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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
Follow this and additional works at:h p://preserve.lehigh.edu/engr-civil-environmental-fritz-lab-reports
is Technical Report is brought to you for free and open access by the Civil and Environmental Engineering at Lehigh Preserve. It has been acceptedfor inclusion in Fritz Laboratory Reports by an authorized administrator of Lehigh Preserve. For more information, please [email protected].
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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2 5E 2
i g Te s t Set up speo1melj : C8:.
1
F i g 5 Specimens af ter tes1;1bg