Compression tests on short steel columns of rectangular cross-sec.pdf

8/14/2019 Compression tests on short steel columns of rectangular cross-sec.pdf

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Lehigh University Lehigh Preserve

Fritz Laboratory Reports Civil and Environmental Engineering

1-1-1953

Compression tests on short steel columns of rectangular cross-section, 1953G. Haaijer

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Recommended CitationHaaijer, G., "Compression tests on short steel columns of rectangular cross-section, 1953" (1953).Fritz Laboratory Reports.Paper 35.h p://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports/35
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VffiLDED CONTINUOUS J . i R A ~ n E SAND THEIR COMPONENTS _ _ . . . . . ~ ~ . . . . . . . . . . . . . . . _ r ~ _ ~ ~

PROGRESS REPORT S

COMPRESSION TESTS O SHORT STEEL COLUMNS

OF RECTANGULAR CROSS SECTION

y

Gaerhard Han1jer

Not f or p ub li ca ti on )

This work has been car r i ed out aa a par t of an i nves t iga t ionsponsored jo in t ly by the Welding Research Council an d the De-partlnent of the Navy wi t h fund_s f u rn i shed y th e folJ ovJing:

American Inst i tum of Steel Construct ionAmerican I ron an d Stee l n s t i t u t

n s t i tu te of Research Lellig11 Uni v erst Column e s e ~ c hC ou nc il A dv is ory )Office of Naval Re se ar ch C o nt ra c t No 39303Bt1.reau o f ShipsBureau of Yards and Docks

Fr i t z Engineering LaboratoryDepartment of Civ i l Engineering an d Mechanics

~ h g hUniversi tyBethlehem, Pennsylvania

June 15 1953

Fr i t z Laboratory Report O 205E-2


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2 5E 2

T L E CONTENTS

n t ~ o d u c t i o n

u m m a ~ yof Theory

Scope of Tests

IV Test Set up and Procedure

V Resul t s

V I Summary

li igu:rea

~ g

5

6


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205E.2

COMPRESSION TESTS SHORT STEEL COLUMNS

OF RECTANGULAR R O S S ~ T I O N S ~ ~

I In t roduct ion _ . : ; I o u ~ 1 . o ~ ..

_ _

Sj.nce 1947 a r e se s ccl} p x ~ o g r a mon ~ e l d e dContinuous

Fran16s Rnd ~ h i rComponents il has been und er wa y a t Fr i t z E n

gineeril : lg Labora to ry. Mult ip le t e s t s on beams, C01Un1l1S and

connec t ions sllowed t h a t some TI lnbers reached the c a l c u l a t e d

p l a s t i c hinge value and sus ta ined i t for a considerable r o t a ~

t i o n I n con t r a ry, o the r sl)eclmens fla.iled prematl1.rely dll e to

l o c a l buckl ing .

The seriousness of s uc h p re ma tu re f a i l u ~ ewas empha-

s ized in Progress Report Q and a study was proposed on loca l

i n e l a s t i c buckJ..ing of structur1al s t e e l members. The o r i g i n a l

program was modified f ol lo win g th e ffilggestions of R es ea rc h

Committee C of the Column Research Council . Hence, t e s t s on

pla te assemblies were included from the beginning.

Testing proceeded along two l ines :

a Tests of sho r t conlpression couponsas proposed in Report

b ) Tests. o f angle specimens

I n thi s pre sen t report th e r e su l t s of t e s t s a) are

presented an d compared with theore t i ca l pred ic t ions .

Progress Report Q , I n e l a s t i c L oo al B uc kli ng of lNF-Secti on s II by Ching Huan Yang an d Lynn S. Beedle

Fr i tz Laboratory Report 205E-l


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205E-2

S U t n 1 ~ ~ yo f Th e ory

-2

J?or s lender co].umns, whi ch bucl{le i n th e e l a s t i c range,

the c r i t i c a l load i s given by the Euler fornmla:

Pe =1T 2 EI

KL i s th.e eQ. .1.ivalent lengtb. i th e f a c t o r K d ep en c1 in e on the

end C O l l C l i t i r) 11 S . For p i n ell:.1s I\: = 1 .0 ; fo r f i x e d 611d IC = O.5I i l 131 16 p l a s t i c r a l l 2 ~ ethe c r i t i c a l s t r eng th llas been

descr ibed , theore t i ca l ly, by two loads :

a) th e tangent modulus load, obtained by rep lac ingthe modulus o f e l e . s t i c ; l t y, E, i n EUle r s formtl1aby th e t angent 1110dulus of elast:1.c1 y

Pt = IT 2 E tI KL 2

b ) the reduced TIloc l us l o a d , deri .ved under the a ssumption t h a t \ ln lo ad in g o cc ur s on some f i b e r so f th e or-oss - sec t ion l1\11 1i11g; b\ lCkl ing. Then th emodulus of e la s t i c i ty i s rep laced by the reducedmodulus

E r _ t ~ E . +;Et) 2

and Pr = rr2 E ~ I . _

KIJ) 2

Shanley cleared up the problem and came to the foloQwing pr in -

c i p a l o n l u s o n s ~

1 . Bending commences at the tang ent modulus load withan increase i n l oad .

