Workshop Note on Pushover Analysis
March 4, 2017 | Author: taraponge43-1 | Category: N/A
Short Description
Download Workshop Note on Pushover Analysis...
Description
IS-CAAD International Seminar on Computer Aided Analysis and Design
Performance Based Design and Push-over Analysis of Buildings Workshop Note
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis Using ETABS and SAP2000 June 18-19, Manila, Philippines For
Association of Structural Engineers Philippines
By
Naveed Anwar Asian Center for Engineering Computations and Software Asian Institute of Technology In Association with
Computers and Structures Inc., Berkeley, California, USA
Acknowledgements
Pushover Analysis, ACECOMS, AIT
• Some of the material presented in these notes is based on following sources: – Class notes by Prof. Worsak Kanok-Nukulchai – Seminar notes from Computers and Structures Incorporated, USA – Notes from various workshops conducted by Naveed Anwar – SAP2000 User and Technical Manuals – ETABS User and Technical Manuals – ATC40, Applied Technology Council, USA – FEMA-273, Federal Emergency Management Agency, USA
Asian Center For Engineering Computations and Software
1
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Pushover Analysis, ACECOMS, AIT
Objectives • Introduce the basic Modeling and Analysis Concepts • To provide an understanding of Static Nonlinear Pushover Analysis for Seismic Performance • To demonstrate the application of Pushover Analysis for buildings using ETABS and SAP2000 and to provide a comparison
Modeling and Analysis
Asian Center For Engineering Computations and Software
2
Pushover Analysis, ACECOMS, AIT
Pushover Analysis Using ETABS and SAP2000
Structural System – Analysis Model STRUCTURE RESPONSES
Pushover Analysis, ACECOMS, AIT
EXCITATION Loads Vibrations Settlements Thermal Changes
Asian Center For Engineering Computations and Software
Displacements Strains Stress Stress Resultants
pv
Structural Model
3
Pushover Analysis Using ETABS and SAP2000
Analysis of Structures ∂σxx ∂σyy ∂σzz + + + pvx = 0 ∂x ∂y ∂z Pushover Analysis, ACECOMS, AIT
pv
Real Structure is governed by “Partial Differential Equations” of various order Direct solution is only possible for: • Simple geometry • Simple Boundary • Simple Loading.
Pushover Analysis, ACECOMS, AIT
The Need for Modeling A - Real Structure cannot be Analyzed: It can only be “Load Tested” to determine response B - We can only analyze a “Model” of the Structure C - We therefore need tools to Model the Structure and to Analyze the Model
Asian Center For Engineering Computations and Software
4
Pushover Analysis Using ETABS and SAP2000
Finite Element Method: The Analysis Tool
• Finite Element Analysis (FEA)
Pushover Analysis, ACECOMS, AIT
– “A discretized solution to a continuum problem using FEM”
• Finite Element Method (FEM) – “A numerical procedure for solving (partial) differential equations associated with field problems, with an accuracy acceptable to engineers”
Pushover Analysis, ACECOMS, AIT
Continuum to Discrete Model
pv 3D-CONTINUM MODEL
CONTINUOUS MODEL OF STRUCTURE
(Governed by partial (Governed by either differential equations) partial or total differential equations)
Asian Center For Engineering Computations and Software
DISCRETE MODEL OF STRUCTURE
(Governed by algebraic equations)
5
Pushover Analysis Using ETABS and SAP2000
From Classical to FEM Solution Equilibrium
Actual Structure
Structural Model
∂σxx ∂σyy ∂σzz + + + p =0 ∂x ∂y ∂z vx Pushover Analysis, ACECOMS, AIT
FEM
Assumptions
Classical
Kr = R
Stress-Strain Law Compatibility
“Partial Differential Equations”
∫σ
t
_
_
“Algebraic Equations” _
ε dV = ∫ pvt udV + ∫ pst uds v
(Principle of Virtual Work)
K = Stiffness r = Response R = Loads
Simplified Structural System Deformations (D)
Loads (F)
Pushover Analysis, ACECOMS, AIT
Fv
D
K
F
F=KD
Asian Center For Engineering Computations and Software
6
Pushover Analysis Using ETABS and SAP2000
The Analysis System STRUCTURE
RESPONSES
EXCITATION
Pushover Analysis, ACECOMS, AIT
pv
• Static • Dynamic
• Elastic • Inelastic
• Linear • Nonlinear
Eight types of equilibrium equations are possible!
The Equilibrium Equations 1. Linear-Static
Elastic
Ku = F
2. Linear-Dynamic
Elastic
Pushover Analysis, ACECOMS, AIT
Mu&&(t ) + Cu& (t ) + Ku (t ) = F (t )
3. Nonlinear - Static Elastic OR Inelastic Ku + FNL = F
4. Nonlinear-Dynamic OR Mu&&(t ) + Cu& (t ) + Ku(t ) + F (t ) NL = FElastic (t ) Inelastic
Asian Center For Engineering Computations and Software
7
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Basic Analysis Types Excitation
Structure
Response
Basic Analysis Type
Static
Elastic
Linear
Linear-Elastic-Static Analysis
Static
Elastic
Nonlinear
Nonlinear-Elastic-Static Analysis
Static
Inelastic
Linear
Linear-Inelastic-Static Analysis
Static
Inelastic
Nonlinear
Nonlinear-Inelastic-Static Analysis
Dynamic
Elastic
Linear
Linear-Elastic-Dynamic Analysis
Dynamic
Elastic
Nonlinear
Nonlinear-Elastic-Dynamic Analysis
Dynamic
Inelastic
Linear
Linear-Inelastic-Dynamic Analysis
Dynamic
Inelastic
Nonlinear
Nonlinear-Inelastic-Dynamic Analysis
Analysis Type
Pushover Analysis, ACECOMS, AIT
The type of Analysis to be carried out depends on the Structural System – The Type of Excitation (Loads) – The Type Structure (Material and Geometry) – The Type Response
Asian Center For Engineering Computations and Software
8
Pushover Analysis Using ETABS and SAP2000
Some More Solution Types
Pushover Analysis, ACECOMS, AIT
• Non-linear Analysis – – – – –
P-Delta Analysis Buckling Analysis Static Pushover Analysis Fast Non-Linear Analysis (FNA) Large Displacement Analysis
• Dynamic Analysis – Free Vibration and Modal Analysis – Response Spectrum Analysis – Steady State Dynamic Analysis
Static Vs Dynamic • Static Excitation
Pushover Analysis, ACECOMS, AIT
– When the Excitation (Load) does not vary rapidly with Time – When the Load can be assumed to be applied “Slowly”
• Dynamic Excitation – When the Excitation varies rapidly with Time – When the “Inertial Force” becomes significant
• Most Real Excitation are Dynamic but are considered“Quasi Static” • Most Dynamic Excitation can be converted to “Equivalent Static Loads”
Asian Center For Engineering Computations and Software
9
Pushover Analysis Using ETABS and SAP2000
Elastic Vs Inelastic • Elastic Material – Follows the same path during loading and unloading and returns to initial state of deformation, stress, strain etc. after removal of load/ excitation
Pushover Analysis, ACECOMS, AIT
• Inelastic Material – Does not follow the same path during loading and unloading and may not returns to initial state of deformation, stress, strain etc. after removal of load/ excitation
• Most materials exhibit both, elastic and inelastic behavior depending upon level of loading.
