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The collapse of welded aluminium plate girders—an experimental study
Fhin-Walled Structures 5 (1987) 247-275
The Collapse of Welded Aluminium Plate Girders---an Experimental Study
H. R. Evans Department of Civil and Structural Engineering, Newport Road, University College, Cardiff CF2 1TA, UK
and M. J. H a m o o d i University of Technology, Baghdad, lraq
(Received 2 November 1986; accepted 13 March 1987)
ABSTRACT Twenty-two tests conducted to study the collapse behaviour of welded aluminium girders are described. The girders are of varying proportions, have transverse or longitudinal web stiffeners and are subjected to different combinations of shear and bending loads. It is observed that, although shear sway mechanisms similar to those for steel girders do develop, the webs of aluminium girders may fracture in the heat affected zones adjacent to the perimeter welds. These fractures develop at some stage during the formation of the collapse mechanism and are the consequence, rather than the cause, of failure. It is shown that the tension field theory, originally developed for steel girders, may overestimate the shear-carrying capacity of aluminium girders and it is concluded that the theory requires some modification before it can be applied with confidence to aluminium girders.
NOTATION
b bf
bs
Clear width of web plate between stiffeners. Width of flange plate. Width of longitudinal stiffener. 247
Thin-Walled Structures 0263-8231/87/$03.50 © Elsevier Applied Science Publishers Ltt England, 1987. Printed in Great Britain
248 d
My Mp
M; mpf mexp t
te t~ Vcr Vexp Vmec
vpw 3/
H. R. Evans, M. J. Hamoodi
Clear depth of web plate between flanges. Plastic m o m e n t of resistance provided by flange plates only. Plastic m o m e n t of resistance of full girder cross-section. Non-dimensional flange strength parameter = Mpf/CF tO-pw. Plastic moment of resistance of the flange plate. Measured bending moment in web panel at failure. Thickness of web plate. Thickness of flange plate. Thickness of longitudinal stiffener. Shear load to produce buckling of web panel. Measured shear load at failure. Shear capacity predicted by mechanism solution. Shear load corresponding to 0.2% proof stress in web. Non-dimensional parameter expressing stiffener rigidity: for transverse stiffeners,
stiffener rigidity Y = web rigidity x web width
stiffener rigidity for longitudinal stiffeners, y = web rigidity x web depth "
O'0-2w, Or0.2f
Proportional elongation of material. Measured 0.2% proof stresses for web and flange material, respectively.
1 INTRODUCTION The accurate prediction of the ultimate load capacity of plate girders has become increasingly important in recent years because of the change from allowable stress to limit state design procedures. As a result of an extensive research study of post-buckling behaviour, a simple tension field theory 1has been developed to predict the collapse loads of welded steel girders. This theory has been incorporated in recently published design codes for steel bridges 2 (BS 5400) and buildings3 (BS 5950) and in the draft of Eurocode 3.4 Currently, the design code for aluminium structures 5 (CP 118) is being rewritten in a limit state format 6 (BS 8118). It is, therefore, necessary to establish whether design methods developed for steel girders can be used to calculate the ultimate load-carrying capacity of welded aluminium girders. The properties of aluminium differ from those of steel in two particularly important respects. Firstly, the elastic modulus of aluminium is only onethird that of steel. Consequently, web buckling will occur at a lower load
Collapse of welded aluminium plate girders
249
Fig. 1. Assumed shear sway failure mechanism associated with the development of a tension field.
and, since the proof stress of aluminium is approximately the same as the yield stress of steel, there will be an even more extensive post-buckling reserve of strength in an aluminium girder than in a steel girder. Because of its greater cost, aluminium is normally only used when saving of self weight is of the utmost importance; it is, therefore essential to take full advantage of the post-buckling reserve of strength. In the second place, the heat input during welding has a much more significant effect on the properties of aluminium than on steel. The resulting loss in material strength within the heat affected zone may lead to a reduction in the ultimate load capacity of aluminium girders. The tension field mechanism solution for steel girders has been described fully elsewhere, i Other than for the illustration of the assumed failure mode in Fig. 1, which shows the development of a yield zone in the web and plastic hinges in the flanges, it will not be considered in any detail here. Instead, this paper will describe an experimental study of the collapse behaviour of aluminium girders fabricated from an alloy (6082) that is particularly susceptible to welding effects. The results of 22 tests on girders of varying proportions, with different web stiffening arrangements and under different loading conditions will be presented and measured load capacities will be compared to those predicted by the tension field theory.
2 E X P E R I M E N T A L P R O G R A M M E AND G I R D E R D E T A I L S The collapse behaviour of a plate girder is particularly influenced by the geometrical characteristics of the girder, by the combination of shear and m o m e n t applied and by the performance of the web stiffeners. The tests
250
H. R. Evans, M. J. H a m o o d i
were planned to study each of these factors in detail and may be conveniently grouped as follows:
Series/--six tests on transversely stiffened girders to study the influence of web slenderness (d/t), and of flange strength (Mp (see notation)). Series 2 - - n i n e tests on transversely stiffened girders to study the influence of web aspect ratio (b/d), of varying levels of co-existent bending moments upon girders loaded predominantly in shear, and of transverse stiffener rigidity. Series 3 - - t w o tests to study the collapse of transversely stiffened girders loaded predominantly in bending. Series 4---five tests to study the influence of longitudinal stiffeners upon girders loaded predominantly in shear. Details of the girders tested in each series will now be described briefly. 2.1 Series 1 tests
In this series, six transversely stiffened girders were loaded predominantly in shear, the general layout of the girders being as illustrated in Fig. 2(a). Accurate dimensions, measured on the fabricated girders, are listed in Table la, together with the geometrical parameters. The web aspect ratio (b/d) was kept constant at 1.47 throughout the six tests. A web slenderness of 280 was considered in the first three tests and an increased slenderness of 375 was considered subsequently. Such slender webs were adopted to ensure early buckling and extensive post-buckling action. The range of variation of flange strength (Mp) considered for each web slenderness is representative of the normal range for steel girders. 2.2 Series 2 tests
Five transversely stiffened girders were fabricated for this series and nine tests were carried out upon them, as detailed in Fig. 2(b) and Table la. Web slenderness and flange strength were kept constant throughout and the spacing of the transverse stiffeners was varied to give web panel aspect ratios (b/d) of 0.97, 0-48 and 0.33 for comparison with the ratio of 1.47 considered in the first series. Different groups of panels were considered in the nine tests, as indicated in Table la. Since each girder was simply supported at its ends and loaded centrally, the various panels were subjected to different combinations of bending moments and shearing forces. This is shown in Fig. 3 where theoretical interaction diagrams 7, defining all combinations of m o m e n t and
Collapse of welded aluminium plate girders
LO°,L_
251
C °,
T PANEL PA2
670
d~30_,
1~4
2 (~ 4 4 2
(a) Girders for series 1 tests.
iq
(c)
I
Girders for series 3 t e s t s . (b) Girders for series 2 tests.
677
~219 _,
14
677
_ , 2 2 1 _~
(d] Girders for series /. tests. (all dimensions in ram) Fig. 2. Details o f test girders.
shear under which the girders would be expected to collapse, are plotted. The moment/shear ratios actually applied to the panels in the tests are indicated by the rays drawn from the origin. The points at which these rays intersect the failure envelope represent the predicted failure loads for the various test panels. Within the region SC of the interaction diagram, the girder will fail under
3
2
1
Test series
AG4 AG1 AG5 AG3 AG2 AG6 AGSI AGS2-TI AGS2-T2 AGS3-T1 AGS3-T2 AGS4-T1 AGS4-T2 AGS5-TI AGS5-T2 AGS6-T1 AGS6-T2
Girder and test
669 669 667 672 671 667 442 219 218 218 218 218 218 144 144 218 105
b (mm) 455 455 457 456 455 456 454 456 457 456 456 456 456 456 455 226 227
d (ram) ~ro.2~
E
bf
1-64 1.60 1.6l 1.21 1.21 1-22 1.20 1.20 1.20 1-20 1.20 1-20 1-20 1.22 1-22 1.20 1.20
285 283 287 259 260 261 279 252 252 252 252 252 252 245 245 252 252
67.8 69-5 67-5 68.1 69-3 68-2 71-5 71-5 71.5 71.5 71.5 71.5 71.5 71.5 71.5 71.5 71.5
101 101 101 10! 101 102 102 103 103 103 102 104 104 102 102 51 51
(ram) (Nmm 2)(kNm 2) (ram)
t
Web detai&
o'0.2f
6-50 9.59 12.60 6.48 9.56 12-90 6-34 6.30 6-30 6.30 6.31 6.32 6-32 6.33 6.33 6.35 6.35
286 300 295 285 301 294 239 239 239 239 239 239 239 239 239 239 239
(ram) (Nmm -2)
tf
Flange details
TABLE la Details of Transversely Stiffened Test Panels
1.47 1.47 1-46 1-47 1.47 1.46 0.97 0-48 0.48 0.48 0-48 0-48 0-48 0.32 0-32 0.96 0.46
b/d
278 284 284 376 376 374 378 380 381 380 380 380 380 372 373 189 189
d/t
Parameters
317 742 1 215 468 1 063 I 90(1 351 386 386 385 385 392 392 392 392 778 778
Mp x 10 -5
PA2 PA2 PA2 PA2 PA2 PA2 PV1,2 PV1,2 PV3,4 PVI,2 PV3,4 PV1,2 PV3,4 PVI 2,3 PV4,5,6 PBI PAl
Test pane&
:z:
.z:
t~o PJi [,3
Collapse o f welded aluminium plate girders
253
the predominant effects of shear. At point C, the failure mode changes from a web shear to a flange bending mode. Figure 3 shows that the m o m e n t / shear combinations sustained by the various panels extend over almost the whole of the predominant shear (SC) range and approach the intermediate point (C) in some cases. Girders AGS2, AGS3 and AGS4 were geometrically identical, other than for the dimensions of the transverse stiffeners. These were deliberately varied, as detailed in Table lb, to allow the possibility of stiffener failure to
TABLE lb Details of Transverse Stiffeners for Panels of Series 2 Tests
Girder and test AGS 1 AGS2-T 1 AGS2-T2 AGS3-T1 AGS3-T2 AGS4-T1 AGS4-T2 AGS5-T1 AGS5-T2
Stiffener a SVC SV 1 SV2 SV1 SV2 SVI SV2 SV1 & 2 SV3 & 4
bs (rnrn)
ts (ram)
y
yL b
y/yc
19.0 13.0 14.0 5.5 11.0 9.5 6.5 19.0 19.0
6.35 6.33 6.33 6.32 6.32 6.33 6.33 6.35 6.35
432 311 383 37 197 133 52 1 3ll 1 311
15 128 128 129 129 128 129 442 451
28.80 2-43 2-99 0-29 1.54 1-04 0.41 2.95 2.95
a All stiffeners double-sided. b R e f e r e n c e 8.
