九州大学学術情報リポジトリ

(1)

九州大学学術情報リポジトリ

Kyushu University Institutional Repository

繰返し載荷を受けるコンクリート充填鋼管部材に対する各種解析モデルの解析精度の比較

白, 涌滔

九州大学大学院人間環境学府空間システム専攻博士後期課程

小俵, 慶太

九州大学大学院人間環境学府空間システム専攻修士課程

河野, 昭彦

九州大学大学院人間環境学研究院都市・建築学部門

松尾, 真太朗

九州大学大学院人間環境学研究院都市・建築学部門

https://doi.org/10.15017/26751

出版情報：都市・建築学研究. 20, pp.101-109, 2011-07-15. 九州大学大学院人間環境学研究院都市・建築学部門

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権利関係：

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都市・建築学研究九州大学大学院人間環境学研究院紀要第20号， 2011年7月 J. of Architecture and Urban Design

，

Kyushu University

，

No.20

，

pp.101 ~ 109

，

July. 2011

繰返し載荷を受けるコンクリート充填鋼管部材に対する各種解析モデルの解析精度の比較

A n a l y t i c a l Comparison o f V a r i o u s Models f o r C o n c r e t e ‑ F i l l e d S t e e l Tubular Columns S u b j e c t e d t o C y c l i c L o a d i n g

白涌 i e *

^，

小俵慶太一河野昭彦料牢，松尾真太朗***

Yongtao BAI* ， K e i t a ODAWARA 料， A k i h i k o KA W ANO 料申 andS h i n t a r o M A TSUO * * *

The hysteresis behaviors of circular and square concrete filled steel tubular were analysed and compared with test results. Local buckling and stiffness degradation are considered for steel model， various simplified analytical models of confined concrete are adopted to veri今theaccuracy of simulations. Comparison results indicate that steel model adopted in analysis program can accurately perform the local buckling and degradation of steel tube. A抗er comparing different types of confined concrete model， the strength degradation of concrete in circular steel tube could be ignored because ofhigh‑level confinement effect， while the strength degradation of the concrete in square steel tube should be considered contrarily. Furthermore， the simplified model based on Sakino & Sun's proposal has the best accuracy on predicting the post‑peak degradation behavior of square concrete fiUed steel tubes.

Keywords: concrete filled steel tubes， beam columns， cyclic loading， constitutive mαterial model， fiber modelαnαlysis コンクリート充填鋼管、柱一梁部材、繰り返し載荷、材料要素モデ、/レ、ファイパモデ、/レ解析

1. INTRODUCTION

Concrete filled steel tube structures have been widely applied in practical civil engineering projects like high‑rise buildings， bridges and industrial structures. This structural style has excellent strength and ductility performances to resist intensive earthquake motions. Meanwile， finite element method has been verfied to be an efficient way to simulate structural performances. Therefore， establishing an accurate constitutive model of materials wil1 be essential to guarantee the accuracy of analysis results. Nevertheless， the entire material behavior of concrete fiUed steel tube structures covering the deterioration after peak caused by local failures such as local buckling or concrete crush hasn't been accurately studied yet.

Various constitutive models of concrete have been proposed to accurately define the pre‑peak and post‑peak behaviors of concrete filled stee1 tube struc加res¹)‑6).

Popovics (1973) primarily proposed the constitutive model

*

空間システム専攻博士後期課程

* *

空間システム専攻修士課程

キ都市・建築学部門

of confined concrete， which wぉmodifiedby Mander et al. 1)， 2). (1988). Sakino & Sun³，4) proposed the empirical formula for computing the constitutive relationship of confined concrete respectively in various sectional steel tubes (2004)，

and homogenous model has been proposed by Usami et al.^S)， 6) (1998). Experimental researches were also conducted on cyclic behavior of concrete filled steel tube beam‑

01umns7)‑1l)

The aim of this study is to veri命accuracyof material models to predict the global behavior of concrete filled steel tubes by adopting fiber model analysis method. Therefore， cyclic behavior of circular and square sectional CFT specimens are compared between test results and analytical results based on the circular CFT tests conducted by A. Elremaily et a1.⁷) and Y. Xiao et a1.⁸¥ and square CFT tests conducted by A. Varma et al. 9)， JめandE. Inai et a.l^l^l).