Linear Vs Nonlinear • Linearity – The response is directly proportional to excitation – (Deflection doubles if load is doubled)
Pushover Analysis, ACECOMS, AIT
• Non-Linearity – The response is not directly proportional to excitation – (deflection may become 4 times if load is doubled)
• Non-linear response may be produced by: – Geometric Effects (Geometric non-linearity) – Material Effects (Material non-linearity) – Both
Asian Center For Engineering Computations and Software
10
Pushover Analysis Using ETABS and SAP2000
Elastic Vs Inelastic • Elastic Material – Follows the same path during loading and unloading and returns to initial state of deformation, stress, strain etc. after removal of load/ excitation
Pushover Analysis, ACECOMS, AIT
• Inelastic Material – Does not follow the same path during loading and unloading and may not returns to initial state of deformation, stress, strain etc. after removal of load/ excitation
• Most materials exhibit both, elastic and inelastic behavior depending upon level of loading.
Linear Vs Nonlinear • Linearity – The response is directly proportional to excitation – (Deflection doubles if load is doubled)
Pushover Analysis, ACECOMS, AIT
• Non-Linearity – The response is not directly proportional to excitation – (deflection may become 4 times if load is doubled)
• Non-linear response may be produced by: – Geometric Effects (Geometric non-linearity) – Material Effects (Material non-linearity) – Both
Asian Center For Engineering Computations and Software
11
Pushover Analysis Using ETABS and SAP2000
Action
Linear-Elastic
Linear-Inelastic
Deformation Action
Deformation
Action
Pushover Analysis, ACECOMS, AIT
Action
Elasticity and Linearity
Nonlinear-Inelastic
Nonlinear-Elastic
Deformation
Deformation
Linear and Nonlinear Linear, Static and Dynamic
Ku = F Pushover Analysis, ACECOMS, AIT
F
FNL
M u&&( t ) + C u& ( t ) + Ku ( t ) = F ( t )
Ku = F
Nonlinear, Static and Dynamic
Ku - FNL = F
Ku + FNL = F u
Mu&&(t ) + Cu&(t ) + Ku(t ) + F (t ) NL = F (t )
Non Linear Equilibrium
Asian Center For Engineering Computations and Software
12
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
The Seven Degrees of Freedom • The General Beam Element may have 7 degrees of freedom • The seventh degree is Warping • Warping is out-of plane distortion of the beam crosssection
ry uy y
u x rx x z uz rz wz
Each section on a beam member can have seven Degrees Of Freedom (DOF) with respect to its local axis.
The Complete DOF Picture uz Ö Axial deformation Ö Axial strain Ö Axial stress ux Ö Shear deformation Ö Shear strain Ö Shear stress
Pushover Analysis, ACECOMS, AIT
uy Ö Shear deformation Ö Shear strain Ö Shear stress rz Ö Torsion Ö Shear strain Ö Shear stress ry Ö Curvature Ö Axial strain Ö Axial stress rx Ö Curvature Ö Axial strain Ö Axial stress wzÖ Warping Ö Axial strain Ö Axial stress
Asian Center For Engineering Computations and Software
13
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
What is Stiffness ? • In structural terms, stiffness may be defined as “Resistance to Deformation” • So for each type of deformation, there is a corresponding stiffness • Stiffness can be considered or evaluated at various levels • Stiffness is also the “constant” in the ActionDeformation Relationship
For Linear Response
u∞F Ku = F K=
F u
The Structure Stiffness Material Stiffness
Cross-section Geometry
Pushover Analysis, ACECOMS, AIT
Section Stiffness
Member Geometry Member Stiffness
Structure Geometry Structure Stiffness
Asian Center For Engineering Computations and Software
14
Pushover Analysis Using ETABS and SAP2000
The Matrices in FEM Global Nodal Deformations T-Matrix Global-Local Cords.
