stressing procedure Position of tendon with respect to top of slab (+ve upwards) Eccentricity of tendon relative to centroid of dimensioning c. s.

: Angle between axis of beam and tendon (0 = Tendon is parallel to beam axis)

CEDRUS–5

Part E Prestressing Module

E 3 Examples

E 3 Examples E 3.1 Flat Slabs

E 3.1.1 Description of problem By means of the floor slab treated below the the individual input steps for the calculation of a prestressed slab are discussed. This provides above all a basic introduction to the method of working with the prestressing module. Actual numbers are introduced in the second example in connection with the dimensioning of the reinforcing steel. It is assumed that the user already knows how to use the Graphics Editor. In order to become familiar with the input of geometrical objects it is recommended to work through the introductory example in the basic module of CEDRUS−5. Further tips are given in the Program’s Help System. The input of the prestressing was simplified in this example, in order to make the description easier.

E 3.1.2 Tabsheet ’Structure’

7.20

2.40

Initially the slab outline, openings and columns are input, whereby all geometrical data may be taken from the diagram given below..

2.40

7.20

19.20

thickness h=0.28 columns 0.4 x 0.4

2.90

8.40

8.40

8.40

8.40

2.90

39.40

Code Materials: Prestressing:

Swisscode (SIA 2xx) Concrete C35/45, Steel B500B, PT steel Y1860. A p =100 mm2 (per strand), f y + 0.9 @ f pk =1670 N/mm2 , f pk = 1860 N/mm2

E 3.1.3 Tabsheet ’Loads’ The following two load cases are considered − Dead load (automatically generated by CEDRUS) − Live load$general (additive) q = −5 kN/m2 (whole slab) The later has to be input. laster, another load case with the action type ’Prestressing’ is automatically added with the input of the prestressing cables.

CEDRUS–5

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Part E Prestressing Module

E 3 Examples

Loadcases (check) Settings

Tablewith tendon data

Table with geom. data

Grafiphics

Checl k

Sup port Tendon

Pre−dimensioning

Group: Settings

Field of list for selecting ten don group

Group: Delete, New

E 3.1.4 Tabsheet ’Prestressing’

Prestressed flat slabs are probably not often designed by the majority of engineers. In order to quickly obtain an overview, therefore, CEDRUS−5 provides a special program for dimensioning the internal field of a floor slab. First we select this dialogue field and input as spans for the internal field lx = 8.4 m and ly = 7.2 m. At the moment we do not specify the slab thickness, i.e. it is determined by the program itself. For the loading the value of q = −5 kN/m2 has to be input and for the prestressing we select the steel ’Y1860’,as well as Ap=100 mm2.

With [Calculate] we obtain a ’proposal’ from the program itself. For different reasons (punching shear, acoustics) we change the suggested slab thickness to h = 0.28 m and we repeat the whole calculation. We now look more closely at the detailed preliminary prestressing sheet (possibly print it out) and then decide upon the following prestres$ sing:

E–18

S

Column strips: 12 strands (3 "bundles of 4") in the x and y directions

S

Field strip: 7 x 1 strand in the x direction, 9 x 1 strand in the y direction

CEDRUS–5

Part E Prestressing Module

E 3 Examples

With respect to our introductory example the following arrangement should then be obtained:

Input of tendons and supports The tendon profile is first drawn with the Graphics Editor in plan view and then brought to the desired vertical position by inputting supports. In order to give a better overview of this procedure the tendon input is divided into the following two groups: Group 1: Tendons in the x−direction Group 2: Tendons in the y−direction We begin with Group 1:

CEDRUS–5

E–19

Part E Prestressing Module

E 3 Examples

Now the first x−tendon is input over the bottom row of columns with the following at$ tributes (due to the long tendon lengths stressing is carried out from both sides):

With the button [Create] the polygon input is started with the Graphics Editors and the discrete points of the tendon curve are input geometrically. In our case the starting point is at the left boundary of the slab at (0.0 / 0.5). For the input of the second point we press the x−key, whereby the mouse can only be moved in a horizontal direction, and we click on the right slab boundary. We complete the polygon input by pressing the key . Now we duplicate the element just input by first selecting it and then using the function ’Duplicate’ from the Context menu with the following parameters:

Distances: 2*0.85

2*0.2 etc.

During the input of the above row, provided the button ’Preview’ in the dialogue win$ dow is selected, the elements to be created are continuously shown (’dimmed’), i.e. im$ mediate checking is possible at all times. After confirming with [OK] all tendons in the x−direction will be generated.

E–20

CEDRUS–5

Part E Prestressing Module

E 3 Examples

In the region of the column strips we still have to change the number of strands. For every column strip we select the three tendons and choose ’Attributes’ from the Context menu. We change the field ,No. of strands’ to the new value ’4’ and confirm with ’Apply’. Now follows the input of the supports. We assume a distance to boundary of 30 mm and that the external diameter of the tendon is 20 mm. The distance from the slab boundary to the line of action of the force in the steel is thus 40 mm for the tendons in the x−direction. In our example, due to the intersection at the middle of the support, this value is increased to 60 mm for the tendons in the y−direction. In an actual application, the geometrical relationships over the supports have to be planned exactly, whereby in the manufacturers’ product documentation of prestressing systems one can find much information regarding this question. For CEDRUS as a cal$ culation program only the centre line of the steel force is of interest. Possible geometri$ cal conflicts,however, may be detected by means of the graphical output (see Checks). The dialogue window is filled with the following values:

With the button [Create] we can place the supports geometrically. The first point is at (2.9/0) and the last point in the y$direction at the top boundary of the slab. The remaining supports are generated again with the function ’Duplicate’ from the Con$ text menu with the following values. Direction vector: dx = 0.0 dy:=1.0 Distances: 8*4.20 (half span length) Now we have to change the attributes of all tendon lowest points. We select all supports in the middle of the field and assign them the attribute ’Lowest Point’ with distance to boundary of 40 mm, as well as in the section ’Minimum Radius’ the value ’free’.

