i

PUSHOVER ANALYSIS OF BRIDGE BENT –

OVERVIEW AND CASE STUDY

Credit Seminar Report

by

Palak Jaykumar Shukla

(Roll Number:P10ST516)

Under the Supervision of

Prof. C. D. Modhera

DEPARTMENT OF APPLIED MECHANICS

SARDAR VALLABHBHAI NATIONAL INSTITUTE OF

TECHNOLOGY

SURAT-395007

GUJARAT (INDIA)

ii

Acceptance Certificate

APPLIED MECHANICS DEPARTMENT

SARDAR VALLABHBHAI NATIONAL INSTITUTE OF TECHNOLOGY

The credit seminar report titled “Pushover analysis of bridge bent- overview and case

study” submitted by Palak Jaykumar Shukla (Roll No. P10ST516) may be accepted for

evaluation.

Supervisor:

Prof. C. D. Modhera

Date:7-10-11

Place: SVNIT, Surat.

iii

Acknowledgement

I express my indebtness to Prof. C. D. Modhera who first motivated me in choosing this

interesting topic and then devoted his time and helped me at every stage during the

preparation of this credit seminar report. I thank him for all his precious time that he has spent

with me during the course of preparation of this report and the critical suggestions that he

made for its improvement. I also thank Prof. M .K. Desai for his help and encouragement

during preparation of this report.

Date : 7-10-11

Palak Jaykumar Shukla

iv

Abstract

The literatures are available on the seismic evaluation procedures of multi-storeyed

buildings using nonlinear static (pushover) analysis. There is no much effort available in

literature for seismic evaluation of existing bridges although bridge is very important structure

in any country. There are presently no comprehensive guidelines to assist the practicing

structural engineer to evaluate existing bridges and suggest design and retrofit schemes. In

order to address this problem, the aims of present study was to carry out seismic evaluation

case study for Rail/road Bridge bent using nonlinear static (pushover) analysis.

The first chapter focuses on the introduction of the subject, where as second chapter

deals with the literature review about pushover procedures, its applications, limitations and

some alternative methods.

The third chapter includes statement of problem for case study. The modelling of

bridge bent is done with software SAP2000 to perform pushover analysis using SAP2000.

In forth chapter the conclusions are drawn from results of analysis are mentioned and

also indicate future scope of study.

v

CONTENTS

Acceptance Certificate ii

Acknowledgement iii

Abstract iv

Contents v

List of figures vi

List of tables vi

Chapter 1 Introduction 1

1.1 GENERAL 1

Chapter 2 Literature Review 3

2.1 Definition of the Non-Linear Static Procedure (Pushover Analysis) - FEMA 273 3

2.2 Performing the Non – Linear Static Procedure (Pushover Analysis) 4 2.3 Use of Pushover Results 10

2.4 Limitations of Pushover analysis 10 2.5 Alternate Pushover analysis procedure 11

Chapter 3 Problem Statement 14

3.1 Model Selected 14

3.1.1 Material Properties 14

Chapter 4 Software Implementation Error! Bookmark not defined.

4.1 Software implementation 15

Chapter 5 Discussions and Conclusions 18

References 21

vi

LIST OF FIGURES

Figure 2-1 Static Approximation Used In the Pushover Analysis ............................................ 3 Figure 2-2 Response Spectrum ............................................................................................... 4

Figure 2-3 Target Displacement ............................................................................................. 4 Figure 2-4 General Response Spectrum .................................................................................. 6

Figure 2-5 Bilinear Relation of Base Shear vs. Roof Displacement Plot ................................. 9 Figure 2-6 Schematic representation of Capacity Spectrum Method (ATC 40) ....................... 9

Figure 3-1 Geometry of problem selected............................................................................. 14 Figure 4-1 Basic SAP2000 model without pushover data ..................................................... 15

Figure 4-2 Frame Hinge Property ......................................................................................... 16 Figure 4-3 Assign pushover hinge ..................................................................................... 16

Figure 4-4 Pushover load case data ...................................................................................... 17 Figure 5-1 Pushover Curve................................................................................................... 18

Figure 5-2 Capacity spectrum curve ..................................................................................... 19

LIST OF TABLES

Table 2-1 Determination of Building Performance Level 5 Table 2-2 Building Performance Level for Given Seismic Event 6

Table 5-1 Pushover output for various earthquake shaking 19

1

Chapter 1

Introduction

1.1 GENERAL

Kinematic hypothesis “Plane sections remain plane during bending “. It becomes a

working hypothesis in analysis of beams and columns considering linear elastic material

behaviour. Virtually all codes are based on these concepts. For this approach, machine design

for cyclic fatigue loading is an excellent field of application However for quasi-static loading

or for catastrophic overloads as well as for missiles, better approximation of material

behaviour are necessary.