Element Nodal Deformations Pushover Analysis, ACECOMS, AIT
N-Matrix Shape Functions
Deformation in Element Space B-Matrix Strain-Deforrmation
Strain In Element Space D-Matrix Stress-Strain
Stress in Element Space
Methods of Dynamic Analysis • For Both Linear and Non-Linear Systems – Step-by-Step Integration – Use of Mode Superposition with Eigen or LoadDependent Ritz Vector for FNA Pushover Analysis, ACECOMS, AIT
• For Linear Systems Only – Transformation of frequency domain and FFT Method – Response Spectrum Method – CQC - SRSS
Asian Center For Engineering Computations and Software
15
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Step by Step Solution Method • Form Effective Stiffness Matrix • Solve Set of Dynamic Equilibrium Equations for Displacement at Each Time Step • For Non-Linear Problems Calculate Member Forces for Each Time Step and Iterate for Equilibrium – Brute Force Method
Pushover Analysis, ACECOMS, AIT
Mode Superposition Method • Generate Orthogonal Dependent Vectors and Frequencies • Form Uncoupled Modal Equations and Solve Using Exact Method for Each Time Increment • Recover Nodal Displacement as a Function of Time • Calculate Member Forces as a Function of Time
Asian Center For Engineering Computations and Software
16
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Load Dependent Ritz Vector • Approximately Three Times Faster than the Calculation of Exact Eigen Vectors • Results in Improved Accuracy using a Smaller Number of LDR Vector • Computer Storage Requirements are Reduced • Can be Used for Non-Linear analysis to Capture Local Static Response
Dynamic Response of Beam
Pushover Analysis, ACECOMS, AIT
100 Pounds
10 @ 12" = 120"
Force
Asian Center For Engineering Computations and Software
Time
17
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Pushover Analysis • • • • •
One Dimensional Static Loads No Energy Dissipation Inertia Forces Not Considered Defined One Failure Mode Higher Mode Effects Neglected
Pushover Analysis, ACECOMS, AIT
Fast Non-Linear Analysis • Evaluate LDR Vectors with Non-Linear Elements Removed and Dummy Elements Added for Stability • Solve All Modal Equations with Non-Linear Forces on the Right Hand Side • Use Exact Integration within Each Time Step • Force and Energy Equilibrium are Satisfied at Each Time Step by Iteration
Asian Center For Engineering Computations and Software
18
Pushover Analysis Using ETABS and SAP2000
Fast Non-Linear Analysis
Pushover Analysis, ACECOMS, AIT
• The FNA Method is Designed for Static and Dynamic Analysis of Non-Linear Structures with a Limited Number of Pre-Defined NonLinear Elements
Pushover Analysis, ACECOMS, AIT
Base Isolation
Asian Center For Engineering Computations and Software
19
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Building Impact
Pushover Analysis, ACECOMS, AIT
Dampers
Asian Center For Engineering Computations and Software
20
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Gaps and Joints
Pushover Analysis, ACECOMS, AIT
Hinges
Asian Center For Engineering Computations and Software
21
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Dampers
Pushover Analysis, ACECOMS, AIT
Linear Viscous Damping • Does not Exist in Normal Structures and Foundations • 5 or 10 Percent modal Damping Values are Often Used to Justify Energy Dissipation Due to Non-Linear Effects • If Energy Dissipation Devices are Used Then 1 Percent Modal Damping should be Used for the Elastic Part of the Structure
Asian Center For Engineering Computations and Software
22
Pushover Analysis Using ETABS and SAP2000
Non-Linear Equilibrium Equations
Pushover Analysis, ACECOMS, AIT
Ma + Cv + Ku + FN = F • Where Ma + Cv + Ku = F − FN Fn= The Global Node Loads due to the Forces in the Non-Linear Elements
Non-Linear Equilibrium Equations
Pushover Analysis, ACECOMS, AIT
Ma + Cv + [K + kE ]u = F − FN + kEu • Where Ke= The Effective Linear Stiffness of the Non-Linear Element are of Arbitrary Values for Zero Damping
Asian Center For Engineering Computations and Software
23
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Uplift
Pushover Analysis, ACECOMS, AIT
Non Linear Static Analysis
Asian Center For Engineering Computations and Software
24
Pushover Analysis Using ETABS and SAP2000
Structure Types • Cable Structures • Cable Nets • Cable Stayed
• Bar Structures Pushover Analysis, ACECOMS, AIT
• 2D/3D Trusses • 2D/3D Frames, Grids
• Surface Structures • Plate, Shell • In-Plane, Plane Stress
• Solid Structures
Global Modeling of Structural Geometry
Pushover Analysis, ACECOMS, AIT
(a) Real Structure
(b) Solid Model
(c) 3D Plate-Frame
(d) 3D Frame
(f) Grid-Plate
(e) 2D Frame Fig. 1 Various Ways to Model a Real Struture
Asian Center For Engineering Computations and Software
25
Pushover Analysis Using ETABS and SAP2000
Some Sample Finite Elements
Pushover Analysis, ACECOMS, AIT
Truss and Beam Elements (1D,2D,3D)
Plane Stress, Plane Strain, Axisymmetric, Plate and Shell Elements (2D,3D)
Brick Elements
Pushover Analysis, ACECOMS, AIT
The Modal Analysis
Asian Center For Engineering Computations and Software
26
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
The Modal Analysis • The modal analysis determines the inherent natural frequencies of vibration • Each natural frequency is related to a time period and a mode shape • Time Period is the time it takes to complete one cycle of vibration • The Mode Shape is normalized deformation pattern • The number of Modes is typically equal to the number of Degrees of Freedom • The Time Period and Mode Shapes are inherent properties of the structure and do not depend on the applied loads
Free Vibration Analysis • Definition – Natural vibration of a structure released from initial condition and subjected to no external load or damping
• Main governing equation -Eigenvalue Problem
[M ] ⎧⎨ u ⎫⎬
⎧•⎫ + [c ] ⎨ u ⎬ + [K ⎩ ⎭t ⎩ ⎭t
Pushover Analysis, ACECOMS, AIT
••
] {u }t
=
{P }t
• Solution gives – Natural Frequencies – Associated mode shapes – An insight into the dynamic behavior and response of the structure
Asian Center For Engineering Computations and Software
27
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
The Modal Analysis • The Modal Analysis should be run before applying loads any other analysis to check the model and to understand the response of the structure • Modal analysis is precursor to most types of analysis including Response Spectrum, Time History, Push-over analysis etc. • Modal analysis is a useful tool even if full Dynamic Analysis is not performed • Modal analysis easy to run and is a fun to watch the animations
Application of Modal Analysis
Pushover Analysis, ACECOMS, AIT
• The Time Period and Mode Shapes, together with animation immediately exhibit the strengths and weaknesses of the structure • Modal analysis can be used to check the accuracy of the structural model – The Time Period should be within reasonable range, (Ex: 0.1 x number of stories seconds) – The disconnected members are identified – Local modes are identified that may need suppression
Asian Center For Engineering Computations and Software
28
Pushover Analysis Using ETABS and SAP2000
Application of Modal Analysis
Pushover Analysis, ACECOMS, AIT
• The symmetry of the structure can be determined – For doubly symmetrical buildings, generally the first two modes are translational and third mode is rotational – If first mode is rotational, the structural is unsymmetrical
• The resonance with the applied loads or excitation can be avoided – The natural frequency of the structure should not be close to excitation frequency
Pushover Analysis, ACECOMS, AIT
Model Creation Tools • • • • • • • • •
