Experimental verification of thin-walled girders with circular holes

J. Construct. Steel Research 13 (1989) 301-316

Experimental Verification of Thin-Walled Girders with Circular Holes

J. Ravinger Institute of Construction and Architecture, Slovak Academy of Sciences, 842 20 Bratislava, Czechoslovakia

& P. Lag6ekov~i Institute for Research and Development of Civil Engineering Structures, 823 66 Bratislava, Czechoslovakia (Received 10 February 1988; revised version received 19 May 1988; accepted 28 September 1988)

ABSTRACT Results are presented of tests of girders "with slender webs having circular holes and rules are offered for an evaluation of the ultimate load.

NOTATION bf bs bw df, ds, dw mM, mq

Width of flange Width of stiffener D e p t h of w e b plate Thickness of flange, stiffener, and web-plate, respectively Buckling reduction coefficient for a slender w e b loaded in bending, and in shear, respectively mql Basic buckling reduction coefficient for a slender w e b loaded in shear mq2 Contribution of the flanges to the buckling reduction coefficient for a slender w e b loaded in shear 301 J. Construct. Steel Research 0143-974X/89/$03.50 (~) 1989 Elsevier Science Publishers Ltd, England. Printed in Great Britain

302

Af, A~,Aw D M~ Mw Mu l, Mu2

QPL

Qw) Qui, Qu2 Ovi Wf, Ww

WpLo

~n.f,%.~,~n.w

J. Ravinger, P. Laggekov6

Area of flange, stiffener, and web plate cross-section respectively Diameter of circular hole Bending ultimate load of the stiffener (assuming D = h - 2d 0 Ultimate load of the slender web Loaded in bending, taking into account the buckling effects Ultimate load of the thin-walled girder with nonreinforced hole, and with reinforced hole, respectively, loaded in bending Ultimate load of the slender web loaded in shear without taking into account the buckling effects Ultimate load of the slender web loaded in shear, taking into account the buckling effects Ultimate load of the thin-walled girder with nonreinforced hole, and with reinforced hole, respectively, loaded in shear Ultimate shear load due to Vierendeel action Cross-section modulus of flanges, and web, respectively Plastic section modulus of one flange with respect to its own axis Yield stress (MPa) respectively

of flange, stiffener, and web,

INTRODUCTION Thin-walled girders probably represent the main constructional component of steel structures. It is frequently required that holes be fabricated in them, e.g. in order to enable passage of service ducts or piping, or for inspection purposes. At the present time, we can also try to decrease the weight of a structure, even in civil engineering construction, by using circular cut-outs. Circular holes are simple to fabricate (by machine cutting) and they do not produce high concentrations of stresses. We shall distinguish between two types of circular holes (Fig. 1): (a) non-reinforced holes and (b) reinforced holes (i.e. holes fringed by a stiffener). Reinforced holes are suitable when the hole and its brim are machine-produced in one working step. If it is intended to improve the load-bearing capacity of the girder by way of welding extra stiffeners on to its web, use of straight stiffeners (Fig. 2) may prove to be more advantageous.

Thin-walled girders with circular holes

t

Ca)

303

lil

(b)

Fig. 1. The cross-sectionof a girder with (a) non-reinforced and (b) reinforced holes.

Fig. 2. Use of straight stiffeners for girders with holes.

EXPERIMENTAL VERIFICATION Figure 3 shows the geometry and notation of the girders tested by the authors. The main material properties are listed in Table 1. The test set-up was similar to that used in the tests on girders with unstiffened slender webs and described in Ref. 1. The test set-up is shown schematically in Fig. 4. Figures 5 and 6 give a general view of the tests. Some girders were tested with the view to check the necessity of using an end stiffener. This end stiffener is indicated by a dashed line in the figures. Girders RGH-1 and RGH-2

The girders were loaded by 12 symmetrically distributed forces (Fig. 7). The collapse of the girders was caused by bending. Girder RGH-3 A

To verify the ultimate load of the end part of the girder, non-symmetrically distributed forces were applied (Fig. 8). The girder had no end stiffener,

o'~.f

293

297

404

462

461

MPa

crlT.f

6-04 259

6-1

11.8

mm

t

Flange

30.0

31-5

33.5

%

e

508

414

642

MPa

at, ,,

Web

or#,.,

2.85 246

3.1

mm

t

Material properties

28.0

20.5

%

e

Yes

No

Yes

No

End stiffener (dashed line, Fig. 3)

t = thickness; crn = yield stress; o-t = rupture stress; e = maximum elongation.

