Thin-Walled Structures 11 (1991) 219-231
Web Crippling of Multi-web Deck Sections
Jit'i S t u d n i ~ k a Department of Steel Structures, Czech Technical University, Thakur Street 7, 166 29 Prague, Czechoslovakia (Received 17 December 1988; accepted 2 June 1989)
ABSTRACT This paper presents the results of an extensive experimental investigation of web crippling loads for multiple web deck sections. One flange loading and two flange loading conditions were testedfor both end and interior reactions. Based on the test data, it can be concluded that satisfactory conformity was obtained with the Canadian cold formed steel standard for interior support conditions. For end support conditions, a slightly modified expression from the Canadian standard is recommended.
NOTATION 1.22 - 0 . 2 2 r Yield strength factor 1.06 - 0.06R < 1.0 B e n d radius factor 1.33 - 0.33tc Yield strength factor 0.5 < (1.15 - 0.15R) < l . 0 B e n d radius factor 0.7 + 0.3(0/90) 2 W e b i n c l i n a t i o n factor Tensile yield strength C l e a r distance b e t w e e n the flats o f flanges m e a s u r e d in the p l a n e o f the w e b H = hw/t W e b s l e n d e r n e s s ratio k D i s t a n c e b e t w e e n e n d o f d e c k a n d e n d o f b e a r i n g plate K =k/t E n d d i s t a n c e ratio 219 Thin-Walled Structures 0263-8231/91/$03.50© 1991 Elsevier Science Publishers Ltd, England. Printed in Great Britain C 1 ~-~
C2 = C3 = C4 = C0= Fy hw
220 m
Mult n
N = n/t
t'c e, F
R = r/t t 0 K" =
J. S t u d n i ~ k a
Distance between edges of adjacent opposite concentrated loads Ultimate bending m o m e n t Bearing length Bearing length ratio Computed load Test load Inside bend radius Inside bend radius ratio Web thickness Angle between plane of web and plane of bearing surface 45 ° < 0 < 9 0 ° Fy/230
1 INTRODUCTION Cold-formed steel multiple web deck sections are used extensively in building construction. Where these sections are supported by end or interior bearing plates, or are subjected to a concentrated load at some point in the span, failure of the deck can occur by web crippling. Bending stress can be also present, but for some combinations of loading and deck profiles the effect of the bending stress is small and may not contribute significantly to failure. Research reported by Baehre 1 has shown that there is negligible interaction between bending and web crippling when M < Mult/3, and Hetrakul and Yu, 2 Wing and Schuster 3 and RatlifP confirmed this opinion. The ultimate web crippling load capacity is a function of a n u m b e r of parameters, namely, the web slenderness ratio H, the inside bend radius ratio R, the bearing length ratio N, the angle of web inclination 0 and the yield strength of steel Fy. Load capacity also depends on the distance between the bearing edges of adjacent opposite concentrated loads or reactions. W h e n this distance m is greater than 1.5 hw one flange loading is considered to occur. Two flange loading occurs when the clear distance between bearing edges is equal to or less than 1.5 hw. Substantial difference is found between end and interior reaction loadings. C a n a d i a n 5 and AISI 6 codes are identical in definition of end and interior reactions, and state that 'end loading or reaction occurs when the distance from the edge of bearing to the end of a m e m b e r is equal to or less than 1.5hw. W h e n the distance is greater there is interior reaction." The objective of this study was to determine the load resistance of
Web crippling of multi-web deck sections
221
multi-web deck sections subjected to end and interior reaction loading P, as shown in Fig. 1. An experimental test program was set up to provide experimental data so that existing methods of computation could be compared and evaluated.
2 TEST PROGRAM The test program was designed to encompass the most important parameter variations that influence the web crippling resistance of multi-web deck sections subjected to end and interior reaction loading. Test specimens were obtained from a Czechoslovak manufacturer, VSZ Kosice. The two types of specimens are shown in Fig. 2. Spreading of the webs during loading was, for some tests, prevented by transverse tie rods which were bolted to the bottom flange of profiles (see Fig. 3). k. 11 m
i
,
I
l'fl
n
C~.)
rrt
t f~t) L
-
-
Fig. 1. Test set-up for (i) end reaction P (ii) interior reaction P.
"~'AT.~-
t
1
T
d-I
1"5G.