be studied. The stiffeners of girders AGS1 and AGS5, as detailed, were designed not to fail. All stiffeners were 'double-sided', i.e. they were positioned symmetrically on each face of the web plate. Table lb gives the rigidity of each stiffener in the direction perpendicular to the plane of the web, as defined by the non-dimensional parameter y. An allowance has been made for the area of fillet weld connecting the stiffener to the web in the calculation of y. The rigidities of the experimental stiffeners are compared to the values specified in the current code of practice 5 (CP 118). The code rigidity is d e n o t e d by yL in Table lb and corresponds to the simple empirical formula established by Cook and Rockey s (yL = 14d3/b3). For the experimental girders the ratio of y/yL is observed to vary from 2-99 to 0.29, with the latter value representing a very flexible stiffener which would be expected to fail.
254
H . R . Evans, M. J. Hamoodi AG$ 3-TI ~ Stifflmcr AG$ 4-T2J
~oF ../~;:~_~
VI c
O.<; o
~V/V~w ,-AGS 2-1"2
v,.
AG5 2-TI AGS 4-TI
•
oi
,~,:,
o
'////I '
04
O.
O.~
0.4
0.3
0.3 0.2
0.~ 0.1
I
0
0[2
i
I
04
,
i
i
0.6
O. i
0.8
_
I.O-MIMp
D
oT.V~" ,
0.8 0.57
0.6i O..= 0.,~
0.5 0.5 0.4
0.3 0.~ 0.1
0.3 0.2 O.]
/D I 0.4 ' 0~.6 = 0,8 '
IIO-'-M/Mp
O
G i r d e r AG S 5 - S e r i e s 2
0.2
0.4
O.b
•Expcrimcntai points ~ C
O.e 0.7 0.8
/ / j/
0.5 0.4 0.3 0.2 0.1 0
D t
0.2
~
0.4
Girder A G S
0.6
0.8
0.8
t.O ~M/Mp
Girder A G S 6 -TI -Series 3
V/v~
i
i
1.0 M/Mp
C
S
I.C O.g
0.8
,Vlvp. o0 .C
i C~
; OI-6
IP/I
1.0
o~~,,O,ST,
O
(~2 1 0 ! 4
i
G i r d e r s A G S 2,3 & / . - S e r i e s 2
/- AGS5-T2
0.~ 0.;
i
0
Girder AG S 1-Series 2
l
failure
i
,
1.0 ~MIMp
6-T2-Series
3.
Fig. 3. M o m e n t / s h e a r interaction diagrams for test girders.
Collapse of welded aluminium plate girders
255
2.3 Series 3 tests
Two tests were conducted upon the single girder fabricated for this series, as shown in Fig. 2c. Web slenderness and flange strength were the same for both tests, see Table la, but the panel aspect ratio was changed from 0.96 in the first test to 0.47 in the second. The specific object to these two tests was to study collapse under high bending moment. The moment/shear interaction diagram in Fig. 3 shows that the applied load combinations for both the test panels lie within the required 'bending mode' region CD of the diagram. 2.4 Series 4 tests
Finally, in series 4, five longitudinally stiffened girders were tested under a predominant shear loading; the girders are illustrated in Fig. 2(d) and girder dimensions are given in Table 2. All five girders were nominally identical, other than for the number and dimensions of the longitudinal stiffeners. The overall dimensions of the five girders were chosen to be similar to those of the unstiffened girder AG3 tested in series 1 to allow the effects of introducing the longitudinal stiffeners to be determined. Girders AGLS1 to AGLS4 were reinforced by two longitudinal stiffeners and girder AGLS5 was reinforced by three stiffeners. The stiffeners were located so as to divide the web into sub-panels of equal depth, this being the o p t i m u m stiffener positioning for a girder under pure shear. In girders A G L S 1 to AGLS4 the dimensions of the longitudinal stiffeners were varied, as shown in Table 2(b), to allow the possibility of stiffener failure to be studied. In the table, the non-dimensional stiffener rigidity 3' is compared to the •" value. As defined by Kloppel and Scheer 9, ~/ is the rigidity value calculated from elastic buckling theory as the minimum rigidity required to ensure that the stiffener remains straight and limits buckling to the adjacent sub-panels of the web. The ratio of 3'/3/" is seen to reduce to a value of only 0-10 for girder AGLS1 indicating probable stiffener failure. The three longitudinal stiffeners of girder AGLS5 were designed not to fail.
3 MATERIAL PROPERTIES All the test girders were fabricated from the heat treatable 6082 (previously designated H30TF) aluminium alloy using shielded argon arc welding. In the absence of a distinct yield point, the 0.2% proof stress (O-o.2)will be adopted as the reference stress for design calculations. Material properties were established by exhaustive testing and measured
Test series
669 669 668 668 669
AGLS 1 AGLS2 AGLS3 AGLS4 AGLS5
454 455 455 454 454
d (mm)
bf
1-20 1.20 1"20 1.23 1"22
2 2 2 2 3
AGLS 1 AGLS2 AGLS3 AGLS4 AGLS5
5.0 22.0 9.0 12.5 28-6
bs (ram)
a All stiffeners double-sided. b Reference 9.
No. of stiffeners"
Girder
279 252 252 281 245
6-30 6.33 6.32 6.33 6-33
ts (mm)
71,5 71 "5 71"5 71"5 71-5
7
15 671 55 125 1 376
102 103 102 104 102
(mm) (Nmm-2)(kNm -2) (mm)
O'0.2f
6.34 6.30 6-30 6-32 6-33
140 140 140 140 163
7 "b
239 239 239 239 239
(mm) (Nmm -2)
tf
E
t
o-o.2~
Flange details
Web details
(b) Details of stiffeners:
b (mm)
Girder
(a) Overall details of panels:
TABLE 2 Details of Longitudinally Stiffened Test Panels
0-10 4.79 0.40 0-90 8.47
3~IY"
1-47 1-47 1-47 1.47 1.47
b/d
378 379 379 369 372
d/t
Parameters No. of
351 386 385 347 392
× 10 5)
stiffness
Mp* longitudinal
Z:
~z
t'O
AG4 AG 1 AG5 AG3 AG2 AG6 AGS 1 AGS2 AGS3 AGS4 AGS5 AGS6
Girder
1.64 1.60 1-61 1.21 1.21 1.22 1.20 1.20 1.20 1.20 1.22 1-20
285 283 287 259 260 261 279 252 252 252 245 252
O'0.2w
(Nmm-2)
I
(mm) 322 323 324 309 313 310 315 317 314 317 317 317
(Nmm 2)
Oru
Web material
8-38 9.66 8-88 15-5 15.3 16.8 16.8 19-2 17.6 17.6 17.3 17.8
× 10-2
"0
31 29 31 25 23 26 36 20 20 20 17 20
6.50 9.59 12.60 6.48 9.56 12-90 6.34 6.30 6-30 6-32 6.33 6.33
(mm)
If
TABLE 3 Typical Material Properties
O'u
286 300 295 285 301 294 239 239 239 239 239 239
305 314 311 305 314 329 336 334 334 334 332 332
(Nmm -2) (Nmm -2)
O'0.2f
Flange material 7~
11.9 11.1 19-6 15.2 15.7 16.3 20-1 21.9 21.9 21.9 21-9 21.9
× 10-2 64 88 87 64 103 39 14 14 14 14 14 14
I'Q
~" 5. ~" -~ E"
t~
H. R. Evans, M. J, Hamoodi
258
proof stresses of web and flange material (cr0.zwand o0.2f)are given in Tables 1 and 2; the elastic modulus (E) of the web material is also tabulated. Strain measurements on the test specimens allowed a representative value of 0-32 to be determined for the Poisson's ratio. Further measured values of material properties are given in Table 3 for the transversely stiffened girders. The ultimate tensile strength (o-,) is listed, together with the proportional elongation ('0) at failure. Although the values of the proof and ultimate stresses remain reasonably constant, considerable variation is noted in the proportional elongation. Lower values of ~9, indicating low ductility, are observed for the thicker web material of girders AG4, AG1 and AG5. An empirical equation defining the relationship between stress and strain for any alloy has been proposed by Ramberg and Osgood, as discussed by Dwight. 10This may be written in the following form: • = E
0.002
where the index n is known as the 'knee factor' and is chosen to ensure that the equation produces a curve passing through the true 0.2% proof stress point. A low value of n produces a rounded curve, whereas a high value of n gives a sharper knee. A simple empirical formula has been proposed by Dwight 1° to allow n to be determined from the standard mechanical properties: /7
--
log, (500~) log, (o'./0"0.2)
Values of the knee factor calculated from this formula are given in Table 3. They are seen to be reasonably consistent for the web material, ranging from 17 to 36, but the flange values for the girders of series 1 are considerably higher than those for the second series; they reach a maximum of 103, indicating a particularly sharp knee to the curve, for AG2. Typical stress/strain curves obtained from the Ramberg-Osgood formula are compared to experimental results in Fig. 4 for typical web and flange material. In both cases the empirical curve, using the n values calculated from Dwight's formula, lies very close to the experimental curve. It is well-known that the 6082 alloy is particularly susceptible to the effects of welding. Mazzolani 11 has shown that the heat affected zone extends a distance of approximately 20 mm from each side of the weld, confirming the assumption of 25 mm made in CP 118. 5 Mazzolani has also indicated that within the heat affected zone, the proof stress of the alloy is reduced by between 45% and 50%. A detailed study by Seah 12 of the particular alloy
Collapse of welded aluminium plate girders
259
300
t"s 2 0 0
Z = u IOO
n - 24.7 I
o,
I
02
0'3
0'4
d.s
0'6
0 .'7
"
O/o Strain ...... - -
Experimental curve Romberg Osgood equation
30C
O4 E
20C
X
lOC
al
/ 0
n = 15.95 I
0.I
I
I
0.2
0.3
I
I
0.4 0.5 Olo Strain
I
0.6
0 I7
Fig. 4. Typical stress/strain curves for web and flange material.
used in the present test series has confirmed Mazzolani's findings, regarding b o t h the extent of the heat affected zone and the amount of the strength reduction.