2. CONSTITUTIVE MODEL OF MATERIALS 2.1 Steel tube

In order to simulate the local buckling and stiffness degradation of steel tube， Ohi & Akiyama's stress‑strain

(3)

model as shown in Fig. 1 is adopted for both circular and square sectional steel tubes.

Where， Es is Young's modulus of steel;σy is the yield stress of steel materials; R_i_n_iis the R' for the first M&P (Mengotto & Pinぬ)12)curve of the skeleton curve which value has been confirmed as 10.0;σ~ is the ultimate stress of steel materials; Ru is the R' for the second M&P curve of the skeleton curve;ヂisfactor to move the skeleton curve;ε1b is strain at local buckling;τib is the rate of buckling negative slope to Young's modulus; rspm is rate of the post‑buckling strength to the buckling strength;τ1b2 is rate ofthe post‑buckling negative slope to Young's modulus.

σ^』

ε

tensl0n

Fig.l Ohi & Akiyama's stress^幽strainmodel of steel tube 2.2 Confined concrete in Circular CFT

From previous study on circular CFT structures， it is clear that confinement effect of concrete in circular steel tube improves both strength and ducti1ity. Therefore， in order to study behavior before and after buckling happened respectively， the stress‑:‑strain model is divided into two parts which respectively is pre‑peak and pos~-peak， and typical simplified model of plain concrete and

∞

nfined concrete in circular tube are shown in Fig. 2.

crmや1・es事lVesn主主111

Fig. 2 Simplified stress‑strain relationship of tbe concrete in circular steel tube

2.2.1 Pre‑peak behavior

The Popovics's model1)， 2) is adopted as the stress‑strain model of pre‑peak part (0三民主fcc， O:=:;εc三εcc)，the formulas

of constitutive model is shown in Eq.(l)， (2). Young's modulus of confined concrete are calculated based on reference 13)ωshown in Eq.(3).

rI &" /ε￨

σc ん^X .L~ ~~ìr (1) r‑1+1 &c/&"∞￨

EC

Ec

‑ ( f c c

ε∞/) (2) Ec = (3.3

点

+6.90).1

削

Pa) (3) Besides， Sakino & Sun's proposa1³，4) is adopted to define the strength ofthe confined concrete as shown in Eq.(4)， and strain co汀espondingto confined strength as shown in Eq.(5)， (6).

σv ，D

ん

= f c

(1+1

釘 × 才

^(7‑Z)^「^{) ( 4 )}

.

1'" i 1 仙， r 1+4.7(K ‑1) 1 K豆1.5

&̲̲ =O.94r _lIl't )xl0-~x~ / .¥

山田 13.4+ 20(K ‑1) I K> 1.5 (5)

K=

日 αu

守 4 ‑ 2 )

^ー^l ⁽⁶⁾

Where， Ec is Young's modulus of confined concrete; D and t are diameter and thickness of steel tube， respectively; σ'c and εc are stress and strain value of confined concrete in pre‑peak period， respectively;f'cc and Gcc are peak stress and corresponding strain， respectively; Ec is Young's modulus; σy is yield s廿ess of steel tube; k is confinement coefficient=4.1 (Rich^紅tet al.)14);α~ is normaIized hoop stress in circular steel tube at ultimate load=‑O.19¹⁵).

2.2.2 Post‑peal五behavior

Researchers³)‑6) proposed various empirical equations on the post‑peak behavior of confined concrete in circular CFT.

While， given the circular steel tubular provide considerable confinement effect on core concrete， the stiffness degradation after peak are ignored in analysis program which is expressed as horizontal line a武erpeak.

2.3 Square CFT

The confinement effect of concrete in rectangular CFT is quite different企omcircular CFT， the stress‑strain model is shown in Fig. 3. Rectangular steel tube rarely improves the strength of confined concrete， whi1e it obviously improves the degradation stiffness of confined concrete compared with plain concrete.

