Feasibility of Capacity Spectrum method for seismic

analysis of concrete bridges for Indian terrain as a step

towards performance based Design Philosophy

Taher S Najmi1 Mayank Desai

2

PG student at SDMCET Dharwad1

Assistant Professor of Applied Mechanics Department at S.V.N.I.T Surat2

tahernajmi721@gamil.com1 , dmayank@gamil.com

2

ABSTRACT

Bridge Structures are of vital importance to our daily activities and economy.

History has shown that such structural systems are vulnerable to earthquakes. Bridge

damage resulting from a significant earthquake could be devastating because casualties

and economical loss are usually large. But they are equally important as residential and

commercial buildings because they are the strategic structures and they serve as passages

and connectors to provide the easy access to the unaffected area for transportation of both

goods and people in post natural calamity needs and emergencies in grief stricken area.

They not only serve as the over-ground paths for crossing the water bodies and valleys,

but they constitute the networked system to connect communities to aid the commerce

and people of the nation.

The principal aim of this study is use the advanced and newly developed analysis

and design procedures. Because this study mainly concentrates on the Seismic safety

aspects of the concrete bridges, it is taken for granted that the bridge under consideration

satisfies all static stress criteria and is serviceable as far as static loading is concerned.

The bridge adopted for the study is safe, serviceable under the condition of no earthquake.

The study carried out here employs implementation of advanced method called Capacity

Spectrum Method as a suggested method for evaluation of the structural capacity of the

bridge for given demand in terms of target displacement posed by Design Basis

Earthquake (DBE) and Maximum Considered Earthquake (MCE). Demand is estimated

both using Response Spectrum and Time History Analyses and Capacity is evaluated

using Nonlinear Static Procedure prescribed in FEMA-273 and ATC-40.

Keywords: Capacity Spectrum Method, Pushover Analysis, Time History Analysis,

DBE, MCE

INTRODUCTION

Bridges give the impression of being rather simple structural systems. Indeed they

have always occupied a special place in the affections of structural designers because

their structural form tends to be a simple expression of their functional requirement. As

such, structural solutions can often be developed that are both functionally efficient and

aesthetically satisfying, as evidenced by the many excellent texts on aesthetic aspects of

bridge design.

Despite, or possibly because of their structural simplicity, bridges in particular

those constructed in reinforced or pre-stressed concrete, have not performed as well as

might be expected under seismic attack. In recent earthquakes in California, Japan, and

Central and South America, modem bridges designed specifically for seismic resistance

have collapsed or have been severely damaged when subjected to ground shaking of an

intensity that has frequently been less than that corresponding to current code intensities.

As will be seen subsequently, this unexpectedly poor performance can in the majority of

cases be attributed to the design philosophy adopted coupled with a lack of attention to

design details. Earthquakes have a habit of identifying structural weaknesses and

concentrating damage at these locations. With building structures, the consequences may

not necessarily be disastrous, because of the high degree of redundancy generally inherent

in building structural systems. This enables alternative load paths to be mobilized if

necessary. Typically, bridges have little or no redundancy in the structural systems. And

failure of one structural element or connection between elements is thus more likely to

result in collapse than is the case with a building. This leads to the above-mentioned

warning that the structural simplicity of bridges may be a mixed blessing. While the

simplicity should lead to greater confidence in the prediction of seismic response, this

also results in greater sensitivity to design errors.

To be able to effectively design either new bridges or retrofit measures for

existing bridges, a clear understanding of potential problem areas is essential. There is no

better way of developing this understanding than by a systematic examination and

categorization of failures and damage that have occurred to bridges in earlier

earthquakes. It has often been said that those who ignore the lessons of history are

doomed to repeat its mistakes. In no area is this truer than in seismic design. It is thus

appropriate, before developing design philosophy or design details, to spend some time

in reviewing past earthquake damage to bridges and common design deficiencies.

