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Comparative tests on endplate beam-to-column connections
J. Cm2struet. Steel Resear~:h30 (1994) 151 175 ,(', 1994 Elsevier Science Limited Printed in Malta. All rights reserved 0143-974X/94,$7.00 EI.SEVIER
Comparative Tests on Endplate Beam-to-Column Connections A. K. Aggarwal D e p a r t m e n t of Civil Engineering, University of Technology, Lae, P a p u a New G u i n e a (Received 9 July 1992: revised version received 13 O c t o b e r 1992; accepted 10 June 1993)
ABSTRACT The paper reports the results of an experimental im'estigation carried out on beam-to-column joints with the aim of comparin,q the behaviour ~flush and extended endplate joints. In the experimental programme, twelve speeimens ~]" beam-column joints were tested under 'static' loads. Four specimens had a flush endplate and the other eight had an extended one. In the latter,.]'our specimens had an extension of endplate on one side of the beam, while the other four had an extension on both side~. In the test specimens, parameters such as endplate thickness and bolt diameter were varied for a constant beam and a constant column cross-section. From the data collected, experimental moment rotation curves were obtained and the end restraint offered by the joints was calculated. In comparison, it is observed that the .flush endplate joints, though havimj rotations similar to the extended endplate joints, have lower load and moment carryin,q capacities.
NOTATION
h by bl Bt B t,
By ds Dr ec J"
Distance from top hole to beam flange Bolt force due to applied vertical shear (V) Distance from the centre of beam flange to centre of bolts (Fig. 3) Maximum permissible bolt load in tension Bt modified for presence of shear as well as tension Maximum permissible bolt force in shear Depth of each stiffener Column depth Distance from bolt hole to column flange edge Clearance between end of beam and face of support 151
152
A. K. A aoarwal
Wi
Specified yield stress of material (250 MPa) Yield stress of column flange material (MPa) Yield stress of web material Bolt gauge, i.e. spacing of two bolt lines Length of weld Effective length of weld Total number of bolts in a connection Bolt pitch, i.e. distance between bolts along a line of bolts Applied tension load per bolt Stiffener design force Maximum permissible load in bolts Strength of the bolt group in shear Maximum permissible longitudinal load/length of fillet weld Maximum permissible load in plate Shear strength of plate Maximum permissible transverse load/length of fillet weld Maximum permissible load on flange welds Maximum permissible load on web welds Q/PlB, generally taken as 0"2 Prying force Column flange capacity adjacent to beam tension flange Root radius of column section Web thickness of member Column web thickness Thickness of endplate Thickness of stiffener Fillet weld leg length Thickness of column flange Maximum permissible shear force on unstiffened web Width of endplate
q51
Hole diameter
Fy Fycf Fyw ,q 1
Iv N P PTB PTS Pbt Pbv P1 Ppt Ppv P, Pwt Pwv q
Q Qm~ rc t tc fi t~ tw
L V,~x
1 INTRODUCTION Although flush and extended endplate beam-to-column connections are fabricated in a similar manner, the variations in geometry and the length of the endplate affect both their design and strength characteristics. The extended endplate joints have been the subject of a significant number of independent studies, but relatively little research information is available for the flush endplate connections. Consequently, the design criteria for
Comparative tests on endplate beam-to-column connections
153
extended endplate joints are well documented but design recommendations for flush endplate joints are based on traditional practices. 1 While the extended endplate joints are normally designed to transfer the plastic moment of the beam to the column, tests carried out on flush endplate joints have indicated that they are limited to moments appreciably lower than the plastic moment of the beam. The maximum moment likely to be transferred across a joint varies and has to be assessed. In the present study, the behaviour and strength characteristics of flush endplate joints are investigated and compared with similar extended endplate specimens. Plastically designed beam-to-column endplate connections are considered to be rigid and capable of transferring both moment and shear force from a beam to the connected column. Basically, the flush endplate connections are similar in construction to the extended endplate joints, the principal difference being the length of the endplate. In the former, the length of the endptate is kept approximately equal to the beam depth, but in the latter, the endplate extends beyond the beam flanges either on one side or on both sides. To fabricate the joints, a beam is welded to an endplate and then the complete assembly is bolted to a column flange normally using high strength friction grip bolts.
2 DESCRIPTION OF TEST SPECIMENS To compare the strength and moment-rotation characteristics of flush and extended endplate joints, twelve specimens were tested under gradually increasing 'static' loads, according to the experimental programme given in Table 1. In four test specimens, the endplate was made equal to the beam depth (flush endplate joint, Fig. l(a), type 1) and the other eight had an extended endplate. In the latter, four specimens had an extension of endplate on one side of the beam (Fig. l(b), type 2), while in the other four, the endplate extended on both sides (Fig. l(c), type 3). Two different diameter (16ram and 20mm) bolts and two different plates (16mm and 20mm) were used in specimens with a constant beam and a constant column cross-section. The beam section used in all tests was 200UB 25-4kg/m and the column 200 UC 46"2 kg/m with British equivalents of 203 x 103 UB 25 and 203 x 203 UC 46 respectively. All specimens were made using BHP sections conforming to the Australian specification AS 12042 with a nominal yield stress of 250 MPa and dimensional tolerances conforming to AS 1227. 3 The measured dimensions of the beam and the column section are given in Table 2.
A. K. Ay,qarwal
154
TABLE 1 Experimental Programme
Specimen No.
Endplate thickness (mm)
Bolt diameter (ram)
No. qf holts./ joint
Joint type
Ct C2 C3 C4
16 t6 20 20
16 20 16 20
4 4 4 4
1 1 1 l
C5 C6 C7 C8
16 16 20 20
I(~ 20 16 20
o 6 6 6
2 2 2
C9 C10 CI 1 C 12
16 16 20 20
16 20 16 2O
~ 8 8 8
3 3 3 3
Type of joint: l, flush endplate; 2, extended endplate, extension one side: 3, extended
endplate, extension both sides. A
/ {a)
(b)
J (c)
Fig. 1. (a) Flush endplate joint (type 1); (b) extended endplate joint (type 2): (cl extended endplate joint (type 3).
The extended endplate joints were designed using the plastic method suggested in the Australian Institute of Steel Construction publication, Design of Structural Connections, 4 and a sketch of a typical extended endplate (type 2) beam-column connection used for testing is shown in Figs 2(a) and 2(b). It may be noted that flush endplate connections are not explicitly considered in the Australian design criteria. Therefore, in the absence of a well-documented design procedure, the flush endplate test specimens were dimensioned similarly to the extended endplate joints.
155
Comparative tests on endplate beam-to-column connections TABLE 2 Dimensions and Plastic M o m e n t of Sections
Section
200 UB 254 200 UC 46.2
D
B
tf
t,v
(mm)
(ram)
(ram)
(mm)
S X 10 3 Mp (mm 3) (kN m)
205.37 206"00
133.73 204-00
7.64 10'92
6'll 8"02
257.t2 502'53
76-88 15026
Fully plastic moments have been calculated using a yield stress of 299 MPa (see Section 2.1 ). - - - -
800
Mirror
i/
1 •
200 UB 25.4
~[
I
lOmm thick ~I J stiffeners
I
¢.D
~ f l ilf
t
Mirror
J;I ii~
G
Stiffeners
~
Hydraulic jack
lit ,i
Base frame ]
r - -
I
]
Fig. 2(a). Test specimen and loading arrangement (type 2 joints).
2.1 Determination of yield stress T o o b t a i n an a c c u r a t e a s s e s s m e n t of the yield stress of the b e a m a n d c o l u m n m a t e r i a l , i4 s p e c i m e n s were subjected to axial tensile load. F o u r s p e c i m e n s were o b t a i n e d f r o m the flanges of each of 200 U B 25-4 a n d 200 U C 46"2 a n d three each were o b t a i n e d f r o m the webs of these sections. An a v e r a g e yield stress for the flange m a t e r i a l was o b s e r v e d to be 2 8 3 _ + 1 2 M P a while the w e b m a t e r i a l had a higher yield stress of
A. K. Aggarwal
156
200 ~-~ 14 140 ~ ~__
i--
i
:'-~':~':'~'i":':"'-'~21
_t
ol
o
Strain-gauged
0"1
.......