C,2.G
t
G'L1
b,:
/
Fig. 2. Tested multiple web decks.
222
J. Studni6ka
I
"~ --
[
i I
T.
t !
po~i~i0n
R
- -
L---r-J
Fig, 3. End support test. Positions of profile. Tie rods t are bolted to the flange.
The specimens were simply supported at the ends and the load was applied at the centre, as shown in Fig. 1. Relatively large end bearing plates were used for these tests to ensure that failure would occur at the interior load position and vice versa for end load position. The distance m from the edge of the interior bearing plate to the interior edge of the exterior bearing plate was changed to obtain the conditions for one flange and two flange loadings. However, the main changeable dimension was the bearing width n (see Fig. 1). For tests at end supports an inclined steel bearing plate was used, following the ECCS Recommendations. 7 The deck specimens were tested in both positions N and R (see Fig. 3). The test load Pt was taken either as the largest load the specimen was able to sustain (after which a sudden decrease in load was experienced), or as the load which a residual deformation of 1.0 m m developed, whichever was the lesser. The complete arrangement for a typical end support test is shown in Fig. 4. [
| TESTING
L~AD
P~:~H ~
~.ELL
~VbRAULIC
I
I
I
Fig. 4. Test arrangement.
~EC.I
3~CK.
H E KJ
Web crippling of multi-web deck sections
223
3 TEST RESULTS 3.1 Interior support Test results for 40 specimens are given in Table 1. The following comments may be made on the results: (1) test loads are not substantially different for the N and R positions of deck; (2) test results are almost linearly influenced by bearing width n; (3) test loads for specimens with ties are greater than without ties. 3.2 End support Test results for 76 specimens are given in Table 2. T h e same three c o m m e n t s as for the interior support results can be m a d e a n d a further two can be added: (4) the influence of distance m on test results is very small; (5) w h e n distance k is increased, the test load also increases, although the influence is not very strong.
TABLE 1 Test Results for Interior Support; Web Crippling Load Pt in kN
VSZ 12 002
Type of deck: Position."
N
VSZ 12 102 R
N
I00
Distance m (mm):
R 160
N = 10
17'70 17 "90
16"20 17-98
18"23 19 "98
17-07 20' 57
N = 40
20"13 21"30
20'83 21"95
20.77 24" 12
20.18 23.10
N = 60
22" 10 23" 12
23' 10 24" 62
22' 12 24-05
23'53 25.03
N = 80
22' 11 22" 13
24"01 24'98
26"07 25' 17
25.19 27.11
N = 100
24"61 24"87
25"15 27-16
28.11 26.38
27.31 27.28
Upper value is valid for deck without ties; bottom value is valid for deck with ties.
J. Studni6ka
224
TABLE 2 Test Results for End Support; Web Crippling Load Pt in k N VSZ 12 002
Type of deck: N
Position:
VSZ 12 102 R
N
R
50
Distance m (ram):
100
20
100
20
100
100
200
100
200
7'63 10'64
8-32 11"83
8'01 9"01
8"59 11-72
9'16 10'34
10'24 10"37
9'38 10"22
10'54 11"20
N=40
11"36 14"11
12'44 15.08
13'16 12'25
13.61 15'00
12'51 13"35
13"07 14"97
11"46 14'36
14'20 15"14
N = 60
12"45 15"67
14"26 15'29
13"14 15'02
15'26 17"23
14"07 13"52
13"58 14"12
12"34 14"91
14"23 15'03
N = 80
15'84 16"98
19'86 18'82
16"92 22"44
18-92 23"40
14.60 13-88
18'41 17"14
14"09 14"74
15'51 15"62
Distance k (ram): N=
10
150
Distance m (mrn):
240
20
100
20
100
100
200
N = 40
12"42
15'80
--
--
11"84
12'99
N = 60
13'71
16"45
--
--
13"33
14'25
N = 80
14'30
18'11
--
--
14"78
17"02
Distance k (ram):
100
200
m
m
Where there are two values of load, the upper value is valid for deck without ties, and the bottom value is valid for deck with ties.