4 TESTING PROCEDURE AND INSTRUMENTATION E a c h test girder was simply supported at its ends and loaded by a vertical central point load. At the start of each test, the initial deformations of the
260
H. R. Evans, M. J. Hamoodi
webs, flanges and stiffeners were measured. Test loads were applied by a servo-controlled hydraulic jack which enabled the load to be applied so as to achieve and maintain a specified deflection. Displacements of the webs and stiffeners were recorded at selected load levels and the strains set up in some girders were recorded. After failure, the residual deflected shapes of the relevant web and flanRe panels were recorded. A large number of results, giving detailed information of girder behaviour, were obtained. These have been presented in detail by Hamoodi 13and will now be summarized for each series of tests in turn.
5 RESULTS F O R SERIES 1 TESTS The six tests in this series were planned to show the infuence of web slenderness and flange strength upon collapse behaviour under predominant shear. Final failure occurred in each test when the web plate fractured in the perimeter regions where the web tension field anchors against the boundary members. These fractures are clearly seen in Fig. 5 particularly in the close-up view in Fig. 5(d). A selection of girders is shown viz. AG4 (moderately slender web, weak flange), AG5 (similar web, strong flange) and A G 3 (very slender web, weak flange). In each case, before web fracture occurred, the girder developed a shear failure mechanism similar to that observed in steel girders. The shear sway action is clearly observed in all the photographs, as are the web buckles and the plastic hinges in the flanges. The load/deflection curves are plotted in Fig. 6a for the three girders of moderate web slenderness and in Fig. 6b for the three girders with very slender webs. The gain in capacity with flange strength is apparent and each curve shows the expected characteristics. During the approach to failure, the slope of the curve decreases rapidly and, a well-defined plastic collapse 'plateau' is observed before final failure occurs due to web fracture. Predicted and measured results are summarised in Table 4 (see notation for definition of terms). The ratio of the experimental failure load (Vexp) to the buckling load (V~r) ranges from 11.9 to 23-4, showing the extensive post-buckling reserve of strength of the test girders. The variation of the Mexp/MFratio from 0.17 to 0.41 shows shear to have been the predominating load action in this first series. The ratio Vexp/Vmecshows the accuracy of the girder capacity (V,~ec) predicted by the tension field mechanism solution.1 Other than for girder AG6, where subsequent inspection showed an end post failure to have occurred in conjunction with the shear sway mechanism, no serious discrepancy is
Collapse of welded aluminium plate girders
261
AG4 Fig. 5(a). View of girder AG4.
Cj 5 Fig. 5(b). View of girder AG5.
262
H. R. Evans, M. J. Hamoodi
Fig. 5(e). View of girder AG3.
AG 3 Fig. 5(d). Close up view of fracture in girder AG3.
Collapse of welded aluminium plate girders 70 f /
-- 6O z ==
""V
f
263
" ~X
___.¢~
_o s o
~ 4c (~~ '< 20 I0
Key
/ / F/ /
~
I S
O
Point of web fracture G_irder AG 4 with M¢= .OO317 . . . . . Girder AG I with M~= .00742 iGirder AG 5withlM ~" = .OI215 I IO IS 20 Central deflection (ram)
Fig. 6(a). Load/deflection curves for girders with web slenderness ratio of 280.
5O z
40 o 30
.~ 20
~ to
f/ // "l/ t~/" ~lr
I 5
~ Point o f w e b fracture ~ Girder AG3 with M ~ = .00468 . . . . . Girder AG2 with Mp~= ,OIO63 - - - - i Girder AG 6 with M ; : .OI 899 I I0 15 Central deflection (mm)
Fig. 6(b). Load/deflection curves for girders with web slenderness ratio of 375.
observed. For the other girders, the theory slightly underestimates the capacity of A G 4 but overestimates in all other cases, with a maximum overestimation of 8% being noted for AG2.
6 R E S U L T S F O R S E R I E S 2 TESTS The nine tests in this series were planned to give information about the c o m b i n e d effects of shear and bending, of panel aspect ratio and of transverse stiffener rigidity. W e b fractures were again observed in all girders at failure, with all stiffeners proving adequate, other than for the very light stiffeners of girders AG3-T1 and AG4-T2. The results obtained are summarised in Table 4.
H. R. Evans. M. J. Hamoodi
264
TABLE 4 Results for Transversely Stiffened Girders
Test series
Girder and test
Vexp (kN)
Vexp
Vexv
Vcr
Vpw
M~xp MF
Vexp Vme¢
1
AG4 AG1 AG5 AG3 AG2 AG6 AGS1 AGS2-T1 AGS2-T2 AGS3-T1 AGS3-T2 AGS4-T1 AGS4-T2 AGS5-T1 AGS5-T2 AGS6-T 1 AGS6-T2
52'3 56.3 69"3 33.9 41-4 44.4 47-0 62.0 63'5 50'0 59.0 60.5 57.0 62.0 68.5 20-0 23.5
11.9 13-2 16"2 19-0 22-5 23.4 19.8 12-4 9.2 12.2 10-4 12" 1 9-5 9-0 7-7 4.1 1.6
0.43 0-47 0.57 0-41 0-50 0.53 0-54 0.78 0.80 0-63 0-74 0.76 0.72 0-79 0.87 0-51 0.59
0"41 0.29 0"27 0.27 0-21 0.17 0-29 0.58 0" 19 0-63 0'33 0.56 0.29 0.52 0.42 1-01 1-16
1-01 0.93 0"98 0.93 0.92 0.81 a 0.96 0.98 0"95 0'82 b 0.90 0.95 0.87 b 0.87 0.93 0.96 c 1. l0
2
3
Failed panel PA2 PA2 PA2 PA2 PA2 PA2 PV2 PV2 PV4 PV1 PV3 PV2 PV3 PV3 PV4 PBI PAl
a E n d post failure. b T r a n s v e r s e stiffener deflection. c Lateral movement of flange.
The combined moment and shear levels applied to the various girder panels have been defined by the rays drawn on the theoretical interaction diagrams in Fig. 3. The actual moment/shear ratio at failure in each test is now superimposed upon the ray for the panel in which failure occurred to give a comparison of theory and experiment. Each of the tests involved a group of sub-panels, as discussed earlier, and although each web panel buckled under shear, final fracture did not always occur in the panel subjected to the highest bending moment. For example, Fig. 7(a) shows girder AGS1 after test where, although extensive buckling of both panels is observed, fracture occurred in panel PV2 with the lower bending moment. Thus, the comparison of values in Table 4 for this test is based on results for PV2 and the experimental point is inserted on the ray for this panel in Fig. 3. These theoretical curves show the expected reduction in shear capacity due to the presence of moments to have been slight. The test results confirm that the shearing action was the prime cause of the fracture in the webs. The effects of a decreasing web aspect ratio upon the collapse behaviour
Collapse of welded aluminium plate girders
AGS
Fig. 7(a). View of girder AGS1.
A GS 4 TEsTI
Fig. 7(b). View of girder AGS4-T1.
265
266
H. R. Evans, M. J. H a m o o d i
Fig. 7(c). View of girder AGS5-T1.
are illustrated by comparing the results obtained earlier for AG3 (b/d = 1.47) to those now presented for the seven tests on AGS1 (b/d = 0-97), AGS2-T1 and AGS2-T2, AGS3-T2 and AGS4-T1 (for all of which b/d = 0.48) and AGS5T1 and AGS5T2 (b/d = 0.32). Views of a selection of these girders after collapse are presented in Fig. 7 for comparison with the earlier view of AG3 in Fig. 5(c). Severe web fracture is clearly apparent for the two girders with low web aspect ratios. Load/deflection curves are plotted in Fig. 8 for girders of varying b/d ratios. Although each curve does just about reach a horizontal failure plateau, this is very much shorter than the well-defined plastic plateau obtained for AG3. The collapse behaviour, therefore, becomes less 'ductile' with a decreasing web aspect ratio. The increase in girder strength with the introduction of intermediate transverse stiffeners is also apparent.