© o J_
~I
~.'"/"'~¢"
"t
© 4
/
Strain-gauged bolt
Fig. 2(b). Details of extended endplate joint (type 2 joints). 315_+ 15 M P a compared with the nominal yield stress of 2 5 0 M P a . The combined average yield stress of the beam and column material was calculated as 299 MPa.
2.2 Bolts All bolts used in the test specimens conformed to the Australian specification AS 12525 for high strength friction grip bolts equivalent to BS 4395 (Part 1).6 In flush endplate joints, four bolts were used in each specimen, while in the extended endplate joints, six and eight bolts were used for type 2 and type 3 joints respectively. All bolts were fully tensioned using a torque wrench which had been previously calibrated for torque versus axial tension for each of the two bolt diameters used in the test specimens. It may be noted that within a bolt group, the load carried by an individual bolt will vary with the tightening method used and the sequence in which tightening takes place. In this case the sequence of bolt tightening followed a consistent pattern. Though the torque control method is only an indirect indicator of bolt tension, it was used in this study because of the easy availability of the equipment and convenience of operation. In each test specimen, two strain-gauged bolts were used and these were tightened with load-indicating washers. The gap between the bolt head and washer was measured under increasing torque. The minimum specified gap was achieved at a torque lower than that obtained from strain-gauged bolts, thus implying a low accuracy for some load-indicating washers. The average axial tension obtained in strain-gauged bolts with
157
Comparative test~s on endplate beam-to-column connections TABLE 3
Average Axial Tension in Strain-Gauged Bolts with Torque Bolt diameter
Torque (N m)
Axial tension (kN)
Breakin.q load {kN)
Proof load (kN)
[ram)
16 20
650 950
80 +_8 130 + 15
124.0 196-0
91-0 145.0
torque for each diameter bolt is given in Table 3 and the minimum breaking and proof loads for each bolt are also shown. It may be noted that the current European practice 7 does not recommend full tensioning (preloading) of bolts in both flush and extended endplate joints, but the Australian design philosophy requires that all high strength bolts be fully tensioned according to AS 1511. 8
3 CALCULATED
BEHAVIOUR
OF TEST SPECIMENS
The maximum allowable load for extended endplate connections was calculated using the Australian design criteria. '~ According to the guide, the design procedure for both types of extended endplate joints is similar. The maximum allowable load on an endplate connection is taken as the lowest action nominally necessary to cause failure of the endplate, of the tension flange bolts or the beam endplate weld. In addition, the design procedure requires that the necessity for column stiffening be checked in the regions of tension, compression and shear. The minimum forces necessary for the various modes of failure for the connections are given in Table 4 and the controlling value is marked with an asterisk in each case. Sample calculations for the figures given in Table 4 for type 2 joints are given in the Appendix. For the flush endplate joints, the design criteria 4 for extended endplate joints were suitably modified. In the design model, it is assumed that the entire tension is taken by the two tension flange bolts and that the shear force carried by the joint is shared equally by all the bolts. An allowance of 20% is made in the bolts to account for the prying forces. Accordingly, the tensile and shear strength of bolts in flush endplate joints was calculated from the following equations: Pb, = 2Bt/(1 + q)
(1)
Pbv = N B v
(2)
A. K. Aggarwal
158
TABLE 4 Calculated Behaviour of Test Specimens Specimen No.
Bolt strength
Plate strength
Weld strength
Column capacity
Shear
Tension
Shear
Bendim/
Tension
Shear
(kN)
(kN)
(kN)
Flange (kN)
Weh
(kN)
(kN)
(kN)
(kN)
c1 c2 C3 C4
233 366 233 366
141 236 141 236
880 880 1100 t100
61. 61. 95* 95*
581 581 581 581
690 690 690 690
497 497 497 497
286 286 286 286
C5 c6 C7 C8
350 549 350 549
298 478 298 478
880 880 I100 1100
196' 196" 308 308
581 581 581 581
690 690 690 690
497 497 497 497
286 286 286* 286*
C9 c10 Cll c12
466 733 466 733
298 478 298 478
880 880 1100 1100
196" 196. 308 308
581 581 581 581
690 690 690 690
497 497 497 497
286 286 286* 286*
Normally the bending strength of an endplate in an extended endplate joint is calculated on the assumption that it bends in double curvature between the bolts and the flange. This has been modified in the case of flush endplate connections and it is proposed that the endplate cantilevers from the centre of the bolt line to the middle of the beam flange (Fig. 3). This modification gives the strength of the endplate in bending as:
Pp, :~ Fyi" wi" t2/'461
(31
/
/
Cantilever
Load
V
[i
Flush endplate
Fig. 3. Bending of flush endptate.
Comparatit,e tests on endplate beam-to-column connections
159
The shear strength of an endplate and the strength of the flange and web welds are assumed to have values similar to those of extended endplate joints. From Table 4, it is observed that the bending strength of the endplate controls the design for almost all the joints with the exception of specimens C7, C8, C l l and C12, where the shear capacity of the column web was critical. It is to be noted that the design criteria given in Ref. 4 are applicable to connections that are statically loaded. Joints subjected to dynamic loads or fatigue applications are not considered within the scope of the guidelines. Therefore, keeping in mind the provisions of these criteria, it was decided to test the specimens under static loads only.
4 LOADING
OF TEST SPECIMENS
All specimens were loaded to failure in discrete increments of load. The connections were assumed to have failed either when large displacements were observed for a constant load or when there was difficulty in maintaining the load. At each load increment, two complete cycles of loading and unloading were carried out to see the effect of a second cycle of loading on the behaviour of the joints.
5 MEASUREMENTS In order to measure the rotations of the joints ( ® - 4~), it was necessary to measure the rotation of the beam ® and the rotation of the column 4). An optical technique, using a pair of ordinary mirrors and theodolites, was used. Separate mirrors were mounted on the beam and column flange close to the connection. Graph papers mounted on vertical boards served as sighting targets. The reflected images of these graph papers observed in the mirrors were viewed using theodolites. A schematic arrangement used for the measurement of rotations is shown in Fig. 4. The rotations of the column base were recorded using a vertical dial gauge for every observation and these values were subtracted from the beam/column rotations. The details of the technique used for the measurement of rotations have also been discussed by the author elsewhere. 9~° It should be noted that only one side of the column flange was loaded and therefore shear deformations in the column web took place. As the rotations have been calculated based on the overall displacements observed, the effect of shear deformations in the column web is included in the observations.
A. K. Aggarwa/
160
Sighting targets
//
Mirror
E i~
/ / ,/
Theodolite
///II\\ "-I
Fig. 4. S c h e m a t i c a r r a n g e m e n t for m e a s u r e m e n t o f r o t a t i o n s .
6 OBSERVED
MODES
OF FAILURE
The twelve specimens tested as a part of the experimental programme are compared in Table 5 for their calculated failure m o m e n t and observed behaviour (experimental failure m o m e n t and shear force) along with experimentally determined in-plane rotations and factor of safety. In all the flush endptate joints, the predicted mode of failure was associated with yielding of the endplate in tension, but the observed behaviour was slightly different. For specimens CI and C2, the failure occurred with yielding of the column flange and large deformations in the area between the column stiffeners (shear zone); a typical deformed shape of the joint is shown in Fig. 5. Some deformation of the endplate was also observed but the deformation of the column flange was more pronounced. At failure, the column web was subjected to 259 kN shear force against the maximum calculated value of 286kN, using a yield stress of where Fy=299 MPa. Comparing the deformation of the plate in specimens C I and C2, it is observed that specimen C1 had a larger deformation resulting from a lower clamping force between the endplate and column flange because of the smaller diameter bolts. In the case of specimens C3 and C4, the endplate suffered practically no deformation and most of the deformation was concentrated in the column flange in the vicinity of the beam tension flange. This behaviour of the joint was expected because the endplate was relatively much thicker than the column flange.
