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.

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

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

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

What is Push-Over Analysis?

What is Push-Over Analysis?

Static Nonlinear Analysis technique, also known as sequential yield

It is one of the analysis techniques recommended by FEMA 273/274

Proper application can provide valuable insights into the expected

Why Push-Over Analysis?

Why Push-Over Analysis?

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

Elastic analysis cannot predict failure mechanism and account for

Certain part will yield when subject to earthquake.

The use of inelastic procedure for design and evolution is an attempt

Analysis Procedure

SAP2000 NL

Create 3D Model

Assign end offsets

Design Structure

Assign Hinge properties

Beams – M3, V2

Columns –PMM, V2

Define Static Pushover

Cases

Gravity Pushover

(Force controlled) DL+0.25LL

Lateral Pushover

(Displacement controlled)

Define Load case(Lateral Load at centre of mass)

Analyze

Run analysis, Run Now

Pushover Analysis Procedure

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

Stairway slabs Transfer load to respective member

Shear Walls Wide Column Elements

Infill walls Equivalent strut method

Foundation

Isolated footings

Single pile

Multiple piles

Plinth beams

Hinged at the bottom of foundation

Fixed at five times the diameter of pile

Fixity of columns at top of pile cap

Frame elements

Modeling of Structural elements

Concrete Properties

• Cube compressive strength, fck ( f’c= 0.8 fck )

• Modulus of Elasticity of concrete ( )

Reinforcing Steel Properties

• Yield strength of steel

• Modulus of Elasticity of steel Es

5000c ckE f

Material Properties

Material Properties

Define - Material

Modeling of Beams and Columns

3D Frame Elements

Cross Sectional dimensions, reinforcement details, material type

Effective moment of inertia

Beams Rectangular 0.5 Ig

T-Beam 0.7 Ig

L-Beam 0.6 Ig

Columns 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

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

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.

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.

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

Hinge Property

0

0.2

0.4

0.6

0.8

1

1.2

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04

Rotation/SF

Mo

men

t/S

FA

BC

DE

IO LSCP

C

1. Point „B‟ corresponds to nominal yield strength and yield rotation y.

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

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

15y or u, whichever is greater.

B Yield state

IO Immediate Occupancy

LS Life Safety

CP Collapse Prevention

C Ultimate state

Three way to model the hinge property for member,

Default Hinge Property

ATC 40

User Defined Hinge Property

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)

ab

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)

• Procedure: For defining Flexure Hinge

Define- Hinge Property

Define New Hinge Property

Hinge Properties – ATC 40 (BEAM)

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)

• Procedure: Defining flexure

hinge

Define - Hinge Property

Define New Hinge Property

Hinge Properties – ATC 40 (Column)

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)

Determination of the Load pattern: (IS 1893 (part 1) : 2002 )

Q3

Q2

Q1

Lateral Load Pattern

Fundamental

natural period

Design Base

Shear

Design Lateral

Force

d

h.Ta

090

WAV hB

2

2

jj

iiBi

hW

hWVQ

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

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

General

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

Step 2

Step 8

Display -

Deformed Shape

Case

Push X

State of the Hinge

Performance Point ( Capacity spectrum- Z )

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

Performance Point

Demand Spectrum

Capacity Spectrum

Effective Period

Display –

Pushover Curve

Period (s)

Sp

ectr

al A

cce

lera

tio

n C

oe

ffic

ien

t (S

a/g

)

EPA = CACV / T

2.5 CA

Demand Spectrum

EPA: Effective Peak Acceleration

2.5CA = Average value of peak

response

2.5CA = Cv / T

Zone II

(0.10)

Zone III

(0.16)

Zone IV

(0.24)

Zone V

(0.36)

At T = 0.40 for Type I

At T = 0.55 for Type II

At T = 0.67 for Type III

Fig.:Construction of a 5 percent –damped elastic response spectrum

Seismic Coefficient, CA

SoilZone 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

Demand Spectrum

Capacity Curve – Push X

EXAMPLE 2

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

General

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 shape

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.

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 vibration

12. Misuse can lead to an erroneous understanding of the performance characteristics

Points to be taken care..