2. The maximum load l i e s between Pt and Pr , Pr beingthe upper l i m i t


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205E 2

Shanley i nd ica ted that the formulas for computing the t a n g e n t ~

modulus load do not app ly when E t = 0, tr since the l i m i t i n g

column load i s then determined by the s t ress at Wlich t h i soccurs .

Yang (Progress Report Q emphasized the appl ica t ion

of the t a n g e n t ~ m o d u l u t h ~ o ~ yto the s t rength of very s ho rt

specimens ( ~ : ( J o l e e . : ~ p l ) 3 s : \ j ~ ( \ n.for Pt a l so a p p l y i n g to th e

strain--ha:rc18Yl:1.:ng : ~ [ t n . g 6 )p nd sugges t ing reasons fo r the i n

crease i n st:: i engt11 abo lG tllG y i e l d load w ith o u t th e necessit ,Y

fo r l a t e r a l s u p p o r t ~

B le io h d is cu s se s the problem on pages 21 and 22 of

h i s book Buck l ing Strength o 1feta l st ructures .

t l Se op e _ 2f Te s t s

The scope of these t e s t s on shor t columns i s to i n v e s

t iga te the behavior of th e column a t and beyond the point a t

which bending s t a r t s espec ia l ly with regard to the tangent

modulus load l as computed from the s t r e s s - s t r a i n curve i n the

s t ra in-hardening range.

V ~. T e st S e t up and Procedureb _

The shor t compression specimens were cu t from the

flange of an 8WF40 sec t ion as sketched in Fig. Dimensions

are shown in Table 10

All specimens were prec i se ly a l igned by means of

s t r a i n read ings taken on two s ides of the specimen with u ~

g e n b e rg e r s t r a i n g p ~ g es (1 inc11 gage l e n g t h . At a l o a d eqtla1.

to one h a l f o f the y i e l d lo ad the I-Iuggenberger gages were r8


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205E--2, -4

placed by a Pater s gage 2-inch gage length) an d a wire was

attached to the specimen connecting t h ~ cen te r l ine of the co l

umn with an 0.001 inch mes dia l in order to measure the l t r l

def l ec t ion of the c e n t e r l i n e .

This se t -up i s shown in Fig, 4 .

s the t s t ~ r n c e e l e c lcont inuous ly, Sim\ll taneous l oad ,

s t r i n an d def lec t ion r e a d i n g s were taken.

Ta bI e 1

18.-9

8 . 8 0

6 .90

0.5456

s

C

I s ; ~ ~ ~ ~ ~ in 1 ~ : r ~ : l _ - _ ~ _ :l - - ~; _ t ; ~ ~4 ~ - - l ~ - : ~ ~ ~ r ~ - : ; ~ T - ;: ~ ~ . _ - ~ : 9 - - -I 03 I 0 .745 0 .543 I 3 .20 II 5 . 9 0 1 0 0 2 I I II 04 I 0.745 0 .543 I 3.65 I 6 .72 11 .6

I

t I0.745 0.545 4.33 7.94

1

I 0.745

0 .750 0.527

0.750 0.527I

b = width, t = th ickness and L = l eng th of specimensTest condi t ions simUlate f ixed ends , therefore l K ~ O 5

: 1

r = r ad iuso f

Gyrat ion i _ ~

b_ _ ~

=V l t ~ 2 ~ ~

i b t~ ; s lenderness r t i o \


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2 5E 2

V. Resul ts

-5

Fig . 1 shows a s t r e s s s t r a i n curve which i s an average

curve obtained from t e s t s on the shor tes t specimens C2 and 03

which showed prac t i ca l ly iden t i ca l r e s u l t s These specimens

were sUff ic ien t ly stocky so tha t the s t r e s s s t r a i n diagram

would not be a f f e c t e d 81gnif icant ly the l eng th .

lr om t;hi s a v e I ~ g es t r e s s -s t r a i n curve , t angent rnoc1ulus

and rec1\.lced.:Jmodl7tlus ~ o ~ l sv ere c o m p u t e d ~and p l o t t e d i n F i g . 2

as a function of the s lenderness r a t i o The low er curve gives

tlle t angen t -modulus and the h ighe r one i s a p l o t of the roduced

modulus r e l a t i o n s h i p . The plo t t ed poin ts i nd ica te the ult imate

s t r eng th of the specimens. I n Fig . 3 curves giv ing the load as

a funct ion of the def lec t ion of the center l ine are p l o t t e d .