2.3.1 Pre‑peak behavior

The pre‑peak behavior of the confined concrete in square CFT is similar to circular CFT as shown. in equation (1)・(3) which is proposed by Popovics1，勾.The confined strength of concrete and strain corresponding to confined strength are calculated as Eq. (7)・(9).

‑102‑

(4)

the model of Usami . et a1.⁵， 6) is also adopted in analysis program to veri今 the accuracy of simplified model mentioned above which is shown in Table 1. Where， v is poisson ratio of steel which is equal to 0.3.

(7) ん=九

f c

Y

C

= 1.67 x D'(‑O.112) (8) (9) ε;c=0.944(1/4)×104

Where D' is the diameter ofthe circularity which has the

same area with the square section. 3. COMPARISON BETWEEN TEST & ANALYSIS Due to strong confinement effect of core concrete from circular steel tube， degradation stiffness a武erpeak is ignored in analysis model. Concrete and steel tube models are established as in 2.1， 2.2. Test matrix of specimens and comparison of moment capacity are shown in Table 2， 3. Loading procedure for test and fiber model analysis 16) is cyc1ic horizontal loading with constant axial loading as shown in Fig.4. Analytical results and tests results⁷)， 8) of hysteresis behavior are compared and shown in Fig.5‑7.

J

_._._._._._{田園孟圃 ?}V

D(B)i

!

L;7今y

3.1 Circular CFT beam columns 2.3.2 Post‑peak behavior

As shown in Fig. 3， the post‑peak model is simplified into linear relationship， the degradation modulus τEc of the post‑ peak period could be computed by two points ofぴい，εい) and (αj'cc，ε'cu) as in Eq. (10). Therefore， the coefficients of αand ε， cu are required to be defined.

rEc=

人 ‑U

^∞

Gcu ^{‑ G}cc

The simplified post‑peak model is calculated based on Sakino & Sun proposae，4) as shown in Table 1. Meanwhile，

(10)

. 凶

wp﹄

't

c

o l・

γ ‑

T・

9 n i u

pLW

︑ 実

ぽ

α e

川武

J U 4

附吋

4t

凶h h U

竹叫

.凶押M d H

山な

n f L

ぼ川

崎

L O o h m

心

/ ︐4 n m w /

︐ 〆

/ o m

〆

ヨゴ刻一

Jプ誌は

︐ 一一一一一一一一一一

vu

一 ⁝ 一 ⁝ 一

⁝ ⁝ ⁝ 一一

一

a M

U

‑

‑ 1

4・

:R1ea r p L s p u

IiP3

Dlj 1..¥之ジ

Fiher divisi:on 0' 1

cit・cular古eclion Fiher m.odel ana.lysis v

k f

機穀物協

Fig. 4 Loading procedure of test and fiber model analysis Fig. 3 Simplified stress‑strain relationship of the

concrete in square section steel tube

Table 1 Parameters for the post‑peak behavior of concrete in square CFT No Simplified model based on

degradation Sakino & Sun's proposall6) Model ofUsami et a1.4_，₅₎

斗 J 手長 = 0 4

rEc

ー

一

ム二三ム

ε叫ーε民

α=1‑土

W

、・ 1̲̲ ，B ."B 電

W =1. 50-17.1xl0-^Jん+2.39， 12λ(一一 1)(~-2rj

耐引ノ T "T

。

Parameters

τEc

α= 1‑':Ecx(ε叫‑ecu) fc α=1‑土

W

笥﹄

﹃fnU

2 0

ヲ

かく

σ

0.fA

一

f

吋 ︒

︿一ト

﹀一

五一

f

川 ︐

U.44

R位R

nu nu

︑₁

15 11 11 1F El la ti

‑‑ J

r o

‑ ‑ A

l n u

+

. 4 4

R

E d

且T O O

U P 2 1 弘一 2 似

A ‑ M

R

FE ES SE El EL n u

r︑MA﹃1A fili‑‑dIlli‑‑L

‑ ‑

叫

向 ︒

G"cu=0.015 N/A

α

G"cu

(5)