Collapse of welded aluminium plate girders
267
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The comparison of experimental and predicted values in Table 4 shows the theory to have overestimated the girder capacity in all cases with the ratio of Vexp/Vmecfor girders with adequate stiffeners varying from 0.87 (AGS5-T1) to 0.98 (AGS2-T1). Although the largest theoretical overestimation is for the panel with the lowest b/d ratio, there is no definite trend. Indeed the Voxp/Vm~ratios obtained for the series 2 tests are similar to those listed for series I where the web aspect ratio was 1.5 throughout. The transverse stiffeners proved fully adequate for all the seven girders discussed so far in this series, even though the stiffener on AGS4-T1 was very light with a Y/YL ratio of only 1.04. However, for the two remaining girders--AGS4-T2 (3'/YL = 0"41) and AGS3-T1 (Y/3'L = 0-29)--the stiffeners proved inadequate, as had been expected. Views of these two girders after failure in Fig. 9 show stiffener deflections perpendicular to the plane of the web and web buckles running through the stiffeners into the adjacent sub-panels. The stiffener failures naturally lead to a considerable theoretical overestimation of the collapse load. When the Y/YL ratio drops from 0.41 to 0.29, the Voxp/Vm~cratio also reduces from 0.87 to 0.82. A tension field analysis of these two panels, assuming them to be completely unstiffened, would give a lower bound to the strength and Vexp/Vmoc ratios of 1"24 and 1.12, respectively. Finally, in Fig. 10a, the ratio of the experimental load to the 0.2% proof load (Vexo/Vp,) is plotted against the stiffener rigidity ratio (Y/YL). The curve shows that the girder strength initially increases rapidly with an increasing
268
H. R. Evans, M. J. Hamoodi
AG S 3 TEsT I
Fig. 9. Views of 2 girders with inadequate stiffeners after failure. Girder AGS4-T2 (top) and Girder AGS3-T1 (bottom).
269
Collapse of welded aluminium plate girders I.IVtxPIvpw
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7 R E S U L T S F O R SERIES 3 TESTS T h e two tests in this series were carried out to investigate collapse behaviour u n d e r high bending m o m e n t , as indicated by the rays drawn on the theoretical interaction diagrams in Fig. 3.
270
H. R. Evans, M. J. H a m o o d i
Fig. 11. View of girder AGS6-T2.
Unfortunately, because of inadequate restraints, some lateral movement of the compression flange occurred at failure in the first test (AGS6-T1.) Consequently, the experimental point lies within the predicted failure envelope in Fig. 3 and Table 4 shows an overestimation of 4% by the theory. However, the second test (AGS6-T2) was entirely successful and the photograph in Fig. 11 gives a clear illustration of a failure mode in which buckling of the compression zone of the web under high bending is combined with an inclined shear buckle. In this case, the experimental point lay well outside the predicted failure envelope and Table 4 (V~xp/Vm~c= 1" 10) shows a safe underestimation of the collapse load by the theory. Girder AGS6-T2 differed from the earlier girders with the same web aspect ratio in two important respects; in the first place, bending was now dominant and, secondly, the web slenderness ratio was reduced significantly. Whereas web fracture had been noted in all the earlier tests, this did not occur in AGS6 where a long plastic failure plateau was obtained in the load/deflection curve.
8 RESULTS F O R SERIES 4 TESTS The five girders tested in this final series were identical to girder AG3 of series 1, other than for the number and dimensions of the longitudinal
Collapse of welded aluminium plate girders
271
TABLE 5 Results for Longitudinally Stiffened Girders
Test series 4
Vexp
V~xp
Vexp
Mexp
Girder
(kN)
V~r
Vpw
Mr
Vexp Vmec
AGLS1 AGLS2 AGLS3 AGLS4 AGLS5
41.5 44.0 43.5 46.5 49.5
3.73 3.94 3.91 3.88 2-52
0.47 0.55 0.55 0.51 0.63
0.38 0-42 0.41 0-43 0-47
0.94~ 1.06 1.06 1.01 1.03
a Longitudinal stiffener failure.
stiffeners employed. The tests were specifically intended to show the influence of these stiffeners upon the collapse behaviour under predominant shear. The longitudinal stiffeners proved fully adequate in all tests other than that on AGLS1 where the stiffeners were extremely light (y/y* = 0.10); even the relatively light stiffeners of AGLS3 and AGLS4 (y/y" = 0.40 and 0-90) proved satisfactory. The plot of girder strength against stiffener rigidity in Fig. 10b shows similar characteristics to that in Fig. 10(a) for transversely stiffened girders. In Fig. 10(b), the 'knee' value, beyond which an increase in longitudinal stiffener rigidity has little influence on girder strength, occurs at a y/y* ratio of around 0.5. Comparison of the measured failure loads given in Table 5 with that for the unstiffened girder AG3 shows a significant gain in strength to have been achieved by stiffening. The failure load of 33.9 kN for AG3 increases to an average of 44-7 kN with the introduction of two adequate stiffeners and to 49-5 kN when a third stiffener is employed. This is largely because of the increase in the initial buckling capacity of the stiffened web. It is very noticeable that the indicator of the extent of post-buckling action (Vexp/V,) decreases from 19.0 for AG3 to only 2.52 for AGLS5. In contrast to the transversely stiffened girders under predominant shear, no fractures occurred in the webs of the longitudinally stiffened girders. Indeed, a well-defined plastic failure plateau was developed in each case before the girder was unloaded, as indicated by the load/deflection plots in Fig. 12. The photographs in Fig. 13 typify the clear shear sway collapse mechanisms developed in each test girder. For all the girders with adequate stiffeners, the tension field theory underestimated the measured collapse load; Table 5 shows the Vexp/Vmec ratio to vary from 1.01 to 1-06. For girder AGLS1, where the stiffeners failed, an analysis of the corresponding unstiffened girder gives a lower bound to the strength and a Vexp/Vm~ratio of 1"13.
H. R. Evans, M. J. Harnoodi
272
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9 CONCLUSIONS The 22 tests reported in this paper have shown that, although welded aluminium girders develop shear sway mechanisms similar to those of steel girders, the webs of aluminium girders may fracture within the heat-affected zones adjacent to the perimeter welds. These fractures occur at some stage during the development of the collapse mechanism and may be regarded as a consequence, rather than the cause, of failure. The fractures are due to a reduction in material ductility and strength within the heat-affected zone which makes it impossible for the large plastic deformations, associated with the formation of a long failure plateau, to be developed in many cases. Long failure plateaus, indicating 'ductile' failures, are obtained for girders with wide web panels, but the length of the plateau decreases as the transverse stiffener spacing is reduced. For webs with very closely-spaced stiffeners, the high local strains arising from a combination of the tensile membrane field of the shear sway action and the secondary out-of-plane bending of the buckling action, result in virtually no failure plateaus and 'brittle' failures. It should be noted, however, that although the web slenderness ratios of the aluminium girders were similar to those for steel girders, the girders were operating much further beyond their buckling loads because of the reduced material stiffness; indeed, in the extreme case, the collapse load was 23 times the buckling load. The secondary out-of-plane bending stresses
Collapse of welded aluminium plate girders
273
AG S 5:
Fig. 13. View of girder AGLS4 (top); view of girder AGLS5 (bottom).
were, therefore, particularly high because of the magnitude of the web buckles developed. When longitudinal stiffeners were employed to control the buckling, ductile failure plateaus with no web fractures were obtained although the collapse loads still approached four times the buckling loads. The tests have illustrated the significant gain in girder strength that can be achieved by employing transverse and longitudinal web stiffeners. It has also been shown that these stiffeners can be approximately proportioned by referring to linear buckling theory. However, since the main expense associated with the provision of stiffeners arises from fabrication rather than
274
H. R. Evans. M. J. Hamoodi
material costs, little economy is lost by increasing the stiffener dimensions b e y o n d the apparent minimum required. Finally, it has been observed that the tension field theory, originally developed for steel girders, may overestimate the shear carrying capacity of welded aluminium girders. This is in contrast to extensive observations for steel girders, where the theory invariably underestimates shear capacity. A l t h o u g h the maximum overestimation noted herein was only 13% and the girders were operating a long way into the post-buckling range and were m a d e of an alloy that was extremely susceptible to loss of strength due to welding, any such overestimation can have serious consequences from the point of view of design calculations. It is thus evident that the tension field theory requires some modification before it can be applied with confidence to the analysis of aluminium girders.
ACKNOWLEDGEMENT The authors wish to thank the Royal A r m a m e n t Research and Developm e n t Establishment for fabricating the test girders and for general support. In particular, the frequent helpful discussions with Dr P. S. Bulson and Mr D. W e b b e r are gratefully acknowledged.
REFERENCES I. Rockey, K. C., Evans, H. R. and Porter, D. M., A design method for predicting the collapse behaviour of plate girders, Proc. Instn. Civ. Engrs. 65 (1978) 85-112. 2. BS 5400, Steel, Concrete and Composite Bridges: Part 3, Code of Practice for Design of Steel Bridges, British Standards Institution, London, 1982. 3. BS 5950, Structural Use of Steelwork in Building: Part 1, Code of Practice for Design in Simple and Continuous Construction, British Standards Institution, London, 1985. 4. Eurocode 3, Common Unified Code of Practice for Steel Structures Draft, EEC, November 1983. 5. CP 118, The Structural Use of Aluminium, British Standards Institution, London, 1969. 6. BS 8118, Draft Code of Practice for the Design of Aluminium Structures, British Standards Institution, London, 1985. 7. Evans, H. R., An appraisal, by full-scale testing, of new design procedures for steel girders subjected to shear and bending, Proc. lnstn. Cir. Engrs. Part 2, 81 (1986) 175-189. 8. Cook, I. T. and Rockey, K. C., Shear buckling of clamped and simply supported infinitely long plates reinforced by transverse stiffeners, Aeronautical Q. XllI (February 1962) 41-70.
Collapse of welded aluminium plate girders
275
9. Kloppel, K. and Scheer, J., Beulwerte Ausgesteifter Rechteckplatten, Wilhelm Ernst and Sohn, Berlin, 1968. 10. Dwight, J. B. Private communication, 1982. 11. Mazzolani, F. M., Proposal to classify the aluminium alloys on the basis of the mechanical behaviour, ECCS Committee 16, doc. 16.74.2, 1974. 12. Seah, H. A., The behaviour of welded aluminium alloy plate girders reinforced with carbon fibre reinforced plastics, MSc Thesis, University College Cardiff, 1984. 13. Hamoodi, M. J., The behaviour of reinforced aluminium web plates in shear loading, MSc Thesis, University College Cardiff, 1983.