Basic Principles of Seismic Design of Concrete Bridges

The newly developed Seismic design of bridges envisages the advanced and more

practical approach to design the bridges which can withstand the earthquake safely for

which it is designed. The newer methodologies of design and analysis procedures have

been implemented to build new bridges and are still being refined to minimize the

earthquake hazards to the bridges. The following are the some of the key points for the

Seismic Design of Bridges:

� Determining the design earthquake(s) for the site

� Determining the seismic hazards at the site

� Determining the seismic demands on the bridge

� Designing and detailing the bridge and its components/elements so that their

capacity meets the performance requirements for the seismic demand.

MODELLING

Software Tools

For modeling and analysis the following software tools are taken help of.

(1) CSI BRIDGE 15 Nonlinear Version (Structural Analysis Program)

A product of

Computers and Structures, Inc.

1995 University Ave, Berkeley,

California.

About CSI BRIDGE 15:

CSI BRIDGE 15 is an eminent and versatile software tool for carrying out the

linear as well as nonlinear finite element analysis of the Bridge. It is equipped with some

of the advanced modeling, analysis and design capabilities. The bridge is modeled using

CSI BRIDGE 15. This software tool is used for Bridge analysis.

DETAILS OF BRIDGE MODEL

The bridge of the following geometry and configuration has been chosen for the

study. The bridge is a simply supported pre stressed concrete box girder bridge

constructed on the medium to hard strata. The bridge is having a total of five equal spans.

The geometry of the bridge along with the necessary span and section data is given on the

following pages. Before modeling the bridge all the sectional properties and required

constants were calculated and are incorporated in model.

FIG 1.1 Cross section details of the Bridge

Table 1.1 Span data

Pier/ Abutment Location (m)

Abutment1 0

Pier1 30

Pier2 60

Pier3 90

Pier4 120

Abutment2 150

FIG 1.2 Isometric View of the Bridge Model

FIG 1.3 Deck Section Details

FIG 1.4 Load case Tree

ANALYSIS

Pushover Analysis:

One such nonlinear static procedure as mentioned above is an analysis called Push

Over analysis. The recent advent of performance based design has brought the nonlinear

static pushover analysis procedure to the forefront. Pushover analysis is a static, nonlinear

procedure in which the magnitude of the structural loading is incrementally increased in

accordance with a certain predefined pattern. With the increase in the magnitude of the

loading, weak links and failure modes of the structure are found. The loading is

monotonic with the effects of the cyclic behavior and load reversals being estimated by

using a modified monotonic force-deformation criteria and with damping approximations.

Static pushover analysis is an attempt by the structural engineering profession to evaluate

the real strength of the structure and it promises to be a useful and effective tool for

performance based design.

The ATC-40 and FEMA-273 documents have developed modeling procedures,

acceptance criteria and analysis procedures for pushover analysis. These documents

define force-deformation criteria for hinges used in pushover analysis. As shown in figure

below, five points labeled A, B, C, D, and E are used to define the force deflection

behavior of the hinge and three points labeled IO, LS and CP are used to define the

acceptance criteria for the hinge. (IO, LS and CP stand for Immediate Occupancy, Life

Safety and Collapse Prevention respectively.) The values assigned to each of these points

vary depending on the type of member as well as many other parameters defined in

theATC-40 and FEMA-273 documents.

Force deformation for Pushover hinge

Capacity spectrum method

One of the methods used to determine the performance point is the Capacity

Spectrum Method, also known as the Acceleration-Displacement Response Spectra

method (ADRS). The Capacity Spectrum method requires that both the capacity curve

and the demand curve be represented in response spectral ordinates.