Table 2 Matrix of the circular sectional CFT specimens Specimens Geome仕icaIproperties

Material properties Axialload References

NO. level

D/t t (即時 D L(即時 !c (MPa) /y(悶a) P/Po CFT‑l 51 6.4 326.4 100 0.33 A. Elremaily & CFT・5 51 6.4 326.4 40 0.4 CFT・6 51 6.4 326.4 70 0.32 A. Azizinamini[7]

CFT・2 34 9.5 323 914

104 372

0.2 CFT‑3 34 9.5 323 104 0.4 CFT‑4 34 9.5 323 40 0.42 Yan Xiao et aI.(8) CI‑CFT3 112 3 336 1500 39.1 303 0.47 1500 1500 1500 CFT‑6

1000 1000 1000

~画、500 _込Z 500 ~ 500

一ー

帽。^ロ

。

一可。回ヨ ‑8 ロ

百EEsm a

‑1000ト，‑1 . ^巴^a

￨一‑喧ー‑Tωests

‑1500

.

‑ ‑ 1 5 0 0

‑80 ‑60 ‑40・20

。

₂₀ ₄₀ ₆₀ ₈₀ ‑80 ‑60 ‑40 ‑20

。

20 40 60 80 ‑80 ‑60 ‑40 ^・20 0 20 40 60 80 Deflection (mm) Deflection (mm) Deflection (mm)

(a) CFT・1び'c=100MPa) (b) CFT・5σ'c=40恥1Pa) (c) CFT・6(f'c=70MPa) Fig. 5 Specimens with the width‑thickness ratio of 51

CFT‑4

CI‑CFf3

Table 3 Moment capacity comparison

、(

zAg・" 〆m

Moment capacity

Nameof MeλP speclmens Test LRFD AnaIysis

瓜4釦a :ロag言Db

。

(kN.m) (凶.m) (kN.m)

CFT‑l 542.4 283.7 518.2 1.05 ^T^国^回³ CFT‑5 450.9 170.5 461.1 0.98

巳E」

。泊 ‑

CFT‑6 511.9 254.6 540.9 0.95

CFT‑2 617.0 455.3 653.4 0.94 .400

CFT‑3 663.3 281.7 634.8 1.04 .10 5.

DriaR

。

atiof%) 10 CFT・4 544.7 205.1 626.9 0.87

Fig. 7 Comparison of moment versus dri抗・ratio between tests envelop and analysis hysteresis

‑104一

(6)

Table 4 Test matri^玄withspecimens

Specimen

ι

^f^'^c ^N_Bô_/_t^m_rⁱ_aⁿ_tâ_i_o^l ^Thⁱ^c^kⁿê^s^s ^Tê^s^t ^P^/^P

。

(mm) length (m) CBC‑32‑80‑1O 600 110 32 8.9 1.5 0.1 CBC・32・80・20 600 110 32 8.9 1.5 0.2 CBC‑48‑80‑1

。

⁶⁶⁰ 110 48 6.1 1.5 0.11 CBC‑48‑80‑20 660 110 48 6.1 1.5 0.22 SR4・A・4・C 295 35.5‑42.4 35 6.0 1.26 0.4 SR4‑A‑9‑C 295 84.5‑94.5 35 6.0 1.26 0.4 SR4‑C^聞4‑C 276 35.5‑42.4 47 4.5 1.26 0.4 SR4‑C‑9‑C 276 84.5‑94.5 47 4.5 1.26 0.4 Fig. 5‑6 shows the comparison of analyticaI and test

horizontaI 10ad‑def1ection curves with different diameter‑ thickness ratio and concrete strength. It is observed that predicted curves mainly have good agreement with test results by using degradation model of steel and no・

degradation model of confined concrete. Besides， moment capacity of specimens⁷) are calculated and compared with test and LRFD code results as shown in Table 3.