Checks Now we want to check individual tendons by selecting a particular tendon and then click on the button shown on the left. In a new dialogue window we should see something like the following diagram

CEDRUS–5

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Part E Prestressing Module

E 3 Examples

In the above A4 page layout the variation of steel stress, the tendon geometry and the deviations forces transmitted by the tendon to the slab are presented. In our case among other things we should check that the negative deviation forces concentrated in the area of the supports (=highest point) are transmitted to the slab. At the highest point we have specified the minimum radius condition and naturally we want the inflexion point with regard to the punching shear check to be near to the supports. With the print entry symbol in the upper left corner of this diagram, if required, can be entered in the print list. Within the input process typical tendons should always be considered and checked in each direction with this function. The dialogue window should never be closed to con$ sider a new tendon, but left in the ’background’ any tendon can be selected and the graphics adjusts itself automatically.

E–22

CEDRUS–5

Part E Prestressing Module

E 3 Examples

The second tendon group is created in the same way with the following steps: S

Define the new Group (2)

S

Input tendon in y−direction: On opening the attributes dialogue reset the input field ’No. of Strands’ to 1. The first tendon starts with (1.10/0.0) and ends at the top slab boundary.

S

One could once again duplicate all tendons with the following instruction: Direction vector: dx = 1.0 dy = 0.0 Distances: 2*0.8 2*0.2 10*0.8 2*0.2 10*0.8 2*0.2 10*0.8 2*0.2 10*0.8 2*0.2 2*0.8 The input of the above line, however, is somewhat lengthy and thus prone to error. As an alternative one could by duplicating just create the first field (Distances: 2*0.8 2*0.2 10*0.8 1*0.2 ) and then create the rest of the tendons by mirroring twice about the corresponding column axes.

S

Increase number of strands for the column strips: Key words: select relevant tendons, increase attribute ’No. of Strands’ once more to 4, [Apply]

S

Input supports over the first row of columns (point on left boundary 0/2.4) with fol$ lowing attributes: Height: ’Highest Point’ with distance to boundary of 60 mm Minimum radius: ’Parabola’

S

Duplicate supports ’Distances’: 4*3.60 (half span length)

S

Change support attributes in middle of field using following attributes: Height: ’Lowest Point’ with distance to boundary of 60 mm Minimum radius: ’free’ After checking the tendon visually with

the input is completed.

Now we leave this window and call the function shown on the left. By this means the deviation and anchorage forces for all prestressing load cases are formed and at the same time a record file is written. If the program encounters incor$ rectly input tendons (intersection with slab boundary, violation of minimum radius condition etc.) a corresponding error message is written. From the information given at the end of the table one can see how large is the sum of the deviation forces. A comparison with the dead load gives: g (dead load) = 25 kN/m3 x 39.40 m x 19.20 m x 0.28 m u+ (sum of all positive deviation forces)

= 5295 kN [ 9524 kN

For each internal field, of the total of 40 strands 24 of them are positioned in the column strips. Only these strands transmit the deviation forces directly to the columns. The ratio u/g therefore can be estimated as follows: u/g = (24/40) x 9524 /5295 [ 1.08 If we compare this value with the preliminary dimensioning: Instead of the suggested 47 strands we have only retained 40 of them. In addition, the distances to the boundary for the tendons running in the y−direction are greater than those assumed in the pre−di$ mensioning. The ratio u/g can also be calculated from a comparison of the two bending deflection diagrams for the load cases dead weight and prestressing. Since prestressing corresponds to a self−weight stress state, the prestressing load case considered by itself has to be fulfil equilibrium, i.e. the sum of all vertical loads must

CEDRUS–5

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Part E Prestressing Module

E 3 Examples

(up to a certain tolerance value) be equal to zero. This can be checked quite easily in the tabsheet ’Loads’ in the tabular output in the last line of the table. The prestressing layout should also be checked once again graphically: Positive and negative deviation forces are presented in different colours and thus it can be seen immediately whether, e.g., the negative deviation forces are actually transmitted to the columns. Tendons input twice, which lie directly on top of each other, are shown by the program in the table of prestressing data with a warning sign. If the number of strands is shown graphically (Context menu ’Attributes’, ’Options’), we can detect such (probably unde$ sired input) immediately, since the corresponding graphical symbols are displayed for each tendon at a different place.