Th e arrows i nd i ca t e the t angen t -modulus l oad as com

puted from the strain-hardening range of the s t r e s s s t r a i n curve.

Fig . 5 shows the specimens a f t e r being t e s t e d


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205E 2 -6

~ S ulm ary

From the load-def lec t ion curves i t i s seen thAt b e n d ~

il1g s t 8 ~ r t sinnned.lately a f t e r r e a c h i n g th e yieJ.d p o i n t e x c e p t

fo r specimens 07 -and 08 which s t a r t to bend somewhat e a r l i e r .

IIoV le,ter t h i s i s not t i le loac1 a t Wllich bend ing C O n l l ~ e r l C e sto i n -

crease r a p i d l y an d i s t hus , no t a U c r i t i c a l load Cons i s t en t

\rvi tlJ. tl lo ory and with ear } i e r t e s t s th e lnaximum 1 cads are smal le r

than the reduced-lnodulus I.oads an d g r e a t e r than the tange11t ..

modulus l o a d s ~

C on si de rin g th e l oad v s . l a t e r a ~d e f l e c t i o n curves o f

F i g . 3 , i t i s e v i d e n t tha.t U J t o the t b . e o r e t i c a l tange11t-modulus

l oad see a r r o v ~ sthe l a t e r a l de f l e c t i on r emains q t1 i t e sY11all.

I n the region o f t h i s load , however, the def l e6 t ion s t a r t s to

increase more r ap id ly. Thus, as nea r ly as can be dBtermined i n

t e s t s bending in the c r i t i c a l sense s t a r t s a t the t a n ~ o n t -

modUlUS l o a d th e tang ent m odu lu s b ein g de-termined i n th e s t r a i n -

harden:tng r ange .

The p r o j e c t Welded. Cont inuous F ralue s and T h e i l ~COln-

ponen t s U i s be ing c a r r i e d out a t F I ~ i t zLalloratory und,er the

gene ra l d ire .c t ion o f L JTnn Stt Bo,o dle C) Br uno r I h i l : ~ l i m D n ni s pro

j e c t d i r o c t o ~o f the s tudy on I n e l a s t i c n R t e h i ~ i t Y


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-

. ~

80

I\

60

t r e s s Ii p s i n

2 I

4 r

I

I ~ _ _ _ _ _ _f / . / / > ~ J

8 V W ~I ~ ~ .l ~ t . ~ 1 f ; Y

compress .o nCOUpOl lS

_i

('0o t J

o 10 20 30

s t r i n i n i n

40 50 603

1 0

F ig Average Stress- t:::2.i.- tJU: 3 Spec.imen8 nd C


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J:

too .

~

b

3Q

o

oI

.

~ e d u e dNf odulus

_ . - - - . - - _ I ~ I

5

oIf

- IJ , - I

I I---r-- fI I

jI

f

I I IL

1

I ~ . II _KL_=n\ _ _t_s L II t , r ~ v I_ : . . . . . . . _ i I . _ _ v d.- - -- . . .--.: .

10 15 - 20 25~ = e f f e c t i v e s lenderness r a t i o CK = 0 .5r

Column Curve a nd O bs er ve d Ultimate S t r e n g t h of Spec imens i n e l a s t i c rangeigo 2

o

l O O J : - - - - - T- - - - - r - - - - I - - - - - - r - - - - = - - - - - . - - - - -I I I I i _ I P 6 r t i o ; 1 I ;

T l ~ r ~ 6\ 9 I \ \ I n l ~ ~i

80 IL I II \ -; I t . r i \ . _ ~ Iu ~ s s . I t ~

k i p s / i I 1 2 J I . . : / / I : i I ~ If 1 I i 1 I60 1 :] - - - T- - -. . - I

I J J

t 1 ~ ~t

/- Tangen t Modulus / . /

4 L- I

I_I C u l :;ima t e s t r e n g t hI

? O l ~Ij

I

ot.. ~ . ~ _ .


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S t r e s s Ip s i n 2

t

1

N

t oOI1

s t r e s s a t t h e o r e t i c a lt a n g e n t m o d u l u s / l o a d

~r C8i

l

1 \

C

C

C2

l1

LJ

ti iI

~

. ~

0

O

~Def lec t ion of Center l ine

t e s t p o i n t\ \ ; -) \ _ ~

_t ' , I _ _ I C - i ~ _ ~ \ ~ . __ _ . _. _L, _ L _ L . . _r; f~ 5 i n -- 1

o

F i g . 3 Average St r e s s vs Latera l Def lec t ion Curves


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i g Te s t Set up speo1melj : C8:.

1

F i g 5 Specimens af ter tes1;1bg

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Compression tests on short steel columns of rectangular cross-sec.pdf