Channel Shaped Reinforced Concrete Compression Members

8/14/2019 Channel Shaped Reinforced Concrete Compression Members

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A C I S T R U C TU R A L JO U R N A L TE CH N IC A L P P E RTi t l e no. 84-S21

Channel Shaped Reinforced Concrete Compression Membersunder Biaxial Bending

by Cheng Tzu Thomas Hsu

f r s M i o t un r\{vrtfHt'nltl an d atialviii 'al irnf\ttt;iiit>n i> I he M renal hand delvrrtttjlion o tia\mll\' Inaded 'hur mui iied t n / i m / m ail.rifarla/I1- M / / / I 'hnnfl-\litJfH' \< . h / f dt".i'n j>rtn't 'durf\.

i .uppiirlt

I r r c g u l a r - s h a p c d s l r u c t u r a l c o n c r e t e m e m h e r s s u h -j ec t ed l o c o m b i n c d b i a x i a l b e n d i n j z a nd a x i a l l oads a resomet imes encoun ie red in dcs i en p rac i i ce ; i n i h e case o tr e in fo reed concre te co lun ins and s h e a r \ \ a l K , c h a n n e l -s h a p e d mcmbcr*. a re u s u a l l y used a s co lun ins or enc lo -s u r e s o f h e e l e v a t o r s h a l t s ( I i y . 1 ) . H o \ \ e \ e r . c u r r e n tb u i l d i n ^ - c o d e p r o v i s i o n s do not p r m i d e g u i d e l i n e s C ordes igning such a n icrnbcr. The reason i \ t t h e nt 'or-m a i i o n on h e b e h a v i o r o i r r e g u l a r - s h a p e d r e i n l o r c e dc o n c r e t e m e m b e r s u n d e r c o m b i n e d b i a x i a l b e n d i n g a nda x i a l load is not \ \ e l l k n o \ \ n . T h e y a re u s u a l l y o \ e r d e -s i g n e d , w h i c h m a y cause th e s t r u c t u r e to be s t i f t e r , a nd

m a y resu l t in loss of d u c t i l i i y \ \ h e n a p p l i e d to se i sn i icr cg ions . T h e p r i m a r y ob j ec t ive o t h i s pape r is to ad -dress t h e s i r e n g t h a nd de l ' o rn ia t iona l behav io r o t c h a n -n c l - s h a p e d r e i n f o r e e d c o n c r e t e m e m b e r s u n d e r i h eab ovc combined l o a d i n g s .

A t o t a l o f f i v e c o l u m n s and s ix shea rwa l l spec imens\vcrc Cabr i ca ed a nd t e s t c d . Of the t o t a l e l e \ e n s p e c i -m e n s , n ine werc m a d e w i i h no rma l conc re t e uh i l e t w owcre f ab r i ca t cd f rom h i g h - s i r e n g i h c o n c r e t e . T h e t e s t si m c s t i g a t c d t he ax ia l l oad , m o n i e n t , d e t l e c t i o n , c u r \ a -t u r e , and s i r c n g l h o C (hese sec t ions , and h e r e su l t s w e r ec o m p a r e d w i t h a n a l y t i c a l p r e d i c t i o n s o f t h e w r i t e r ' sc o m p u t e r p r o g r a m . '; Based on the C i n d i n g s o f bo th ex -p e r i m e n t a l a n d a n a l y t i c a l r e s u l t s , a m e t h o d is reconi-m e n d e d fo r poss ible des ign p rac t i ce .