Fig. A–12 Tendon with single stand

Two tendons each with single strand

E 3.1.5 Tabsheet ’Calculation’

In our example we are interested above all in the additionally required reinforcing steel, which we want to determine with the aid of a beam section dimensioning. To ensure that the corresponding results are available, first of all we have to make the correspon$ ding specification in the tabsheet ’Calculation’ . By default the program creates limit state specifications for ’!Ultimate Load’ and ’!Serviceability’. We produce now a new specification, stored by the program under the term ’Prestres$ sing=Resistance’, by selecting the function on the left and inputting the values shown in the dialogue below:

For the calculation of the action effect the limit state specification ’!Ultimate Load’ the following factors are used:

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CEDRUS–5

Part E Prestressing Module

E 3 Examples

LIMIT STATE SPECIFICATION code: SIA 162 ACTION: !dead load permanent L1: [1.00] Loadcase 1 ACTION: !imposed load plus where decisive L2: [1.00] Loadcase 2 ACTION: !Prestressing permanent L3: [1.00] Loadcase 3 LIMIT STATE SPECIFICATION: !Ultimate (ULS) Limit state: !Ultimate (ULS) Actions Design situations No. Name 1 2 –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 0 !Dead load 1.3 0.8 1 !Imposed load 1.5 1.5 2 !Prestressing 1 1

With regard to the last line it should be noted that of the prestressing forces only the constraints are used if the beam section dimensioning is carried out for ’As: Prestres$ sing=Resistance’.

E 3.1.6 Tabsheet ’Results’ Now we change to the tabsheet ’Results’, and in the column ’Results for’ we choose the line ’As: PT=Resistance’ Then we input over the first row of columns a beam section of width 1.50 m and an axial force factor = 1.00 and examine the corresponding result, i.e. the required addi$ tional reinforcing steel. With this the introductory example comes to a conclusion. In practice, however, one would still have to produce an extensive documentation, but we will leave this out. In the sense of a checklist the most important points in the calculation of a prestressed floor slab are summarized once more in the next section in abbreviated form.

E 3.1.7 Checklist The following checklist reiterates the most important points which have to be con$ sidered in a prestressed floor slab using CEDRUS$5: S

Input of the outline in plan and of the loads in the basic module of CEDRUS$5. An ’empty’ load case of action type ’Prestressing’ also has to be introduced in order to be able later to include the loads generated by the prestressing module.

S

Specify reinforcement and prestressing layout qualitatively (width of column strips, gradation of reinforcement etc), clarify geometrical relationships at points of inter$ section (fix distances to boundaries).

S

Floor slab with uniform arrangement of columns: − Carry out pre−dimensioning (with the CEDRUS pre−dimensioning program) − Select number of strands − Provide additional reinforcement possibly in boundary and special areas Geometrically complex floor slab: determination of a fictitious reinforcing steel using conventional CEDRUS dimen$ sioning methods (beam sections). Then convert to prestressing cross sections corre$ sponding to the ratio of the two steel stresses. Reminder: This factor depends on whether a prestressing with or without bonding is chosen (failure stress or existing prestressing steel stress)

CEDRUS–5

S

Input prestressing force

S

Compare bending deflections due to permanent loads and prestressing in all fields and if necessary adjust prestressing force

E–25

Part E Prestressing Module

E–26

E 3 Examples

S

Ultimate load verification: Determine additional reinforcing steel with the means provided by CEDRUS

S

Check stresses (Note: CEDRUS only calculates moments, so the axial force has to be estimated). Aim: As few cracks as possible immediately after prestressing

S

Check punching shear

S

Produce layout plan etc (possibly with export of DXF files to a CAD program)

CEDRUS–5

Part E Prestressing Module

E 3 Examples

E 3.2 Two Span Beams E 3.2.1 Problem description By means of this example the explanations of chapter E 2.4.2 are documented numeri$ cally. For this purpose a simple system was deliberately chosen, so that the values can also be obtained by hand calculations. Structure type Slab Code: Swisscode Materials: Concrete C25/30, (−>E c = 32 kN/mm2, n + 0.17) Steel B500B, Boundary distances for reinforcing steel = 30 mm Structure: 2 span beam (2 x11.80 m x 3.00 m) with linear bearings (walls: height=3 m,Young=3.5e7 kN/m2, support: freely rotational, wall stiffnes) and columns in the middle of the field (0.40 m x 0.40 m, Area support: settlement=column stiffness, rotations=free) Slab thickness: d = 0.35 m Prestressing: According to Fig. A−13 and Fig. A−14 Prestressing with no bonding, vert. variation with standard elements 4 strands (Y1860) "in field" distributed according to sketch 4 strands as "bundle" (Y1860) over columns according to sketch Area per strand: Ap = 100 mm2, Rmin = 2.5 m, friction coefficient: m = 0.19/rad, Da = 0.004 rad/m Stressing procedure: force at start = 0.75 f pk ( f pk = 1860 N/mm2) Wedge draw−in = −6 mm FE mesh: Max. size of elements 1 m Load cases: Dead load (automatically generated) Live load q = −5 kN/m2 (whole slab), Cathegory storage area Prestressing (automatically generated) Procedure: S Input slab with above dimensions and loads. S Input prestressing with prestressing module S Define longitudinal section (beam of width 3 m) and perform dimensioning

Lowest point of support: Distance to boundary = 50 mm

Highest point of support Distance to boundary = 50 mm Minimum radius

Lowest point of support: Distance to boundary= 50 mm 1.50

Column

5.00

6.8

1.50

6.8

11.8

5.00 11.8

Fig. A–13 Slab outline with tendons

L=0.8 –0.00 –0.10 –0.20

5.00

10.00

15.00

20.00

L=0.8

Parabola with minimum radius Fig. A–14 Longitudinal section with tendon profile

CEDRUS–5

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Part E Prestressing Module

E 3 Examples

.