Defining Individual Nodes and Elements Using Graphical Modeling Tools Using Numerical Generation Using Mathematical Generation Using Copy and Replication Using Subdivision and Meshing Using Geometric Extrusions Using Parametric Structures
Asian Center For Engineering Computations and Software
29
Pushover Analysis Using ETABS and SAP2000
Graphic Object Modeling
Pushover Analysis, ACECOMS, AIT
• Use basic Geometric Entities to create FE Models • Simple Graphic Objects – – – –
Point Object Line Object Area Object Brick Object
Represents Node Represents 1D Elements Represents 2D Elements Represents 3D Elements
• Graphic Objects can be used to represent geometry, boundary and loads • SAP2000, ETABS and SAFE use the concept of Graphic Objects
Pushover Analysis, ACECOMS, AIT
Modeling Objects and Finite Elements • Structural Members are representation of actual structural components • Finite Elements are discretized representation of Structural Members • The concept of Graphic Objects can be used to represent both, the Structural Members as well as Finite Elements • In ETABS, the Graphic Objects representing the Structural Members are automatically divided into Finite Elements for analysis and then back to structural members for result interpretation
Asian Center For Engineering Computations and Software
30
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Design Methods and Concepts
From Loads to Stresses
Pushover Analysis, ACECOMS, AIT
Applied Loads
Building Analysis
Member Actions
Cross-section Actions
Material Stress/Strain
Asian Center For Engineering Computations and Software
From Strains to Response
The Response and Design Material Response
Section Response
Member Response
Building Response
Load Capacity
31
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
From Serviceability to Performance
From Serviceability to Performance
Pushover Analysis, ACECOMS, AIT
• Satisfying one design level does not ensure that other design levels will be satisfied – Serviceability design only ensures that deflections and vibrations etc. for service loads are within limits but says nothing about strength – Strength design ensures that a certain factor of safety against overload is available within a member or a cross-section but says nothing about what happens if load exceeds design level – Performance design ensures that structure as a whole reaches a specified demand level. Performance design can include, both service and strength design levels
Asian Center For Engineering Computations and Software
32
Pushover Analysis Using ETABS and SAP2000
From Serviceability to Performance
Pushover Analysis, ACECOMS, AIT
• The entire response of structure or a member can be determined, in an integrated manner from the ActionDeformation Curve A – Serviceability B – Cracking Limit C – Strength Limit D – Failure Limit
P
∆
The Cross-section Response Material Stress-Strain Curves Cross-section Dimensions
Performance
Pushover Analysis, ACECOMS, AIT
Given P value
Given Moments
Given Axial Load
P-M Curve
M-M Curve
Moment-Curvature Curves
•Moment for Given Curvature •Curvature for Given Moment •Yield Moment •Stiffness •Ductility
•Moment for Given Load •Load for Given Moment •Capacity Ratio
Asian Center For Engineering Computations and Software
Strength
Capacity Interaction Surface
Given Moment Direction
•Mx for Given My •My for Given Mx •Capacity Ratio
33
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Original Cross-sections
Plain concrete shape
Compact Built-up steel section
Reinforced concrete section
Composite section
Compact Hot-rolled steel shape
Reinforced concrete, composite section
Pushover Analysis, ACECOMS, AIT
Sections After Strengthening
Asian Center For Engineering Computations and Software
34
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Capacity Interaction Surface P
My
Mx
Pushover Analysis, ACECOMS, AIT
P-M and M-M Interaction Curves
Asian Center For Engineering Computations and Software
35
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
The Moment Curvature Curve
Pushover Analysis, ACECOMS, AIT
Cross-section Stresses
Asian Center For Engineering Computations and Software
36
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Strength and Performance • In Strength Design, every member and every cross-section must satisfy strength equation • Even if all members and sections are designed for strength, the structure may not perform well in case of overload • In Performance Based Design, only a few members on the critical load path need to perform well for the structure to perform well • Therefore for strengthening of structures, we may only need to strengthen members or section in the critical load path
Members on Critical Load Path
Pushover Analysis, ACECOMS, AIT
• In Performance Based Design, only a few members on the critical load path need to perform well for the structure to perform well • Therefore for strengthening of structures, we may only need to strengthen members or section in the critical load path
Asian Center For Engineering Computations and Software
37
Pushover Analysis Using ETABS and SAP2000
What Effects Serviceability? • Anything that reduces cracking – The presence of appropriate amount of reinforcement at appropriate locations
Pushover Analysis, ACECOMS, AIT
• Anything that increases stiffness – Reasonable sizes and proportions of member cross-sections
• Anything that reduces Creep/ Shrinkage – Presence of compressive reinforcement
• Anything that improves Durability – High strength concrete – Proper cver and protection of rebars
What Effects Strength? • The basic Material Strength
Pushover Analysis, ACECOMS, AIT
– Concrete crushing strength – Reinforcement yield strength
• The Cross-section Dimensions • The amount of Rebars • The framing conditions
Asian Center For Engineering Computations and Software
38
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
What Effects Performance? • Performance is generally of concern for lateral loads such as earthquake and wind • The main factor that effects performance is the Ductility of the members on the critical load path • In frame structures, the design of the joints between columns and beams is critical • The performance of shear walls if great importance for lateral load demands
Pushover Analysis, ACECOMS, AIT
• Ductility can be defined as the “ratio of deformation and a given stage to the maximum deformation capacity” • Normally ductility is measured from the deformation at design strength to the maximum deformation at failure
Asian Center For Engineering Computations and Software
Load
Ductility – Definition and Usage
Yield/ Design Strength
Dy
Du
Deformation Ductility = Dy / Du
39
Pushover Analysis Using ETABS and SAP2000
What Effects Ductility! • The most important factor effecting ductility of reinforced concrete cross-section is the confinement of concrete
Pushover Analysis, ACECOMS, AIT
– Amount of confinement steel – Shape of confinement steel
• Other factors include: – – – – –
Presence of Axial Load Stress-strain curve of rebars Amount of rebars in tension Amount of rebars in compression The shape of cross-section
Action – Deformation Curves
Pushover Analysis, ACECOMS, AIT
• Relationship between action and corresponding deformation • These relationships can be obtained at several levels – – – –
The Structural Level: Load - Deflection The Member Level: Moment - Rotation The Cross-section Level: Moment - Curvature The Material Level : Stress-Strain
• The Action-Deformation curves show the entire response of the structure, member, cross-section or material
Asian Center For Engineering Computations and Software
40
Pushover Analysis Using ETABS and SAP2000
How to Get Action-Deformation Curves • By actual measurements – Apply load, measure deflection – Apply load, measure stress and strain