A C I S t ruc tu ra l Journa l / May June 1987

COMNEN COLUHN

E L E VAT O H M A T

/>. l~Simplified sketches o f sowc principal applica-iions of irregular shaped reinforeed concrete columnsand shearwalis in huildings

RESEARCH S I G N I F I C A N C ET h i s s t u d y o f l o a d a n d d e l o r m a t i o n b e h a v i o r o

c h a n n e l - s h a p e d co lumns a nd s h e a r w a l l s \ \ a s a imed a tprov id ing gu idc l incs C or des ign ing such a m e m b e r u n d c rcombined b iax ia l be nd in g and ax ia l comprcss ion . Bothn o r m a l - s t r e n g t h a nd h i g h - s t r e n g t h concre tes u e r e used

R e t e n e d A p i 16 . l Y N * . ,m d r e i i e e i l u n d e ? I n - i n i i i c p u M k . i t u > n pohiies< i i p % r i ( z h i I ' H", - Vr j i e n t J t i < i v u i e i e I n s i i i u i c M I n j i l m r e ^ e r i e d . i n t h i i l i n fi l i c m a k i n >i i t inpies n t i l r x s pc r rn i - iS ion 1 1 nh i .L i r i i - J l t c > n i t o v i i p v n t h i propnc l t i r > . l ' e i i i n c i i : J U I I IN M O I I i l l t c p u b l i v l i e d n i t h e M . i t i l i \ p t i l il* > 1 < /N/'I . urul Journal 1 1 re. en e il h v in 1 , \

201


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, - l f / memtv

trtt'mtifr < >

.1(7 ( omrn

{ m\fr\il i .

r ( Hrng-fiu boma* Htu n f rl l lh,- \tr* J?r\,-\ "

U / 1M / ( >inniilt,-t' 441. K,'i

/feo 4.'?. l> f l f l i t i n o < < I L

Itl/i' ( m i t - r v / i . i j f l t i \ltdil fi'rti;irn't'rini> rm-, in ( jnjiiu in

i-\\u' ul l ' i n f mi 1 n iir iinmcntal

l'irt r i ( ( ii 'i'' ' ( tn'unjn and f> are t h e c o l u m n m i d h c i g h t d e f l e c t i o nc o m p o n e n t s i n the x - and the \ - d i r e c t i o n s , r e s p e c l i v e l y.

T h e m o m e n t - a x i a l l o a d - c u r v a t u r e r e l a t i o r i s h i p s u e r eused l o c a l c l a t e t h e ax i a l l oad v a l u /* ( v v i t h o u t ac-c o u n t i n g f o r c o l u m n d e f l e c i i o n . T h e a x i a l load v a l u P, ( w h i c h accou iHs f or c o l u m n s d e f l e c t i o n s f> and .)w c r c d e r i v e d in the f o l l o w i n g e q u a t i o n s

P (c

\(c.

w h c r c e , a nd 1, a r e t h e e c c e n t r i c i t i e s a l o n g x - a n d y -a x c s , r e s p e c t i v c l y.

E X P E R I M E N TA L P R O G R A MA t o l a l o t " I I s p e c i m e n s v s e r e t e s t e d i n t he p r e s e n t

s t u d y . H v e s p e c i m e n s v v e r e d e s i g n e d a s s h o r t , t i e d c o l -u m n s ( I ' i g . ? ) , and the o t h e r s i x s p e c i m e n s v v e r e c o n -s l r u c l c d a s s h o r l s h e a r v v a l l s ( I ' i g - 4 ) . P h y s i c a l c h a r a c -l e r i s t i c s of t h e t ' i v e c o l u m n s and s ix s h e a r v v a l l s t e s t e da r e s h o v v n in Ta b l e I and F ig . 3 and 4 . I he t e s t i n gf r a m e c o n s t r u c t e d f o r t h i s e x p e r i m e n t a l p r o g r a m i ss h o w n i n F i g . 5 , a n d t h e a c t u a l e x p e r i m e n t a l s e t u p f o rt h e t c s t i n g s is s h o w n in F i g . 6 and 7 .