Conversion of Pushover curve to Capacity Spectrum Curve

To convert a spectrum from the standard Sa (Spectra Acceleration) vs. T (Period) format

found in the building codes to ADRS format, it is necessary to determine the value of Sdi

(Spectral Displacement) for each point on the curve, SaiTi This can be done with the

equation:

(1.1)

(1.2)

(1.3)

(1.4)

(1.5)

(1.6)

RESULTS & DISCUSSION

In order to run the pushover analysis, the first requirement is the moment

curvature analysis data of the bridge pier section and the specification of push load

pattern. However, here, the hinges are defined using the FEMA-356 definitions and two

types of push pattern namely uniform and modal have been defined.

The target displacements are set up using the response spectrum and time history

analysis and control node which in this study is the c.g of the superstructure at each bent

beam is pushed to the target displacement. The hinge formation is controlled by

displacement control.

Figure 1.5 Response spectrums of DBE and MCE for medium soil site

Table 1.2 Modal Periods and Frequencies

Output Case

Text Step Type

Text Step Num

Unitless

Period

Sec

Frequency

Cyc/sec

Circ Freq

rad/sec

Eigen value

rad2/sec2

MODAL Mode 1 0.232134 4.3079 27.067 732.62

MODAL Mode 2 0.221893 4.5067 28.316 801.81

MODAL Mode 3 0.18305 5.463 34.325 1178.2

MODAL Mode 4 0.174454 5.7322 36.016 1297.2

MODAL Mode 5 0.159506 6.2694 39.392 1551.7

MODAL Mode 6 0.151901 6.5832 41.364 1711

MODAL Mode 7 0.139517 7.1676 45.035 2028.2

MODAL Mode 8 0.138598 7.2151 45.334 2055.2

MODAL Mode 9 0.133809 7.4733 46.956 2204.9

MODAL Mode 10 0.116974 8.5489 53.714 2885.2

MODAL Mode 11 0.114503 8.7334 54.874 3011.1

MODAL Mode 12 0.114396 8.7416 54.925 3016.7

Push Over Analysis

1) Uniform Pushover analysis data for BENT-2 in X direction

Table 1.3 Pushover Curve for Bent-2

Step

Displacement

m

Base Force

KN

A

to

B

B

to

IO

IO

to

LS

LS

to

CP

CP

To

C

C

to

D

D

to

E

Beyond

E

Total

0 0.000701 0 24 0 0 0 0 0 0 0 24

1 0.01656 228894.053 22 2 0 0 0 0 0 0 24

2 0.123735 1383578.171 8 4 7 3 0 2 0 0 24

3 0.169624 1829723.123 0 5 3 6 2 8 0 0 24

4 0.178239 1867301.906 0 2 4 6 3 9 0 0 24

Table 1.4 Pushover Curve Demand Capacity for Bent-2

Step

Teff

Beff

SdCapacity

m

SaCapacity

Alpha

PFPhi

0 0.111125 0.05 0.003933 0 1 1

1 0.111125 0.05 0.096564 2.038123 0.866561 0.962152

2 0.122177 0.062595 0.658095 11.93058 0.894823 1.054876

3 0.12469 0.069962 0.899284 15.67675 0.900584 1.058249

4 0.125238 0.072701 0.92461 15.98066 0.901602 1.081537

Figure 1.5 Capacity and Demand of Bent 2 for DBE in ADRS

Figure 1.6 Capacity and Demand of Bent 2 for MCE in ADRS

2) Modal Pushover analysis data for BENT-2 in X direction

Table 1.5 Pushover Curve for Bent-2

Step

Displacement

m

Base Force

KN

A

to

B

B

to

IO

IO

to

LS

LS

to

CP

CP

To

C

C

to

D

D

to

E

Beyond

E

Total

0 0.000701 0 24 0 0 0 0 0 0 0 24

1 0.018018 88921.385 23 1 0 0 0 0 0 0 24

2 0.054574 221609.583 3 10 8 0 0 2 0 1 24