As shown in Fig. 7， analytical result of CトCFT3has accurate prediction with test results by adopting material model as mentioned in 2.1， 2.2.

3.2 Square CFT

Square CFT beam‑colutnns are analysed and comp訂ed with cyclic horizontal loading (constant axial loading) tests

conducted by Varma， Ricles et a1.⁹)， 10) and E. Inai et al.^l¹).

Different material models of steel (no degradation in Fig. 8(a); Ohi &Akiyama's model with local buckling and degradation in Fig. 8 (b・d)，Fig. 9・11); concrete (no degradation in Fig. 8‑11 (b); model based on Sakino &

Sun's proposal in Fig. 8(d)， 9・l1(a);model based on the proposal of U sami et al. in Fig. 8(

，の

9・11(

の )

are adopted in analysis program to veri今thesimulation accuracy of each model.

Test matrix of specimens is shown in Table 4， and comparison results of horizontal loading versus displacement hysteresis curves are respectively shown in Fig. 8~12.

Authors

Vanna， R.icles et a.1⁹， 10)

E. Inai et a.1¹¹¹

800

400

5

^2ω

︒

∞

4∞

4

唱縄問︾ご

gz︒

N = ︒

出

‑6∞

‑800

‑12 ‑8 ‑4 0 D/Dy

(吟Nopost‑peak degradation of steel

CBC・32・80・20(Us畑 ietal)

400 5200

宮 o

z

‑4∞

‑6∞

‑800

・12 ‑8 ‑4 0 4

01 Dy (Dy=14.6mm)

(c) Model ofUsarni at al.

12

400

玄色

。

‑司君

‑400

‑6∞

‑800

旬E

‑12 12

800

‑4 0 4

D IDy (Dy=14.6mm)

(b) No post‑peak degradation of concrete

CBC・32‑80‑20(Sakino)

400

!

²⁰⁰

~ ^‑²⁰⁰

出

‑400

‑600

12 ‑12 ‑8 ‑4 0 D/Dy (Dy=14.6mm)

(d) S北白0&Sun's model

12

Fig. 8 Comparison of the horizontalload‑displacement responses the CBC・32・80‑20

(7)

800 600 400 400

~;.;f，'句s，，勾q・，a

^A'3

r

^・ ^ー^a^j^E^?^，^l^l^{i 4 e}^，^.^r

^~~∞

るZ{

200

t t . t / l l i

^・眠。 _f_.^，¹

'

，，

‑‑euoe

;~' l //flll ^~;'l^，^/^'^. o

'司

'

"

‑

。 o

~ e ^‑²^日^日

‑600

z ^o

12

~:.I ./.. _L.I_il1~

4∞

ー12

‑600ト -.-1.て二，~..f/. .li

lラ

‑8 4

内U n u n U 0 0 2 4

( Zu u

‑ ud w

︒ 二 56

︒N =

︒ 国

‑400

12

400 宮古己200

"0

帽。

‑ 0

'

"

z

g

♀00 国0

‑400

‑600

‑800 '‑‑‑‑'‑‑‑'‑‑‑‑‑'・・ ^E ・800I ' 1 ‑800

・12 ‑8 ‑4 0 4 8 12 ・12 ‑8 ‑4 0 4 8 12 ‑10 ‑S 0 5 10

D/Dy D/Dy D/Dy

(吋Sakino'smodel (b) No post‑pe^北degradation (c) Model ofUsami at aI. Fig. 11 Comparison ofthe horizontalload‑displacement responses CBC‑48‑80^・20