Fy/,~/3
(kN m) (3)
(kN m) (2)
11.91 11-91 18.54 18.54
38.26 38.26 53-09 53.09
38-26 38.26 53.09 53.09
(I)
CI C2 C3 C4
C5 C6 C7 C8
C9 CIO C11 C12
75-26 71.20 75-04 73.70
77.00 82-60 84-00 84.00
51.30 51.30 52.65 55-35
Observed max. moment (expt)
Calculated max. moment (theoretical)
Specimen No.
112.0 106.0 112-0 110.0
110.0 118-0 120.0 120.0
76.0 76.0 78.0 82-0
(kN) (4)
Max. shear (expt)
1.97 1-86 1-41 1.39
2.01 2-16 1.58 1.58
4.31 4.31 2.84 2-98
FS(observed moment)/ (theoret. moment) (5) = (3)/(2)
1.16 1.10 1.15 1.13
1.18 1.27 1.29 1.29
0.79 0.79 0.81 0.85
FS = (observed moment)/ (nominal moment) (6) = (3)/65.0
TABLE 5 Observed and Calculated Behaviour with Factor of Safety
81.85 54.70 89.30 87.50
67"09 79'60 90-85 108-54
83'80 94.60 8740 86"90
(7)
Total cumulative rotation x 10 3 rad (in the plane of joint)
e~
A.K. ,4,q,qarwal
162
Fig. 5. Typical defo,med shape of type l joint.
Specimens C5 and C6 with 16mm thick endplates and 16mm and 20 mm diameter bolts respectively failed with the yielding of both the column flange and the endplate. The yield pattern of the column flange was similar (Fig. 6) to that observed by Packer and Morris. ~ The actual yield load (389 kN) can be compared with the calculated yield load for this pattern (330 kN), the agreement being not unreasonable, given the simplifications inherent in the predicted values. Fixed edge
. . . . .
~111-
" [
r
~1 oi
'
I/
/
0
'
\
j
~'-
5/W
i_ Fixed edge
!
~,~_n ......,,~__m__.D..l
i Section
CC, DD '
_
F i g . 6. Y i e l d
,,L2~ i
~
Section
Section
AA
BB ni
i paHern
I\~r a ~ t i l t e n c d
column
flange
Comparatit,e tests on endplate beam-to-column connections
163
For specimens C7 and C8 with 20 mm thick endplates, very little deformation of the endplate was observed and most of the deformation was concentrated in the column flange in the vicinity of the beam tension flange, where the plastic hinges formed. Specimens C9 and C ll with 16ram diameter bolts and 16ram and 2 0 m m endplates respectively depicted unexpected behaviour. The moments (measured on the face of the column) transferred across the connection by both these specimens were greater than those for specimens C12 and CI0 with 20ram diameter bolts. The bolt group symmetric to the tension flange was subjected to 380 kN against the calculated maximum value of 298 kN, giving evidence of significant reserve strength. This large difference between the observed and the theoretical strength values of bolts can partly be explained in terms of 'prying force' (endplate bearing against column flange), which is considered in the design criteria and reduces the theoretical strength of bolts by 20% in most of the cases. Kennedy e t ~ll. 12 while reviewing different design criteria comment on the Australian design rules by writing: 'Grundy, Thomas and Bennett 13 have eliminated a number of problems by arbitrarily increasing the bolt load by 20% to account for prying. While this is not an exact solution, one might argue that it is probably sufficient to give a safe, if not efficient design in most practical cases.'
7 TEST RESULTS It is observed from Table 5 (col. 3) that all flush endplate joints were unable to transfer the nominal plastic moment (65"0 kN m) of the beam across the joint while all extended endplate joints transferred moments larger than the plastic moment. (It may be noted that the nominal plastic m o m e n t of the beam has been calculated using the nominal yield stress of steel (250 M Pa) together with the plastic modulus of the beam section. The plastic m o m e n t of the beam section calculated using the actual dimensions and the observed yield stress of the material (Table 2 values) has not been used because of limited practical significance.) The shear force (jack force) transferred across the flush endptate joints varies from 76 kN to 82 kN which corresponds to a m o m e n t ranging from 0'79 Mp to 0"85 Mp. Similar shear force and m o m e n t values for extended endplate joints range from 106kN to 120kN and 1-10 Mp to 1"29 Mp respectively. According to the EC37 classification, flush endplate joints fall into the category of partial-strength joints while the extended endplate joints are classified as full-strength connections.
A. K. Aggarwal
164
Unexpectedly, Table 5 also indicates that type 2 joints sustained moments larger than type 3 joints. Normally, it is expected that additional bolts in a joint would enhance its stiffness, but test results indicate that both type 2 and type 3 joints have similar cumulative in-plane rotations. The factor of safety (Table 5, col. 5), calculated using the experimentally determined moment (jack force (col. 4) × moment arm) and the maximum theoretical moment, indicates values ranging from 2"84 to 4-31 for flush endplate joints and from 1.39 to 2.01 for extended endplate connections. It may be noted that the maximum theoretical failure moment for a joint has been obtained by multiplying the controlling failure load (obtained from Table 4) by the distance between the beam flanges. The high factor of safety shown by the joints could be attributed to the plate strength because the design criteria make a very conservative assessment of their strength. The Australian design rules suggest the use of a thick endplate in contrast to the British Codes of Practice which favour the use of a thin endplate (Chapter 5, Commentary to the AISC manual4). According to the plastic design model, a 20"4mm endplate is required to transfer the nominal plastic moment (65.0 kN m) of the beam, but it has been observed that a 16 mm endplate is satisfactory under static loads. According to EC3, all bolted connections are expected to have a partial factor of safety of 1-25, but the Australian design criteria 4 do not specify any such value. The criteria suggest that all components of a bolted endplate joint are unlikely to fail simultaneously and therefore a varying factor of safety could be expected for different elements of a joint. However, the factor of safety observed in extended endplate joints designed using the existing guidelines varies from 1"39 to 2-01. According to the British design practice, l the flush endplate connections are 'only capable of developing a moment capacity appreciably less than that of the beam'. The statement suggests that the flush endplate joints can transfer moments lower than the plastic moment of resistance of the beam but the exact percentage is not specified and has to be assessed. With limited experimental evidence, the results of the present study indicate (Table 5, col. 6) that on average 0"81 Mp is transferred across the joint.
8 MOMENT
ROTATION CURVES
One of the objectives of this investigation was to determine the momentrotation curves for the bolted endplate connections and to determine their end restraint. The extended endplate connections are assumed to be fully rigid in their behaviour and are therefore considered to maintain rotational continuity between the beam and the column under all conditions of
Comparative tests oll endplate beam-to-column connections
165
loading. It has, however, been observed that for most rigid connections including the extended endplate, the initial geometry changes under load and the assumptions inherent in the analysis are violated. It is therefore desirable to analyse frames using a semi-rigid method provided welldocumented m o m e n t - r o t a t i o n curves for joints are readily awtilable. Most criteria suggesting the plastic method of design require joints to have sufficient rotational capacity, but the desired magnitude of rotation is generally not specified. Horne and Morris ~4 while looking at the desired rotation capacity for joints report that Suttees ~5 suggested 3 0 X 10 _3 rad as an acceptable value for hinge rotation for beam-tocolumn connections in multi-storey frames. The results of the present study indicate that the cumulative in-plane rotation for all specimens at failure was large and varied from 54.7 x 10 -3 to 108-54 x 10 3 rad. The Australian design rules do not specify any value for joint rotation capacity, but EC3 suggests that if the moment of resistance of a beamto-column joint is 1.2 times the plastic moment of the beam, then the rotation capacity of the connection need not be checked. As all type 2 joints transferred moments larger than 1'2 Mp, it was unnecessary to check their rotation capacity. From the data collected, a m o m e n t rotation curve for each test joint was obtained separately and from the plots it was possible to assess the end restraint (connection stiffness) for each specimen. Three sets of combined plots for each of the three different types of test joints are shown in Fig. 7(a) for type 1, Fig. 7(b) for type 2 and Fig. 7(c) for type 3 specimens. The end restraint of a connection has been defined as a proportionate complement of/~ where /~ is the slope of the m o m e n t - r o t a t i o n curve at zero rotation and is represented by: /~ = tan ~(® - (b)/(M)
(4)
The average end restraint shown by type 1 connections is 86%, while for types 2 and 3 it is 91% and 88% respectively. Even though the end restraint shown by endplate joints is fairly large, it is lower than what is normally assumed in the analysis of frames with 'rigid' joints. It is seen that maximum end restraint is provided by type 2 joints and the minimum by type 1 (flush endplate)joints. Unexpectedly, the behaviour of type 3 joints is intermediate between type 2 and type 1 joints. The additional bolts and increased length of plate in type 3 joints did not improve their stiffness. To compare the m o m e n t rotation behaviour of three different types of test specimens, two sets of plots of moment versus cumulative rotation were obtained for specimens C1, C5 and C9 (Fig. 8(a)) and for specimens
A. K
66
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E 6O 0
.~
,
20
0
20
'~0 6'0 80 ' Rotation of joint (®-(~) x 10-3 rad
I(]0
'
120
Fig. 7(a). Moment versus total cumulative rotation for type 1 joints 100.