Table 1.6 Pushover Curve Demand Capacity for Bent-2

Step

Teff

Beff

SdCapacity m

SaCapacity

Alpha

PFPhi

0 0.159506 0.05 0.012845 0 1 1

1 0.159506 0.05 0.27151 0.85469 0.802773 1.216005

2 0.178002 0.085606 0.777427 2.018377 0.847191 1.286295

Figure 1.7 Capacity and Demand of Bent 2 for DBE in ADRS

Figure 1.8 Capacity and Demand of Bent 2for MCE in ADRS

1) Uniform Pushover analysis data for BENT-2 in Y direction

Table 1.7 Pushover Curve for Bent-2

Step

Displacement

m

Base Force

KN

A

to

B

B

to

IO

IO

to

LS

LS

to

CP

CP

To

C

C

to

D

D

to

E

Beyond

E

Total

0 -4.69E-14 0 24 0 0 0 0 0 0 0 24

1 0.012847 95711.696 22 2 0 0 0 0 0 0 24

2 0.015327 110071.083 18 6 0 0 0 0 0 0 24

3 0.025219 135437.849 10 14 0 0 0 0 0 0 24

4 0.04313 158478.134 4 18 2 0 0 0 0 0 24

5 0.127501 211318.033 0 2 12 8 0 2 0 0 24

6 0.143904 217138.747 0 2 12 4 2 4 0 0 24

7 0.150302 215871.466 0 2 12 0 4 6 0 0 24

Table 1.8 Pushover Curve Demand Capacity for Bent-2

Step

Teff

Beff

SdCapacity

m

SaCapacity

Alpha

PFPhi

0 0.152461 0.05 -1.08625E-12 0 1 1

1 0.152461 0.05 0.313331384 0.887761 0.831886 0.950645

2 0.154034 0.057525 0.368688581 1.023326 0.829954 0.963869

3 0.170076 0.115527 0.56017648 1.275392 0.819391 1.043815

4 0.196888 0.175326 0.894652039 1.519896 0.804545 1.117753

5 0.279229 0.232348 2.479596464 2.094386 0.778529 1.192211

6 0.291373 0.237839 2.782279151 2.158244 0.776304 1.199203

7 0.297776 0.244713 2.897617062 2.152099 0.773977 1.202664

Figure 1.9 Capacity and Demand of Bent 2 for DBE in ADRS

Figure 2.0 Capacity and Demand of Bent 2 for MCE in ADRS

2) Modal Pushover analysis data for BENT-2 in Y direction

Table 1.9 Pushover Curve for Bent-2

Step

Displacement

m

Base Force

KN

A

to

B

B

to

IO

IO

to

LS

LS

to

CP

CP

To

C

C

to

D

D

to

E

Beyond

E

Total

0 -4.69E-14 0 24 0 0 0 0 0 0 0 24

1 0.013311 68371.549 22 2 0 0 0 0 0 0 24

2 0.015937 77689.352 18 6 0 0 0 0 0 0 24

3 0.030399 104071.641 12 12 0 0 0 0 0 0 24

4 0.147419 174919.98 0 2 12 2 2 6 0 0 24

5 0.148117 174817.23 0 2 12 2 2 6 0 0 24

Table 2.0 Pushover Curve Demand Capacity for Bent-2

Step

Teff

Beff

SdCapacity

m

SaCapacity

Alpha

PFPhi

0 0.174454 0.05 -3.17802E-13 0 1 1

1 0.174454 0.05 0.09696525 0.717175 0.735606 0.931196

2 0.177325 0.062018 0.114258623 0.817932 0.732891 0.946159

3 0.199121 0.119079 0.198620265 1.127621 0.712138 1.038203

4 0.322732 0.220768 0.850850212 1.838829 0.733995 1.175295

5 0.323517 0.221772 0.854606142 1.838004 0.733893 1.17567

Figure 2.1 Capacity and Demand of Bent 2 for DBE in ADRS

Figure 2.2 Capacity and Demand of Bent 2for MCE in ADRS

Time History

The requirements for the mathematical model for Time-History Analysis are

identical to those developed for Response Spectrum Analysis. The damping matrix

associated with the mathematical model shall reflect the damping inherent in the building

at deformation levels less than the yield deformation. Time-History Analysis shall be

performed using time histories prepared according to the requirements given below.