As shown in Fig. 8 (a)， it is observed that ignoring the According to由ecomp訂ison results in Fig. 8‑10， material degradation of steel mainly lead ωoverestimation concrete models based on Sakino & Sun's proposal and of hysteresis area and gradient in post‑peak region. As proposal of Usami et al. have nearly ωcurate predictions， shown in Fig. 8・11(b) Ignoring of the concrete material while when the width‑thickness ratio becomes larger and degradation will only reduce the gradient in post‑peak axial load level keeps high， the former model has more region， which results in the overestimate ofmember's after accurate results as shown in Fig. 10. Specimens¹¹⁾are only peak behavior. Therefore， post‑peak degradations of steel analysed by using simplified model based on Sakino &

and concrete as shown in Fig. 1・3are essential to be Sun's proposal and Ohi &Akiyama's model of steel with considered， and concrete model based on the proposals of local buckling and degradation as shown in Fig. 12. Sakino and Sun's proposal and model ofUsami et al. have In Fig. 12ラ the analytical results have acceptable better agreement with te坑results. underestimate compared with test curves， and analytical

ハU

(8)

‑3ω

・0.04 ・0.02 0 0.02 0.04 0.06 ‑0.06 ・0.04 ・0.02 0 0.02

e e

(c) SR4C4C (d)SR4C9C Fig. 12 Hysteresis comparison of test and analytical results

CBC・32‑80・20 CBC‑32・&0‑20

results can accurately simulate the stiffness of p^{印刷}peak and post‑peak periods. Besides， the moment capaci句of prediction values and test values are SR4A4C (Mua=166.83kNm， M

ー

=187kNm);SR4A9C (Mua=213kNm， M_u_e=225kNm); SR4C4C (Mua=128kNm， _Mu_e=151kNm);

SR4C9C (Mua=172kNm， _Mu_e=202kNm); respectively. The corresponding ratio between test and analytical results (MueIMua) are 1.12， 1.06， 1.18， 1.17. It indicates that analysis program in this comparison is creditable and stable to simulate square CFT structures.

3.3 Degradation modulus (τEc)

Post‑peak degradation of represents the behavior after CFT structures happening local buckling， which also express the ductility performance after structure achieving

200

100

:z E 0

.話、..‑

~

‑100

ー200

‑3∞

‑0.06 ‑0.04 ・0.02

。

0 0.02 0.04 0.06

(a) SR4A4C

300

200

100

~ 至。

~

‑200

‑300

‑0.06

800

0 ふ陪

・

⁝:

・: 下山口

白

︑ リ均

一町

︑⁝

h

j

由

﹄一同

也 ︑

山﹁吋立ブ・

同v .

L1 11

﹄1Eト

sl i‑

‑L '1 1 0 0 0 0 0 0 0 0 0 0 AZ ua

匂)

200ト1・;)...1'1'."， (~f~\H.:n:~k (k'Rri!d~詰lcn

D‑U路!nl

モr.s~~?(m!.! !>‑:. SH!.i l∞ トlー三，‑Test

strength. The values of degradation gradient are derived from the peak‑point of local‑buckling happened and peak point of ending circle企omhysteresis curves in Fig. 8・10 (Ohi &Akiyamaラsmodel of steel with local buckling &

degradation; various degradation models of concrete)， and connecting them together to form descending curve after peak as presented in Fig. 13‑15.

From Fig. 13・15，it is observed that ignoring degradation of concrete always overestimate the post‑peak behavior of square CFT members. The other two Models with considering the degradation of concrete exhibit homogenous results and are relatively accurate to simulate post‑peak behavior of square CFT.

300

200

100

( E

至。、

̲

， 2

‑¥00

‑200

‑300

‑0.06 ‑0.04 ‑0.02 0 0.02 0.04 0.06

8

(b) SR4A9C

300

200

100

至。E

~

‑100

‑200

0.04 0.06

ー100 1‑

吋>-Ncωr.:(~J"!'，:}teω:gr!ldat!<:f{

D‑Usami

か ~:rlkiJぬよ:らW.ì

‑也ーTest

‑200

‑300

(

豆} 4∞ : :t:

‑500

‑600

‑700

‑800

4 ~ ~ ~ 4 ~ 4 ~

D/ I>y ^D/I>y

(a) Positive direction (b) Negative direction Fig. 13 Comparison of the descending slope of CBC・32・80‑20

(9)

CBC・.J2・80‑10 ーーγーーー一ー「一

1 田昌 T号事ー訟苫ヂえと巴~":.~...~-~二一 .