E 3.2.2 Results

Results of dimensioning for ultimate load in the field at x = 4.83 Limit state specification:

Beam section: Table of As:

Table of tendons

Summary of section forces (from As−Table) M d
(g ) q) = (1.35* 255.9 + 1.5*146.23) M p
(P @ e ) M z) P@e Mz (with constraint factor = 1.0) Ȁ M d
(g ) q ) M z) (= external action)

= = = = =

564.8 kNm −104.6 −127.0 +22.4 587.2 kNm

By comparison: maximum field moment from beam theory M(q) + 9 q
l 2 + 9 @ 15 @ 11.82 + 146.85 128 128 Prestressing check (from prestressing record) å Po [ 6.52 o/oo Då + 0.0 (prestressing without bonding) P + 0.00652 E s A s + 1017 kN (cf. above) P * e = 0.125 * 1017 = 127.1 kNm (cf. above) Prestressing forces at dimensioning level: N p + gP + 1017 kN p .

E–28

According to SIA 262, 4.2.3.3 one must apply the resistance factor of the PT steel to the yield stress and not on the E-modlulus. Therefore the prestressing force must not be reduce here.

CEDRUS–5

Part E Prestressing Module

E 3 Examples

Dimensioning (x c and z estimated or taken from cross section program) Concrete compression zone : x c [ 62.3 mm Inner lever arm : z [ 285.5 mm MȀ Total required tensile force : z d +2057 kN Reinforcing steel : 2057 * 1017 + 2392 mm2 500ń1.15

åc å s1

xc

Concrete compression zone

Mp

z

Prestressing

Np

e

å p + åp o ) Då p å s2

P

Strain plane

Forces acting on concrete due to prestressing

Fig. A–15 Cross section dimensioning

By comparison: Dimensioning for ultimate load, prestressing with bonding The difference between this and the previous dimensioning is that the additional strains in the prestressing steel are taken into account: å Po [ 6.52 o/oo Då + 4.6 o/oo Prestressing with bonding: program supplies assumed maximum strain in reinforcing steel = 5 o/oo, thus Då at height of prestressing ca. 4.6 o/oo) å P [ 11.1 o/oo Yield limit exceeded

s fp=1600 fpd=1391

σp

Ep=195 kN/mm2

fpk=1860 fpk/γs=1617

å 0.0111

0.00713

εud=0.02

Fig. A–16 Material law for prestressing steel used in this example

s P [ 1461 N/mm2 (hardening: (1617−1391)*(11.1−7.13)/(20−7.13) ) P + s P A p = 1169 kN Dimensioning: Concrete compression zone Inner lever arm Total required tensile force Reinforcing steel

CEDRUS–5

: : : :

x c [ 63 mm z [ 284 mm Md/z = 587/0.284 = 2068 kN (2068−1169)/(500/1.15) = 2068 mm2

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Part E Prestressing Module

E 3 Examples

Dimensioning for serviceability, szul = 200 N/mm2 Prestressing without bonding, Results in field at x = 4.83 Limit state specification:

This limit state specification was generated automatically with the analysis parameter set ’AP1’ associated to it: The specification of ss,adm can be made in the menu ’Set$ tings>Analysis parameter’ for the set ’AP1:Serviceability’. Table of As values:

Hand calculation or calculation with cross section program (e.g. FAGUS) Action: Md= Md_max + (Mp_max − P*e) = 256 + 0.8*146 + (−104.6 + 127) = 395.2 kN Prestressing: å Po [ 6.52 o/oo Då + 0.0 (Prestressing without bonding) P + 0.00652 E s A s = 1017 kN As−dimensioning: Concrete compression zone Inner lever arm Total required tensile force Reinforcing steel

: : : :

x c [ 84 mm z [ 278 mm Md/z =1422 kN (1422−1014)*103/200 = 2040 mm2

Dimensioning for serviceability, Prestressing with bonding Prestressing: å Po [ 6.52 o/oo Då + 0.89 o/oo (addit. strain from steel stress 200 N/mm2 at the level of the tendon) P + 0.00741 E s A s = 1156 kN As−dimensioning: Concrete compression zone Inner lever arm Total required tensile force Reinforcing steel

E–30

: : : :

x c [ 84.6 mm z [ 275.7 mm Md/z =1433 kN (1433−1156)*103/200 = 1385 mm2

CEDRUS–5

Part E Prestressing Module

E 3 Examples

E 3.3 Tips and Tricks E 3.3.1 Duplication of groups Often one needs to investigate different alternatives. For this purpose tendons and sup$ ports need to be copied from one group to the next. The following key combinations are necessary for this (in abbreviated form): 1. 2. 3. 4.

(select all tendons and supports) (copy all tendons) Create new group (insert all objects)

Regarding point 1: If for example the support dialogue is open, with only the supports (all of them) are selected.

E 3.3.2 Generating possibilities Compared to CEDRUS−3 the number of specific tendon generating possibilities has been reduced. To compensate for this the functions of the Graphics Editor, which are identical in all Cubus Windows programs, have been considerably extended. Often one direction with the extended ’Duplicate’ command can be generated almost in a single operation (in the case of an unsuccessful attempt don’t forget the ’Undo’ function !). For skew or irregular slab boundaries the ’Trim’ function can be useful (in a first step gener$ ate tendons over the slab boundary and then select and trim all elements together which are too long).