Pushover Analysis, ACECOMS, AIT
Pushover Analysis, ACECOMS, AIT
• By computations – Use material models, cross-section dimensions to get Moment-Curvature Curves
• By combination of measurement and computations – Calibrate computation models with actual measurements – Some parameters obtained by measurement and some by computations
The Moment Curvature Curve
Asian Center For Engineering Computations and Software
41
Pushover Analysis Using ETABS and SAP2000
The Moment-Curvature Curve
Pushover Analysis, ACECOMS, AIT
• Probably the most important action-deformation curve for beams, columns, shear walls and consequently for building structures • Significant information can be obtained from Moment Curvature Curve to compute: – – – – – – – –
Yield Point Failure Point Ductility Stiffness Crack Width Rotation Deflection Strain
What is Curvature
Pushover Analysis, ACECOMS, AIT
e
• In geometry, it is rate of change of rotation • In structural behavior, Curvature is related to Moment • For a cross-section undergoing flexural deformation, it can computed as the ratio of the strain to the depth of neutral axis
Asian Center For Engineering Computations and Software
C
Curvature = e / C (radian / unit length)
42
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
How to Read M-Phi Curve
Outputs from M-Phi Curve
Pushover Analysis, ACECOMS, AIT
2 -Failure Point
Asian Center For Engineering Computations and Software
1 -Yield Point
3 - Ductility =
ϕy ϕu
43
Pushover Analysis Using ETABS and SAP2000
Outputs from M-Phi Curve 4 - Stiffness of the Section at given M and Phi
M EI M EI =
Pushover Analysis, ACECOMS, AIT
φ=
φ
5 - Slope of the section at given Moment b
M dx EI a
θ =∫
Outputs from M-Phi Curve 6 - Deflection of the section at given Moment
⎛M⎞ ∆ = ∫ ⎜ ⎟x dx EI ⎠ a⎝ Pushover Analysis, ACECOMS, AIT
b
7 - Strain at given Moment
ε = φc
c = distance from the NA to the point where strain is required
Asian Center For Engineering Computations and Software
44
Pushover Analysis Using ETABS and SAP2000
Outputs from M-Phi Curve 8 - Crack Width at given crack spacing
W = εs X
φ
Pushover Analysis, ACECOMS, AIT
W = φyX
εs
9 - Crack Spacing at given crack width W X=
εs
X=
W φy
Outputs from M-Phi Curve - Summary Plot M-Phi Curve
EI =
Determine curvature at known moment
φ
Pushover Analysis, ACECOMS, AIT
Determine Flexural Stiffness (EI)
θ =
b
M
∫ EI
⎛M ⎞ ∆ = ∫⎜ ⎟ x dx EI ⎠ a ⎝ b
M
Determine Deflection
ε = φc
dx
a
Determine Slope
X =
Determine Strain
W
W = εsX
εs
Asian Center For Engineering Computations and Software
Determine Crack Spacing/Width
45
Pushover Analysis Using ETABS and SAP2000
Outputs from M-Phi Curve - Example For M=600 Phi = 0.00006 From M-Phi Diagram
Pushover Analysis, ACECOMS, AIT
EI =
M
φ
EI=600x12/0.00006 EI=1.2E8 k-in^2
Slope at Mid Span b
M dx EI a =600x7.5x144/1.2E8
θ =∫
=0.0054 rad
Outputs from M-Phi Curve - Example Deflection at Mid Span
⎛M ⎞ ∆ = ∫ ⎜ ⎟x dx EI ⎠ a⎝ Pushover Analysis, ACECOMS, AIT
b
=600x7.5x144x15x12/(6x1.2E8) =0.162 in
Strain in Steel
ε = φc M = 600 k-ft, y=16 =0.00006x16 =0.00096
Asian Center For Engineering Computations and Software
φ
εs
46
Pushover Analysis Using ETABS and SAP2000
Outputs from M-Phi Curve - Example Crack Width Assuming crack spacing of 18 in
Specified Crack Spacing = X
W = εs X
φ
NA
Pushover Analysis, ACECOMS, AIT
=0.00096 x 18 =0.01728 in
Crack Spacing
y
Rebar Centroid
εs
W
Assuming crack width of 0.02 in
X=
W
εs
=0.02/0.00096 =20.8 in
M-Phi Curve and Ductility Effect of Axial Load Effect of Compression Steel Effect of Confinement Model Effect of Confinement Shape
Pushover Analysis, ACECOMS, AIT
• • • •
Asian Center For Engineering Computations and Software
47
Pushover Analysis Using ETABS and SAP2000
Axial Load and Ductility Effect of Axial Load on Ductility 700 600 500
Pushover Analysis, ACECOMS, AIT
400
Axial Load =0 300
Axial Load =0.2Pu
200
Axial Load =0.4Pu
100
Axial Load =0.6Pu Axial Load =0.8Pu
0 -0.0002
0.0000 -100
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
0.0014
0.0016
0.0018
C ur v a t ur e ( r a d/ i n)
Compression Steel and Ductility Effects of Compression Rebars on Ductility 700 600 500 400 300
a: Duct ilit y Rat io =2.65 b: Duct ilit y Rat io =3.32
200
Pushover Analysis, ACECOMS, AIT
c: Duct ilit y Rat io =4.68 d: Duct ilit y Rat io =9.25
100 0 -0.0005
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
0.0040
-100
Asian Center For Engineering Computations and Software
C ur v a t ur e ( r a d/ i n)
48
Pushover Analysis Using ETABS and SAP2000
Confinement Model and Ductility Effect of Concrete Confinement Model on Ductility of Cross-Section 350
300
Pushover Analysis, ACECOMS, AIT
Moment (kip-ft)
250
200
Whitney Rectangle Mander Circular Confined
150
Mander Pipe Filled 100
50
0 0
0.001
0.002
0.003
0.004
0.005
0.006
Curvature (rad/in)
Confinement Steel and Ductility Effect of Confinement Steel Spacing on Ductility 160 140
Moment (kip-ft)
Pushover Analysis, ACECOMS, AIT
120
100
Spacing = 3in 80
Spacing = 6 in
60
Spacing = 12 in
40
20 0 -0.0005
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
-20
Asian Center For Engineering Computations and Software
Curvature (in/rad)
49
Pushover Analysis Using ETABS and SAP2000
Confinement Shape and Ductility Effect of Confinement Shape on Ductility 350
300
250
200
Pushover Analysis, ACECOMS, AIT
150
100
M ander Rectangular Confined M ander Circular Confined
50
Whitney Rect angle
0 (0. 0010)
0. 0000
0. 0010
0. 0020
0. 0030
0. 0040
0. 0050
0. 0060
0. 0070
-50 C ur vat ur e ( r ad/ i n)
Introducing
Pushover Analysis, ACECOMS, AIT
Pushover Analysis
Asian Center For Engineering Computations and Software
50
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
The Pushover Analysis • An alternate method of analysis for carrying out the Performance Based Design • Pushover analysis is carried out after the Linear Analysis has been done and Serviceability and Strength design has been completed • Pushover analysis is most suitable for determining the performance, specially for lateral loads such as Earthquake or even wind
Why Pushover Analysis
Pushover Analysis, ACECOMS, AIT
• Buildings do not respond as linearly elastic systems during strong ground shaking • Improve Understanding of Building Behavior – - More accurate prediction of global displacement – - More realistic prediction of earthquake demand on individual components and elements – - More reliable identification of “bad actors”
• Reduce Impact and Cost of Seismic Retrofit – - Less conservative acceptance criteria – - Less extensive construction
• Advance the State of the Practice
Asian Center For Engineering Computations and Software
51
Pushover Analysis Using ETABS and SAP2000
Performance Based Design - Basics • Design is based not on Ultimate Strength but rather on Expected Performance
Pushover Analysis, ACECOMS, AIT
– Basic Ultimate Strength does not tell us what will be performance of the structure at Ultimate Capacity
• Performance Based Design Levels – – – – –
Fully Operational Operational Life Safe Near Collapse Collapse
Pushover Analysis, ACECOMS, AIT
Pushover Spectrum
Asian Center For Engineering Computations and Software
52
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Pushover Demand Curves
Pushover Analysis, ACECOMS, AIT
Earthquake Push on Building
Asian Center For Engineering Computations and Software
53
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
The Pushover Curve
Pushover Analysis, ACECOMS, AIT
Pushover Capacity Curves
Asian Center For Engineering Computations and Software
54
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Demand Vs Capacity
Non-linearity in Pushover • Material nonlinearity at discrete, user-defined hinges in frame/line elements. 1. Material nonlinearity in the link elements.
