Non Linear Analysis Pushover

Introduction of Pushover Analysis

“Everything should be made as simple as possible. But not simpler.”

-Einstein

Overview

1. What is pushover analysis? 2. Why Pushover Analysis ? 3. Analysis Procedure. 4. Examples. 5. Point to be considered.

What is Push-Over Analysis? 

Push-over analysis is a technique by which a computer mode



The intensity of the lateral load is slowly increased and the se



Push-over analysis can provide a significant insight into the w

What is Push-Over Analysis?

Why Push-Over Analysis?

 Static Nonlinear Analysis technique, also known as sequential y

 It is one of the analysis techniques recommended by FEMA 273/

 Proper application can provide valuable insights into the expect

Why Push-Over Analysis?

 To get the performance level of structure in case of seismic load

 Elastic analysis cannot predict failure mechanism and account f

 Certain part will yield when subject to earthquake.

 The use of inelastic procedure for design and evolution is an att

Analysis Procedure

SAP2000 NL

Pushover Analysis Procedure Create 3D Model

Gravity Pushover (Force controlled) DL+0.25LL Lateral Pushover (Displacement controlled)

Assign end offsets Define Load case (Lateral Load at centre of mass)

Design Structure Analyze Assign Hinge properties Beams – M3, V2 Columns –PMM, V2

Define Static Pushover Cases

Run analysis, Run Now

Establish Performance point Base shear Vs Roof Displacement Sequential Hinge Formation

Modeling of Structural elements Beams and columns

3D Frame elements

Slab

Diaphragm action (ignore the out of plane stiffness)

Load

Assign load to respective member

Beam column joints

End offsets (Rigid zone factor 1)

Inclusion of appendages

Include water tanks, cantilever slabs

Modeling of Structural elements Stairway slabs

Transfer load to respective member

Shear Walls

Wide Column Elements

Infill walls

Equivalent strut method

Foundation Isolated footings

Hinged at the bottom of foundation

Single pile

Fixed at five times the diameter of pile Fixity of columns at top of pile cap

Multiple piles Plinth beams

Frame elements

Material Properties Concrete Properties

• Cube compressive strength, fck ( f’c= 0.8 fck ) • Modulus of Elasticity of concrete ( Ec  5000 f ck ) Reinforcing Steel Properties

• Yield strength of steel • Modulus of Elasticity of steel Es

Material Properties Define - Material

Modeling of Beams and Columns  3D Frame Elements

 Cross Sectional dimensions, reinforcement details, material type  Effective moment of inertia Beams

Columns

Rectangular

0.5 Ig

T-Beam

0.7 Ig

L-Beam

0.6 Ig 0.7 Ig

Modeling of Beams Define – Frame/Cable Sections

Modeling of Columns Define – Frame/Cable Sections

Modeling of Beam Column Joints Select Frame Sections

Modeling of Slab Select Joints at each floor and assign different diaphragm to each floor

Modeling of Hinge

Performance Level 

A performance level describes a limiting damage condition which may be considered satisfactory for a given building and a given ground motion.



The limiting condition is described by the physical damage within the building, the threat to life safety of the building’s occupants created by the damage, and the post earthquake serviceability of the building.



The four building performance levels: 1. Operational 2. Immediate occupancy 3. Life safety 4. Structural Stability

Performance Level 

Operational: This is the performance level related to functionality and any required repairs are minor.



Immediate Occupancy: This corresponds to the most widely used criteria for essential facilities. The building’s spaces and systems are expected to be reasonably usable.

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Life Safety: This level is intended to achieve a damage state that presents an extremely low probability of threat to life safety, either from structural damage or from falling or tipping of nonstructural building component.

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Structural Stability: This damage state addresses only the main building frame or vertical load carrying system and requires only stability under vertical loads.

Moment Rotation Curve for a Typical Element 1. Point „B‟ corresponds to nominal yield strength and yield rotation y.

1.2

C

B

1

Moment/SF

2. Point „C‟ corresponds to ultimate strength and ultimate rotation u, following which failure takes place.

Hinge Property

Yield state

IO

Immediate Occupancy

LS Life Safety

IO

0.8

B

LS

CP

CP Collapse Prevention C

0.6

Ultimate state

0.4

D

0.2

E

A

0 0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Rotation/SF

3. Point „D‟ corresponds to the residual strength, if any, in the member. It is usually limited to 20% of the yield strength, and can be taken into account provided the calculated ultimate rotation is less than 15 y. 4. Point „E‟ defines the maximum deformation capacity and is taken as 15y or u, whichever is greater.

Hinge Property  Three way to model the hinge property for member,  Default Hinge Property  ATC 40  User Defined Hinge Property

Default Hinge Property  Default hinge properties can not be modified.  They also can not be viewed because the default properties are section dependent.  The default properties can not be fully defined by the program until the section to which they are apply has been identified. Thus, to see the effect of the default properties, the default property should be assigned to a frame element, and then the resulting generated hinge property should be viewed.  The built-in default hinge properties for concrete members are generally based on Tables 9.6, 9.7 and 9.12 in ATC-40.  You should review any generated properties for their applicability to your specific project.

Default Hinge Properties • Select the member. • Assign – Hinge property

Default Hinge Properties

Hinge Properties – ATC 40 (BEAM)

a

b

c

Hinge Properties – ATC 40 (BEAM) • Moment Rotation curve for beam: Following values are required to define Moment Rotation curve for a element.