、

^{山匂}

一句E

一回

ー

̲ . . . .

^Vー

一司旬』ー ‑ ̲ ・7 、・・ー，

ι… ー ..;.... ，..~胃、ι_h旬、 ‑ ，・・』ー匂・::-..~.-...;.ー町戸崎白

・、

‑800 I

5 6 7 8 ‑8 ‑7 ‑6 ‑5 ‑4

DIDy DI均

(a) Positive direction (b) Negative direction Fig. 14 Comparison of the descending slope of CBC‑32・80・10

CBC‑48‑80・10 80

。

700 600 500

歪{ _}刊。

~ 300 200 100

。

800 700 600 500

~ ⁴⁰⁰

}

= ロ

300

ロ喧:t=::"山』山町切目白山〕叩回目--_..~・山町四回目や 4 匂住之一日

‑̲・hこニミ'‑・円削" 主_{一ー‑‑̲二.}.....i.. . .

崎町品，、

ヤ‑‑‑‑̲ご輪....~.。

一』句....白

‑8∞

5 6 7 8 9 ‑9 ・8 ‑7 ‑6 ‑5

DI均 DI均F

(a) Positive direction (b) Negative direction Fig. 15 Comparison oftbe descending slope of CBC‑48‑80‑10

fc=100，.IY=600

z∞

100

。

BIt=32，fc=100

‑1000

. . _E

捌 .; ..3ωo 宮E

a ‑4000

~ E・50ω

Q.)

Q

同6000

‑7∞0 100 200

‑10

。

CBC‑32・80・10

̲̲，一一_「ー一‑一‑r‑

..G..)‑' N{~ co誌はt:t(，.，:d<場開，i;草間日 fトUsami

。

・ S:.ki町、品::iJ.問

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(a) Considering/y ₍_b₎_C_o_n_s_i_d_e_r_i_n_g_B_/_t (c) Consideringf'c Fig. 16 Comparison ofthe post‑peak gradients ofthe confined concrete in square CFT

Thus， the post‑peak gradient of出esetwo modelsω0.74・0万(ろ: 200・600)). Besides， considering the shown in Table 1 are calculated and compared based on comparisons between analysis and tests， simplified model

由eparameters of cylinder strength of concrete び'c)，the based on Sakino & Sun's proposal exhibits more accurate yield strength of steel (ろ)and the width‑thickness ratio of predictions on degradation gradient than model based on steel旬bes(B/t). Comparison results are shown in Fig. 16. the proposal of Usami et a ，.lbecause the later one will

As shown in Fig. 16， the

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mp訂isonsindicate白atwhen 'show too conservative resu]ts when parameters change. the concrete s仕ength or width‑thickness ratio become

smaller， the above two models would exhibit better agreement on degradation modulus when the yield strength of steel becomes larger， the degradation modulus of above two models basically kept the same ratio， (ratio of rEc between Sakino & Sun's model and model of Usami at al. chang回 0.52・0.7(B/t: 100‑30); 0.54心.74ぴ"c: 100‑20);

4. CONCLUSIONS

An analytical

∞

mparison of circular and square CFT beain‑colurnns under cyclic loadings (constant axial loadings， cyclic horizontal loadings) between FEM simulation and test is conducted to veriかtheprediction

‑108一

(10)

accuracy of different material models. Conclusions based on analytical investigation can be summarized as follows.

1. The fiber model analysis adopted in this study is accurate and reliable to simulate CFT beam‑columns and other homogenous structures， according to the global performances of analytical results.

2. Based on the comparison results of circular CFT beam‑columns， confined concrete exhibits high level confinement by circular steel tube， the comparison results have good agreement by ignoring the strength degradation of concrete after peak.

3. Since the behavior of confined concrete in square steel tube is improved not as much as circular CFT， the stiffness degradation should not be ignored. Otherwise， the post‑peak behavior will be overestimated according to the prediction results.