Many earthquake events showed that extrapolations of the elastic solution into the

inelastic range of structural behaviour are unrealistic. A far better approximation of the actual

behaviour of structure near collapse can be obtained by assuming plastic behaviour of

members and joints. These analyses often referred as pushover analysis.

The static pushover analysis is a partial and relatively simple intermediate solution to

the complex problem of predicting force and deformation demands imposed on structures and

their terms are static and analysis. Static implies that static method is being employed to

represent a dynamic phenomenon; a representation that may be adequate in many cases but it

doomed to failure sometimes. Analysis implies that a system solution has been created already

and the pushover is employed to evaluate the solution and modify it as needed. The pushover

does not create the good solutions, it only evaluates solutions. If engineer starts with a poor

lateral system, the pushover analysis may render the system acceptable through system

modifications, or prove it to be unacceptable, but it will not provide a safe path to a good

structural system.

The pushover is part of an evaluation process and provides estimates of demands

imposed on structure and elements. Evaluation implies that imposed demands have to be

compared to available capacities in order to assess acceptability of the design. It is fair to say

that at this time deformation capacities cannot be estimated with great confidence, not for new

elements and less so for elements of existing structures. Recognizing this limitation, the task

is not to perform an evaluation process that is relatively simple but captures the essential since

neither seismic input nor capacities are known with accuracy.

2

The attention for existing bridges is comparatively less. However, bridges are very

important components of transportation network in any country. The bridge design codes, in

India, have no seismic design provision at present. A large number of bridges are designed

and constructed without considering seismic forces. Therefore, it is very important to evaluate

the capacity of existing bridges against seismic force demand. There are presently no

comprehensive guidelines to assist the practicing structural engineer to evaluate existing

bridges and suggest design and retrofit schemes. In order to address this problem, the present

work aims to carry out a seismic evaluation case study for a railroad bridge bent using

nonlinear static (pushover) analysis with SAP 2000.

3

Chapter 2

Literature Review

2.1 Definition of the Non-Linear Static Procedure (Pushover Analysis) - FEMA 273

The Non – Linear Static Procedure or Pushover Analysis is defined in the Federal Emergency

Management Agency document 273 (FEMA 273) as a non – linear static approximation of

the response a structure will undergo when subjected to dynamic earthquake loading. The

static approximation consists of applying a vertical distribution of lateral loads to a model

which captures the material non–linearities of an existing or previously designed structure,

and monotonically increasing those loads until the peak response of the structure is obtained

on a base shear vs. roof displacement plot as shown in figure 2-1.

Figure 2-1 Static Approximation Used In the Pushover Analysis

The desired condition of the structure after a range of ground shakings, or Building

Performance Level, is then decided upon by the owner, architect, and structural engineer. The

Building Performance Level is a function of the post event conditions of the structural and

non – structural components of the structure.

Based on the desired Building Performance Level, the Response Spectrum for the design

earthquake may be determined. The Response Spectrum gives the maximum acceleration, or

Spectral Response Acceleration, a structure is likely to experience under the design ground

shaking given the structure’s fundamental period of vibration, T. This relation is shown

qualitatively in figure 2-2. From the Response Spectrum and Base Shear vs. Roof

Displacement plot, the Target Displacement δt, may be determined. The Target Displacement

represents the maximum displacement the structure will undergo during the design event.

One can then find the maximum expected deformations within each element of the structure

4

at the Target Displacement and redesign them accordingly. The Target Displacement is

shown qualitatively in figure 2-3

Figure 2-2 Response Spectrum Figure 2-3 Target Displacement

2.2 Performing the Non – Linear Static Procedure (Pushover Analysis)

The steps in performing the Non – Linear Static Procedure or Pushover Analysis are:

1) Determine the gravity loading and the vertical distribution of the lateral loads.