• Ast • Asc

• fc ’ • V • bw

• d

Hinge Properties – ATC 40 (BEAM)

Units: • V (pound), 1 lb = 4.45 N • fc’ (lb/in2), 1 lb / in2 = 0.006895 MPa • bw , d (in), 1 in = 25.4 mm • ρ = Ratio of nonprestressed tension reinforcement • ρ’ = Ratio of nonprestressed compression reinforcement • ρbal = Reinforcement ratio producing balanced strain condition

Hinge Properties – ATC 40 (BEAM) • Performance level for element

Hinge Properties – ATC 40 (BEAM)

Hinge Properties – ATC 40 (BEAM) • Procedure: For defining Flexure Hinge Define- Hinge Property Define New Hinge Property

Hinge Properties – ATC 40 (Column) • Moment rotation curve for column: Following values are required to define the hinge property. • P • Ag • fc’ • V • bw • d

Hinge Properties – ATC 40 (Column)

Hinge Properties – ATC 40 (Column) • Performance level for element

Hinge Properties – ATC 40 (Column)

Hinge Properties – ATC 40 (Column) • Procedure: Defining flexure hinge Define - Hinge Property

Define New Hinge Property

User Defined Hinge Property (Beam) • Develop the Moment rotation relationship based upon given cross section, R/F, Spacing of stirrup.

User Defined Hinge Property (Beam)

User Defined Hinge Property (Column)

User Defined Hinge Property (Column)

Pushover Cases Three Different Pushover Cases are defined as listed below:

1. Gravity push, which is used to apply gravity load 2. Push X, is the lateral push in x – direction (Eqx) , after gravity push 3. Push Y, is the lateral push in y – direction (Eqy) , after gravity push

Pushover - Gravity

Joint – roof centre of mass

Force Controlled – Refers to systems which are not permitted to exceed their elastic limits

Pushover - Gravity

1.

Design Basis Earthquake + Life Safety (2% total drift)

2.

Maximum Considered Earthquake + Collapse Prevention (4% total drift)

Lateral Load Pattern Determination of the Load pattern: (IS 1893 (part 1) : 2002 ) Fundamental natural period

Ta 

Design Base Shear

VB  Ah W

Design Lateral Force

Wi hi Qi VB Wj hj 2

0.09h d

Q3

Q2

2

Q1

Assign the lateral load at centre of mass at each floor. Do the dynamic analysis to get the mass participation in first mode and time period of structure.

Pushover - Lateral Define Analysis Case

Pushover - Lateral

Deformation Control – Refers to systems which can, and are permitted to, exceed their elastic limit in a ductile manner. Force or stress levels for these components are of lesser important than the amount or extent of deformation beyond the yield point

Analyze Run Analysis

Run Now

Result The sequence of Hinge Formation The Capacity Spectrum Base shear Vs Roof Displacement

EXAMPLE 1

General Building Type

RC frame with un-reinforced brick infill

Year of construction

--------------------

Number of stories

Ground + 3 Storey

Plan dimensions

30 m  8.8 m

Building height

12.8 m above plinth level

Type of footing

Isolated footing

Time Period (Dynamic analysis) – 0.95 s Mass participation(Mode I) – Y = 95 % Mass participation(Mode II) – X = 95 %

3D Model

Assigned Hinge User Defined Hinge Property

State of the Hinge at every Increase in Lateral load Display Deformed Shape Case Push X Step 8 Step 2

State of the Hinge

Performance Point ( Capacity spectrum- Z ) Display – Pushover Curve Demand Spectrum Capacity Spectrum

Effective Period Performance Point

Teff = 1.338s

βeff = 10.3% V = 1761 kN D = 0.073 m = 0.57% of H Sa = 0.137 m/s2 Sd = 0.061 m/s

Spectral Acceleration Coefficient (Sa/g)

Demand Spectrum 2.5 CA

EPA: Effective Peak Acceleration 2.5CA = Average value of peak response

EPA = CA

CV / T

Period (s)

Fig.:Construction of a 5 percent –damped elastic response spectrum Zone II (0.10)

Zone III (0.16)

Zone IV (0.24)

Zone V (0.36) At T = 0.40 for Type I

2.5CA = Cv / T

At T = 0.55 for Type II At T = 0.67 for Type III

Demand Spectrum

Seismic Coefficient, CA Soil

Zone II (0.10)

Zone III (0.16)

Zone IV (0.24)

Zone V (0.36)

Type I

0.10

0.16

0.24

0.36

Type II

0.10

0.16

0.24

0.36

Type III

0.10

0.16

0.24

0.36

Seismic Coefficient, CV Type I

0.10

0.16

0.24

0.36

Type II

0.14

0.22

0.33

0.49

Type III

0.17

0.27

0.40

0.60

Capacity Curve – Push X

EXAMPLE 2

General Building Type

RC frame with un-reinforced brick infill

Year of construction

--------------------

Number of stories

Ground + 7 Storey

Plan dimensions

27.3 m  12.6m

Building height

24 m above plinth level

Type of footing

Isolated footing

Time Period (Dynamic analysis) – 2.19 s Mass participation(Mode I) – Y = 94 % Mass participation(Mode II) – X = 5 %

3D Model

State of the Hinge

Capacity spectrum-X

Performance point does not exist.

Capacity spectrum-Y

Performance point does not exist.

Capacity Curve – Push X

Points to be taken care.. 1.

Do not underestimate the importance of the loading or displacement

2.

Know your performance objectives before you push the building.

3.

If it is not designed, it cannot be pushed.

4.

Do not ignore gravity loads.

5.

Do not push beyond failure unless otherwise you can model failure.

6.

Pay attention to rebar development and lap lengths.

Points to be taken care.. 7.

Do not ignore shear failure mechanisms.

8.

P-Delta effects may be more important than you think.

9.

Do not confuse the Push-over with the real earthquake loading.

10.

First mode, in which mass participation should be maximum.

11.

This is generally valid for building with fundamental periods of vibrati

12.

Misuse can lead to an erroneous understanding of the performance ch