The Collapse of Welded Aluminium Plate Girders---an Experimental Study
H. R. Evans Department of Civil and Structural Engineering, Newport Road, University College, Cardiff CF2 1TA, UK
and M. J. H a m o o d i University of Technology, Baghdad, lraq
(Received 2 November 1986; accepted 13 March 1987)
ABSTRACT Twenty-two tests conducted to study the collapse behaviour of welded aluminium girders are described. The girders are of varying proportions, have transverse or longitudinal web stiffeners and are subjected to different combinations of shear and bending loads. It is observed that, although shear sway mechanisms similar to those for steel girders do develop, the webs of aluminium girders may fracture in the heat affected zones adjacent to the perimeter welds. These fractures develop at some stage during the formation of the collapse mechanism and are the consequence, rather than the cause, of failure. It is shown that the tension field theory, originally developed for steel girders, may overestimate the shear-carrying capacity of aluminium girders and it is concluded that the theory requires some modification before it can be applied with confidence to aluminium girders.
NOTATION
b bf
bs
Clear width of web plate between stiffeners. Width of flange plate. Width of longitudinal stiffener. 247
Thin-Walled Structures 0263-8231/87/$03.50 © Elsevier Applied Science Publishers Ltt England, 1987. Printed in Great Britain
248 d
My Mp
M; mpf mexp t
te t~ Vcr Vexp Vmec
vpw 3/
H. R. Evans, M. J. Hamoodi
Clear depth of web plate between flanges. Plastic m o m e n t of resistance provided by flange plates only. Plastic m o m e n t of resistance of full girder cross-section. Non-dimensional flange strength parameter = Mpf/CF tO-pw. Plastic moment of resistance of the flange plate. Measured bending moment in web panel at failure. Thickness of web plate. Thickness of flange plate. Thickness of longitudinal stiffener. Shear load to produce buckling of web panel. Measured shear load at failure. Shear capacity predicted by mechanism solution. Shear load corresponding to 0.2% proof stress in web. Non-dimensional parameter expressing stiffener rigidity: for transverse stiffeners,
stiffener rigidity Y = web rigidity x web width
stiffener rigidity for longitudinal stiffeners, y = web rigidity x web depth "
O'0-2w, Or0.2f
Proportional elongation of material. Measured 0.2% proof stresses for web and flange material, respectively.
1 INTRODUCTION The accurate prediction of the ultimate load capacity of plate girders has become increasingly important in recent years because of the change from allowable stress to limit state design procedures. As a result of an extensive research study of post-buckling behaviour, a simple tension field theory 1has been developed to predict the collapse loads of welded steel girders. This theory has been incorporated in recently published design codes for steel bridges 2 (BS 5400) and buildings3 (BS 5950) and in the draft of Eurocode 3.4 Currently, the design code for aluminium structures 5 (CP 118) is being rewritten in a limit state format 6 (BS 8118). It is, therefore, necessary to establish whether design methods developed for steel girders can be used to calculate the ultimate load-carrying capacity of welded aluminium girders. The properties of aluminium differ from those of steel in two particularly important respects. Firstly, the elastic modulus of aluminium is only onethird that of steel. Consequently, web buckling will occur at a lower load
Collapse of welded aluminium plate girders
249
Fig. 1. Assumed shear sway failure mechanism associated with the development of a tension field.
and, since the proof stress of aluminium is approximately the same as the yield stress of steel, there will be an even more extensive post-buckling reserve of strength in an aluminium girder than in a steel girder. Because of its greater cost, aluminium is normally only used when saving of self weight is of the utmost importance; it is, therefore essential to take full advantage of the post-buckling reserve of strength. In the second place, the heat input during welding has a much more significant effect on the properties of aluminium than on steel. The resulting loss in material strength within the heat affected zone may lead to a reduction in the ultimate load capacity of aluminium girders. The tension field mechanism solution for steel girders has been described fully elsewhere, i Other than for the illustration of the assumed failure mode in Fig. 1, which shows the development of a yield zone in the web and plastic hinges in the flanges, it will not be considered in any detail here. Instead, this paper will describe an experimental study of the collapse behaviour of aluminium girders fabricated from an alloy (6082) that is particularly susceptible to welding effects. The results of 22 tests on girders of varying proportions, with different web stiffening arrangements and under different loading conditions will be presented and measured load capacities will be compared to those predicted by the tension field theory.
2 E X P E R I M E N T A L P R O G R A M M E AND G I R D E R D E T A I L S The collapse behaviour of a plate girder is particularly influenced by the geometrical characteristics of the girder, by the combination of shear and m o m e n t applied and by the performance of the web stiffeners. The tests
250
H. R. Evans, M. J. H a m o o d i
were planned to study each of these factors in detail and may be conveniently grouped as follows:
Series/--six tests on transversely stiffened girders to study the influence of web slenderness (d/t), and of flange strength (Mp (see notation)). Series 2 - - n i n e tests on transversely stiffened girders to study the influence of web aspect ratio (b/d), of varying levels of co-existent bending moments upon girders loaded predominantly in shear, and of transverse stiffener rigidity. Series 3 - - t w o tests to study the collapse of transversely stiffened girders loaded predominantly in bending. Series 4---five tests to study the influence of longitudinal stiffeners upon girders loaded predominantly in shear. Details of the girders tested in each series will now be described briefly. 2.1 Series 1 tests
In this series, six transversely stiffened girders were loaded predominantly in shear, the general layout of the girders being as illustrated in Fig. 2(a). Accurate dimensions, measured on the fabricated girders, are listed in Table la, together with the geometrical parameters. The web aspect ratio (b/d) was kept constant at 1.47 throughout the six tests. A web slenderness of 280 was considered in the first three tests and an increased slenderness of 375 was considered subsequently. Such slender webs were adopted to ensure early buckling and extensive post-buckling action. The range of variation of flange strength (Mp) considered for each web slenderness is representative of the normal range for steel girders. 2.2 Series 2 tests
Five transversely stiffened girders were fabricated for this series and nine tests were carried out upon them, as detailed in Fig. 2(b) and Table la. Web slenderness and flange strength were kept constant throughout and the spacing of the transverse stiffeners was varied to give web panel aspect ratios (b/d) of 0.97, 0-48 and 0.33 for comparison with the ratio of 1.47 considered in the first series. Different groups of panels were considered in the nine tests, as indicated in Table la. Since each girder was simply supported at its ends and loaded centrally, the various panels were subjected to different combinations of bending moments and shearing forces. This is shown in Fig. 3 where theoretical interaction diagrams 7, defining all combinations of m o m e n t and
Collapse of welded aluminium plate girders
LO°,L_
251
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shear under which the girders would be expected to collapse, are plotted. The moment/shear ratios actually applied to the panels in the tests are indicated by the rays drawn from the origin. The points at which these rays intersect the failure envelope represent the predicted failure loads for the various test panels. Within the region SC of the interaction diagram, the girder will fail under
3
2
1
Test series
AG4 AG1 AG5 AG3 AG2 AG6 AGSI AGS2-TI AGS2-T2 AGS3-T1 AGS3-T2 AGS4-T1 AGS4-T2 AGS5-TI AGS5-T2 AGS6-T1 AGS6-T2
Girder and test
669 669 667 672 671 667 442 219 218 218 218 218 218 144 144 218 105
b (mm) 455 455 457 456 455 456 454 456 457 456 456 456 456 456 455 226 227
d (ram) ~ro.2~
E
bf
1-64 1.60 1.6l 1.21 1.21 1-22 1.20 1.20 1.20 1-20 1.20 1-20 1-20 1.22 1-22 1.20 1.20
285 283 287 259 260 261 279 252 252 252 252 252 252 245 245 252 252
67.8 69-5 67-5 68.1 69-3 68-2 71-5 71-5 71.5 71.5 71.5 71.5 71.5 71.5 71.5 71.5 71.5
101 101 101 10! 101 102 102 103 103 103 102 104 104 102 102 51 51
(ram) (Nmm 2)(kNm 2) (ram)
t
Web detai&
o'0.2f
6-50 9.59 12.60 6.48 9.56 12-90 6-34 6.30 6-30 6.30 6.31 6.32 6-32 6.33 6.33 6.35 6.35
286 300 295 285 301 294 239 239 239 239 239 239 239 239 239 239 239
(ram) (Nmm -2)
tf
Flange details
TABLE la Details of Transversely Stiffened Test Panels
1.47 1.47 1-46 1-47 1.47 1.46 0.97 0-48 0.48 0.48 0-48 0-48 0-48 0.32 0-32 0.96 0.46
b/d
278 284 284 376 376 374 378 380 381 380 380 380 380 372 373 189 189
d/t
Parameters
317 742 1 215 468 1 063 I 90(1 351 386 386 385 385 392 392 392 392 778 778
Mp x 10 -5
PA2 PA2 PA2 PA2 PA2 PA2 PV1,2 PV1,2 PV3,4 PVI,2 PV3,4 PV1,2 PV3,4 PVI 2,3 PV4,5,6 PBI PAl
Test pane&
:z:
.z:
t~o PJi [,3
Collapse o f welded aluminium plate girders
253
the predominant effects of shear. At point C, the failure mode changes from a web shear to a flange bending mode. Figure 3 shows that the m o m e n t / shear combinations sustained by the various panels extend over almost the whole of the predominant shear (SC) range and approach the intermediate point (C) in some cases. Girders AGS2, AGS3 and AGS4 were geometrically identical, other than for the dimensions of the transverse stiffeners. These were deliberately varied, as detailed in Table lb, to allow the possibility of stiffener failure to
TABLE lb Details of Transverse Stiffeners for Panels of Series 2 Tests
Girder and test AGS 1 AGS2-T 1 AGS2-T2 AGS3-T1 AGS3-T2 AGS4-T1 AGS4-T2 AGS5-T1 AGS5-T2
Stiffener a SVC SV 1 SV2 SV1 SV2 SVI SV2 SV1 & 2 SV3 & 4
bs (rnrn)
ts (ram)
y
yL b
y/yc
19.0 13.0 14.0 5.5 11.0 9.5 6.5 19.0 19.0
6.35 6.33 6.33 6.32 6.32 6.33 6.33 6.35 6.35
432 311 383 37 197 133 52 1 3ll 1 311
15 128 128 129 129 128 129 442 451
28.80 2-43 2-99 0-29 1.54 1-04 0.41 2.95 2.95
a All stiffeners double-sided. b R e f e r e n c e 8.
be studied. The stiffeners of girders AGS1 and AGS5, as detailed, were designed not to fail. All stiffeners were 'double-sided', i.e. they were positioned symmetrically on each face of the web plate. Table lb gives the rigidity of each stiffener in the direction perpendicular to the plane of the web, as defined by the non-dimensional parameter y. An allowance has been made for the area of fillet weld connecting the stiffener to the web in the calculation of y. The rigidities of the experimental stiffeners are compared to the values specified in the current code of practice 5 (CP 118). The code rigidity is d e n o t e d by yL in Table lb and corresponds to the simple empirical formula established by Cook and Rockey s (yL = 14d3/b3). For the experimental girders the ratio of y/yL is observed to vary from 2-99 to 0.29, with the latter value representing a very flexible stiffener which would be expected to fail.