4. For the post‑peak model of confined concrete in square CFT， Simplified models based on different proposals have different analytical results. Analytical results by adopting simplified model indicate that Sakino

& Sun's proposal can accurately predict the behavior of confined concrete in square CFT， while the proposal of U sami et al may generate underestimation of the post‑peak behavior of confined concrete in square CFT.

REFERENCES

1) Popovics S: A Numerical Approach to the Complete Stress‑Strain Curves for Concrete. Cement Concrete Researches， Vol. 3， No. 5， pp. 583‑99， 1973.

2) Mander J. B， Priestly J. N and Park R: Theoretical Stress‑Strain Model for Confined Concrete， Journal of Structural Engineering， Vol. 114， No. 8

，

^p^p^.¹⁸⁰⁴^‑

26， 1988.

3) Sakino K. and Sun Y: Stress‑Strain Curve of Concrete Confined by Rectilinear Hoop， Journal of Structural and Construction Engineering， No. 461， pp. 95‑104， 1994.

4) Kenji Sakino， Hiroyuki Nakahara， Shosuke Morino， and Isao Nishiyama: Behavior of Centrally Loaded Concrete‑Fi11ed Steel‑Tube Short Colurnns， Journal of Structural Engineering， Vo. l130， No. 2， pp. 180‑8， 2004.

5) T. Usami， H.B. Ge: Cyclic Behaviour ofThin‑Walled SteeI Structures‑Numerical Analysis， Thin‑walled Structures， No. 32， pp. 41‑80， 1998.

6) K.A.S. Susantha， Hanbin Ge and Tsutomu Usami:

Uniaxial Stress‑Strain Relationship of Concrete

Confined by Various Shaped Steel Tubes， Engineering S仕uctures，No. 23， pp. 1331‑47，2001. 7) Ahmed Elremaily， Atorod Azizinamini: Behavior and

strength of circular concrete‑filled tube columns， Journal of Constructional Steel Research， No. 58， pp.

1567・91ラ2002.

8) Yan Xiao， Wenhui He， Kang‑kyu Choi: Confined Concrete‑Filled Tubular Columns， Joumal of Structural Engineering， Vol. 131， No. 3， pp. 488・197， 2005.

9) A.H. Varma， James M. Ricles， Richard Sause， Le‑Wu Lu: Seismic Behavior and Design of High^働Strength Square Concrete‑Filled Steel Tube Beam Columns， Journal of Structural Engineering， Vol. 130， N o. 2， pp.

169・179，2004.

10) A.H. Varma， James M. Ricles， Richard Sause， Le‑Wu Lu: Seismic Behavior and Modeling of High‑Strength Composite Concrete‑FiIled Steel Tube (CFT) Beam‑

Colurnns， Journal of Constructional Steel Research， No. 58， pp. 725・758，2002.

11) Eiichi Inai， Akiyoshi Mukai， Makoto Kai， Hiroyoshi Tokinoya， Toshiyuki Fukumoto and Koji Mori: Behavior of Concrete‑Filled SteeI Tube Beam Columns， Journal of Structural Engineering， Vol. 130， No. 2， pp. 189‑202，2004.

12) Mengotto M.， Pinto P. E: Method of Analysis for Cyclically Loaded R. C. Frames Including Changes in Geometry and Non‑elastic Behaviour of Elements Under Combined Normal Force and Bending， IABSE Congress Reports of the Working Commission， Band 13， 1973.

13) Martinez et al.: Spirally Reinforced High‑Strength Concrete Columns， ACI Journal， Vol. 81， No. 35， pp. 431・42，1984.

14) Richart F. E.， Brandzaeg A. and Brown R. L: The Failure of Plain and Spirally Reinforced Concrete in Compression， Univ. I1linois， Engineering Experimental Station， Urbana， Il1， Bulletin No. 190，

1929.

15) Architectural Institute of Japan (AIJ): Recommendations for Design and Construction of Concrete Fi11ed Steel Tubular Structures， Tokyo， 2008. 16) A. Kawano， K. Sakino: Seismic Resistance of CFT Trusses， Engineering Structures， Vol. 25， pp. 607・19， 2003.

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