-__!
80
co
...___
c8
g 4o-I /Y~
i It 2o~!
/
',
0
I
20
40
do
~o
i;o
12o
Rotation of joint (®-(~) x 10 -3 rad
Fig. 7(b). M o m e n t
versus total c u m u l a t i v e r o t a t i o n for type 2 oints.
100 t~
C10
-~ 80-] . . . . ,!
- L - - '-' . . . . . "~= 60
o~ o
,'
-
~ /
-
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20
-
~
l
C9~
~
~
J
.
Ct2
~
,
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- - T ............T . . . . . . . . I
40 60 80 Rotation of joint (®-(~) x 10 3 rad
.
.
.
.
.
.
] Mnofbeam
l
lOO
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12o
Fig. 7(c). Moment versus total cumulative rotation for type 3 joints.
Comparatit~e tests
on
endplate beam-to-column connections
167
C3, C7 and C l l (Fig. 8(b)). Both these sets had 16 mm diameter bolts but the former had 16 mm endplates and the latter 20 mm plates. It is also seen from the plots that the curves are virtually linear in the beginning, and after the initial phase the connection stiffness reduces owing to softening in the connection. This behaviour could possibly result from yield in the column web/flange. Once the connection has softened, its stiffness again becomes approximately constant but at a lower value. At the junction where the stiffness of the joint changes, a 'knee' is formed and the moment at which this forms seems to vary with the type of joint. For
Ioo
80 E
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z
Mpofbeam
E 60
~.~._~
c~
40 o
I t I I
~ 20
I
0
L
20
0
' '
40 6 Rotation of joint ((~-0) x 10-3 rad
1 0
120
Fig. 8(a). Effect of joint type on m o m e n t r o t a t i o n b e h a v i o u r (specimens C1, C5 and C9).
lOO
E
C7
80
z
60 E 40-
:~ 20 o
I
o
'
2'o
.
. 40 . .
.
60
80 '
'
1o 0
120
Rotation of joint (~-~) x 10-3 rad
Fig. 8(b). Effect of joint type on m o m e n t r o t a t i o n behaviour (specimens C3, C7 and C11).
168
A, K. Aggarwal
flush endplate joints, the knee formed around 28 kN m (0'43 My), but for extended endplate joints this behaviour was observed approximately at 42 kN m (0-65 Mp) for type 3 joints and 52 kN m (0"8 Mp) for type 2 joints. The effect of endplate thickness on the behaviour of joints was also considered and plots of moment versus cumulative rotation were obtained for specimens C2 and C4 (Fig. 9(a)) (type 1 joints), specimens C5 and C7 (Fig. 9(b)) (type 2 joints) and specimens C10 and CI 2 (Fig. 9(c))(type 3 joints). It is observed from Fig. 9(a) that both specimens have identical behaviour over almost the entire range of loading. In the initial stages, specimen C2 with a 16 mm endplate shows a higher stiffness than specimen C4 with a 20 mm endplate, but around a moment of 30 kN m its behaviour changes and it has bigger joint rotations for identical moments on the joints. In the case of type 2 joints, specimen C5 shows better ductility than C7 up to a moment of 65-0 kN m, and beyond this the curves for the two specimens almost overlap. In the case of type 3 joints, both specimens have similar moment-rotation curves for amost the entire range of loading. However, the maximum in-plane rotation of joint C12 is higher than that of C10. The effect of bolt diameter on the moment rotation behaviour of joints was also evaluated for a constant plate thickness and a constant beam and column cross-section using two different diameter bolts. Plots showing the variation of moment with cumulative rotation are shown in Figs 10(a) for specimens C3 and C4, Fig. 10(b) for specimens C5 and C6 and Fig. 10(c) for specimens C9 and C10. It is observed from Fig. 10(a) that both specimens (C3 and C4) have identical behaviour over almost the entire range of loading. For the same m o m e n t on the joints, test specimen C3 with 16 mm bolts shows marginally higher rotations that specimen C4 with 20 mm diameter bolts. An almost similar pattern is seen in the other two sets. However, in the case of specimens C9 and C10 (Fig. 10(c)), the joint with 16 mm diameter bolts is comparatively more flexible.
9 CONCLUSIONS From the comparative tests done on endplate beam-to-column joints, the following conclusions can be drawn: (1) The flush endplate joints have lower load and moment carrying capacities than similar specimens having extended endplates. The results of the tests indicate that on average 81% of the nominal moment of the beam is transferred across the joint. However, the experimental evidence is small. (2) Unexpectedly, the moment resisted by joints having an extension of endplate on one side (type 2) is higher than similar specimens having an extension of endplate on both sides. Statical considerations alone might
Comparative tests on endplate beam-to-column connections
E
'°°80ql C4 C2
g E 40-
~ 20 i i t
0 0
i
'1
20
i
40
i
1
60
i
I
I
80
100
120
Rotation of joint (®-¢) x 10 .3 rad
Fig. 9(a). Effect of endplate on moment rotation behaviour for type I joints. 100
~
A 80 E
Z v E
6O
C7
E 40
o :~ 20 p i
0
2C
40
60
i
i
80
Rotation o f joint (®-$) x 10 -3
1O0
120
rad
Fig. 9(b). Ffie,:t of endp;ate on moment rotation behaviour for type 2 joit~.ts. 1(10 F
.....
i
8:)-~ ~-
i
CIO
_~_____6 C 12
L r:.
/)w
f° :~ 20
J? n
~0
4;
6;
8'0
10'0
120
Rotation of joint ((3-$) x 10 .3 rad
Fig. 9(c). Effect of endp!ate on moment rotation behaviour for type 3 joints.
t69
.4. K. Ag,qarwal
70 100.
E
--
8O
Z
] I
E 60 5
C4
g 40
c
E o
:~ 20
l
T
20
O
i
l
I
i
I
i
i
40 60 80 Rotation of joint (0-0) x I0 -3 rad
T
T -
100
120
Fig. lO(a). Effect of bolt d i a m e t e r on m o m e n t - r o t a t i o n b e h a v i o u r for type 1 joints.
-!
100
E
]
_.,r-~'j' C6
80
~
c
5
!
Z
60
'5
8 c
40
o
20
i I i
0
t
t
20
~
......
T
T"
I
7-
....
--r
40 60 80 Rotation of joint (®-~) x 10-3 rad
T
100
I
120
Fig. 10(b). Effect of bolt d i a m e t e r o n m o m e n t - r o t a t i o n b e h a v i o u r for type 2 joints. 100
E
--
80C
l
O
~ C 9
"5
g E 40-
20
4;
80
80
lOO
Rotation of joint (0-(~) x 10-3 rad
Fig. lO(c). Effect o f bolt d i a m e t e r o n m o m e n t r o t a t i o n b e h a v i o u r for type 3 joints.