E 3.3.3 Checks When generating a load case all necessary checks are carried out (minimum radii, inter$ section of slab boundary etc). If an incorrectly input tendon is encountered, a corresponding error message appears on the screen, the object is marked graphically and the reason for the error is given in the corresponding table. For at least each characteristic tendon a longitudinal section should be considered (par$ allel tendons intersecting the same support have a similar or identical profile). Besides the x’−z profile, often, it can also be tested whether the desired profile was in fact input correctly by means of the deviation forces (="curvature diagram").

E 3.3.4 Detecting tendons lying on top of each other See Example 1, Checks (last section)

E 3.3.5 Reference height of supports with different slab thicknesses For the determination of the z−coordinate of a support both support end points (or the position shifted inwards by a small tolerance value) are decisive, as is shown in the

CEDRUS–5

E–31

Part E Prestressing Module

E 3 Examples

example given below. If these exhibit the same height the input is admissible. For the supports in all the intermediate zones the same z−coordinate is used. However, if, as in the case shown below, the input is made with reference to the bottom slab boundary, with 2Lowest support point ... Distance to boundary ... 2, strictly speak$ ing this statement holds only for the two external zones.

H

Support

H

T

T

T = Support defined as lowest point H = Support defined as highest point Fig. A–17 Support height with different slab thicknesses

To enable external prestressing, no check is carried out on whether the tendons measured in the vertical direction lie within the slab. If the end point of the support lies in the area of intersection of two downstanding beams of different thickness, the greater height is used.

E–32

CEDRUS–5

Part F Dynamic Analysis

F 1 Natural Vibrations

Part FDynamic Analysis F 1 Natural Vibrations F 1.1 Basic Theory The optional module Dynamics of CEDRUS5 permits the analysis of natural vibrations for slabs with general mass distributions. As results you get circular frequencies, corre sponding mode shapes and participation factors. For this purpose the following eigenvalue problem must be solved: ([K] * w i 2[M]){F i} + {0} where: wi {f i } [M] [K]

: : : :

eigenvalue (circular frequency) of i−th mode mode shape of i−th mode mass matrix stiffness matrix

The mode shapes (eigenmodes) are normalized as follows: {F i}T[ M ]{F i} + 1 The modal participation factors are defined as follows:

Pi +

NJNj 1 0 0..

T

[M]{F i}

F 1.2 Mass Distribution The mass distribution consists of specific masses, distributed masses (polygonal or along a line) and concentrated masses, just like a normal load specification with differ ent units (i.e. mass/unit volume, mass/unit length or area, mass). Therefore you have to specify the mass distribution in the load register of CEDRUS−5’s interface. Here you can define so−called ’mass load cases’, which correspond to a specific mass distribution that can be used in a dynamic analysis. For the numerical analysis the mass distribution is transformed into translatory (in Z− direction) acting concentrated masses in the nodes of the FE−mesh, i.e. the mass matrix has only diagonal nonzero elements. .

CEDRUS–5

’Exotic’ mass distributions can lead to numerical convergence problems (e.g. it is impossible to calculate more eigenvalues than the number of nodes with associated concentrated masses). Generally the mass of the slab should be considered, thus avoiding these problems.

F–1

Part F Dynamic Analysis

F 1 Natural Vibrations

F 1.3 Input parameters An analysis of natural vibrations requires the following input parameters: S

The number of the (mass) load case corresponding to the mass distribution.

S

The number of modal shapes to be calculated (starting with the smallest frequency).

S

The load case numbers for the resulting modal shapes (i.e. eigenvectors). Here you must specify the number for the first mode only, because all additional modes are saved under consecutive numbers. Make sure to define numbers that do not exceed 999 or do not conflict with already existing load cases. In CEDRUS−5’s result register you can address each modal shape with its unique load case number.

S

A tolerance value for the required accuracy (default value is 1E−8).

F 1.4 Output of Results As results you get the modal shapes (eigenmode) that can be viewed graphically and numerically just like displacements and the table of frequencies and participation factors of all calculated eigenvalues. Example 1 − 3D view of an eigenmode :

Eigenmode 9, mass distribution L_100, scale factor 2.0000

F–2

CEDRUS–5

Part F Dynamic Analysis

F 1 Natural Vibrations

Example 2 − Table of frequencies and participation factors: Frequencies for mass distribution L_100 ======================================== Nr. Omega^2 Omega Frequency Period Participationfact. [rad/sec]^2 [rad/sec] [Hz] [sec] −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− −− 1 0.541 0.735 0.117 8.546034 3.914 2 21.199 4.604 0.733 1.364647 2.170 3 45.260 6.728 1.071 0.933946 0.000 4 165.992 12.884 2.051 0.487682 1.272 5 421.818 20.538 3.269 0.305926 0.000 6 636.570 25.230 4.016 0.249033 0.909 7 1255.112 5.428 5.638 0.177353 0.000 8 1737.189 41.680 6.634 0.150750 0.707 9 2716.417 52.119 8.295 0.120554 0.000 10 3871.275 62.220 9.903 0.100984 0.579 −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− −− Sum of equiv. masses (square of participation factors) 23.312 Total mass 25.000