RP-2 RP-3

BRH-3 BRH-3 B

BRH- 1 BRH-2

RGH-3 A RGH-3 B

RGH-1 RGH-2

Girder

13-0 17.0

39-0

32.0 33-0

31"0

22.0

20.0

16-0 18-5

PI~ w

Shear near the support

Bending in the middle and torsion ofthe compression flange

Lateral buckling of the tension flange

Shear through first hole

Lateral buckling of the tension flange and shear

Bending in the middle

Character o f failure

TABLE1 S u m m a r y o f t h e T e s t R e s u l t s a n d Comparison with Theory

(5) (9)

(9)

(3)

(11)

(3)

Eqn for calculation o f P1v

1.12 1.07

1.02

1"01 1"04

0"98

1-29

1'18

t'01 1"17

PI.

PI, v,

o,

cm

k.o 4~

Thin-walled girders with circular holes

END,STIFFENER

J R GH4 JRGH-2 1RGH-3]

(-

i

~P ! PORT~280G I

825

305

i

Q

Q

G

[ = 600 __1_ 600 ~ = 600 =l= 600 =1__ 600 8850•2

~lLA'iSoo i

A-A' ~

IBRH-I IBRH-2IBRH-3 ] •

3.1

B-B'

{~

3.l'~-.-~

LB'60o.I_ 600 LBOi02 I 825 I_ tj -

465oi~

; - _J

A-A'

I-- 525 _1

L A' 6O0 _[-_ 6O0 =1

i

B

~

525 =1_

Fig. 3. The geometry and notation of the test girders.

460

60

60

riO

Fig. 4. Test set-up: 1, test girder; 2, loading arms; 3, support of loading arms; 4, attachment of test girder; 5, loading beam; 6, support of test girder; 7, loading jacks (200 kN); 8, loading jacks (100 kN).

306

d. Ravin¢er. P. La.i(ekov~i

Fig. 5. General view of a girder in the testing position.

Fig. 6. A view of the loading arms.

307

Thin-walled girders with circular holes

IRGH-I RGH-21

p,J [k N]

~[ PIMAX:1.85kN

L'1' L'1

15

107

i 11.611 660

t

-'- [crn]

10

6.o,~ [kN] •

®

I

GIRDER RGH-1 5-

GIRDER RGH-2 I

~

5

42 x ~kNcrn]

v~ 6-

150

200

25o

~mmY

Fig. 7. The load-deflecnon curves for test girders RGH-1 and RGH-2,

and considerable horizontal displacements of the tension flange were then detected (Fig. 9). After the m a x i m u m load (20 kN) had been reached the girder was quickly unloaded to be used in the following investigation. Girder RGH-3 B

An end stiffener (60 m m x 8 m m ) was welded and the other end part of the girder was then tested (Fig. 8). A shear collapse mechanism was observed (Fig. 10). Girder BRH-I

This was a symmetrically loaded girder without an end stiffener (Fig. 1 l). Considerable horizontal displacements of the tension flange combined with shear distortion near the support characterized the collapse mechanism (Fig. 10). Girders BRH-2 and BRH-3

These girders were fitted with end stiffeners. Twisting of the compression flange in the n e i g h b o u r h o o d of the hole in the central part of the girder caused collapse in this case (Figs 10 and 11).

J. Ravin,~er, P. La~Pekovti

308

20+ :

/ --

;_ ~ _ ; I

~

I~ /~,'/ II J'.~/// l/,~///~/ /,"

2j

~ _ . . . . __;. . . . . .

"/ / //~/'/ ////

*

j

e

- - - - G I R D E R WITH END STIFFENER RGH-3/B ....

10

20 !

i

i

[

/

~.[~1~.,~ END SECT'ON

GIRDER WrTHOUT END STIFFENER RGH-B'A

30

~-°'°~5°(:°~[2:I I::'°;~: t ; 12°1:

40 lmm] zP1MaX= 2 2 0 kN

vc

Icm} . . . . . /

;'

i

I'I ltt

Y

,o~_-/g_~

: / #/ / f ' ~

I

MIDDLE SECTION

o %--

!

}

'

....

.~

~7,

:

G,ROERWITH END STIFFENER RGH-31B

i

GIRDER WITHOUT END STIFFENER RGH-31A

i

~ ~Mh >

Fig. 8. The load-deflection curves for test girder RGH-3.

/ '

-t,~

e - ¸¸

~4

Fig. 9. A close-up view of the horizontal displacements of the tension flange.

797.P~

Thin-walled girders with circular holes

Fig. 10. Girders after tests.

309

J. Ravinger, P. La~(ekovti

310

[kl---~.I

[

,'

i

WITHOUT END STIFFENER

,

,

WITH END STIFFENER p 1=33kN p1

L--

WITH END STIFFENER I

~.32,N

,,

--

,'_

U

[cm]

#1 ,X/"/1

I #/ ;

#

II I'/

_...z'

/ ~

/ /V /'//~

~

,

,

201

-~

~

////J

'; it/ / / ~lM MAx=<34+Sxp ~ V ~ / / t

,' ! / II

, v.