Comparative tests on endplate beam-to-column connections
171
indicate the merits of type 2 joints but further work under varying loads may show contradictory disadvantages. (3) The disign criteria make a conservative assessment of the plate strength in bending, thus resulting in a high factor of safety for the joints. The reserve strength in the plate could not be related to any other factor except the joint modelling technique. (4) Maximum end restraint (91%) is shown by type 2 joints and the minimum (86%) by flush endplate joints. Unexpectedly, the end restraint shown by type 3 joints (88%) is lower than for type 2 connections. (5) The moment rotation curves for all three types of joints indicate an almost similar pattern with an almost linear initial phase, followed by another portion with a substantially reduced stiffness. The change-over from high stiffness to a lower value seems to depend on the geometry of the joint. For the flush endplate joints the stiffness was reduced around 28 kN m, but for type 2 joints the transition occurred around 52 kN m. (6) Strength-ductility characteristics of joints reveal that flush endplate joints have an average in-plane rotation of 88-2 × 10 3 tad while type 2 and 3 joints have an average rotation of 86-5 x 10 -3 and 78'4 × 10 -3 rad respectively. The ductility shown by all three types of joints is sufficient to permit the use of a plastic method for their design. (7) For a constant endplate thickness, smaller diameter bolts reveal better ductility because of the small initial clamping force between the endplate and the column flange. Finally, the need to formulate an improved design criterion for flush endplate joints is necessary because of the popularity of the joint in structural steelwork. The areas requiring modification for extending the existing guidelines have been identified.
ACKNOWLEDGEMENTS The financial support given by the Papua New Guinea University of Technology for this project is gratefully acknowledged. Words of appreciation are also extended to the technical and secretarial staff in the Department of Civil Engineering.
REFERENCES 1. Pask, J. W., M a n u a l on Connections [i~r B e a m and Column
Construction.
Publication No. 9/82, British Constructional Steelwork Association~ London. 1982.
A. K. Aggarwal
172
2. Standards Association of Australia, AS 1204, Weldable Structural Steels-Ordinary Weldable Grades. SAA, Sydney, Australia, 1980. 3. Standards Association of Australia, AS 1227, General Requirements for the Supply of Hot-Rolled Steel Plates, Sections, Piling and Bars ,fi)r Structural Purposes. SAA, Sydney, Australia, 1980. 4. Hogan, T. J. & Thomas, I. R., Design o[ Structural Connections, 3rd edn (first published 1978). Australian Institute of Steel Construction, Sydney, Australia, 1988. 5. Standards Association of Australia, AS 1252, General Grade High Strength Steel Bolts with Associated Nuts and Washers.lor Structural En,qineerin,q. SAA, Sydney, Australia, 1973. 6. British Standards Institution, BS 4395, High-Strength Friction-Grip Bolts and Associated Nuts and Washers [or Structural Engineering, Part 1: General Grade. BSI, London, 1969. 7. European Committee for Standardisation, EC 3, Design q/'Steel Structures, Part 1.1: General Rules and RulesJbr Buildings. ENV 1993-1-1, Brussels, Feb. 1992. 8. Standards Association of Australia, AS 1511, High Stren.qth Structural Boltin.q Code. SAA, Sydney, Australia, 1984. 9. Aggarwal, A. K. & Coates, R. C., Moment-rotation characteristics of bolted beam-column connections. J. Construct. Steel Res., 6(4) (1986) 303 18. 10. Aggarwal, A. K., Behaviour of flexible beam-to-column connections. Proceedings q[" the Second National Structural Engineering Confi, rence, Adelaide, Australia. National Conference Publication No. 90/10, 1990, pp. 462 7. 11. Packer, J. A. & Morris, L. J., A limit state design method for the tension region of bolted beam column connections. Struct. Engr, 5(10) (1977). 12. Kennedy, A. N., Vinnakota, S. & Sherbourne, A. N., The split-tee analogy in bolted splices and beam-column connections. Proceedimts of the International Conlerence on Joints in Structural Steelwork, Teesside Polytechnic, U K, 1981. 13. Grundy, P., Thomas, 1. R. & Bennett, I. D., Beam-to-column moment connections. J. Struct. Div. ASCE, STI (1980) 313-30. 14. Horne, M. R. & Morris, L. J., Plastic Desi.qn qflJ~w-Rise Frames. Constrado Monograph, Granada, London, 1981. 15. Packer, J. A. & Morris, L. J., A limit state design method for thc tension region of bolted beam-to-column connections (Discussion by Suttees). Struct. Enqr, 56 (1978).
APPENDIX SAMPLE
CALCULATION FOR VALUES TYPE 2 JOINTS
GIVEN
I N T A B L E 4:
Bolt strength (i) Strength of the bolt g r o u p in shear
= N ' B ~ where Bv = 1/0-6 x (strength of bolt in shear) = 1/0.6 × ( 3 5 ) - 5 8 . 3 for 1 6 r a m bolts
(_'otttptlralit'e tests or1 fildplafe [~t'tlm-lo-COlllt~'ltl connections
or 6 x 583 = 349.8 k N for 6 bolts/'joint = 1/'0-6 x (55)=91"6 for 20 mm bolts or 6 × 9 1 . 6 = 5 4 9 . 6 k N for 6 bolts/joint (ii) Strength of the bolt g r o u p in tension Bt. = Bt,~./1
(bvj/(Bv) 2
where (b,.),v = 117/'6= t9'5 k N
B t, =
(19-5) 2 - - 57 x 0"942 = 53"7 k N for 16 mm bolts (58'3)
57 x ~/1
Bt,=88 x
•/
(19"5)2 1-- ( 9 1 . 6 ~ = 8 8 x 0"977=86-0 k N for 2 0 m m bolts
1 ( 4 x 53.7"] Put =O'6k, i + 0 ' 2 ] = 2 9 8 ' 3 kN for 16 mm bolts
1 ( 4 x 86-0"] Pb, = 0-6k i +~7~ j = 477-8 k N for 20 mm bolts
Plate strength (i) Bending Fv x PP' -
!4' i
X t~
b 250 x 200 x t 2 65"0
= 769-2 × ti2
where t~ is the thickness of plate. For plate thickness 16 mm, Pp, = 196"9 k N 20 mm, Pp, = 307.7 k N
173
A.K. Aggarwal
174
(ii) P l a t e s t r e n g t h in s h e a r Ppv = 2 x 0"55 x fly x w i x fi = 2 x 0"55 x 250 x 200 x ti
= 55 x ti k N F o r p l a t e t h i c k n e s s 16 mm, Ppv = 8 8 0 k N 20 m m , Ppv = 1100 k N
Weld strength
(i)
F l a n g e weld
Pwt -
2xPt
x l,
0.6
w h e r e lv = l - 2tw
Iv = ( 1 3 3 " 4 x 2 - 5 " 8 4 ) - 2 = 248"96 m m
x 6
2x0-7 Pwt - - x 248"96 0"6 = 580-9 k N (for 6 m m welds) (ii) W e b w e l d
Pwv --
2xPt 0"6
where
x lv 1,. = l - 2 t w •=(203"2--2
x 7"82) x 2 = 3 7 5 " 1 2 m m
1 , = 3 7 5 " 1 2 - - 2 x 6"0 = 363-12 m m Pwv --
2 x 363.12 0.60
x 0"57 = 689"9 k N
(for 6 m m welds)
C o l u m n strength C a p a c i t y o f unstiffened c o l u m n s e c t i o n in t e n s i o n / c o m p r e s s i o n Qmc = Fy~r" T~ [ 3 ' 1 4 + 2 ( e c + p - ~bl)/f]
Comparative tests on endplate beam-to-column connections
175
where
f =(,q-tc- 2"r~)/2 OF
f = ( 1 4 0 - 8 - 0 2 - 2 x 10.2)/2.0 = 111-58/2 = 55.79 Qmc = 283 x 10-922 [3.14 + 2(30 + 130 - 22)/55.79] = 272.9 k N W h e n the c o l u m n is stiffened b y t w o full d e p t h 6 m m thick stiffeners, the a d d i t i o n a l force o n a c c o u n t o f stiffeners P~s = (0-6" Fyw" t~" d~)2 PTs = 0 " 6 x 315 x 6 x
(206 - 8"02) x 2 2
= 224"5 k N T o t a l c a p a c i t y o f c o l u m n flange w i t h stiffeners = 272-9 + 224.5 = 497.4 k N
Column web shear capacity V:,.x = 0 ' 5 5 " Fyw" De" tc
= 0 ' 5 5 x 315 x 206 x 8"02 = 286"2 k N
Comparative Tests on Endplate Beam-to-Column Connections A. K. Aggarwal D e p a r t m e n t of Civil Engineering, University of Technology, Lae, P a p u a New G u i n e a (Received 9 July 1992: revised version received 13 O c t o b e r 1992; accepted 10 June 1993)
ABSTRACT The paper reports the results of an experimental im'estigation carried out on beam-to-column joints with the aim of comparin,q the behaviour ~flush and extended endplate joints. In the experimental programme, twelve speeimens ~]" beam-column joints were tested under 'static' loads. Four specimens had a flush endplate and the other eight had an extended one. In the latter,.]'our specimens had an extension of endplate on one side of the beam, while the other four had an extension on both side~. In the test specimens, parameters such as endplate thickness and bolt diameter were varied for a constant beam and a constant column cross-section. From the data collected, experimental moment rotation curves were obtained and the end restraint offered by the joints was calculated. In comparison, it is observed that the .flush endplate joints, though havimj rotations similar to the extended endplate joints, have lower load and moment carryin,q capacities.