A l l s p e c i m e n s v v c r c l e s t e d and s tud ied fo r t h e i r c o m -p l e t e b c h a v i o r u n d e r c o m b i ne d b i a x i a l b e n d i n g and ax -ia l c o m p r e s s i o n , a nd wcrc used t o e x a m i ne s o m c o f t h ev a r i a b l e s i n v o l v c d , such a s s t e e l y i e ld s t r e n g t h , n o r m a l -a n d h i g h - s t r c n g t h c o n c r e t e , a n d e c c e n t r i c i t i e s . T h e

ACI S t ruc tu ra l Journa l / May June 1987


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specimens were p in-ended .T he b r acke l s in bo ih ends o f the specimens were d e-

signed and h e a v i l y r e inforced to p r e v e n t local f a i lu res Fig. 4 and 6) . For co lumn spec imens C h a n n e l Sec t ionA ) , ih e b racke ts were conf ined w i t h a foo t - long steelt u b e on each end , and the gap b e t w e en th e s teel tubesand t h e o r i g ina l b r ack e t s w as g r o u t e d w i t h 5000 p s ic o n c r e t e , as s h o w n in F ig . 6 . A1I f i v e c o l u m n s w e r er e in fo r ced l ong i t ud i na l l y by 22 N o . 3 b a r s w i t h steelyield s t r e n g t h / = 51 .8 ks i . O f the t o t a l s ix shearwal lsp ec im ens Ch a nne l Sec t i on B) , f ou r s p e c i m ens w e ref a b r i c a t e d w i t h n o rma l conc re t e a n d t w o w i t h h i g h -s t r e n g t h c o n c r e t e . A l l s h e a r w a l l s p e c im e n s w e r e r e in -fo r c e d l ong i t ud ina l l y by 18 No. 3 bars w i t h tw o d i f f e rent s tee l y ie ld s t rengths , as seen in Table 1 . These lon-g i tud ina l bars we re held together by 'vin. lies at spac-ings 2.5 to 4 in. center- to ce rner. T h e l ies and l o n g i t u -d i n a l bars were l i ed toge ther us ing No. 16 gage b i n d i n g

Table 1 Specimen detailsSpetimcnnumbcr

u-

.K

4c

5,

*> >

%

8> .

*>

IQh

llh

I>pco MamI.TOSS vcciion' b a r %

A :: No 1.A :: N O i

A :: NO - - - - - -

A :: NO 3-

A :: N O .B 1 8 No 3.B 1 8 No 3

B 1 8 N o 1

f -B 1 8 N o 1.

B 18 No 3

B 18 No l

' . / . i. i h 4 :

51 8 3W.14 I X 2 5 6 4

5 1 8 '662,4 1 (i 1 0 f> 4 ... * i .

5 1 8 j:r ;4 i K i 6 4

5 1 8 3 M W 4 1 5 : < ; 6 4

6 5 6j:ii i*:*:*: * 1 56 < '(sj:.u 4 u : H Mft i *6 ( ~6.:Wi4' 4 '54 > 0 8 ^ ' t. 5

6* 62'vtl 4 9 1 1 (> f> 1 lO h

llh. . _

B

B IB I

i

B 1B

Bt

f'rom leM repul s .T ' r o m P .: l rom

A n a l v s i * r e p u l s ,kips

'

102.4

103 .1

102.4

103.6

120.0

100.2

91.0

70.5

6 3 . 1

124.0

102.7

-

93.

, 86.3

6 7 . 5

60.0

t

95.3

T C . I r e b u l l k i p s

108.31

1 1 9 6 5

1 0 3 . 1 5

1 0 7 2 8

1 2 1 7 2

UP.28

9 .99

66.112

ir 5991 61

A \ c r a p c

/ *

/*-,

1.058

1 . 1 6 1

1.007

1.016

1 . 0 1 4

1.07 I

1.07 1

1.05.1

1 046

0.912

1 0 3 3

/ _.

1 . 1 4 5

1 . 1 . 1 5

1 1 0 0

1 1 0 0

1.028

0.982

1.082

Table 3 Ultmate moment capacity

Fig I0Specimens of Channel Section B after failure

206

Anahsis r c s u l t s .