2) Determine the desired Building Performance Level.

3) Calculate the Seismic Hazard.

4) Compute the maximum expected displacement or Target Displacement, δt.

Each of these steps are described in the sections following.

1) Determine the Vertical Distribution of the Lateral Loads

In addition to the gravity loads, the first thing that can be determined is the vertical

distribution of the lateral loads. The gravity loads to be used in the Pushover Analysis are

dDcalculated by equation [1], while the vertical distribution of lateral loads is given by

the FEMA 273 Cvx loading profile reproduced as equation [2].

[1]

Where, QG is equal to the total gravity force, QD is equal to the total dead load effect, QL

is equal to the effective live load effect, defined as 25% of the unreduced live load, and

QS is equal to 70% of the full design snow load except where the design snow load is less

than thirty pounds per square foot in which case it is equal to 0.0.

[2]

5

The Cvx coefficient represents the lateral load multiplication factor to be applied at floor level

x, wx represents the fraction of the total structural weight allocated to floor level x, hx is the

height of floor level x above the base, and the summation in the denominator is the sum of

these values over the total number of floors in the structure, n. The parameter k varies with

the structural fundamental period, T. k is 1.0 for T less than or equal to 0.5 seconds and 2.0

for T greater than or equal to 2.5 seconds. For shorter, stiffer structures, the fundamental

period will be small and the variation of the lateral loading over the height of the building will

approach the linear distribution for a k value equal to 1.0. For taller, more flexible structures,

the fundamental period will be greater and the variation of the lateral loading over the height

of the structure will approach the non – linear distribution for k equal to 2.0. The implication

of this is that for stiffer structures the higher mode response of the structure will be less

significant and the lateral loading can enforce purely first mode response. As the structure

becomes more flexible however, the higher mode effects become much more important and

the k value attempts to account for this by adjusting the lateral load distribution

2) Building Performance Level Determination

The next thing that may be determined is the Building Performance Level. The Building

Performance Level is the desired condition of the building after the design earthquake decided

upon by the owner, architect, and structural engineer, and is a combination of the Structural

Performance Level and the Non–Structural Performance Level. The Structural Performance

Level is defined as the post – event conditions of the structural building components. This is

divided into three levels and two ranges. The levels are, S – 1: Immediate Occupancy, S – 3:

Life Safety, and S – 5: Collapse Prevention, are shown in Table 2-1.

Table 2-1 Determination of Building Performance Level

Structural Level Non Structural Level Operational Immediate

Occupancy Life Safety Hazards

Reduced Damage Not Limited

N-A N-B N-C N-D N-E Immediate Occupancy S-1 1-A 1-B Range Between S-1 & S-3 S-2 Life Safety S-3 3-C Range Between S-3 & S-5 S-4 Collapse Prevention S-5 5-E

The owner, architect, and structural engineer can now decide what Building Performance

Level they want their building to achieve after a range of ground shakings which are expected

to occur at a given design location (Table 2-2). The values K and P shown in bold in Table 2-

2 correspond to the performance one achieves when designing by the Uniform Building Code

6

(UBC). This corresponds to Life Safety after a 10% probability of exceedance in 50 year

event and Collapse Prevention after a 2% probability of exceedance in 50 year event,

respectively.

Table 2-2 Building Performance Level for Given Seismic Event

Seismic Event Building Performance Level 1-A 1-B 3-C 5-E

50% /50 years A B C D 20% /50 years E F G H 10% /50 years I J K L 2% /50 years M N O P

3) Calculation of the Seismic Hazard

An important parameter that must be determined for the Pushover Analysis is the Seismic

Hazard of a given location. The Seismic Hazard is a function of:

1) The Building Performance Level

2) The Mapped Acceleration Parameters (found from contour maps included with FEMA

273)

3) The Site Class Coefficients (which account for soil type)

4) The effective structural damping

5) The Fundamental Structural Period

the General Response Spectrum can be formulated for the design event being considered. The

General Response Spectrum is shown qualitatively in Figure 2-4.

Figure 2-4 General Response Spectrum

The General Response Spectrum is a function of the many site and design event specific

parameters which are related by a complicated system of equations. However, once it has

been developed, since it is a function only of site location parameters and the design event

7

under consideration, it becomes a very useful tool as it describes the maximum acceleration a

structure, with a given fundamental period, must endure during the design event.