Time-History Analysis shall be performed with no fewer than three data sets (two

horizontal components or, if vertical motion is to be considered, two horizontal

components and one vertical component) of appropriate ground motion time histories that

shall be selected and scaled from no fewer than three recorded events. Appropriate time

histories shall have magnitude, fault distances, and source mechanisms that are consistent

with those that control the design earthquake ground motion. Where three appropriate

recorded ground motion time history data sets are not available, appropriate simulated

time history data sets may be used to make up the total number required. For each data

set, the square root of the sum of the squares (SRSS) of the 5%-damped site-specific

spectrum of the scaled horizontal components shall be constructed. The data sets shall be

scaled such that the average value of the SRSS spectra does not fall below 1.4 times the

5%-damped spectrum for the design earthquake for periods between 0.2T seconds and

1.5T seconds (where T is the fundamental period of the building).

Results of Time History Analysis

Figure 2.3 Displacement history of Bent 2 in X direction

Figure 2.4 Displacement history of Bent 2 in Y direction

CONCLUSION

� It is evident from the study that capacity spectrum method of paves strong

theoretical basis for evaluation of the structural capacity for given demand in

terms of displacement and load levels.

� Response spectrum analysis and Time history analysis are required beforehand in

order to employ capacity spectrum method to set the target displacement and load

levels for displacement or force based non-linear static (pushover) analysis.

� The bridge model, MCE overestimates the target displacement approximately by

20%, which is still less than displacement at performance point. This indicates that

the model of bridge used for the study is safer even for MCE.

� Modal push pattern in X direction with modal time period of T = 0.1595 sec. give

better push load distribution in order to reach target displacement giving good

number of steps as compared to uniform push patterns.

� Modal push pattern in Y direction with modal time period of T = 0.1744 sec.

gives better push load distribution in order to reach target displacement giving

good number of steps as compared to uniform push patterns.

� Results of Non linear static pushover analysis are compared with acceptance

criteria prescribed in FEMA-273 and ATC-40 document in order to meet the

serviceability criteria of structure. However capacity spectrum method employing

NSP gives freedom to the user to harness Non-linearity of structural material and

geometry in terms of custom ductility ratio meeting collapse prevention levels at

the most.

REFERENCES

Research Papers

1) Applied Technology council (ATC). (1996) “Seismic Evaluation and Retrofit of

Concrete Buildings”: Vol. 1, ATC-40, Redwood city calif.

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Buildings, FEMA 356 Report, prepared by the American Society of Civil

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Seismic Safety Council, published by the Federal Emergency Management

Agency, Washington, D.C.

5) ATC, 1997b, NEHRP Commentary on the Guidelines for the Seismic

Rehabilitation of Buildings, FEMA 274 Report, prepared by the Applied

Technology Council, for the Building Seismic Safety Council, published by the

Federal Emergency Management Agency, Washington, D.C.

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Design Standards and Manuals

1. IS 456 -2000 and IS 1893 -2002 (Part – I)

2. IS 2911 Part – 4 Load Test on Pile

3. IRC: 6 -2000 Part-II Standard Specification and Code Practice for road

bridges.

Text Books

1. Bridge engineering, Wai-Fan Chen, Lian Duan, CRC Press.

2. Seismic design and retrofit of bridges, M. J. Preistly, F. Seibal, G. M. Calvi,

John willey and Sons.

3. Seismic Design Aids for Nonlinear Pushover Analysis of Reinforced Concrete

and steel bridges, Jeffrey Ger, Fronklin Y. Cheng, CRC Press.

4. Foundation Analysis and Design, Joseph E. Bowels P.E, S.E

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