CEDRUS–5

F–3

Part F Dynamic Analysis

F–4

F 1 Natural Vibrations

CEDRUS–5

Part G Walls

G 1 Introduction

Part G Walls G 1 Introduction The optional module ’Walls’ allows for the linear elastic analysis and dimensioning of plates subjected to pure in−plane or combined bending/inplane action. If licensed you can choose between the follwing 3 structure types:

Due to the full integration into the user interface of the slab analysis program, the data input for the walls program is very similar to the slab part. Thus this manual for walls does only handle the aspects that are specific to the analysis of walls. For all the other topics, that both modules have in common, please refer to the part A 2 of this manual. The following sections concentrate on the specialities of a wall analysis, i.e. the model for geometry, loads and the output and outline some specialties realated to combined bending/inplane action. The structure type ’slab with normal forces’ is particularly usefull for prestressed slabs, where the distribution of the normal forces due to the anchorage and deviation forces can be investigated. For details see G 3.1.

G 2 Basic Theory G 2.1 Element Model and Solution Method The module walls a Finite Element (FE) program for the linear elastic analysis of plates subjected to in−plane action. The element models used are triangular and quadrilateral elements of arbitrary shape with the three displacement degrees of freedom DX, DY (displacement in directions X and Y) and RZ (rotation about the Z axis) in the corner nodes. RZ

Z Y X

ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ ÎÎÎÎÎÎÎ

DY

ÎÎÎÎÎ ÎÎÎÎÎ ÎÎÎÎÎ ÎÎÎÎÎ ÎÎÎÎÎ ÎÎÎÎÎ DX

In−plane action, not bending action is considered. The stiffness matrices and the load vectors are built according to the socalled ’Free−Formulation’ method. This method

CEDRUS–5

G–1

Part G Walls

G 2 Basic Theory

does provide accurate results for deformations and stresses. The most important proper ties of the element models are: S

shape functions for deformations as linear combinations of eigenmodes.

S

consistent distributed and initial element loads.

S

stress results in corners as well as in the center of the element (four−node elements only).

For a detailed study of this element model refer to the following: S

P.G. Bergan, M.K. Nygard: 7Finite elements with increased freedom in choosing shape functions", Intl. J. of Num. Meth. in Engineering, 20 (1984), P 643664.

S

M.K. Nygard: 7The Free Formulation for Nonlinear Finite Elements with Application to Shells", Thesis, Institutt for Statikk, Universitete Trondheim.

The FE method in CEDRUS−5 essentially involves the following steps: 1. Determination of the element matrices for the hybrid method. 2. Determination of the load vectors (right hand sides of the system of equations). 3. Summation of the element stiffness matrices to form the global stiffness matrix. 4. Solution of the resulting system of equations for the unknown nodal displacement parameters (possibly iteratively in the case of supports that do not take tension). 5. Calculation of the section forces in the elements for the now known nodal displace ment parameters. One should observe that the FE method is an approximate numerical method. The numerical solution, however, converges for an ever finer element mesh, within the limits of numerical accuracy, to the exact theoretical solution of Kirchhoff’s plate bending theory.

G 2.2 Modelling G 2.2.1 Geometry The geometry of the plan outline is basically fixed by the following conditions: S

Outline: An arbitrary closed polygon.

S

Recesses and openings: Arbitrary closed polygons.

S

Point supports: Points for the definition of support conditions for single nodes. The direction of the node can be chosen at will (i.e. skew supports are possible).

S

Line supports: Lines or polygons for the definition of support conditions. Inter nally a series of point supports are generated. The direction of the supported nodes is taken from the orientation of the line is located on.

S

Material separators: Lines or polygons which divide up the slab into several zones with different material attributes.

S

Lines of symmetry: Along these lines the slab may bend but normal to them it may not rotate. Thus one has a special type of linear support, which may only lie on the slab boundary

G 2.2.2 Thickness and Material The structure can be subdivided by separator lines into several zones. For each zone the material model has to be specified. In CEDRUS5 the two material models Isotropic and Orthotropic are supported and explained in this section. In the description of the material models the following nota tion is used:

G–2

CEDRUS–5

Part G Walls

G 2 Basic Theory

sx , sy ,txy : ex , ey ,gxy :

inplane stresses (corresponding) strains elastic modulus and Poisson’s ratio

E,n :

Isotropic Material Isotropic material is directionally independent and is completely described by two elas tic constants, i.e. the modulus of elasticity (or Young’s modulus) E and Poisson’s ratio n. The program allows for two different models, the plane stress and the plane stretching model. Plane Stress In plane stress it is assumed, that the stress perpendicular to the middle plane of the wall vanish (sz = 0 ), which is a good model for thin walls. The relationship between inplane strains and stresses is governed by the following elasticity matrix (i.e. a matrix containing the elastic constants): εx εy

1 =

fE E

γxy εz =

ν

σz =

0

1

ν

0

σx

ν

1

0

σy

0

0

2 (1+ν)

τxy

( σx + σy )

E

fE = factor of the stiffness (deafult=1.0)

Plane Stretching In plane stretching it is assumed, that the strain perpendicular to the middle plane of the wall vanish (ez = 0 ), which is a good model for walls of infinite (or very high) thick ness. The relationship between inplane strains and stresses is governed by the follow ing elasticity matrix: εx εy

1+ν =

ν

0

σx

ν

1−ν

0

σy

0

0

2

τxy

fE E

γxy

.