4) Calculation of the Target Displacement

There are two approaches to calculate target displacement:

a) Displacement Coefficient Method (DCM) of FEMA 356

The Target Displacement, i.e. the maximum displacement the structure is expected to undergo

during the design event, can now be obtained. The target displacement is calculated from the

following equation:

[3]

Where the value C0 is a modification factor that relates spectral displacement and

likely building roof displacement. Values for C0 are tabulated in FEMA 273 as a function of

the total number of stories of the structure.C1 is a modification factor which relates expected

maximum inelastic displacements to displacements calculated for linear elastic response.

Values for C1 are obtained from:

[4]

[5]

Te is the effective fundamental period of the structure and is defined as given in equation

[11]. To is the characteristic period of the response spectrum, defined as the period associated

with the transition from the constant acceleration segment of the spectrum to the constant

velocity segment of the spectrum and is calculated as

[6]

Where Bs and Bl are Damping Coefficients given in FEMA 273

SXS is the final design short period spectral response acceleration parameter, and

SX1is the final design spectral response acceleration parameter at a one second period, can be

determined from:

[7]

[8]

Where Fa ,Fv,Ss and Sl is tabulated in FEMA 273

8

R is the ratio of elastic strength demand to calculated yield strength coefficient. Values for R

are obtained from:

[9]

Sa is the Response Spectrum Acceleration, in g’s, (where g must be in consistent units,

usually in/s2 ) at the effective fundamental period and damping ratio of the building in the

direction under consideration . Vy is the yield strength calculated using the results of the

Pushover Analysis, where the non – linear force – displacement curve of the building is

characterized by a bilinear relation as shown in figure 2-5. W is the total dead load and

anticipated live load, as calculated by equation 1. C0 is as defined above .

C2 is a modification factor that represents the effect of hysteresis shape on the

maximum displacement response of the structure. Values for C2 are tabulated in FEMA 273

and are a function of Building Performance Level, framing type, and the fundamental period

of the structure.

C3 is a modification factor to represent increased displacements due to dynamic P – ∆

effects. For buildings with positive post – yield stiffness, C3 shall be set equal to 1.0. For

buildings with negative post – yield stiffness, C3 shall be calculated from:

[10]

Values for R and Te are obtained from equations [9] and [11] respectively, and α is the ratio

of post – yield stiffness to effective elastic stiffness, where the non – linear force –

displacement relation is characterized by a bilinear relation as shown in figure 2-5.

The effective fundamental period of the structure in the direction under consideration, Te

may be calculated from:

[11]

Where T is the elastic fundamental period of the structure (in seconds), in the direction under

consideration, calculated by elastic dynamic analysis. Ki is the elastic lateral stiffness of the

building in the direction under consideration and is found from the initial stiffness of the non

– linear base shear vs. roof displacement curve as shown in Figure 2-5. Ke is the effective

lateral stiffness of the building in the direction under consideration and is defined as the slope

of the line which connects the point of intersection of the post – yield stiffness line with the

9

horizontal line at the yield base shear value to zero, while intersecting the original base shear

vs. roof displacement curve at 60% of the yield base shear value. Ki and Ke are shown in

Figure 2-5.

b) Capacity Spectrum Method (ATC 40)

The basic assumption in Capacity Spectrum Method is also the same as the previous one. That

is, the maximum inelastic deformation of a nonlinear SDOF system can be approximated

from the maximum deformation of a linear elastic SDOF system with an equivalent period

and damping. This procedure uses the estimates of ductility to calculate effective period and

damping. This procedure uses the pushover curve in an acceleration-displacement response

spectrum (ADRS) format. This can be obtained through simple conversion using the dynamic

properties of the system. The pushover curve in an ADRS format is termed a ‘capacity

spectrum’ for the structure. The seismic ground motion is represented by a response spectrum

in the same ADRS format and it is termed as demand spectrum (Figure 2-6).