254
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Collapse of welded aluminium plate girders
255
2.3 Series 3 tests
Two tests were conducted upon the single girder fabricated for this series, as shown in Fig. 2c. Web slenderness and flange strength were the same for both tests, see Table la, but the panel aspect ratio was changed from 0.96 in the first test to 0.47 in the second. The specific object to these two tests was to study collapse under high bending moment. The moment/shear interaction diagram in Fig. 3 shows that the applied load combinations for both the test panels lie within the required 'bending mode' region CD of the diagram. 2.4 Series 4 tests
Finally, in series 4, five longitudinally stiffened girders were tested under a predominant shear loading; the girders are illustrated in Fig. 2(d) and girder dimensions are given in Table 2. All five girders were nominally identical, other than for the number and dimensions of the longitudinal stiffeners. The overall dimensions of the five girders were chosen to be similar to those of the unstiffened girder AG3 tested in series 1 to allow the effects of introducing the longitudinal stiffeners to be determined. Girders AGLS1 to AGLS4 were reinforced by two longitudinal stiffeners and girder AGLS5 was reinforced by three stiffeners. The stiffeners were located so as to divide the web into sub-panels of equal depth, this being the o p t i m u m stiffener positioning for a girder under pure shear. In girders A G L S 1 to AGLS4 the dimensions of the longitudinal stiffeners were varied, as shown in Table 2(b), to allow the possibility of stiffener failure to be studied. In the table, the non-dimensional stiffener rigidity 3' is compared to the •" value. As defined by Kloppel and Scheer 9, ~/ is the rigidity value calculated from elastic buckling theory as the minimum rigidity required to ensure that the stiffener remains straight and limits buckling to the adjacent sub-panels of the web. The ratio of 3'/3/" is seen to reduce to a value of only 0-10 for girder AGLS1 indicating probable stiffener failure. The three longitudinal stiffeners of girder AGLS5 were designed not to fail.
3 MATERIAL PROPERTIES All the test girders were fabricated from the heat treatable 6082 (previously designated H30TF) aluminium alloy using shielded argon arc welding. In the absence of a distinct yield point, the 0.2% proof stress (O-o.2)will be adopted as the reference stress for design calculations. Material properties were established by exhaustive testing and measured
Test series
669 669 668 668 669
AGLS 1 AGLS2 AGLS3 AGLS4 AGLS5
454 455 455 454 454
d (mm)
bf
1-20 1.20 1"20 1.23 1"22
2 2 2 2 3
AGLS 1 AGLS2 AGLS3 AGLS4 AGLS5
5.0 22.0 9.0 12.5 28-6
bs (ram)
a All stiffeners double-sided. b Reference 9.
No. of stiffeners"
Girder
279 252 252 281 245
6-30 6.33 6.32 6.33 6-33
ts (mm)
71,5 71 "5 71"5 71"5 71-5
7
15 671 55 125 1 376
102 103 102 104 102
(mm) (Nmm-2)(kNm -2) (mm)
O'0.2f
6.34 6.30 6-30 6-32 6-33
140 140 140 140 163
7 "b
239 239 239 239 239
(mm) (Nmm -2)
tf
E
t
o-o.2~
Flange details
Web details
(b) Details of stiffeners:
b (mm)
Girder
(a) Overall details of panels:
TABLE 2 Details of Longitudinally Stiffened Test Panels
0-10 4.79 0.40 0-90 8.47
3~IY"
1-47 1-47 1-47 1.47 1.47
b/d
378 379 379 369 372
d/t
Parameters No. of
351 386 385 347 392
× 10 5)
stiffness
Mp* longitudinal
Z:
~z
t'O
AG4 AG 1 AG5 AG3 AG2 AG6 AGS 1 AGS2 AGS3 AGS4 AGS5 AGS6
Girder
1.64 1.60 1-61 1.21 1.21 1.22 1.20 1.20 1.20 1.20 1.22 1-20
285 283 287 259 260 261 279 252 252 252 245 252
O'0.2w
(Nmm-2)
I
(mm) 322 323 324 309 313 310 315 317 314 317 317 317
(Nmm 2)
Oru
Web material
8-38 9.66 8-88 15-5 15.3 16.8 16.8 19-2 17.6 17.6 17.3 17.8
× 10-2
"0
31 29 31 25 23 26 36 20 20 20 17 20
6.50 9.59 12.60 6.48 9.56 12-90 6.34 6.30 6-30 6-32 6.33 6.33
(mm)
If
TABLE 3 Typical Material Properties
O'u
286 300 295 285 301 294 239 239 239 239 239 239
305 314 311 305 314 329 336 334 334 334 332 332
(Nmm -2) (Nmm -2)
O'0.2f
Flange material 7~
11.9 11.1 19-6 15.2 15.7 16.3 20-1 21.9 21.9 21.9 21-9 21.9
× 10-2 64 88 87 64 103 39 14 14 14 14 14 14
I'Q
~" 5. ~" -~ E"
t~
H. R. Evans, M. J, Hamoodi
258
proof stresses of web and flange material (cr0.zwand o0.2f)are given in Tables 1 and 2; the elastic modulus (E) of the web material is also tabulated. Strain measurements on the test specimens allowed a representative value of 0-32 to be determined for the Poisson's ratio. Further measured values of material properties are given in Table 3 for the transversely stiffened girders. The ultimate tensile strength (o-,) is listed, together with the proportional elongation ('0) at failure. Although the values of the proof and ultimate stresses remain reasonably constant, considerable variation is noted in the proportional elongation. Lower values of ~9, indicating low ductility, are observed for the thicker web material of girders AG4, AG1 and AG5. An empirical equation defining the relationship between stress and strain for any alloy has been proposed by Ramberg and Osgood, as discussed by Dwight. 10This may be written in the following form: • = E
0.002
where the index n is known as the 'knee factor' and is chosen to ensure that the equation produces a curve passing through the true 0.2% proof stress point. A low value of n produces a rounded curve, whereas a high value of n gives a sharper knee. A simple empirical formula has been proposed by Dwight 1° to allow n to be determined from the standard mechanical properties: /7
--
log, (500~) log, (o'./0"0.2)
Values of the knee factor calculated from this formula are given in Table 3. They are seen to be reasonably consistent for the web material, ranging from 17 to 36, but the flange values for the girders of series 1 are considerably higher than those for the second series; they reach a maximum of 103, indicating a particularly sharp knee to the curve, for AG2. Typical stress/strain curves obtained from the Ramberg-Osgood formula are compared to experimental results in Fig. 4 for typical web and flange material. In both cases the empirical curve, using the n values calculated from Dwight's formula, lies very close to the experimental curve. It is well-known that the 6082 alloy is particularly susceptible to the effects of welding. Mazzolani 11 has shown that the heat affected zone extends a distance of approximately 20 mm from each side of the weld, confirming the assumption of 25 mm made in CP 118. 5 Mazzolani has also indicated that within the heat affected zone, the proof stress of the alloy is reduced by between 45% and 50%. A detailed study by Seah 12 of the particular alloy
Collapse of welded aluminium plate girders
259
300
t"s 2 0 0
Z = u IOO
n - 24.7 I
o,
I
02
0'3
0'4
d.s
0'6
0 .'7
"
O/o Strain ...... - -
Experimental curve Romberg Osgood equation
30C
O4 E
20C
X
lOC
al
/ 0
n = 15.95 I
0.I
I
I
0.2
0.3
I
I
0.4 0.5 Olo Strain
I
0.6
0 I7
Fig. 4. Typical stress/strain curves for web and flange material.
used in the present test series has confirmed Mazzolani's findings, regarding b o t h the extent of the heat affected zone and the amount of the strength reduction.
4 TESTING PROCEDURE AND INSTRUMENTATION E a c h test girder was simply supported at its ends and loaded by a vertical central point load. At the start of each test, the initial deformations of the
260
H. R. Evans, M. J. Hamoodi
webs, flanges and stiffeners were measured. Test loads were applied by a servo-controlled hydraulic jack which enabled the load to be applied so as to achieve and maintain a specified deflection. Displacements of the webs and stiffeners were recorded at selected load levels and the strains set up in some girders were recorded. After failure, the residual deflected shapes of the relevant web and flanRe panels were recorded. A large number of results, giving detailed information of girder behaviour, were obtained. These have been presented in detail by Hamoodi 13and will now be summarized for each series of tests in turn.