NOTATION
h by bl Bt B t,
By ds Dr ec J"
Distance from top hole to beam flange Bolt force due to applied vertical shear (V) Distance from the centre of beam flange to centre of bolts (Fig. 3) Maximum permissible bolt load in tension Bt modified for presence of shear as well as tension Maximum permissible bolt force in shear Depth of each stiffener Column depth Distance from bolt hole to column flange edge Clearance between end of beam and face of support 151
152
A. K. A aoarwal
Wi
Specified yield stress of material (250 MPa) Yield stress of column flange material (MPa) Yield stress of web material Bolt gauge, i.e. spacing of two bolt lines Length of weld Effective length of weld Total number of bolts in a connection Bolt pitch, i.e. distance between bolts along a line of bolts Applied tension load per bolt Stiffener design force Maximum permissible load in bolts Strength of the bolt group in shear Maximum permissible longitudinal load/length of fillet weld Maximum permissible load in plate Shear strength of plate Maximum permissible transverse load/length of fillet weld Maximum permissible load on flange welds Maximum permissible load on web welds Q/PlB, generally taken as 0"2 Prying force Column flange capacity adjacent to beam tension flange Root radius of column section Web thickness of member Column web thickness Thickness of endplate Thickness of stiffener Fillet weld leg length Thickness of column flange Maximum permissible shear force on unstiffened web Width of endplate
q51
Hole diameter
Fy Fycf Fyw ,q 1
Iv N P PTB PTS Pbt Pbv P1 Ppt Ppv P, Pwt Pwv q
Q Qm~ rc t tc fi t~ tw
L V,~x
1 INTRODUCTION Although flush and extended endplate beam-to-column connections are fabricated in a similar manner, the variations in geometry and the length of the endplate affect both their design and strength characteristics. The extended endplate joints have been the subject of a significant number of independent studies, but relatively little research information is available for the flush endplate connections. Consequently, the design criteria for
Comparative tests on endplate beam-to-column connections
153
extended endplate joints are well documented but design recommendations for flush endplate joints are based on traditional practices. 1 While the extended endplate joints are normally designed to transfer the plastic moment of the beam to the column, tests carried out on flush endplate joints have indicated that they are limited to moments appreciably lower than the plastic moment of the beam. The maximum moment likely to be transferred across a joint varies and has to be assessed. In the present study, the behaviour and strength characteristics of flush endplate joints are investigated and compared with similar extended endplate specimens. Plastically designed beam-to-column endplate connections are considered to be rigid and capable of transferring both moment and shear force from a beam to the connected column. Basically, the flush endplate connections are similar in construction to the extended endplate joints, the principal difference being the length of the endplate. In the former, the length of the endptate is kept approximately equal to the beam depth, but in the latter, the endplate extends beyond the beam flanges either on one side or on both sides. To fabricate the joints, a beam is welded to an endplate and then the complete assembly is bolted to a column flange normally using high strength friction grip bolts.
2 DESCRIPTION OF TEST SPECIMENS To compare the strength and moment-rotation characteristics of flush and extended endplate joints, twelve specimens were tested under gradually increasing 'static' loads, according to the experimental programme given in Table 1. In four test specimens, the endplate was made equal to the beam depth (flush endplate joint, Fig. l(a), type 1) and the other eight had an extended endplate. In the latter, four specimens had an extension of endplate on one side of the beam (Fig. l(b), type 2), while in the other four, the endplate extended on both sides (Fig. l(c), type 3). Two different diameter (16ram and 20mm) bolts and two different plates (16mm and 20mm) were used in specimens with a constant beam and a constant column cross-section. The beam section used in all tests was 200UB 25-4kg/m and the column 200 UC 46"2 kg/m with British equivalents of 203 x 103 UB 25 and 203 x 203 UC 46 respectively. All specimens were made using BHP sections conforming to the Australian specification AS 12042 with a nominal yield stress of 250 MPa and dimensional tolerances conforming to AS 1227. 3 The measured dimensions of the beam and the column section are given in Table 2.
A. K. Ay,qarwal
154
TABLE 1 Experimental Programme
Specimen No.
Endplate thickness (mm)
Bolt diameter (ram)
No. qf holts./ joint
Joint type
Ct C2 C3 C4
16 t6 20 20
16 20 16 20
4 4 4 4
1 1 1 l
C5 C6 C7 C8
16 16 20 20
I(~ 20 16 20
o 6 6 6
2 2 2
C9 C10 CI 1 C 12
16 16 20 20
16 20 16 2O
~ 8 8 8
3 3 3 3
Type of joint: l, flush endplate; 2, extended endplate, extension one side: 3, extended
endplate, extension both sides. A
/ {a)
(b)
J (c)
Fig. 1. (a) Flush endplate joint (type 1); (b) extended endplate joint (type 2): (cl extended endplate joint (type 3).
The extended endplate joints were designed using the plastic method suggested in the Australian Institute of Steel Construction publication, Design of Structural Connections, 4 and a sketch of a typical extended endplate (type 2) beam-column connection used for testing is shown in Figs 2(a) and 2(b). It may be noted that flush endplate connections are not explicitly considered in the Australian design criteria. Therefore, in the absence of a well-documented design procedure, the flush endplate test specimens were dimensioned similarly to the extended endplate joints.
155
Comparative tests on endplate beam-to-column connections TABLE 2 Dimensions and Plastic M o m e n t of Sections
Section
200 UB 254 200 UC 46.2
D
B
tf
t,v
(mm)
(ram)
(ram)
(mm)
S X 10 3 Mp (mm 3) (kN m)
205.37 206"00
133.73 204-00
7.64 10'92
6'll 8"02
257.t2 502'53
76-88 15026
Fully plastic moments have been calculated using a yield stress of 299 MPa (see Section 2.1 ). - - - -
800
Mirror
i/
1 •
200 UB 25.4
~[
I
lOmm thick ~I J stiffeners
I
¢.D
~ f l ilf
t
Mirror
J;I ii~
G
Stiffeners
~
Hydraulic jack
lit ,i
Base frame ]
r - -
I
]
Fig. 2(a). Test specimen and loading arrangement (type 2 joints).
2.1 Determination of yield stress T o o b t a i n an a c c u r a t e a s s e s s m e n t of the yield stress of the b e a m a n d c o l u m n m a t e r i a l , i4 s p e c i m e n s were subjected to axial tensile load. F o u r s p e c i m e n s were o b t a i n e d f r o m the flanges of each of 200 U B 25-4 a n d 200 U C 46"2 a n d three each were o b t a i n e d f r o m the webs of these sections. An a v e r a g e yield stress for the flange m a t e r i a l was o b s e r v e d to be 2 8 3 _ + 1 2 M P a while the w e b m a t e r i a l had a higher yield stress of
A. K. Aggarwal
156
200 ~-~ 14 140 ~ ~__
i--
i
:'-~':~':'~'i":':"'-'~21
_t
ol
o
Strain-gauged
0"1
.......