Figure 2-5 Bilinear Relation of Base Shear vs. Roof Displacement Plot

Figure 2-6 Schematic representation of Capacity Spectrum Method (ATC 40)

The equivalent period (Teq) is computed from the initial period of vibration (Ti) of the

nonlinear system and displacement ductility ratio (μ). Similarly, the equivalent damping ratio

(βeq) is computed from initial damping ratio (ATC 40 suggests an initial elastic viscous

10

damping ratio of 0.05 for reinforced concrete building) and the displacement ductility ratio

(μ).

2.3 Use of Pushover Results

Pushover analysis has been the preferred method for seismic performance evaluation of

structures by the major rehabilitation guidelines and codes because it is conceptually and

computationally simple. Pushover analysis allows tracing the sequence of yielding and failure

on member and structural level as well as the progress of overall capacity curve of the

structure. The expectation from pushover analysis is to estimate critical response parameters

imposed on structural system and its components as close as possible to those predicted by

nonlinear dynamic analysis. Pushover analysis provides information on many response

characteristics that cannot be obtained from an elastic static or elastic dynamic analysis.

These are;

a) estimates of interstory drifts and its distribution along the height

b) determination of force demands on brittle members, such as axial force demands on

columns, moment demands on beam-column connections

c) determination of deformation demands for ductile members

d) identification of location of weak points in the structure (or potential failure modes)

e) consequences of strength deterioration of individual members on the behaviour of

structural system

f) identification of strength discontinuities in plan or elevation that will lead to changes

in dynamic characteristics in the inelastic range

g) verification of the completeness and adequacy of load path

h) Pushover analysis also exposes design weaknesses that may remain hidden in an

elastic analysis. These are story mechanisms, excessive deformation demands,

strength irregularities and overloads on potentially brittle members.

2.4 Limitations of Pushover analysis

Many publications have demonstrated that traditional pushover analysis can be an extremely

useful tool, if used with caution and acute engineering judgment, but it also exhibits

significant shortcomings and limitations, which are summarised below:

a) One important assumption behind pushover analysis is that the response of a MDOF

structure is directly related to an equivalent SDOF system. Although in several cases the

11

response is dominated by the fundamental mode, this cannot be generalised. Moreover,

the shape of the fundamental mode itself may vary significantly in nonlinear structures

depending on the level of inelasticity and the location of damages.

b) Target displacement estimated from pushover analysis may be inaccurate for structures

where higher mode effects are significant. The method, as prescribed in FEMA 356,

ignores the contribution of the higher modes to the total response.

c) It is difficult to model three-dimensional and torsional effects. Pushover analysis is very

well established and has been extensively used with 2-D models However, little work has

been carried out for problems that apply specifically to asymmetric 3-D systems, with

stiffness or mass irregularities. It is not clear how to derive the load distributions and how

to calculate the target displacement for the different frames of an asymmetric building.

Moreover, there is no consensus regarding the application of the lateral force in one or

both horizontal directions for such buildings.

d) The progressive stiffness degradation that occurs during the cyclic nonlinear earthquake

loading of the structure is not considered in the present procedure. This degradation leads

to changes in the periods and the modal characteristics of the structure that affect the

loading attracted during earthquake ground motion.

e) Only horizontal earthquake load is considered in the current procedure. The vertical

component of the earthquake loading is ignored; this can be of importance in some cases.

There is no clear idea on how to combine pushover analysis with actions at every

nonlinear step that account for the vertical ground motion.

f) Structural capacity and seismic demand are considered independent in the current method.

This is incorrect, as the inelastic structural response is load-path dependent and the

structural capacity is always associated with the seismic demand.

2.5 Alternate Pushover analysis procedure

Pushover Analysis procedure, as explained in FEMA 356, is primarily meant for regular

buildings with dominant fundamental mode participation. There are many alternative

approaches of pushover analysis reported in the literature to make it applicable for different

categories of irregular buildings.

These comprise (i) Modal pushover analysis (Chopra and Goel, 2001),

(ii) Modified modal pushover analysis (Chopra et. al., 2004),

(iii) Upper bound pushover analysis (Jan et. al., 2004),

12

(iv) Adaptive pushover analysis

2.6 Application of Pushover analysis to Bridges

Au, et al. (2001) evaluated vibration analysis of bridges under moving vehicles. The

authors reported that, vehicle-bridge interaction is a complex dynamic phenomenon,

depending on many parameters which include the type of bridge and its natural frequencies of

vibration, vehicle characteristics, vehicle speed, the number of vehicles and their relative

positions on the bridge, roadway surface irregularities, etc. The authors finalized the

interaction between the moving vehicles and the bridge is a nonlinear problem. And FEM is

certainly the most versatile and powerful method, while FSM is particularly suitable for

regular plate-type bridges.