5 RESULTS F O R SERIES 1 TESTS The six tests in this series were planned to show the infuence of web slenderness and flange strength upon collapse behaviour under predominant shear. Final failure occurred in each test when the web plate fractured in the perimeter regions where the web tension field anchors against the boundary members. These fractures are clearly seen in Fig. 5 particularly in the close-up view in Fig. 5(d). A selection of girders is shown viz. AG4 (moderately slender web, weak flange), AG5 (similar web, strong flange) and A G 3 (very slender web, weak flange). In each case, before web fracture occurred, the girder developed a shear failure mechanism similar to that observed in steel girders. The shear sway action is clearly observed in all the photographs, as are the web buckles and the plastic hinges in the flanges. The load/deflection curves are plotted in Fig. 6a for the three girders of moderate web slenderness and in Fig. 6b for the three girders with very slender webs. The gain in capacity with flange strength is apparent and each curve shows the expected characteristics. During the approach to failure, the slope of the curve decreases rapidly and, a well-defined plastic collapse 'plateau' is observed before final failure occurs due to web fracture. Predicted and measured results are summarised in Table 4 (see notation for definition of terms). The ratio of the experimental failure load (Vexp) to the buckling load (V~r) ranges from 11.9 to 23-4, showing the extensive post-buckling reserve of strength of the test girders. The variation of the Mexp/MFratio from 0.17 to 0.41 shows shear to have been the predominating load action in this first series. The ratio Vexp/Vmecshows the accuracy of the girder capacity (V,~ec) predicted by the tension field mechanism solution.1 Other than for girder AG6, where subsequent inspection showed an end post failure to have occurred in conjunction with the shear sway mechanism, no serious discrepancy is
Collapse of welded aluminium plate girders
261
AG4 Fig. 5(a). View of girder AG4.
Cj 5 Fig. 5(b). View of girder AG5.
262
H. R. Evans, M. J. Hamoodi
Fig. 5(e). View of girder AG3.
AG 3 Fig. 5(d). Close up view of fracture in girder AG3.
Collapse of welded aluminium plate girders 70 f /
-- 6O z ==
""V
f
263
" ~X
___.¢~
_o s o
~ 4c (~~ '< 20 I0
Key
/ / F/ /
~
I S
O
Point of web fracture G_irder AG 4 with M¢= .OO317 . . . . . Girder AG I with M~= .00742 iGirder AG 5withlM ~" = .OI215 I IO IS 20 Central deflection (ram)
Fig. 6(a). Load/deflection curves for girders with web slenderness ratio of 280.
5O z
40 o 30
.~ 20
~ to
f/ // "l/ t~/" ~lr
I 5
~ Point o f w e b fracture ~ Girder AG3 with M ~ = .00468 . . . . . Girder AG2 with Mp~= ,OIO63 - - - - i Girder AG 6 with M ; : .OI 899 I I0 15 Central deflection (mm)
Fig. 6(b). Load/deflection curves for girders with web slenderness ratio of 375.
observed. For the other girders, the theory slightly underestimates the capacity of A G 4 but overestimates in all other cases, with a maximum overestimation of 8% being noted for AG2.
6 R E S U L T S F O R S E R I E S 2 TESTS The nine tests in this series were planned to give information about the c o m b i n e d effects of shear and bending, of panel aspect ratio and of transverse stiffener rigidity. W e b fractures were again observed in all girders at failure, with all stiffeners proving adequate, other than for the very light stiffeners of girders AG3-T1 and AG4-T2. The results obtained are summarised in Table 4.
H. R. Evans. M. J. Hamoodi
264
TABLE 4 Results for Transversely Stiffened Girders
Test series
Girder and test
Vexp (kN)
Vexp
Vexv
Vcr
Vpw
M~xp MF
Vexp Vme¢
1
AG4 AG1 AG5 AG3 AG2 AG6 AGS1 AGS2-T1 AGS2-T2 AGS3-T1 AGS3-T2 AGS4-T1 AGS4-T2 AGS5-T1 AGS5-T2 AGS6-T 1 AGS6-T2
52'3 56.3 69"3 33.9 41-4 44.4 47-0 62.0 63'5 50'0 59.0 60.5 57.0 62.0 68.5 20-0 23.5
11.9 13-2 16"2 19-0 22-5 23.4 19.8 12-4 9.2 12.2 10-4 12" 1 9-5 9-0 7-7 4.1 1.6
0.43 0-47 0.57 0-41 0-50 0.53 0-54 0.78 0.80 0-63 0-74 0.76 0.72 0-79 0.87 0-51 0.59
0"41 0.29 0"27 0.27 0-21 0.17 0-29 0.58 0" 19 0-63 0'33 0.56 0.29 0.52 0.42 1-01 1-16
1-01 0.93 0"98 0.93 0.92 0.81 a 0.96 0.98 0"95 0'82 b 0.90 0.95 0.87 b 0.87 0.93 0.96 c 1. l0
2
3
Failed panel PA2 PA2 PA2 PA2 PA2 PA2 PV2 PV2 PV4 PV1 PV3 PV2 PV3 PV3 PV4 PBI PAl
a E n d post failure. b T r a n s v e r s e stiffener deflection. c Lateral movement of flange.
The combined moment and shear levels applied to the various girder panels have been defined by the rays drawn on the theoretical interaction diagrams in Fig. 3. The actual moment/shear ratio at failure in each test is now superimposed upon the ray for the panel in which failure occurred to give a comparison of theory and experiment. Each of the tests involved a group of sub-panels, as discussed earlier, and although each web panel buckled under shear, final fracture did not always occur in the panel subjected to the highest bending moment. For example, Fig. 7(a) shows girder AGS1 after test where, although extensive buckling of both panels is observed, fracture occurred in panel PV2 with the lower bending moment. Thus, the comparison of values in Table 4 for this test is based on results for PV2 and the experimental point is inserted on the ray for this panel in Fig. 3. These theoretical curves show the expected reduction in shear capacity due to the presence of moments to have been slight. The test results confirm that the shearing action was the prime cause of the fracture in the webs. The effects of a decreasing web aspect ratio upon the collapse behaviour
Collapse of welded aluminium plate girders
AGS
Fig. 7(a). View of girder AGS1.
A GS 4 TEsTI
Fig. 7(b). View of girder AGS4-T1.
265
266
H. R. Evans, M. J. H a m o o d i
Fig. 7(c). View of girder AGS5-T1.
are illustrated by comparing the results obtained earlier for AG3 (b/d = 1.47) to those now presented for the seven tests on AGS1 (b/d = 0-97), AGS2-T1 and AGS2-T2, AGS3-T2 and AGS4-T1 (for all of which b/d = 0.48) and AGS5T1 and AGS5T2 (b/d = 0.32). Views of a selection of these girders after collapse are presented in Fig. 7 for comparison with the earlier view of AG3 in Fig. 5(c). Severe web fracture is clearly apparent for the two girders with low web aspect ratios. Load/deflection curves are plotted in Fig. 8 for girders of varying b/d ratios. Although each curve does just about reach a horizontal failure plateau, this is very much shorter than the well-defined plastic plateau obtained for AG3. The collapse behaviour, therefore, becomes less 'ductile' with a decreasing web aspect ratio. The increase in girder strength with the introduction of intermediate transverse stiffeners is also apparent.
Collapse of welded aluminium plate girders
267
7 ~. Z "o
o
50
25 ~"
f
.¢"
A G 3 - b/d - 1.47
ie -
• O
...... , G s , ,Gs=-
-
.....
I
~
I
b
Jd-0.97 ld.O,8
AG S 5 - b/d ~ 0 . 3 2 I I0
I
I IS
Central deflection, 6ram
Fig. 8. Load/deflection curves for transversely stiffened girders of differing web aspect ratio.
The comparison of experimental and predicted values in Table 4 shows the theory to have overestimated the girder capacity in all cases with the ratio of Vexp/Vmecfor girders with adequate stiffeners varying from 0.87 (AGS5-T1) to 0.98 (AGS2-T1). Although the largest theoretical overestimation is for the panel with the lowest b/d ratio, there is no definite trend. Indeed the Voxp/Vm~ratios obtained for the series 2 tests are similar to those listed for series I where the web aspect ratio was 1.5 throughout. The transverse stiffeners proved fully adequate for all the seven girders discussed so far in this series, even though the stiffener on AGS4-T1 was very light with a Y/YL ratio of only 1.04. However, for the two remaining girders--AGS4-T2 (3'/YL = 0"41) and AGS3-T1 (Y/3'L = 0-29)--the stiffeners proved inadequate, as had been expected. Views of these two girders after failure in Fig. 9 show stiffener deflections perpendicular to the plane of the web and web buckles running through the stiffeners into the adjacent sub-panels. The stiffener failures naturally lead to a considerable theoretical overestimation of the collapse load. When the Y/YL ratio drops from 0.41 to 0.29, the Voxp/Vm~cratio also reduces from 0.87 to 0.82. A tension field analysis of these two panels, assuming them to be completely unstiffened, would give a lower bound to the strength and Vexp/Vmoc ratios of 1"24 and 1.12, respectively. Finally, in Fig. 10a, the ratio of the experimental load to the 0.2% proof load (Vexo/Vp,) is plotted against the stiffener rigidity ratio (Y/YL). The curve shows that the girder strength initially increases rapidly with an increasing
268
H. R. Evans, M. J. Hamoodi
AG S 3 TEsT I
Fig. 9. Views of 2 girders with inadequate stiffeners after failure. Girder AGS4-T2 (top) and Girder AGS3-T1 (bottom).
