ELASTO-PLASTIC RESPONSE OF STEEL BRIDGE PIER BASE JOINT UNDER SEISMIC LOADING.pdf

Prof. Masahiro SAKANO, peg03032@nifty.com

Kansai University, Osaka, Japan

Yuji NISHIGAKI, one_life0617yuji@yahoo.co.jp

Graduate School of Engineering, Kansai University, Osaka, Japan

Yorkio KAWAKAMI, yoriko-kawakami@hanshin-exp.co.jp

Hanshin Expressway Corporation

ELASTO-PLASTIC RESPONSE OF STEEL BRIDGE PIER BASE JOINT

UNDER SEISMIC LOADING

SPR Ęś YSTO-PLASTYCZNA ODPOWIED Ź POŁ Ą CZENIA PODSTAWY KONSTRUKCJI NO Ś NEJ

MOSTU STALOWEGO NA OBCI Ąś ENIE SEJSMICZNE

Abstract In this study, the elasto-plastic response of a whole structure, including both superstructures and

substructures, was estimated by means of dynamic elasto-plastic finite element analysis, and the elasto-plastic

strain history at the top end of triangular ribs was estimated by means of static elasto-plastic finite element

analysis using the results obtained by dynamic elasto-plastic finite element analysis. As a result, displacement

response of the steel bridge pier can be estimated by means of dynamic elasto-plastic finite element analysis. The

maximum displacement response

Streszczenie W pracy analizowano spręŜysto-plastyczne zachowanie się całej konstrukcji obejmującej przęsła

oraz konstrukcję wsporczą za pomocą dynamicznej analizy metodą spręŜysto-plastycznych elementów

skończonych. Przebieg zmienności odkształceń spręŜysto-plastycznych na górnym wierzchołku trójkątnego

Ŝebra szacowano za pomocą analizy statycznej z wykorzystaniem spręŜysto-plastycznych elementów

skończonych wykorzystując wyniki otrzymane z analizy dynamicznej metodą spręŜysto-plastycznych

elementów skończonych. W efekcie przemieszczenia stalowej konstrukcji wsporczej mostu mogły być

oszacowane na podstawie analizy dynamicznej za pomocą spręŜysto-plastycznych elementów skończonych. W

przypadku współczynnika tłumienia 0,03 maksymalne przemieszczenie δmax wierzchołka filara wynosiło 207

mm, natomiast przemieszczenie minimalne δ min było –291 mm. Wykorzystując statyczną analizę spręŜysto-

plastyczną metodą elementów skończonych wykazano, iŜ maksymalny zakres zmienności odkształceń ∆ع ymax

górnego wierzchołka trójkątnych Ŝeber moŜe przekroczyć 20%.

1. Introduction

In the 1995 Hyogoken-Nanbu Earthquake, a rigid steel frame bridge pier was fractured at

its base joint, as shown in Fig. 1. Cracks were developed at the top of triangular ribs between

column and base plate, and connected one another. Eventually, more than a half section of the

column failed 1) . These cracks are presumed to have been initiated at the fillet weld toe on the

column side near the top end of the triangular ribs, and propagated from the northwest corner

to the northeast and southwest corners connecting each other. There is a possibility that

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min is -291mm at the

top of column in the case of a 0.03 damping coefficient. By means of static elasto-plastic finite element analysis,

it was shown that there was a possibility that the maximum strain range (De ymax ) can exceed 20% at the top end

of triangular ribs.

max is 207mm and the minimum displacement response

extremely low cycle fatigue cracks could be developed by excessive cyclic loading during the

earthquake. In this study, the elasto-plastic response of the whole structure, including both

superstructures and substructures, was estimated by means of dynamic elasto-plastic finite

element analysis, and the elasto-plastic strain history at the top end of triangular ribs was

estimated by means of static elasto-plastic finite element analysis using the results obtained

through dynamic elasto-plastic finite element analysis.

Fig. 1. Cracks connecting the top ends of triangular ribs

2. Elasto-Plastic Response of a Whole Steel Pier

2.1 Analytical Method

Fig. 2 shows the analyzed steel bridge pier and superstructures. Fig. 3 shows its analytical

model. Dynamic elasto-plastic finite element analysis was conducted using a three-

dimensional beam element. The large-mass method was applied in order to shake the ground

directly using the seismic acceleration record (N-S direction) measured at the Osaka Gas

Fukiai Plant during the Hyogoken-Nanbu Earthquake (see Fig. 4). The beam element was

supposed to be a uniform box section, neglecting longitudinal and transverse stiffeners and

filled concrete. Material properties were supposed as follows;

Young’s modulus: 200GPa

Poisson’s ratio: 0.3

Unit mass of steel: 7850kg/m 3

Yield stress: 235MPa

The damping coefficient: 0.03 and 0.05

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North Side

South Side

Section 1

Section 2

Section 3

Section 4

1561

1500

1450

Section 1

（ SM570 ）

Section 2

（ SS400 ）

Section 5

1500

Section 6

1450

Section 3

（ SM490B ）

Section 4

（ SS400 ）

3 4

1450

G.L.

2300

15126

2000

1000

19126

Section 5

（ SM490B ）

Section 6

（ SM400A)

〔 Unit of length ： mm 〕

Fig. 2. Analyzed steel bridge pier and superstructures

500

-500

Time (s)

Fig. 3. Analytical model of the steel pier and superstructures

North Side

South Side

1000

14126

100 0

15 0 0

Filled with Concrete

G.L.

Fractured

Base Joint

Fig. 4. Seismic acceleration record of N-S direction at the Osaka Gas Fukiai Plant

Front View

Side View

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2.2 Analytical Results

Fig. 5 shows displacement response at the top of the north column. The horizontal axis

represents time t (s), and vertical axis represents relative displacement of the north column top

to its bottom. Solid and broken lines show the displacement response in cases of damping

coefficients 0.03 and 0.05, respectively. The maximum displacement response

max is 207mm

and the minimum displacement response

min is -291mm in the case of a 0.03 damping

coefficient, while

d max is 155mm and

d min is -233mm in the case of a 0.05 damping

coefficient.

300

200

100

-100

Damping

Coefficient

-200

0.03

0.05

-300

Time t (s)

Fig. 5. Displacement response at the top of the north column

3. Elasto-plastic Strain History of Steel Pier Base Joint with Triangular Ribs

3.1 Analytical Method

Fig. 6 shows an analytical model for the static analysis. Static elasto-plastic finite element

analysis was conducted using three-dimensional shell elements for the north column where

cracks were detected, and three-dimensional beam elements for the other beam and column

members. Fig. 7 shows the cyclic stress-strain curve 2) used in the static analysis. The base

plate at the bottom end of the column was completely restrained. The displacement obtained

in the dynamic elasto-plastic analysis was applied to the top of the column, and then elasto-

plastic strain history at the top end of the triangular ribs was estimated.

800

600

400

200

Fig. 6. Analytical model for static elasto-plastic finite element

Strain (%)

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-8.7×10 -2

-12.5×10 -2

-1.1×10 -2

-4.9×10 -2

6.5×10 -2

2.7×10 -2

14.1×10 -2

10.3×10 -2

21.6×10 -2

17.8×10 -2

Fig. 7. Cyclic Stress-Strain curve used in the static elasto-plastic analysis

Beam Element

Shell Element Model

Fig. 8. Longitudinal strain distribution near the top end of the triangular ribs

-10

-20

Fig. 9. Strain history at the top of the northwest triangular rib

Time (s)

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