Chung and Hamed (2003), University of Maryland performed seismic analysis of

bridges using displacement based approach. A three-span bridge of 97.5 meters (320 ft) in

total length was analyzed using both the Nonlinear Static Procedure/Displacement Coefficient

Method and nonlinear time-history. Nine time-histories were implemented to perform the

nonlinear time-history analysis. Three load patterns were used to represent distribution of the

inertia forces resulting from earthquakes. Demand (target) displacement, base shear, and

deformation of plastic hinges obtained from the Nonlinear Static (Pushover) Procedure are

compared with the corresponding values resulting from the nonlinear time history analysis.

Analysis was performed using two levels of seismic load intensities (Design level and

Maximum Considered Earthquake level). Performance of the bridge was evaluated against

these two seismic loads. Comparison shows that the Nonlinear Static Procedure gives

conservative results, compared to the nonlinear time history analysis, in the Design Level

while it gives more conservative results in the Maximum Considered Earthquake level.

Chiorean (2003) evaluated a nonlinear static (pushover) analysis method for

reinforced concrete bridges that predicts behaviour at all stages of loading, from the initial

application of loads up to and beyond the collapse condition. The author developed line

elements approach, which are based on the degree of refinement in representing the plastic

yielding effects. The method has been developed for the purpose of investigating the collapse

behaviour of a three span pre-stressed reinforced concrete bridge of 115m in total length.

ENDO et al. (2004) performed analytical study on seismic performance evaluation of

long span suspension bridge steel tower. This paper presents the limit state evaluation of the

steel tower structures of a long-span suspension bridge against large-scale earthquakes. A

13

series of pushover analyses using two types of analytical models with shell and fiber elements

and nonlinear dynamic analyses were conducted. The strength and damage progress

characteristics obtained from two analytical models and methods were compared. Based on

the analytical results, the acceptable ductility capacity for the steel tower structure exceeding

the elastic limit was proposed. Furthermore, the results from both the pushover analysis and

nonlinear dynamic analysis showed good agreement.

Muljati and Warnitchai (2007) investigated the performance of Modal Pushover

Analysis (MPA) to predict the inelastic response of the continuous bridge decks with no

intermediate movement joints. The authors reported that the performance of MPA in

nonlinear range shows a similar tendency with MPA in linear range. Being an approximate

method, MPA gives an acceptable accuracy beside of simplicity and efficiency in calculation.

Kapposa et al. (2010) used Modal Pushover analysis as means of seismic assessment

of bridge structure. They investigated the extension of the modal pushover method to bridges,

and also its applicability in the case of complex bridges. To this effect, a real, long and curved

bridge is chosen, designed according to current seismic codes; this bridge is assessed using

the aforementioned three nonlinear analysis methods. Comparative evaluation of the

calculated response of the bridge illustrates the applicability and potential of the modal

pushover method for bridges, and quantifies its relative accuracy compared to that obtained

through the ‘standard’ pushover approach.

Capron (2010) perform pushover analysis on I-155 bridge near Caruthersville,

Missouri based seismic evaluation of a 7,100 foot (2,164 m) long bridge located near the New

Madrid Seismic Zone in southeastern Missouri. The evaluation includes the existing

structure, and the substructure retrofitted with column jackets, cap-beam modifications, and

seismic isolation bearings. The evaluation shows that the existing structure has 30% to 40%

of the displacement capacity required for the 500 year design level, and significantly less than

required for the 1,000 and 2,500 year levels; that retrofits can improve performance to the 500

year level; and that isolation bearings can improve performance of the main spans.

