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FUNDERMENTAL EXAMINATION ONHYSTERESIS MODEL OF STEEL MEMBERSBY EXPERIMENTAL RESULT OF SHAKINGTABLE TEST

Satoshi Yamada, Shoichi Kishikiand Yu Jiao

TokyoInstitute of Technology

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Introduction! Shaking table test is the most effective

method to examine the earthquake resistant

performance of structural systemundersevere earthquake.

! Experimental results are also effective toexamine the hysteresis models used in

response analysis.

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Introduction! With the development of computer and

numerical analysis methods, response

prediction of steel structures based on timehistory analysis is gaining more and morepopularity. Different hysteresis models ofstory, member and material are being used.

It has become an important topic that howhysteresis models influence the results ofresponse analysisin evaluating earthquake-resistance performances of steel frames.

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Introduction! At first, experimental method of full scale real time

shaking table test of partial steel frame is brieflyintroduced. Using this system, structuralperformances of steel structures, i.e. plasticdeformation capacity of beam-to-column connectiondetermined by brittle fracture, was investigated.

! One feature of this experimental method is its simpleset-up as to be considered a SDOF system.

! So experimental results can be easily used toexamine the hysteresis models used in responseanalysis.

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Introduction! Next, fundamental examination of hysteresis

model of steel members used in response

analysis is discussed. SDOF systems with bi-linear models as well as multi-linear elasto-plastic models considering Bauschinger effectwere considered in the response analysis.

Models with their parameters that matchedthe experimental results wellwere examined.

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Shaking Table

Test

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Shaking Table Test

Movie

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Shaking Table Test

Example of Experimental Results

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Response Analysis

Data for examination

! One of the experimentalresults is used as thereference to comparewith analytic responses.

! Specimen is full-scalepartial frame with wide

frange section beam ofRH-600x300x12x25andRHS section column ofBBox-500x500x22.

H-600!300!12!25

-500!500!22

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Response AnalysisData for examination

! NS component of JMAKobe Record which was

scaled to a peak velocityof 1.0 m/s, was used inthe excitation.

! Steel beam of thespecimen was plastifiedbut not rupturedunderthe first excitation, andthe column remainedelastic

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Response Analysis

Spring-mass Vibration Model

1

2 34

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Response Analysis

ParameterParameters of the hysteresis model were:

1) Types of hysteresis model (2 types)

Bi-linear(including elastic-perfectly plastic) modelsand Multi-linearelasto-plastic models consideringBauschinger effect; (Akiyama and Takahashi 1990)

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Response Analysis

Parameter

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Response Analysis

Parameter2) Yield point (5 levels)

Nominal yielding strength of SM490A (According tothe Japanese Code, F=325 N/mm2), 1.1 F, 1.2 F, 1.3F, and the result of tensile strength test (369 N/mm2)(1.135 F)

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Response Analysis

Parameter3) Second stiffness (6 levels)

Second stiffness ratio (k2/ke): 0, 1%, 2%, 3%, 4%,

5%

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Response Analysis

Estimation! Estimation of the analytic response compared with

the experimental data was based on the summed

squared errors of load (eQ) and displacement (e!) atfree beam-end according to the time history

response.eQ="(Qa,i-Qe,i)

2 (1)

e

!="(!a,i

-!e,i

)2 (2)

Qe,iis the experimental load, Qa,iis the analytic load,!#,$is the experimental free beam-end displacement,

!a,iis the analytic free beam-end displacement

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Error Indicators of Bi-linear hysteresis

modelsk2/ke=0.0 k2/ke=0.01k2/ke=0.02k2/ke=0.03k2/ke=0.04k2/ke=0.05

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Comparison of the Load-Deformation

Relationships

1.1F, K2/Ke=0.02

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Error Indicators of Multi-linear elasto-plastic

models considering Bauschinger effectk2/ke=0.0 k2/ke=0.01k2/ke=0.02k2/ke=0.03k2/ke=0.04k2/ke=0.05

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Comparison of the Load-Deformation

Relationships

1.2F, K2/Ke=0.02

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Comparison of the Load-Deformation

Relationships

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CONCLUSION! Analytic responses of a series of Bi-linear and Multi-linear

hysteresis models were compared to the result of a full-scaleshaking table test, and models with their analytic responsesclose to the experimental result were pointed out.

! Analytic responses of Bi-linear models with yielding point slightlylower than their tensile test strength and the second stiffnessratio set to 2%~3% had better correspondence with theexperimental result.

! In case of multi-linear models considering Bauschinger effect,when using Bi-linear skeleton curve, analytic responses of

models with yielding point slightly higher than their tensile teststrength and the second stiffness ratio set to 2%~3% wereclose to the experimental result.

! Furthermore, the difference between analytic responses andexperimental result were smaller when Bauschinger effect wastaken into account in hysteresis models.