1−ν

εz =

0

σz =

ν ( σx + σy )

fE = factor of the stiffness (deafult=1.0)

The user must specify the thickness of the wall even in the plane stretching model. If one wants to analyze a wall of unit width, which is the natural choice for plane stretching analysis, the thickness must be explicitly set to 1.0.

Orthotropiv Material Orthotropic material exhibits different properties in the two directions x and y normal to one another. It is described by the following elasticity matrix:

CEDRUS–5

G–3

Part G Walls

G 2 Basic Theory

εx εy

=

γxy

d11

d12

0

σx

d21

d22

0

σy

0

0

d33

τxy

(d12 = d21 d12 *d21 must be fulfilled. The xdirection (material direc tion) is selectable.

G 2.2.3 Point Supports For every point support a local x−direction can be specified. All the input and output refers to this orientation. The stiffness terms sdx , sdy (for displacements) and srz (for rotation) can be defined: sdx sdy srz

: spring stiffness in direction of node : spring stiffness perpendicular to direction of node : rotation stiffness around Zaxis

G 2.2.4 Line Supports The boundary conditions of a wall con be specified with line supports as well. Inter nally, a line support is a series of point supports with local orientations according to the direction of the line. The stiffness terms sdl , sdn (for displacements) and srz (for rota tion) can be defined: sdl sdn srz

: longitudinal spring stiffness (= in direction of the line) per unit length : normal spring stiffness (= perpendicular to the line) per unit length : rotation stiffness around Zaxis per unit length

G 2.2.5 Lines of Symmetry Lines of symmetry are special line supports, along which the wall is free to move while the displacements perpendicular to the line and the rotations are blocked. Symmetry conditions are really only meaningful at wall boundaries, which is why lines of symme try are only allowed to lie on the plan outline.

Lines of symmetry

Lines of symmetry are used to demarcate parts of the wall in the model, be it a genuine line of symmetry or if by means of a symmetry condition one obtains the most favorable boundary condition. Note, that with symmetry conditions the loads too always act sym metrically. An example of genuine symmetry is given by the circular plate − even if with the condi tion of a symmetrically acting load it is rather academic. Here the input of a sector with the corresponding symmetry conditions along the radial boundaries suffices. Line supports on lines of symmetry are permitted. If a line support should work as a line of symmetry, one has to block the longitudinal displacement and the rotation. Note: An eventually provided spring stiffness must divided by two. Point supports on lines of symmetry are allowed. The direction of the support must however correspond to the direction of the line. Note: An eventually provided spring stiffness must divided by two.

G–4

CEDRUS–5

Part G Walls

G 2 Basic Theory

G 2.2.6 Loads CEDRUS5 permits the following types of load: 1) Area loads (i.e. loads per unit area) Rectangular or arbitrary polygons for: − body force (e.g. dead or selfweigh in X and Y) − uniformly distributed force in X and Y − differential temperature loading − initial strain (strain X, Y and XY) 2) Line loads Constant or trapezium distributed − longitudinal force Fl : force in direction of the line − normal force Fn : force perpendicular to the line (counter clockwise) The direction of the line load goes from the first point P1 to P2. l n Fn P2 Y

Fl X

P1

3) Point loads − forces in X and Y 4) Displacements of point supports (the corresponding displacement parameters of the support nodes have to be blocked) − displacement in X and Y − rotation around Z The load types 1) to 3) are independent of the FE mesh, so that they can be arbitrarily arranged geometrically. Loads are combined to individual load cases, which can be combined or superimposed in any way for the calculation of the results. The load cases can be assigned to particular action types, like dead weight loads, surcharge loads, imposed loads etc., whereby in standard cases a load superposition automatically carried out by the program to deter mine the design section quantities is possible.

G 2.3 Results

G 2.3.1 Raw Results The solution algorithms of CEDRUS5 produce raw results for each load case input: S

The nodal displacements

S

Reactions of the supports

S

Section forces at the element centers in global coordinate directions

S

Section forces at the element corners in global coordinate directions, which are then immediately and zonewise converted to averaged nodal values and are not given as separate values

These calculated and binary stored raw results serve as a basis for determining the re sults types described below in the desired form of presentation.

CEDRUS–5

G–5

Part G Walls

G 2 Basic Theory

G 2.3.2 The Structuring of the Output of Results Output results are not created unless the user specifically demands them. Firstly, it is defined for what the results are required (e.g. load case number), then comes the choice of the quantities (e.g. section forces), a possible component (e.g. mx) and finally the presentation form (e.g. isolines), which can still be influenced by certain parameters. From a list one first chooses for what the results are wanted. The list contains S

All input load cases

S

Any defined load case combinations

S

All automatically or manually produced limit state specifications

S

Required reinforcement

Load case combinations are fixed combinations of load cases provided with arbitrary factors, of which the user can define as many as desired. In the output of results they are treated in exactly the same way as individual load cases.