14

Chapter 3

Problem Statement and Software implementation

3.1 Model Selected

Non linear static pushover analysis will be performed on railroad bridge bent using SAP2000

to determine its ultimate lateral deflection capability. The analysis model confugation is

shown below:

Figure 0-1 Geometry of problem selected

3.1.1 Material Properties

Concrete:

Grade of concrete : M35 grade , Ec = 500 * √fck N/mm2

Steel:

HYSD reinforcement of grade Fe 415 conforming to IS: 1786 is used

3.1.2 Load cases:

I) Dead load: Superstructure load w :794.20 KN/m

II) Pushgrav

15

3.2 Software implementation

1. Create the basic computer model (without the pushover data) in the usual manner as

shown in Figure 4-1. The graphical interface of SAP2000 makes this a quick and easy

task.

Model Generation

Figure 0-2 Basic SAP2000 model without pushover data

2. Define properties and acceptance criteria for the pushover hinges as shown in Figure

4-2. The program includes several built-in default hinge properties that are based on

average values from ATC-40 for concrete members and average values from FEMA-

273 for steel members. These built in properties can be useful for preliminary

analyses, but user- defined properties are recommended for final analyses. This

example uses default properties. Locate the pushover hinges on the model by selecting

one or more frame members and assigning them one or more hinge properties and

hinge locations as shown in Figure 4-3

16

3. Define the pushover load cases. In SAP2000 more than one pushover load case can be

run in the same analysis. Also a pushover load case can start from the final conditions

of another pushover load case that was previously run in the same analysis. Typically

the first pushover load case is used to apply gravity load and then subsequent lateral

pushover load cases are specified to start from the final conditions of the gravity

pushover. Pushover load cases can be force controlled, that is, pushed to a certain

defined force level, or they can be displacement controlled, that is, pushed to a

specified displacement. Typically a gravity load pushover is force controlled and

lateral pushovers are displacement controlled. SAP2000 allows the distribution of

lateral force used in the pushover to be based on a uniform acceleration in a specified

direction, a specified mode shape, or a user-defined static load case. The dialog box

shown in Figure 4.4 shows how the displacement controlled lateral pushover case

“Push_grav” used for this example.

Figure 0-3 Frame Hinge Property Figure 0-4 Assign pushover hinge

17

Figure 0-5 Pushover load case data(push_grav)

4. Run the static nonlinear pushover analysis.

18

Chapter 4

Discussions and Conclusions

The following procedure should be used to get the results of the pushover analysis 1. Obtained pushover curve is shown in Figure 5.1.

Figure 0-1 Pushover Curve(load cae push_grav)

2. Obtained capacity spectrum curve as shown in Figure 5.2. Note that one can

interactively modify the magnitude of the earthquake and the damping information on

this form and immediately see the new capacity spectrum plot. The performance point

for a given set of values is defined by the intersection of the capacity curve (green)

and the single demand spectrum curve (yellow).

19

Figure 0-2 Capacity spectrum curve (push_grav)

3. Member forces should be reviewed on a step-by-step basis i.e. typically step 3 is given

in Figure 5-3.

Results of the pushover analysis are summarized in the Table 5-1. The model bridge bent is

analyzed for three level of ground shakings and corresponding base shear (V), displacement

(D), spectral acceleration (Sa), Spectral displacement (Sd), and effective time periods (Teff) are

obtained

Table 0-1 Pushover output for various earthquake shaking

Earthquake Level

ca cv V (kN) Sa

m/s2 Sd

m Teff

(sec)

Beff

Level 1 0.9 0.9 4298.534 1.323 0.028 0.291 0.178 Level 2 0.4 0.4 3249.068 1.00 0.014 0.238 0.050 Level 3 0.2 0.2 1624.53 0.5 7.042*10-3 0.238 0.050

Conclusions:

The main objective of this study was to overview the pushover method for seismic behaviour

and performance of bridge bent. The typical bridge geometry was selected for the present

study and pushover analysis was performed using SAP2000 computer code.

It is observed that the seismic behaviour of the bridge bent is mostly controlled by the

stiffness of the bridge columns. The results of the Pushover analysis suggest that the first

20

hinge development is observed near the pile cap of the bridge bent and corresponding hinges

are developed near the deck level within the bride column.

The pushover analysis is very powerful tool to carry out non-linear static analysis of bride

bent under seismic loads. The selected bridge bent is analyzed for thee performance level

earthquake shakings and obtained results are tabulated elsewhere in the report. It is observed

that the bridge bent has largest level of load (base shear and spectral displacement) under the

most severe shaking of the earthquake (i.e. level 1) and subjected to less load under

corresponding other level of earthquakes. However, under each level of earthquake shaking

the formation of the plastic hinges within the bent geometry governs the structural safety. The

present study outlines the typical methodology used for the checking the bridge structure

under earthquake loading for performance based design or retrofitting of the existing brides of

almost any geometry.