© o J_
~I
~.'"/"'~¢"
"t
© 4
/
Strain-gauged bolt
Fig. 2(b). Details of extended endplate joint (type 2 joints). 315_+ 15 M P a compared with the nominal yield stress of 2 5 0 M P a . The combined average yield stress of the beam and column material was calculated as 299 MPa.
2.2 Bolts All bolts used in the test specimens conformed to the Australian specification AS 12525 for high strength friction grip bolts equivalent to BS 4395 (Part 1).6 In flush endplate joints, four bolts were used in each specimen, while in the extended endplate joints, six and eight bolts were used for type 2 and type 3 joints respectively. All bolts were fully tensioned using a torque wrench which had been previously calibrated for torque versus axial tension for each of the two bolt diameters used in the test specimens. It may be noted that within a bolt group, the load carried by an individual bolt will vary with the tightening method used and the sequence in which tightening takes place. In this case the sequence of bolt tightening followed a consistent pattern. Though the torque control method is only an indirect indicator of bolt tension, it was used in this study because of the easy availability of the equipment and convenience of operation. In each test specimen, two strain-gauged bolts were used and these were tightened with load-indicating washers. The gap between the bolt head and washer was measured under increasing torque. The minimum specified gap was achieved at a torque lower than that obtained from strain-gauged bolts, thus implying a low accuracy for some load-indicating washers. The average axial tension obtained in strain-gauged bolts with
157
Comparative test~s on endplate beam-to-column connections TABLE 3
Average Axial Tension in Strain-Gauged Bolts with Torque Bolt diameter
Torque (N m)
Axial tension (kN)
Breakin.q load {kN)
Proof load (kN)
[ram)
16 20
650 950
80 +_8 130 + 15
124.0 196-0
91-0 145.0
torque for each diameter bolt is given in Table 3 and the minimum breaking and proof loads for each bolt are also shown. It may be noted that the current European practice 7 does not recommend full tensioning (preloading) of bolts in both flush and extended endplate joints, but the Australian design philosophy requires that all high strength bolts be fully tensioned according to AS 1511. 8
3 CALCULATED
BEHAVIOUR
OF TEST SPECIMENS
The maximum allowable load for extended endplate connections was calculated using the Australian design criteria. '~ According to the guide, the design procedure for both types of extended endplate joints is similar. The maximum allowable load on an endplate connection is taken as the lowest action nominally necessary to cause failure of the endplate, of the tension flange bolts or the beam endplate weld. In addition, the design procedure requires that the necessity for column stiffening be checked in the regions of tension, compression and shear. The minimum forces necessary for the various modes of failure for the connections are given in Table 4 and the controlling value is marked with an asterisk in each case. Sample calculations for the figures given in Table 4 for type 2 joints are given in the Appendix. For the flush endplate joints, the design criteria 4 for extended endplate joints were suitably modified. In the design model, it is assumed that the entire tension is taken by the two tension flange bolts and that the shear force carried by the joint is shared equally by all the bolts. An allowance of 20% is made in the bolts to account for the prying forces. Accordingly, the tensile and shear strength of bolts in flush endplate joints was calculated from the following equations: Pb, = 2Bt/(1 + q)
(1)
Pbv = N B v
(2)
A. K. Aggarwal
158
TABLE 4 Calculated Behaviour of Test Specimens Specimen No.
Bolt strength
Plate strength
Weld strength
Column capacity
Shear
Tension
Shear
Bendim/
Tension
Shear
(kN)
(kN)
(kN)
Flange (kN)
Weh
(kN)
(kN)
(kN)
(kN)
c1 c2 C3 C4
233 366 233 366
141 236 141 236
880 880 1100 t100
61. 61. 95* 95*
581 581 581 581
690 690 690 690
497 497 497 497
286 286 286 286
C5 c6 C7 C8
350 549 350 549
298 478 298 478
880 880 I100 1100
196' 196" 308 308
581 581 581 581
690 690 690 690
497 497 497 497
286 286 286* 286*
C9 c10 Cll c12
466 733 466 733
298 478 298 478
880 880 1100 1100
196" 196. 308 308
581 581 581 581
690 690 690 690
497 497 497 497
286 286 286* 286*
Normally the bending strength of an endplate in an extended endplate joint is calculated on the assumption that it bends in double curvature between the bolts and the flange. This has been modified in the case of flush endplate connections and it is proposed that the endplate cantilevers from the centre of the bolt line to the middle of the beam flange (Fig. 3). This modification gives the strength of the endplate in bending as:
Pp, :~ Fyi" wi" t2/'461
(31
/
/
Cantilever
Load
V
[i
Flush endplate
Fig. 3. Bending of flush endptate.
Comparatit,e tests on endplate beam-to-column connections
159
The shear strength of an endplate and the strength of the flange and web welds are assumed to have values similar to those of extended endplate joints. From Table 4, it is observed that the bending strength of the endplate controls the design for almost all the joints with the exception of specimens C7, C8, C l l and C12, where the shear capacity of the column web was critical. It is to be noted that the design criteria given in Ref. 4 are applicable to connections that are statically loaded. Joints subjected to dynamic loads or fatigue applications are not considered within the scope of the guidelines. Therefore, keeping in mind the provisions of these criteria, it was decided to test the specimens under static loads only.
4 LOADING
OF TEST SPECIMENS
All specimens were loaded to failure in discrete increments of load. The connections were assumed to have failed either when large displacements were observed for a constant load or when there was difficulty in maintaining the load. At each load increment, two complete cycles of loading and unloading were carried out to see the effect of a second cycle of loading on the behaviour of the joints.
5 MEASUREMENTS In order to measure the rotations of the joints ( ® - 4~), it was necessary to measure the rotation of the beam ® and the rotation of the column 4). An optical technique, using a pair of ordinary mirrors and theodolites, was used. Separate mirrors were mounted on the beam and column flange close to the connection. Graph papers mounted on vertical boards served as sighting targets. The reflected images of these graph papers observed in the mirrors were viewed using theodolites. A schematic arrangement used for the measurement of rotations is shown in Fig. 4. The rotations of the column base were recorded using a vertical dial gauge for every observation and these values were subtracted from the beam/column rotations. The details of the technique used for the measurement of rotations have also been discussed by the author elsewhere. 9~° It should be noted that only one side of the column flange was loaded and therefore shear deformations in the column web took place. As the rotations have been calculated based on the overall displacements observed, the effect of shear deformations in the column web is included in the observations.
A. K. Aggarwa/
160
Sighting targets
//
Mirror
E i~
/ / ,/
Theodolite
///II\\ "-I
Fig. 4. S c h e m a t i c a r r a n g e m e n t for m e a s u r e m e n t o f r o t a t i o n s .
6 OBSERVED
MODES
OF FAILURE
The twelve specimens tested as a part of the experimental programme are compared in Table 5 for their calculated failure m o m e n t and observed behaviour (experimental failure m o m e n t and shear force) along with experimentally determined in-plane rotations and factor of safety. In all the flush endptate joints, the predicted mode of failure was associated with yielding of the endplate in tension, but the observed behaviour was slightly different. For specimens CI and C2, the failure occurred with yielding of the column flange and large deformations in the area between the column stiffeners (shear zone); a typical deformed shape of the joint is shown in Fig. 5. Some deformation of the endplate was also observed but the deformation of the column flange was more pronounced. At failure, the column web was subjected to 259 kN shear force against the maximum calculated value of 286kN, using a yield stress of where Fy=299 MPa. Comparing the deformation of the plate in specimens C I and C2, it is observed that specimen C1 had a larger deformation resulting from a lower clamping force between the endplate and column flange because of the smaller diameter bolts. In the case of specimens C3 and C4, the endplate suffered practically no deformation and most of the deformation was concentrated in the column flange in the vicinity of the beam tension flange. This behaviour of the joint was expected because the endplate was relatively much thicker than the column flange.