1

n

I

~.?Zj_~J._

/i/

01

!

///

.

v

20

i

~,~l

I

3 [ ram]

[',

I',

SECTION

,'/

END

I

r~ - ~- ~

5

1'0

MIDDLE SECTION

15

[mrr

Fig. I 1. The load-deflection curves for test girders B R H - I , BRH-2, and BRH-3.

IBRH-3,8] [kN]

[kN]i I

4:,%Ax 39kN

404

/ ,/

i

1'1~ p 1~1571 ~

30

h oo0ooo ~.'7

20----

3o4

rl

½,-

3 • 60.3so

/ ".-Z---~ MM~,X=333 * ~P

10

101~ /

f t //

! I

I F

.....

END SECTION

MIDDLE SECTION

]LATERAL BUCKLING]

/

vo

3 [mm)

5

; 10

Fig. 12. The load~teflection curves for test girder BRH-3B.

1~j

or" [m m)

Thin-walled girders with circular holes

311

r~q NON-REINFORC ED HOLES --

[kMl P lSJ

REINFORCED HOLES ~M~=17.0kN

/

2

.rP~AX=I 3.0 I ,.3L

i

boooooooood

g

/

/

,

672x~

Imm]

10

Fig. 13. The load-deflection curves for test girders RP-2 and RP-3.

®

©

M

®

®

iI

'in

i

I

®

I

I

®

I

i

@

'I

I

Fig. 14. A girder with non-reinforced holes: (a) loading by bending; (b) web buckling edge conditions in the region of a hole; (c) effective cross-section; (d) distribution of stresses at the beginning of loading; (e) distribution of stresses at the plastification of the cross-section (low depth-to-thickness ratio of web plate); (f) distribution of stresses in the post-buckling range (high depth-to-thickness ratio of web plate).

J. Ravinger, P. Lagdekovti

312

Girder BRH-3 B The same girder, after it had been reinforced in the deformed portion, was then tested with a non-symmetrical load distribution (Fig. 12). Shear failure near the support occurred. Girders RP-2 and RP-3 (Figs 10 and 13) The girders collapsed due to shear deformation of the first and second holes. The failure was slow, and the deformed girders proved to be capable of sustaining a load near the collapse load.

E V A L U A T I O N OF T H E T E S T R E S U L T S Girders with slender webs with circular holes are outside design standards. A modern computer technique enables us to model the behaviour of even such a complicated type of structure, but even so finally we must formulate some rules which could be used by designers. The authors offer the idea for the evaluation of the ultimate load in accordance with the Czechoslovak design standard (Ref. 2). The derived equations can be used as design rules if the yield stresses are changed to the factored resistances. (a) Girder loaded in bending: non-reinforced holes The behaviour of the girder with non-reinforced holes loaded in bending is shown in Fig. 14. Compression stresses produce the buckling of the web and then we have a non-symmetrical distribution of the m e m b r a n e stresses. Introduction of an effective depth of the web plate in its compression part gives a non-symmetrical cross-section. This leads to more complex and time-consuming calculation and, moreover, it would be difficult to satisfy the need for continuous transition to the rules proposed for the case of a girder with a zero hole (D = 0). A simple and sufficiently accurate procedure consists in using linear interpolation between the ultimate load of a girder without a hole and that of a girder with a hole having its diameter equal to the depth of the web plate. This gives the following formula: Mu1 = Wf. orn, f + Mw(1 - D/bw)

where Wf = elastic section modulus of the flanges

(1)

Thin-walled girders with circular holes

313

Mw = raM. W,~. g,,w i

(2)

2

Ww = z bw dw = elastic section modulus of the web plate

mM = 1 4 5 d w l b , , , ~ n , , , ,

-- 1

(3)

= buckling reduction coefficient of a slender web loaded in bending

®

®

®

®

®

@

,,.gN

( © )M

I]1'

-

N

-

N

Fig. 15. A girder loaded in bending, with reinforced holes.

(b) Girder loaded in bending: reinforced holes (Fig. 15) A n a l o g o u s l y to the p r e v i o u s case of girders with n o n - r e i n f o r c e d h o l e s , w e can r e c o m m e n d l i n e a r i n t e r p o l a t i o n also for the case of girders with r e i n f o r c e d openings: Mu2 = Wf. o-n,f + Mw(1 - D/bw) + MsD/bw

(4)

where Ms = As. o'fl,s, y --- ultimate bending m o m e n t of the stiffener As = bs.ds-<5dw.d~ = area of the stiffener cross-section reduced with regard to the 'shedding' of membrane stresses from the web into the stiffener y = bw-ds

(c) Girder loaded in shear: non-reinforced holes T o start with, it s h o u l d b e n o t e d at this j u n c t u r e that the i n f l u e n c e o f a h o l e is m o s t p r o n o u n c e d with girders l o a d e d in s h e a r (cf. Fig. 16). T o c h a r a c t e r i z e the u l t i m a t e l o a d b e h a v i o u r of a g i r d e r l o a d e d in s h e a r

J. Ravinger, P. Lagdekovd

314

QPLf)\

.