Future Scope of Study

The present bridge bent is analyzed using adopted typical bridge geometry and the study

should be extended using the actual bridge geometry of typical bridges of Surat city. The

earthquake shaking levels are selected arbitrarily adjusting he Ca and Cv to modify the

standard earthquake given in ATC 40. However, the present study may have more value if the

ground shaking levels are obtained using probabilistic seismic hazard analysis for specific

bridge site of Surat city.

21

REFERENCES

1. Applied Technology Council, ATC-40 (1996) “Seismic Evaluation and Retrofit of

Concrete Buildings”, Volume 1-2, Redwood City, California.

2. Au, FTK, Chengand, YS and Cheung, YK (2001) “Vibration analysis of bridges under

moving vehicles and trains”, Engineering Structures, vol. 30, 54-66.

3. Capron Mark R.(2010), “Pushover analysis of the I-155 bridge near

Caruthersville,Missouri”. Project work report, Jacobs Engineering, St. Louis,Missouri.

4. Chintanapakdee, C. and Chopra, A.K. (2004) “Seismic response of vertically irregular

frames: Response history and modal pushover analyses”. ASCE Journal of Structural

Engineering. 130(8), 1177-1185.

5. Chiorean, CG (2003) “Application of pushover analysis on reinforced concrete bridge

model”, 4th European Workshop on the Seismic Behaviour of Irregular and Complex

Structures, Thessaloniki, Greece.

6. Chopra, A.K., and Goel, R.K. (2001). “Modal Pushover procedure to estimate seismic

demand of Building: Theory and Preliminary Evaluation”. Report No. PEER 2001/03 ,

Pacific Earthquake Engineering Research Center, University of California, Berkeley,

California.

7. Chopra, A.K., and Goel, R.K. (2002). “A modal pushover analysis procedure for

estimating seismic demands for buildings”. Earthquake Engineering and Structural

Dynamics,31, 561-582.

8. Chopra, A.K. and Goel, R.K. (2004) “A modal pushover analysis procedure to

estimate seismic demands for unsymmetric-plan buildings”. Earthquake Engineering

and Structural Dynamics. 33, 903-927.

9. Chung C. Fu and Hamed AlAyed (2003), “Seismic analysis of bridges using

Displacement-Based Approach”,University of Maryland.

22

10. ENDO Kazuo, KAWATOH Chihiro and UNJOH Shigeki (2004), “Analytical study

on seismic performance evaluation of long-span suspension bridge steel tower”. 13th

World Conference on Earthquake Engineering, Canada. Paper No.944

11. Federal Emergency Management Agency (FEMA) (1997) “NEHRP Guidelines for the

Seismic Rehabilitation of Buildings”, FEMA-273.

12. Federal Emergency Management Agency (FEMA) (2000) “Prestandard and

Commentary for the Rehabilitation of Buildings”, FEMA-356.

13. Jan, T.S.; Liu, M.W. and Kao, Y.C. (2004), “An upper-bond pushover analysis

procedure for estimating the seismic demands of high-rise buildings”. Engineering

structures. 117-128.

14. Kappos A. J. , Paraskeva T.S. and Sextos A.G. (2010), “Modal Pushover analysis as a

means for the seismic assessment of bridge structures”, Proceedings of the 4th

European Workshop on the Seismic behaviour of Irregular and Complex Structures,

Thessaloniki, Greece, Paper No. 49.

15. Muljati Ima and Warnitchai P. (2007), “A modal pushover analysis on multi-span

concrete bridges to estimate inelastic seismic responses”, Civil Engineering

Dimension, Vol. 9, No. 1, 33-41.

16. SAP 2000 (2007). “Integrated Software for Structural Analysis and Design”, Version

14.0. Computers & Structures, Inc., Berkeley, California

17. Tjhin, T., Aschheim, M. and Hernandez-Montes, E. (2006) “Observations on

reliability of alternative multiple mode pushover analysis methods”. ASCE Journal of

Structural Engineering. 132(3), 471-477.

23