Spccimennumbcr

le

2c

3c

4c

5c

6y

R y9>

Typc o f ,c r o s s scc t ion

A

A

A

A ,A

B

B

B

B

kip-in

A / . ,

3 0 7 . 1

28.1.4

307.1

3 6 1 . 8

300.2

252 3

2 5 5 . 2

2 1 7 . 5

212 .4

Ai.

184.3

185.5

184 3

186.1

180.2

3 7 3 . 0

3 ^6 7

3 2 1 . 1

3 1 3 . 1

IC M rcsulls, kip-n.

A / . ' ' A/. A / . ' M.11 2 4 . 9 1 5 6 19 5 2 3 1

1.129 145 215 .4 25 8

.109.5 .118.4 1 8 5 . 219

.175.5 195.2 193.1 225 9i J

304.3 .126.2 1 8 2 . 6 2 3 6 . 8

270 ,3 306 .2:3 9 9 . 7 | 4 5 5 . 9t ^

2 7 4 . 8 304 .2 '405 .7 415 .9

2 2 9 , 1 2 4 8 . 1 118.2 144.2

2 2 2 . 5 2 3 3 . 7 .128.1 3 3 0 . 9i t t i

I0h

llh

B

B

'LxpcrimcnUl .W.. / .' -xpcumcnia l Af. . P.

from ihc load-ilcflctiiiin tu

3 1 2 . 5 i

*.116.8

e. , M, / . f f . * A , ) ; Af..

462.0

467.7

P. e.

2%. 1 3 5 2 . 8 , 4 3 8 . 1 4 5 8 . 1

2 8 8 . 8 3 3 1 . 9 4 2 6 . 4 4 4 5 . 1

fi . t hcrc A , A , iihiameil

A CI S tr u c t u r a l Journa l / May-June 1987


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(4) and (6) were used fo r compara t ive s tudy in the fo l -lowing equat ions

and

(6a)


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Load contour and design formulas for channelsections

T h e load contours a nd t h r e e - d i m e n s i o n a l f a i lu re s u r -faces n a v e f o r m e d th e b a s i s o f c u r r e n des ign proce-dures f o r r e in fo rced conc re t e co lum ns subject to b iax-i a l b e n d i n g an d a x i a l c ompre s s i on in the v a r i o u s n a -

t ional codes T h e l oad -comour me lhod i nvo lves cu t t ingth e f a i lu re sur face a t a constam va lu of P. to give aload contour i n t e r a c t i o n re lat ing A /n, and Mn. Fig 16and 17 show sets of l oad con tou r s at va r ious v a l e s ofP n. To deve lop a des ign e q u a l i o n , th e d i m e n s i o n l e sload c o n t o u r s a re n eeded . T he genera l nondimens iona

300

250

200

150

100

EXP. M >246.IUpt -lfi.

EXPERIMENTAL

O THCORET1CAL

NOTE: EXP. NVPU+t

(I/4U I0')

a

350

300

tftO

20O

. I5 O

100

50

SPECIMEN yEXP U 344.2 UH -1

A EXPERIMENTAL

O THEOHCT1CAL

NOTE EXP M. -P(*.+6

0 2 4 6

b 4


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equa t i on for the load c on t ou r a t cons t anP, m ay beexpressed in the fo l lowing f o r m " ( o r ano the r s im i l a r

A/, A f,A/,,

1 (8)

where a, a n d a : a re expone nls tha t depend on the d i -m e n s i o n s o f the c r o s s s e c t i o n , t h e r e i n f o r c e m e n ta m o u n t a n d l o c a t i o n , c o n c r e t e s t r e n g t h , s tee l y i e l dstress, and a m o u n t o f concre te cover.