Quo

°1Q __ 10

~ REINFORCED HOLE REINFORCED HOLE 0 t.I1 '

~/ ~Ov-i--

D/b. 1.

O.

Fig. 16. The ultimate load of a girder loaded in shear versus the d i a m e t e r of the hole.

@ I

Fig. 17. The Vierendeel action of the girder.

and having non-reinforced openings in its web, we use an idea proposed by N a r a y a n a n & R o c k e y , 3 i.e. a linear interpolation between (1) the ultimate toad of a girder without holes (D = 0), due account of course being taken of the buckling of the web, and (2) the ultimate load due to the Vierendeel action of the girder flanges (i.e. for D = bw). The latter case means that the shear force is carried by the flanges only, so that the collapse of such a girder is due to plastic bending of these flanges. Thus, Qu1 =

Qu0(1 - D/bw) + QviD/bw

(5)

Thin-walled girders with circular holes

315

where Q u o -m w ---

mq. Aw. 0"6~rn ,~

(6)

bw. d,~ (7)

m q = m q ! + mq2

buckling reduction coefficient mql =

75dw/bw~n,w~

1

basic buckling reduction coefficient for a slender web loaded in shear mq2 -----O.05Aw/Af<_0 - 1 5

describes the influence of the flanges, and Qvi -- ultimate load due to the Vierendeel action For a simple supported girder shown in Fig. 17, we have Qvi = 1/a(26ra.f- WpLo-- PI. r) -- Pl

(8)

where WpLo is the plastic section modulus of one flange with respect to its own axis. (d) Girder loaded in shear: reinforced holes We use an interpolation p r o c e d u r e similar to that employed in the previous case, but for the calculation of the ultimate load of a girder without holes (D = 0) we neglect buckling effects. It is in the nature of things that the m a x i m u m ultimate load of a girder with an opening cannot be higher than the ultimate load of the related girder without a hole, the web buckling effects being taken into account in its determination (eqn

(6)). Thus, Qu2 = QpL(1 - D/bw) + QviD/bw <- Quo

(9)

where QPI_ =

0.6Aw. ern.w; Aw = bw.dw

(10)

ANALYSIS OF THE TEST RESULTS OBTAINED The proposed formulae were c o m p a r e d with the load-carrying capacities of the girders tested (Table 1). For the interaction between bending and

316

J. Ravinger, P. Lag6ekovd

shear, we used the formula: (M/Mu) 2 + (Q/Ou) 2 = 1

(11)

Good agreement between the test results and the predicted ultimate loads was obtained. Furthermore, it was proved that collapse did occur in that part of the girder for which it was predicted by calculation.

CONCLUSION The tests have proved that it is advantageous to use end stiffeners and that it is very useful to use cut-outs with a brim, i.e. reinforced holes (see the differences between the ultimate loads of girders RP-2 and RP-3 in Fig. 13). The formulae presented above make it possible to calculate the ultimate loads of thin-walled girders with openings. This paper did not deal, however, with the problem of the influence of holes upon the overall stiffness of the girders studied.

BIBLIOGRAPHY 1. Ravinger, J., Girders with unstiffened slender webs. J. Constructional Steel Research, 3(2) (1983) 14-22. 2. CSN 73 1401 Design of Steel Structures (Czechoslovak Design Standard). Praha, 1983. 3. Narayanan, R. & Rockey, K. C., Ultimate load capacity of plate girders with webs containing circular cut-outs. Proc. Instn Civ. Engrs, 71(2) (Sept. 1981) 845-62. 4. Redwood, R. G., Baraud, H. & Daly, M. J., Tests of thin-web beams with web holes. J. Struct. Div. ASCE, 104(ST3) (March 1978) 577-96. 5. Hoglund, T., Strength of thin-plate I-girders with circular or rectangular web holes. Building Statics and Structural Engineering. The Royal Institute of Technology, Stockholm, Bull. No. 87, 1970. 6. Narayanan, R. & Der-Avanessian, N. G., Design of slender webs having rectangular holes. J. Struct. Eng., No. 4 (April 1985) 777-87. 7. Ravinger, J., Girders with holes in webs. In ECCS Colloquium on Stability of Plate and Steel Structures, Ghent University, 6--8 April 1987, pp. 101-5.