The quantities for load cases and load case combinations Deformations: With the deformations it is a question of disablement in x− and y−direction as well as the rotations about the Zaxis, respectively, in each node of the FE mesh. The rotations of nodes not acting as supports are output in the global coordinate system. For point and line supports the xdirection of the input object is adopted and the ydirection nor mal to it. The xaxis of line supports shows the support direction. Stresses: The stresses in a wall consist of the components sx ,sy ,txy . The following figure shows the forces acting on an infinitesimal slab element: y

τxy τxy

σy

σy y

σz

σx

τxy

τxy

σx

σx x

τxy τxy

x

f

x

σy The output of the wall section stresses is carried out in zonewise definable output direc tions. The transformation formulas for a free direction f are as follows (Mohr’s circle for the stresses): s x + sx cos 2 f ) s y sin 2 f ) 2t xy sin f cos f s y + sx sin 2 f ) s y cos 2 f * 2t xy sin f cos f t xy + (sx * s y) sin f cos f ) t xy(cos2 f * sin 2 f) In zones with plane stress the stresses in z−direction vanish, while the following rela tions governs the zones with plane stretching : Depending of the output format principal stresses s1 and s2 are calculated.

G–6

CEDRUS–5

Part G Walls

G 2 Basic Theory

s z + n(sx ) sy) In addition the output of nominal stresses is possible:

Ǹ(s * s )  ) (s *2 s )  ) (s * s )  2

2

von Mises:

s eqM +

Tresca:

s eqT + Ť(s1 * s3)Ťs 1 u s 2 u s3

1

2

2

3

3

1

2

Section forces: The section forces consist of the components nx , ny and nxy ,which correspond to the stresses (sx ,sy ,txy . ) multiplied by the thickness of the wall. Therefore the same trans formation formulas can be used.. Reactions: The reactions, arranged node−wise, are output according to the individual supports. In the graphical output of the line supports the possibility exists, of combining the nodal reactions in sections, provided the section length is given.

Quantities for limit state specifications (envelope values) Deformations: One can obtain the envelope values of the displacements. Reactions: One can obtain the envelope values of for point and line supports. Reinforcement forces: The section forces nx , ny and nxy are combined to reinforcement forces according to the combination rules specified in the limit state specifications. The reinforcement forces at a point are the four forces required to determine the rein forcement in two orthogonal directions. Their calculation is based on the wellknown linearised plasticity conditions: nax> = Max ( nx +nxy , nx −nxy ) nax< = Min ( nx +nxy , nx −nxy ) nay> = Max ( ny +nxy , ny −nxy ) nay< = Min ( ny +nxy , ny −nxy ) with: nax> nax< nay> nay<

maximum reinf. force in xdirection (=tension −> reinforcement) minimum reinf. force in xdirection (=compression−> concrete) maximum reinf. force in ydirection (=tension −> reinforcement) minimum reinf. force in ydirection (=compression−> concrete)

The output directions are defined for each zone.

Required reinforcement The required reinforcement of the wall in two orthogonal directions ax and ay is deter mined on the basis of design limit values of the reinforcement moments described

CEDRUS–5

G–7

Part G Walls

G 2 Basic Theory

above. It is assumed, that all the tensional forces are taken by the reinforcement and all the compressive forces are taken by the concrete. The output directions and the materials are defined for each zone.

Forms of Presentation

Limit state values:

point and line reactions

Sections *)

/

Axonometrical

displacements

Tables

Load cases and load case combina tions:

Principle values

Contour plot

Results and their form of presentation:

Numerical/grafical

The following table provides information about the possible forms of presentation for the different derived quantities:

/

/

/

/

/

/

/

stresses

/

/

/

/

/

section forces

/

/

/

/

/

nominal stresses

/

/

/

/

displacements

/

/

/

/

/

reactions

Reinforcement:

/

reinforcement forces

/

/

/

/

reinforcement sections

/

/

/

/

*) Sections: These are simple sections through the corresponding contour plot. In the case of design limit values and reinforcement these section results can only be deter mined in zones, whose output direction coincides with that of the section direction or the normal to it, respectively.

G–8

CEDRUS–5

Part G Walls

G 3 Slab with Normal Forces

G 3 Slab with Normal Forces G 3.1 Model ’Slabs with normal forces’ (SwN) are a combination of slobs with pure bending and walls with pure membrane action. Therefore the nodes of a SwN model have 6 degree of freedoms, DZ, RX, RY from the slab aund DX, DY, RZ from the wall. The SwN model of CECRUS5 does cover structures with a continous middle plane only. i.e. zones with different thickness are all interconnected without eccentricity.

This applies to downstanding beams as well. Therefore, if you start a new project as a slab and enter (eccentrically connected) downstanding beams, after a change of the structure type to SwN (see. G 3.2) the beamzones will be centrically connected. The feature SwN is especially tailored for pre and posttensioned flat slabs, which are not affected by this restriction. In order to input all the data needed to properly model a combined slabwall system, the attributedialogs of the supports (e.g. walls and columns) have two tabsheets regarding the support conditions:

CEDRUS–5

G–9

Part G Walls

G 3 Slab with Normal Forces

G 3.2 Changing the Structural Type Having initially choosen the structural type of a new project, there are some restrictions in changing it later. This is shown in the following graph:

Slab

Wall

Slab with normal forces

Axonometrical

/

/

/

/

point and line reactions

/

/

/

/

stresses

/

/

/

/

/

section forces

/

/

/

/

/

nominal stresses

/

/

/

DZ

Limit state values:

displacements

/

/

/

/

reactions

/

/

/

reinforcement forces

/

/

/

Reinforcement:

G–10

reinforcement sections

Sections

Tables

Load cases and load case combina tions:

Principle values

displacements

Contour plot

Numerical/grafical

Results and their form of presentation:

Beam sections

G 3.3 Results

/

/

/

/ /

CEDRUS–5