Fig. 18 and 19 show some of the d imens ion less loadc o n t o u r s a t p resens t u d y. T he v a r i a b l e s i n v o l v e d inFig. 18 and 19 are the m x i m u m concre te compressives t r e n g t h / ' , the steel yield stress/, an d types o f c h a n -nel sections. As s h o w n in these f i g u r e sa, and n : in -crease fo r larger vales o f P,. T he ca lculated v a le s o fa, an d a : va ry f rom 1 .5 to more than 2 .0 . F o r p rac t icadesign purposes, it seems s a t i s fac to ry to t ak e u , = u :as 1.5 for a n y c h a n n e l - s h a p e d sec t ions , w h i c h is ( hes a m e as for a r ec tangula r sec t ion . From t he p resen ts tudy, i t seems tha t the h igher v a lu o f a, and . m ay

be used {see the f o l lo w i n g des ign examples) for p rac t i -cal design.

SIGN E X M P L E

Select a compress ion m e m b e r w i t h t h i n - w a l l e d c h a n -nel shaped cross section to t a k e the f o l l o w i n g u l t m a t eloads: Pu = 32.6 kips , Mu = 100.6 kip- in . . and V / _=148.5 kip-in. Use/ = 2964 psi, and/ = 65.76 ksi .

Solut ionStep T ry a c h a n n e l - s h a p e d c r o s s s e c t i o n a s

s h o w n in Fig . 2 .Step 2 Try 18 No. 3 bars as i l l u s t r a t e d in F ig . 2 .T h u s , pt = 0 .049, sa y 4 .9 pe rcen t , w h i c h is b e twecn 1

o o

1 X O O 3O O 400 9

H m k . p t - m )

Fig, 16Load conours for Channel Section A

AC I S t r u c t u r a l J o u r n a l / M a y - J u n e 1987

and 8 percent o f gross rea a s pe rmi t ted by the ACIB u i l d i n g Code . " P rac t ica l ly, va les o f 3 6 pe rcen ta re c o m m o n ly used.

Step 3 Use o = 0.7 for t ied c o l u m n . Th en

P, P/o 46.6 kips. V / A /a l/o = U 3 . 7 k i p - i n .

A/,. = A/B./o = 2 1 2 . 2 k i p - i n .

t XX 4O O 9 O O

OO CXJ WO 4O O 500 600

Fig. I7(a) and b)-Load contours for Cha nnel SeclionB

209


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11/11

slightly overestimate those of experimental tesis.ever, a satisfactory agreement w as still achieved. Theexperimental load-deflection and moment -cu rva tu recurves obtained ("rom th e present t e s t s were also notedto be in good agreement w i t h ana ly t ica l results fromzero up to the mximum moment capacity of the sec-tion.

The design procedures in ihis paper require de tcr-mining th e strength in teract ion diagrams and ihe loadcontour equations; the load contour method wiih a -a. = 1.5 for rectangular section w as used in the designexample, and has been found to be on the conservat ivoside as compared w i th th e present analylical and exper-imental results. Even with , = t* . = 2.0, the load con-tour equation still achieves a consrvam e solution.

Recent s tudies by Pos ton e t a l.14 showed t h a t theplane-section assumption in their axial load-moment-curvature computer analysis program for the design ofslender, nonprismatic, and hollow bridge piers is validonly if the unsupported wall length-to-thickness ratiodoes not exceed s ix . As mentioned earl ier, a similar as-sumption was made in developing ihe present ax ia l

l o a d - m o m e n t - c u r v a t u r e compute r p rogram for theanalysis of i rregular shaped, shor t , and t ied columnsand shearwalls . Examination of data from this t e s t asshown in Tables 2 and 3 reveis that no strength reduc-tion of any kind is indicated for any spccimens exceptSpecimens lO h an d llh, w h i c h w c r c fabricaied w i t hhigh-strength concrete.