4 COMPARISON OF TEST LOADS A N D C O M P U T E R LOADS The AISI specification 6 and the Canadian code 5 were used to compute the ultimate web crippling load Pc. As the method of permissible stress is used in the AISI specification, multiplying all equations from clause C 3.4 by the safety factor of 1.85 was necessary. As the Canadian standard is in limit state terms, no corrections were necessary except for the missing resistance factor 0s. Terms in the AISI specification were converted to SI units. Dimensions from Fig. 2 and the measured yield strength Fy = 260 MPa were used for computation of Pc. Computed values Pc are given in Appendix 1.
Web crippling of multi-web deck sections
225
4.1 Interior support Only one flange loading was examined for interior support tests. Comparison of test results Pt with ultimate computed web crippling loads Pc (using the AISI 1986 specification and the Canadian 1984 standard) is shown in Figs 5 and 6. The solid line in the figures represents perfect
~.0
a Q ig
,$
0.8
g
_* ..........
. .......
......
o
VSI ~'tOq *
I
0
. , ?- .....
÷.
6
a '
I
r/o
'
I
~'0
*
60
I
I
8O
I
J'
N
10o
Fig. 5. Test load Pt vs computed load Pc, using AISI specifications. Interior support.
1.'2
~.0
0
a
a
0.6
....
-~ . . . . . . . . . .
-~- ......
~
. . . . . .
o
o
s.- ......
t._
0 0
'
0
!
~0
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I
r~0
'
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80
I
,
N
100
Fig. 6. Test load P, vs computed load Pc, using C A N 3 - - S136. Interior support.
226
J, Studni~ka
correlation (Pt--Pc); the dashed lines are _+ 20% limits, which are acceptable scatter limits for tests of this type, based on previous research. It can be seen that better conformity was reached in Fig. 6, in which almost all results are within + 20% limits over the full range of the bearing lengths. However the mean value o f Pt/Pc of 0.867 with coefficient of variation 0.073 is somewhat disturbing A small n u m b e r of tests makes it impossible to draw firmer conclusions.
4.2 End support Both one and two flange loadings were used in these tests. Comparison of test results Pt with computed load Pc shows that the test results are in reasonable harmony with predicted values of web crippling end support load (see Figs 7 and 8). However, increasing the distance k over boundary value 1.5 hw did not increase the test loads in such a way that they could be compared with the computed loads for interior support. Using the test results, a new slightly modified expression was developed, following the Canadian standard: P = lOt2Fy(sinO) (1 - 0.1r) (1 - 0.1x//R) (1 - H/500) (1 + K/15H)
(1 + 0.005N)
(1)
Equation (1) predicts the web crippling capacity for end reaction for both one and two flange loading if K < 3H. The other limitations from CAN3--S136 are still fully valid. Comparison of eqn (1) with test data in Fig. 9 shows very good prediction of this expression. This is indicated by the values of the mean (1.018) and coefficient of variation (0.136) of Pt/Pc. Computed loads according to eqn (1) are given in Appendix 2.
5 CONCLUSIONS Based on the comparisons of the results of 40 interior support and 76 end support tests with different methods of computation, the following conclusions were reached: (1) The Canadian cold formed steel specification 5 predicted the web crippling capacities reasonably well for interior support conditions. (2) The use o f e q n (1) resulted in better prediction of the web crippling capacity for end support than any of the existing methods. Equation (1) is equally valid for one flange loading and two flange loading. (3) Tests with end support did not confirm the Canadian and AISI provision that increasing the distance from edge of the bearing
Web crippling of multi-web deck sections
P
227
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z
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lbo
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Fig. 7. C o m p a r i s o n of test results with computed load. End support, VSZ 12 002.
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228
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Web crippling of multi-web deck sections
229
4.'2
4.0 R
0.6 ~5Z i~O0~
VS~Z i~iO~
K-~O
o
K = I00
•
K=iO0 K~O0
0
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60
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~0
Fig. 9. Test load Pt vs computed load Pc, using eqn (1). End support. plate to the e n d o f rnulti-web d e c k c a n b r i n g substantial increase o f w e b crippling capacity.