Pushover Analysis, ACECOMS, AIT
• Gap (compression only), hook (tension only), uniaxial plasticity base isolators (biaxial plasticity and biaxial friction/pendulum)..
2. Geometric nonlinearity in all elements. • Only P-delta effects • P-delta effects plus large displacements
3. Staged (sequential) construction. • Members can be added or removed in a sequence of stages during each analysis case.
Asian Center For Engineering Computations and Software
55
Pushover Analysis Using ETABS and SAP2000
Important Considerations
Pushover Analysis, ACECOMS, AIT
• • • •
Nonlinear analysis takes time and patience Each nonlinear problem is different Start simple and build up gradually. Run linear static loads and modal analysis first • Add hinges gradually beginning with the areas where you expect the most nonlinearity. • Perform initial analyses without geometric non-linearity. Add P-delta effects, and large deformations, much later.
Pushover Analysis, ACECOMS, AIT
Important Considerations • Mathematically, static nonlinear analysis does not always guarantee a unique solution. • Small changes in properties or loading can cause large changes in nonlinear response. • It is Important to consider many different loading cases, and sensitivity studies on the effect of varying the properties of the structure • Nonlinear analysis takes time and patience. Don’t Rush it or Push to Hard
Asian Center For Engineering Computations and Software
56
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Procedure for Pushover Analysis • Create a model just like for any other analysis. • Define the static load cases, if any, needed for use in the static nonlinear analysis (Define > Static Load Cases). • Define any other static and dynamic analysis cases that may be needed for steel or concrete design of frame elements. • Define hinge properties, if any (Define > Frame Nonlinear Hinge Properties). • Assign hinge properties, if any, to frame/line elements (Assign > Frame/Line > Frame Nonlinear Hinges). • Define nonlinear link properties, if any (Define > Link Properties).
Pushover Analysis, ACECOMS, AIT
Procedure for Pushover Analysis • Assign link properties, if any, to frame/line elements (Assign > Frame/Line > Link Properties). • Run the basic linear and dynamic analyses (Analyze > Run). • Perform concrete design/steel design so that reinforcing steel/ section is determined for concrete/steel hinge if properties are based on default values to be computed by the program. • For staged construction, define groups that represent the various completed stages of construction. • Define the static nonlinear load cases (Define > Static Nonlinear/Pushover Cases).
Asian Center For Engineering Computations and Software
57
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Procedure for Pushover Analysis • Run the static nonlinear analysis (Analyze > Run Static Nonlinear Analysis). • Review the static nonlinear results (Display > Show Static Pushover Curve), (Display > Show Deformed Shape), (Display > Show Member Forces/Stress Diagram), and (File > Print Tables > Analysis Output). • Perform any design checks that utilize static nonlinear cases. • Revise the model as necessary and repeat.
Performance Based Design and
Pushover Analysis Technical Background By:
Iqbal Suharwardy, PhD, S.E Director Development Computers and Structures Inc., Berkeley, USA
Asian Center For Engineering Computations and Software
58
Pushover Analysis Using ETABS and SAP2000
Performance Check for Structures • Purpose
Pushover Analysis, ACECOMS, AIT
– How will a structure perform when subjected to a give level of earthquake? • Definition of Structural Performance • Definition of Earthquake Level • Determination of performance level
Performance Check for Structures • Process – Recently released guidelines for Seismic Rehabilitation of Buildings:
Pushover Analysis, ACECOMS, AIT
• ATC-40 • ATC-33 (FEMA 273 and 274)
– SEAOC Vision 2000 Framework
Asian Center For Engineering Computations and Software
59
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Types of Performance Checks • Linear Static Analysis • Linear Dynamic Analysis • Non Linear Static Analysis (Pushover Analysis) • Non Linear Dynamic Analysis
Pushover Analysis, ACECOMS, AIT
Performance Check Using Pushover
Asian Center For Engineering Computations and Software
60
Pushover Analysis Using ETABS and SAP2000
Steps in Performance Check
Pushover Analysis, ACECOMS, AIT
• • • •
Construct Pushover Curve Select Earthquake Level to check Select Performance Level to check Select acceptance criteria for each Performance Level • Verify Acceptance – ATC-40 Method – ATC-33 Method
Constructing Pushover Curve • Define Structural Model – Elements – Strength-Deformation properties
Pushover Analysis, ACECOMS, AIT
• Define Loads – Gravity – Lateral Load Patterns
• Select Control Displacements or Drifts • Perform Pushover Analysis
Asian Center For Engineering Computations and Software
61
Pushover Analysis Using ETABS and SAP2000
Pushover Modeling (Elements)
Pushover Analysis, ACECOMS, AIT
• Types – – – – – – –
Truss – Yielding and Buckling 3D Beam – Major direction Flexural and Shear Hinging 3D Column – P-M-M Interaction and shear Hinging Panel Zone – Shear Yielding In-Fill Panel – Shear Failure Shear Wall – P-M-Shear Interaction! Spring – for foundation modeling
Pushover Analysis, ACECOMS, AIT
Pushover Modeling (Properties)
Asian Center For Engineering Computations and Software
62
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Pushover Modeling (Beam Element)
Pushover Analysis, ACECOMS, AIT
Pushover Modeling (Column Element)
Asian Center For Engineering Computations and Software
63
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Pushover Modeling (Column Element)
Pushover Modeling (Loads) • Start with Gravity Loads – Dead Load – Same Portion of Live Load
Pushover Analysis, ACECOMS, AIT
• Select Lateral Load Patterns – – – –
Uniform Code Static Lateral Load Distribution First Mode Combination of Modes
Asian Center For Engineering Computations and Software