KNOWLEDGMENTS

The financia Mjpporl o ihc N ew Jersey Institulc o tcchno o\d s e^cra l consu l lmg cnginccrmg com pa mcs in Nc Jersey and N cw

York is graicfully a c k n o w l c d g c d . Ihc exper imenta l w o r k and p an oth c compuiations o ihc p rcscm s iudy w c r c conduc t ed h> ihc author's gradate studcnls hclwccn 1 9 K O and I 9 S 5 : D Chidamharrao,S. Ya l a m a r t h y. ti. Hannoush. H. tihadum. N Paicl, \ H. \Vang ,and J. H. Yc h Ihcit cflom are also greatK apprcc ia icd .

NOT TIONA, g ross c ross -scc t iona l a rca.-1 lolal a rca of mam r cmfo rccmcn te , ccccn t r ic i ty along x -ax i se . c c c c n t n c i t y a long y - a x i s

/' ultmate Mrcnglh o f concrete/. s tccl yicld stress/. Mec s i rcss a ullimalckd d i s lancc from mximum c o m p r c s M v e .oi icrete s t r a m to

neu t r a l ax i s( (o ta l length o f cohimn(" cffccmc length o columnAf., nominal bcnding moment ahoui x - ax i sAf.. nominal bendmg momen t about \ - a x i sAf , A f _ capacil) al ax ia l load I', w h c n A f . is / e roA, - A,. capacil> a l ax ia load /'_ w h c n A /, is / e roA/.. o A/..A/.. o A/..A, bcndmg momciu .iboui \ - a \ i sA/. hcndmg momenl ahoul y - a x i sP -- ax i a l load \aluc/* mx imum i.'ompre'.Mon capacilv of ihc cohimii1 or shcar-

w a l l

P,

axia l load \aluc ( w u h o u l accnunling fo r column or shcar-wall dcflccuon)P, = axia l load \aluc (accounimg fo r column or s h c a r w a l l de -

fleclion)

nominal axial loadP. = ot Uatcrloo Press , 1980. pp. HN-H5.

4. Chidambatrao, I).. "lichaMor o (.'hjmiel-Shaped KtmlorccdC'oncrc le Columns undcr Combined Biaxia l Bcndmg and C o m p r e s -sion," MSc tlicsis. Nc\ Jerse> Instnuic o" I echtiolog\ N c w a r k . -\ug1983, IOS pp.

5. Ya l a m a r t h > . S ., "UchaMor o I hm-\d Channc l ShapedRcinlorccd C 'oncrc le C'olunuis

undcr C ornbmcd

Biaxia l Bonding and

Comprcssion," \1Sc ihcsi\ N'c Je r sey Insinulc o Icchnoloi\N c w a r V. \1a> 1984. H pp .

6 Hannoush. d . "UchaMor of High S t r cng ih I r regular ShapedRc in fo r ce d Concre te Columns undcr t ombincd Biaxia l Bcndmg andComprcssion." MSc Ilicsis. N ew 1etsc> Insiiiutc o I e c h n o l o g > ,N c w a r k , Ma> 1985 , % pp.

". Matlivk. Alan H.. "Roiational C apaci(> o Hmgmg Regions mRcin fo rced Conc re t e Bcams." f-U \ura \ttvtianu~ 1- f Rrintoru-dConcrelf, SP-12 , American C o n c r e t e Insinuic Am er i c a n Socicl\Cnil I:ngmccrs. Detroit. 1965. pp 143-181.

H. C o r l ey, \V, (icnc. "Rotaiional Ca paci l> o f Rc in fo rced C o n c r e teBcams." Pmit cdin^. ASCI , V. 92, SI4, Ocl. 1966. pp 1 2 1 1 -W >

9 . Brcslcr. Bon-.. "Design Critcna fot R c i n f o r c e d Column'. undcr

A x i a l I oad and Biaxial Bcndmg." A( I J < M K--M . Pre>cef

Channel Shaped Reinforced Concrete Compression Members

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