REFERENCES 1. Baehre, R., Sheet metal panels for use in building construction: current research project in Sweden, Proc. 3rd Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, 24-25 November 1975. 2. Hetrakul, N. & Yu, Wei-Wen., Cold-formed steel I - - beams subjected to combined bending and web crippling. Thin-Walled Structures, Proc. Int. Confat the University of Strathclyde, Glasgow. Granada Publications, 1980, pp. 413-19. 3. Wing, B. A. & Schuster, R. M., Web crippling of multi-web deck sections subjected to interior one flange loading, Proc. 8th Specialty Conference on Cold-Formed Steel Structures, St Louis, MO, 11-12 November, 1986. 4. Ratliff, C. D., Interaction of concentrated loads and bending in C-shaped beams, Proc. 3rd Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla, 24-25 November 1975. 5. Canadian Standards Association, CAN3 -- S136 - - M84, Cold formed Steel Structural Members, Toronto, 1984. 6. American Iron and Steel Institute, Specification for the Design of ColdFormed Steel Structural Members, 1986 Edn, Washington DC, 1986. 7. European Recommendations for Steel Construction: The Testing of Profiled Metal Sheets, Publ. 20, ECCS Committee TC 7, 1978.
230
J. Studni~ka
APPENDIX 1 EXPRESSION FOR ULTIMATE WEB C R I P P L I N G LOADS
(1) AISI specifications One flange loading: End reaction Pc =
1 3 t 2 r C 3 C 4 C o ( 179 -
0.33H)(1 + 0.01N)
Interior reaction Pc =
13t2xC1C2Co(291 -
0.4H) (1 + 0.007N)
when N > 60 the factor (1 +0.007N) may be replaced by (0.75 + 0-011N). Two flange loading: End reaction Pc =
1 3 t 2 r C a C 4 C o ( 132 -
0.31H) (1 + 0.01N)
Interior reaction Pc =
13t2rCtC2Co( 417 -
1.22/4) (1 + 0.0013N)
(2) C A N a - - s l a 6 - - M 8 4 One flange loading: End reaction Pc =
lOt2FysinO( 1 -
0-1r) (1 - 0.1x/R ) (1 - 0-002/4)
(1 + 0.005N) Interior reaction Pc =
18t2FysinO( 1 -
0.1x) (1 - 0.075v/R ) (1 - 0.001H)
(1 + 0.005N) Two flange loading End reaction Pc =
lOt2FysinO( 1 -
0.1x) (1 - 0.01v/R) (1 - 0.002/-/)
(1 + 0.01N) Interior reaction Pc -- 1 8 t 2 F y s i n O ( 1 -
0.2r) (1 - 0.03v/R) (1 - 0.0015H)
(1 + 0.01N) W h e n t is in mm, Fy in MPa and 0 in degrees, Pc will be in Newtons. Computed loads for multi-web decks VSZ 12 002 and VSZ 12 102 (each with six webs) are given in Table A1.
231
Web crippling of multi-web deck sections TABLE A1 Web Crippling Load Pc (kN) Type of deck: Loading:
VSZ 12 002 One flange End lnterior
Reaction:
VSZ 12 102
Two flange e
i
One flange e
Two flange
i
e
i
N--10
9"98 20"66 7 " 1 6 25"69 10"69 21"38 11"20 20'73
9 " 3 7 19"74 6'58 23.04 9 " 9 8 20'70 10"45 19"72
N=40
12"70 24.71 9.10 26'68 11-93 2 3 . 6 1 8 " 3 8 23.94 12"22 24"43 14"26 26"39 11.40 23.66 13"31 25'11
N - - 60
14"52 27"42 10.41 27"34 13"63 26"21 9 " 5 8 24"53 13"24 26"47 16"30 30"16 12.63 25"63 15'21 28-69
N=80
16"34 31"47 11.71 28"00 15"34 30.09 10"78 25'12 14"26 28'50 18.33 33-93 13"31 27"60 17"11 32"28
N = 100
18"15 35"72 13-01 28"66 17'05 15'28 30"54 20"37 37'70 14'26
34"15 11"98 25"71 29"58 19"01 35"87
Upper value is AISI result; bottom value is CAN result.
APPENDIX 2 C O M P U T E D LOADS USING EQN (1) Web crippling loads for tested decks VSZ 12 002 and VSZ 12 102 are given in Table A2. TABLE A2 Web Crippling Load Pc (kN) According to eqn (1) VSZ 12 002
Type of deck." Loading."
Both one flange and two flange
Reaction: Ratio K."
VSZ 12 102
end
end
20
100
100
200
N = 10
10"97
12"11
10"81
11"64
N=40
12"55
13"84
12"35
13"30
N = 60
13"59
15"00
13"39
14"42
N = 80
14"64
16" 16
14"42
15"53