64
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis (Control) • Force Controlled Analysis • Deformation Controlled Analysis – Roof Displacement – Generalized Displacement Definitions Pushover Analysis, ACECOMS, AIT
• Story Drift
• Limit of Analysis – Instability – Loss of Gravity Load Carry Capacity – Excessive Distortions
Pushover Analysis (Solution Schemes) • Event by Event Strategies – Manual
Pushover Analysis, ACECOMS, AIT
• Newton-Raphson Type Strategies – Constant Stiffness iteration – Tangent Stiffness iteraton
• Problem of Degradation of Strength • Ritz Method (Reduced Space) Strategies
Asian Center For Engineering Computations and Software
65
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Pushover Analysis (Results)
Pushover Analysis, ACECOMS, AIT
Use of Pushover Curve (ATC-40) • • • • •
Construct Capacity Spectrum Estimation of Equivalent Damping Determine Demand Spectrum Determine Performance Point Verify Acceptance
Asian Center For Engineering Computations and Software
66
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Use of Pushover Curve (ATC-40)
Pushover Analysis, ACECOMS, AIT
Use of Pushover Curve (ATC-40)
Asian Center For Engineering Computations and Software
67
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Use of Pushover Curve (ATC-40)
Pushover Analysis, ACECOMS, AIT
Use of Pushover Curve (ATC-40)
Asian Center For Engineering Computations and Software
68
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Use of Pushover Curve (ATC-40)
Pushover Analysis, ACECOMS, AIT
Use of Pushover Curve (ATC-40)
Asian Center For Engineering Computations and Software
69
Pushover Analysis Using ETABS and SAP2000
Use of Pushover Curve (FEMA-273) (Displacement Coefficient Method)
Pushover Analysis, ACECOMS, AIT
• Estimate Target Displacement • Verify Acceptance
Use of Pushover Curve (FEMA-273) • Estimation of Target Displacement Estimate effective elastic stiffness , Ke Estimate post yield stiffness, Ks Estimate effective fundamental period, Te Calculate target roof displacement
Pushover Analysis, ACECOMS, AIT
– – – –
Asian Center For Engineering Computations and Software
70
Pushover Analysis Using ETABS and SAP2000
Use of Pushover Curve (FEMA-273) • Estimation of Target Displacement Co, Relates spectral to roof displacement C1, Modifier for inelastic displacement C2, Modifier for hysteresis loop shape C3, Modifier for second order effects
Pushover Analysis, ACECOMS, AIT
– – – –
SAP2000/ETABS Pushover Options
Pushover Analysis, ACECOMS, AIT
• Full 3D implementation • Single Model for – – – – – –
Linear Static Analysis Linear Response Spectrum Analysis Linear Time History Analysis Non Linear Time History Analysis Non Linear Static Pushover Analysis Steel and Concrete Design
Asian Center For Engineering Computations and Software
71
Pushover Analysis Using ETABS and SAP2000
SAP2000/ETABS Pushover Options
Pushover Analysis, ACECOMS, AIT
• Generally Follows ATC-40 and FEMA-273 • Available Pushover Element Types – – – – – – –
Truss – Yielding and Buckling 3D Beam – Major direction Flexural and Shear Hinging 3D Column – P-M-M Interaction and shear Hinging Shell, Solids, etc (Considered Linear) Panel Zone – (later) Shear Wall – (Later) Non-Linear Spring – (Later)
Pushover Analysis, ACECOMS, AIT
SAP2000/ETABS Pushover Options
Asian Center For Engineering Computations and Software
72
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
SAP2000/ETABS Pushover Options
SAP2000/ETABS Pushover Options • Strength – Deformation and P-M-M curves can be calculated by program for:
Pushover Analysis, ACECOMS, AIT
– Steel beams (FEMA-273) – Steel columns (FEMA-273) – Shear Hinges in EBF Links (FEMA-273) – Concrete Beams (ATC-40) – Concrete Columns (ATC-40) – Shear hinge in Coupling Beams (ATC-40)
Asian Center For Engineering Computations and Software
73
Pushover Analysis Using ETABS and SAP2000
SAP2000/ETABS Pushover Options • Gravity Load Analysis
Pushover Analysis, ACECOMS, AIT
– Nodal Loads – Element Loads – Load Controlled Analysis
• Pushover Analysis – Starts from Gravity loads – Nodal Load Patterns (User, Modal, Mass) – Multi-Step Displacement or Drift Controlled
SAP2000/ETABS Pushover Options
Pushover Analysis, ACECOMS, AIT
• Available Results for each step of Loading – – – – – – –
Base Shear Element Forces Section Forces Joint Displacement Drifts Element hinge Deformations Limit Points reached
Asian Center For Engineering Computations and Software
74
Pushover Analysis Using ETABS and SAP2000
SAP2000/ETABS Pushover Options
Pushover Analysis, ACECOMS, AIT
• Pushover Curve Post-Processing (ACT-40) – – – – – –
Conversion to Capacity Spectrum Calculation of Effective Period (per step) Calculation of Effective Damping (per step) Calculation of Demand Spectrum (per step) Location of Performance Point Limit Points (acceptable criteria) reached
SAP2000/ETABS Pushover Options • Visual Display for Each Step – Deformed Shape – Member Force Diagrams – Hinge Locations and Stages
Pushover Analysis, ACECOMS, AIT
• Graphs – – – – –
Base Shear VS Roof Displacement Capacity Curves Demand Curves Demand Spectra at different Damping Effective Period Lines
Asian Center For Engineering Computations and Software
75
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Examples
Pushover Analysis, ACECOMS, AIT
Example 1
Asian Center For Engineering Computations and Software
76
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Base Shear Vs Displacement
Pushover Analysis, ACECOMS, AIT
Capacity Spectrum
Asian Center For Engineering Computations and Software
77
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Example 2
Example 2
Desired Behavior
Pushover Analysis, ACECOMS, AIT
2100
Asian Center For Engineering Computations and Software
1700 1000
0.1
0.6
0.8
Measured Axial Displacement at Joint 2 (in)
78
Pushover Analysis Using ETABS and SAP2000
Find Column E • Determine Column E to give Appropriate Initial Stiffness:
Pushover Analysis, ACECOMS, AIT
Column
PL = (1700 *12*12)/(24*24*0.1) A∆ E=
= 4250 Ksi