269
Collapse of welded aluminium plate girders I.IVtxPIvpw
0.819F I AGS4-T2
AG$
4 -1"I
~ O ~
1
s 2.,2
O
A s3-T2
o.:AG S I
0,2 I
0
0.5
I
1
1.0
1.5
I
2.0
I
2.5
I
3.0
l
3.5
I
4.0
I
4.5
I ,.. 5.0 'l'V"yL
(a) VcxpI O.I~
VPw
0.6
AGLS3 A~LS2
A~LS 4 O.4 kG3
O.2
0
I
0.5
I
1.0
I
I.S
I
2.0
I
2.5
L
3.0
I
3.5
l
4.0
l
4.5
I
5.0 y/~,
(b) Fig. 10. Variation of ultimate load capacity with stiffener rigidity: (a) transversely stiffened girders; (b) longitudinallystiffened girders. (*indicatesstiffener failure in test girder.) stiffener rigidity but then gradually approaches a plateau at a value of 7/7L of a r o u n d 1.0. A n increase in stiffener rigidity beyond this 'knee value' does not lead to any significant increase in girder strength.
7 R E S U L T S F O R SERIES 3 TESTS T h e two tests in this series were carried out to investigate collapse behaviour u n d e r high bending m o m e n t , as indicated by the rays drawn on the theoretical interaction diagrams in Fig. 3.
270
H. R. Evans, M. J. H a m o o d i
Fig. 11. View of girder AGS6-T2.
Unfortunately, because of inadequate restraints, some lateral movement of the compression flange occurred at failure in the first test (AGS6-T1.) Consequently, the experimental point lies within the predicted failure envelope in Fig. 3 and Table 4 shows an overestimation of 4% by the theory. However, the second test (AGS6-T2) was entirely successful and the photograph in Fig. 11 gives a clear illustration of a failure mode in which buckling of the compression zone of the web under high bending is combined with an inclined shear buckle. In this case, the experimental point lay well outside the predicted failure envelope and Table 4 (V~xp/Vm~c= 1" 10) shows a safe underestimation of the collapse load by the theory. Girder AGS6-T2 differed from the earlier girders with the same web aspect ratio in two important respects; in the first place, bending was now dominant and, secondly, the web slenderness ratio was reduced significantly. Whereas web fracture had been noted in all the earlier tests, this did not occur in AGS6 where a long plastic failure plateau was obtained in the load/deflection curve.
8 RESULTS F O R SERIES 4 TESTS The five girders tested in this final series were identical to girder AG3 of series 1, other than for the number and dimensions of the longitudinal
Collapse of welded aluminium plate girders
271
TABLE 5 Results for Longitudinally Stiffened Girders
Test series 4
Vexp
V~xp
Vexp
Mexp
Girder
(kN)
V~r
Vpw
Mr
Vexp Vmec
AGLS1 AGLS2 AGLS3 AGLS4 AGLS5
41.5 44.0 43.5 46.5 49.5
3.73 3.94 3.91 3.88 2-52
0.47 0.55 0.55 0.51 0.63
0.38 0-42 0.41 0-43 0-47
0.94~ 1.06 1.06 1.01 1.03
a Longitudinal stiffener failure.
stiffeners employed. The tests were specifically intended to show the influence of these stiffeners upon the collapse behaviour under predominant shear. The longitudinal stiffeners proved fully adequate in all tests other than that on AGLS1 where the stiffeners were extremely light (y/y* = 0.10); even the relatively light stiffeners of AGLS3 and AGLS4 (y/y" = 0.40 and 0-90) proved satisfactory. The plot of girder strength against stiffener rigidity in Fig. 10b shows similar characteristics to that in Fig. 10(a) for transversely stiffened girders. In Fig. 10(b), the 'knee' value, beyond which an increase in longitudinal stiffener rigidity has little influence on girder strength, occurs at a y/y* ratio of around 0.5. Comparison of the measured failure loads given in Table 5 with that for the unstiffened girder AG3 shows a significant gain in strength to have been achieved by stiffening. The failure load of 33.9 kN for AG3 increases to an average of 44-7 kN with the introduction of two adequate stiffeners and to 49-5 kN when a third stiffener is employed. This is largely because of the increase in the initial buckling capacity of the stiffened web. It is very noticeable that the indicator of the extent of post-buckling action (Vexp/V,) decreases from 19.0 for AG3 to only 2.52 for AGLS5. In contrast to the transversely stiffened girders under predominant shear, no fractures occurred in the webs of the longitudinally stiffened girders. Indeed, a well-defined plastic failure plateau was developed in each case before the girder was unloaded, as indicated by the load/deflection plots in Fig. 12. The photographs in Fig. 13 typify the clear shear sway collapse mechanisms developed in each test girder. For all the girders with adequate stiffeners, the tension field theory underestimated the measured collapse load; Table 5 shows the Vexp/Vmec ratio to vary from 1.01 to 1-06. For girder AGLS1, where the stiffeners failed, an analysis of the corresponding unstiffened girder gives a lower bound to the strength and a Vexp/Vm~ratio of 1"13.
H. R. Evans, M. J. Harnoodi
272
71
Z .1¢
>
"~
o
50
~...-- ~ - - ' a
/ ~ - ~ .
-, . . . . .~,...,
25
j/ '
AGLS 3 - 2 Stiff¢ncrs~ ~(l~r~= 0 . 4 0 AGLS 4-2Stiffencrs~ ~fl~'~= O . 0 0
, O
AG,LS S-3 S m f ~ r = ~ V m * - e. 47 5
J
IO
IS
--
Centrol deflection, 6ram
Fig. 12. Load/deflectioncurvesfor differentlongitudinallystiffenedgirders.
9 CONCLUSIONS The 22 tests reported in this paper have shown that, although welded aluminium girders develop shear sway mechanisms similar to those of steel girders, the webs of aluminium girders may fracture within the heat-affected zones adjacent to the perimeter welds. These fractures occur at some stage during the development of the collapse mechanism and may be regarded as a consequence, rather than the cause, of failure. The fractures are due to a reduction in material ductility and strength within the heat-affected zone which makes it impossible for the large plastic deformations, associated with the formation of a long failure plateau, to be developed in many cases. Long failure plateaus, indicating 'ductile' failures, are obtained for girders with wide web panels, but the length of the plateau decreases as the transverse stiffener spacing is reduced. For webs with very closely-spaced stiffeners, the high local strains arising from a combination of the tensile membrane field of the shear sway action and the secondary out-of-plane bending of the buckling action, result in virtually no failure plateaus and 'brittle' failures. It should be noted, however, that although the web slenderness ratios of the aluminium girders were similar to those for steel girders, the girders were operating much further beyond their buckling loads because of the reduced material stiffness; indeed, in the extreme case, the collapse load was 23 times the buckling load. The secondary out-of-plane bending stresses
Collapse of welded aluminium plate girders
273
AG S 5:
Fig. 13. View of girder AGLS4 (top); view of girder AGLS5 (bottom).
were, therefore, particularly high because of the magnitude of the web buckles developed. When longitudinal stiffeners were employed to control the buckling, ductile failure plateaus with no web fractures were obtained although the collapse loads still approached four times the buckling loads. The tests have illustrated the significant gain in girder strength that can be achieved by employing transverse and longitudinal web stiffeners. It has also been shown that these stiffeners can be approximately proportioned by referring to linear buckling theory. However, since the main expense associated with the provision of stiffeners arises from fabrication rather than
274
H. R. Evans. M. J. Hamoodi
material costs, little economy is lost by increasing the stiffener dimensions b e y o n d the apparent minimum required. Finally, it has been observed that the tension field theory, originally developed for steel girders, may overestimate the shear carrying capacity of welded aluminium girders. This is in contrast to extensive observations for steel girders, where the theory invariably underestimates shear capacity. A l t h o u g h the maximum overestimation noted herein was only 13% and the girders were operating a long way into the post-buckling range and were m a d e of an alloy that was extremely susceptible to loss of strength due to welding, any such overestimation can have serious consequences from the point of view of design calculations. It is thus evident that the tension field theory requires some modification before it can be applied with confidence to the analysis of aluminium girders.
ACKNOWLEDGEMENT The authors wish to thank the Royal A r m a m e n t Research and Developm e n t Establishment for fabricating the test girders and for general support. In particular, the frequent helpful discussions with Dr P. S. Bulson and Mr D. W e b b e r are gratefully acknowledged.
REFERENCES I. Rockey, K. C., Evans, H. R. and Porter, D. M., A design method for predicting the collapse behaviour of plate girders, Proc. Instn. Civ. Engrs. 65 (1978) 85-112. 2. BS 5400, Steel, Concrete and Composite Bridges: Part 3, Code of Practice for Design of Steel Bridges, British Standards Institution, London, 1982. 3. BS 5950, Structural Use of Steelwork in Building: Part 1, Code of Practice for Design in Simple and Continuous Construction, British Standards Institution, London, 1985. 4. Eurocode 3, Common Unified Code of Practice for Steel Structures Draft, EEC, November 1983. 5. CP 118, The Structural Use of Aluminium, British Standards Institution, London, 1969. 6. BS 8118, Draft Code of Practice for the Design of Aluminium Structures, British Standards Institution, London, 1985. 7. Evans, H. R., An appraisal, by full-scale testing, of new design procedures for steel girders subjected to shear and bending, Proc. lnstn. Cir. Engrs. Part 2, 81 (1986) 175-189. 8. Cook, I. T. and Rockey, K. C., Shear buckling of clamped and simply supported infinitely long plates reinforced by transverse stiffeners, Aeronautical Q. XllI (February 1962) 41-70.
Collapse of welded aluminium plate girders
275
9. Kloppel, K. and Scheer, J., Beulwerte Ausgesteifter Rechteckplatten, Wilhelm Ernst and Sohn, Berlin, 1968. 10. Dwight, J. B. Private communication, 1982. 11. Mazzolani, F. M., Proposal to classify the aluminium alloys on the basis of the mechanical behaviour, ECCS Committee 16, doc. 16.74.2, 1974. 12. Seah, H. A., The behaviour of welded aluminium alloy plate girders reinforced with carbon fibre reinforced plastics, MSc Thesis, University College Cardiff, 1984. 13. Hamoodi, M. J., The behaviour of reinforced aluminium web plates in shear loading, MSc Thesis, University College Cardiff, 1983.