Find Column Deflection • Determine Elastic Column Lengthening when loading from 1700 to 2100 K:
Pushover Analysis, ACECOMS, AIT
Column = [(2100-1700) *12*12)]/(24*24*4250) PL ∆= = 0.0235 in
AE
Asian Center For Engineering Computations and Software
79
Pushover Analysis Using ETABS and SAP2000
Find Column Deflection • Determine Elastic Column Lengthening when loading from 2100 to 1000 K:
Pushover Analysis, ACECOMS, AIT
Column = [(2100-1000) *12*12)]/(24*24*4250) PL ∆ = = 0.0647 in
AE
Find Column Deflection
Pushover Analysis, ACECOMS, AIT
• Determine Elastic Column Lengthening when loading from 1000 to 0 K: Column
PL ∆ = = 1000 *12*12)/(24*24*4250) AE = 0.0588 in
Asian Center For Engineering Computations and Software
80
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Find Hinge Properties
Pushover Analysis, ACECOMS, AIT
Hinge Properties
Asian Center For Engineering Computations and Software
81
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Pushover Curve
Pushover Analysis, ACECOMS, AIT
Example 3
Asian Center For Engineering Computations and Software
82
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Example 3
Pushover Analysis, ACECOMS, AIT
Example 3
Asian Center For Engineering Computations and Software
83
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
With W12x190 Brace
Pushover Analysis, ACECOMS, AIT
With W8x10 Brace
Asian Center For Engineering Computations and Software
84
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Conversion to ADRS Spectra ATC-40
Response Spectrum Conversion
Pushover Analysis, ACECOMS, AIT
• Acceleration-Displacement Response Spectra (ADRS) • Every Point on a Response Spectrum curve has a unique – – – –
Spectral Acceleration, Sa Spectral Velocity, Sv Spectral Displacement, Sd Time, T
Asian Center For Engineering Computations and Software
85
Pushover Analysis Using ETABS and SAP2000
Response Spectrum Conversion • For Each value or Sai and Ti determine the value of Sdi using the equation 2
Pushover Analysis, ACECOMS, AIT
T S di = i 2 S ai g 4π
• Spectral Acceleration and Displacement at period Ti are given by
S ai g =
2π Sv Ti
S di =
Ti Sv 2π
Pushover Analysis, ACECOMS, AIT
Capacity Spectrum Conversion • Capacity Spectrum from Capacity or Pushover Curve • Point by Point conversion to first mode spectral coordinates • on capacity curves are converted to Sai and Sdi on capacity Vicorresponding and ∆roof spectrum using:
S ai =
Vi W
α1
Asian Center For Engineering Computations and Software
S di =
∆ roof
(PF × φ 1
1, roof
)
86
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Moment Hinge Properties Using M-Fi Curve
Procedure • Plot M-Fi curve for cross-section • Estimate EI value from M-Fi Curve using the following equation M EI M EI =
Pushover Analysis, ACECOMS, AIT
φ=
φ
• Calculate Rotations from Curvature using: b
θ =∫
Asian Center For Engineering Computations and Software
a
M dx EI
87
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Example • Reinforced Concrete Beam-Column CrossSection • 24”x24” • Reinforced with 12 #9 bars • Length is 12 ft
Example
Pushover Analysis, ACECOMS, AIT
370
0.00028
Asian Center For Engineering Computations and Software
88
Pushover Analysis Using ETABS and SAP2000
Example
Pushover Analysis, ACECOMS, AIT
EI =
M
φ
• So EI = 370/0.00028 = 1321428.6 b M M θ = Ip θ = ∫ dx EI EI a • So θ = 0.00336 rad • Find θ for other Moment Values and input in Hinge Property
Considerations
Pushover Analysis, ACECOMS, AIT
• Keep moment Constant over hinge length when integrating or integrate over the whole member length with actual moment diagram • Only one value of EI at Yield is sufficient • Ip = h/2
Asian Center For Engineering Computations and Software
89
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
Comparisons of SAP2000 and ETABS
SAP2000 vs ETABS • SAP2000 – General Purpose FEA Software
Pushover Analysis, ACECOMS, AIT
– Classic Finite Element Software – Steel, and Concrete Frame Element Design – Shear Wall Design Not Supported – Fewer Automated Meshing Options – Does not Support Composite Design
Asian Center For Engineering Computations and Software
• ETABS – Specialized FEA Software for Building analysis and design – Fully Object based Modeling and Design – Steel, concrete, composite Frame Element design – Supports Shear wall design – Full and practical auto meshing options – Supports Composite Design
90
Pushover Analysis Using ETABS and SAP2000
SAP2000 vs ETABS • SAP2000
• ETABS
– General output related to nodes and elements is reported
– Floor wise representation of results such as story drift, floor mass participation, story shear, etc.
Pushover Analysis, ACECOMS, AIT
– General Report (text files) – Professional Report – Powerful load cases, combinations, envelopes, multiple case, etc. – Cables, Dampers, and NL Links and Hinges
– Relatively less ability to handle load combinations – Only Nonlinear links and Hinges
SAP2000 vs ETABS • SAP2000 – Supports Solid Elements
– Does not support solid elements – Powerful grid system definition and editing
Pushover Analysis, ACECOMS, AIT
– Relatively low versatility for defining and editing grid systems
• ETABS
Asian Center For Engineering Computations and Software
91
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
ETABS Pushover
Pushover Analysis, ACECOMS, AIT
ETABS Pushover
Asian Center For Engineering Computations and Software
92
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
ETABS Pushover
Pushover Analysis, ACECOMS, AIT
SAP2000 Pushover
Asian Center For Engineering Computations and Software
93
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
SAP2000 Pushover
Pushover Analysis, ACECOMS, AIT
SAP2000 Pushover
Asian Center For Engineering Computations and Software
94
Pushover Analysis Using ETABS and SAP2000
Pushover Analysis, ACECOMS, AIT
SAP2000 Pushover
Pushover Analysis, ACECOMS, AIT
SAP2000 Pushover
Asian Center For Engineering Computations and Software
95
Pushover Analysis, ACECOMS, AIT
Pushover Analysis Using ETABS and SAP2000
Asian Center For Engineering Computations and Software
96
View more...
Comments