Fy/,~/3
(kN m) (3)
(kN m) (2)
11.91 11-91 18.54 18.54
38.26 38.26 53-09 53.09
38-26 38.26 53.09 53.09
(I)
CI C2 C3 C4
C5 C6 C7 C8
C9 CIO C11 C12
75-26 71.20 75-04 73.70
77.00 82-60 84-00 84.00
51.30 51.30 52.65 55-35
Observed max. moment (expt)
Calculated max. moment (theoretical)
Specimen No.
112.0 106.0 112-0 110.0
110.0 118-0 120.0 120.0
76.0 76.0 78.0 82-0
(kN) (4)
Max. shear (expt)
1.97 1-86 1-41 1.39
2.01 2-16 1.58 1.58
4.31 4.31 2.84 2-98
FS(observed moment)/ (theoret. moment) (5) = (3)/(2)
1.16 1.10 1.15 1.13
1.18 1.27 1.29 1.29
0.79 0.79 0.81 0.85
FS = (observed moment)/ (nominal moment) (6) = (3)/65.0
TABLE 5 Observed and Calculated Behaviour with Factor of Safety
81.85 54.70 89.30 87.50
67"09 79'60 90-85 108-54
83'80 94.60 8740 86"90
(7)
Total cumulative rotation x 10 3 rad (in the plane of joint)
e~
A.K. ,4,q,qarwal
162
Fig. 5. Typical defo,med shape of type l joint.
Specimens C5 and C6 with 16mm thick endplates and 16mm and 20 mm diameter bolts respectively failed with the yielding of both the column flange and the endplate. The yield pattern of the column flange was similar (Fig. 6) to that observed by Packer and Morris. ~ The actual yield load (389 kN) can be compared with the calculated yield load for this pattern (330 kN), the agreement being not unreasonable, given the simplifications inherent in the predicted values. Fixed edge
. . . . .
~111-
" [
r
~1 oi
'
I/
/
0
'
\
j
~'-
5/W
i_ Fixed edge
!
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i Section
CC, DD '
_
F i g . 6. Y i e l d
,,L2~ i
~
Section
Section
AA
BB ni
i paHern
I\~r a ~ t i l t e n c d
column
flange
Comparatit,e tests on endplate beam-to-column connections
163
For specimens C7 and C8 with 20 mm thick endplates, very little deformation of the endplate was observed and most of the deformation was concentrated in the column flange in the vicinity of the beam tension flange, where the plastic hinges formed. Specimens C9 and C ll with 16ram diameter bolts and 16ram and 2 0 m m endplates respectively depicted unexpected behaviour. The moments (measured on the face of the column) transferred across the connection by both these specimens were greater than those for specimens C12 and CI0 with 20ram diameter bolts. The bolt group symmetric to the tension flange was subjected to 380 kN against the calculated maximum value of 298 kN, giving evidence of significant reserve strength. This large difference between the observed and the theoretical strength values of bolts can partly be explained in terms of 'prying force' (endplate bearing against column flange), which is considered in the design criteria and reduces the theoretical strength of bolts by 20% in most of the cases. Kennedy e t ~ll. 12 while reviewing different design criteria comment on the Australian design rules by writing: 'Grundy, Thomas and Bennett 13 have eliminated a number of problems by arbitrarily increasing the bolt load by 20% to account for prying. While this is not an exact solution, one might argue that it is probably sufficient to give a safe, if not efficient design in most practical cases.'
7 TEST RESULTS It is observed from Table 5 (col. 3) that all flush endplate joints were unable to transfer the nominal plastic moment (65"0 kN m) of the beam across the joint while all extended endplate joints transferred moments larger than the plastic moment. (It may be noted that the nominal plastic m o m e n t of the beam has been calculated using the nominal yield stress of steel (250 M Pa) together with the plastic modulus of the beam section. The plastic m o m e n t of the beam section calculated using the actual dimensions and the observed yield stress of the material (Table 2 values) has not been used because of limited practical significance.) The shear force (jack force) transferred across the flush endptate joints varies from 76 kN to 82 kN which corresponds to a m o m e n t ranging from 0'79 Mp to 0"85 Mp. Similar shear force and m o m e n t values for extended endplate joints range from 106kN to 120kN and 1-10 Mp to 1"29 Mp respectively. According to the EC37 classification, flush endplate joints fall into the category of partial-strength joints while the extended endplate joints are classified as full-strength connections.
A. K. Aggarwal
164
Unexpectedly, Table 5 also indicates that type 2 joints sustained moments larger than type 3 joints. Normally, it is expected that additional bolts in a joint would enhance its stiffness, but test results indicate that both type 2 and type 3 joints have similar cumulative in-plane rotations. The factor of safety (Table 5, col. 5), calculated using the experimentally determined moment (jack force (col. 4) × moment arm) and the maximum theoretical moment, indicates values ranging from 2"84 to 4-31 for flush endplate joints and from 1.39 to 2.01 for extended endplate connections. It may be noted that the maximum theoretical failure moment for a joint has been obtained by multiplying the controlling failure load (obtained from Table 4) by the distance between the beam flanges. The high factor of safety shown by the joints could be attributed to the plate strength because the design criteria make a very conservative assessment of their strength. The Australian design rules suggest the use of a thick endplate in contrast to the British Codes of Practice which favour the use of a thin endplate (Chapter 5, Commentary to the AISC manual4). According to the plastic design model, a 20"4mm endplate is required to transfer the nominal plastic moment (65.0 kN m) of the beam, but it has been observed that a 16 mm endplate is satisfactory under static loads. According to EC3, all bolted connections are expected to have a partial factor of safety of 1-25, but the Australian design criteria 4 do not specify any such value. The criteria suggest that all components of a bolted endplate joint are unlikely to fail simultaneously and therefore a varying factor of safety could be expected for different elements of a joint. However, the factor of safety observed in extended endplate joints designed using the existing guidelines varies from 1"39 to 2-01. According to the British design practice, l the flush endplate connections are 'only capable of developing a moment capacity appreciably less than that of the beam'. The statement suggests that the flush endplate joints can transfer moments lower than the plastic moment of resistance of the beam but the exact percentage is not specified and has to be assessed. With limited experimental evidence, the results of the present study indicate (Table 5, col. 6) that on average 0"81 Mp is transferred across the joint.
8 MOMENT
ROTATION CURVES
One of the objectives of this investigation was to determine the momentrotation curves for the bolted endplate connections and to determine their end restraint. The extended endplate connections are assumed to be fully rigid in their behaviour and are therefore considered to maintain rotational continuity between the beam and the column under all conditions of
Comparative tests oll endplate beam-to-column connections
165
loading. It has, however, been observed that for most rigid connections including the extended endplate, the initial geometry changes under load and the assumptions inherent in the analysis are violated. It is therefore desirable to analyse frames using a semi-rigid method provided welldocumented m o m e n t - r o t a t i o n curves for joints are readily awtilable. Most criteria suggesting the plastic method of design require joints to have sufficient rotational capacity, but the desired magnitude of rotation is generally not specified. Horne and Morris ~4 while looking at the desired rotation capacity for joints report that Suttees ~5 suggested 3 0 X 10 _3 rad as an acceptable value for hinge rotation for beam-tocolumn connections in multi-storey frames. The results of the present study indicate that the cumulative in-plane rotation for all specimens at failure was large and varied from 54.7 x 10 -3 to 108-54 x 10 3 rad. The Australian design rules do not specify any value for joint rotation capacity, but EC3 suggests that if the moment of resistance of a beamto-column joint is 1.2 times the plastic moment of the beam, then the rotation capacity of the connection need not be checked. As all type 2 joints transferred moments larger than 1'2 Mp, it was unnecessary to check their rotation capacity. From the data collected, a m o m e n t rotation curve for each test joint was obtained separately and from the plots it was possible to assess the end restraint (connection stiffness) for each specimen. Three sets of combined plots for each of the three different types of test joints are shown in Fig. 7(a) for type 1, Fig. 7(b) for type 2 and Fig. 7(c) for type 3 specimens. The end restraint of a connection has been defined as a proportionate complement of/~ where /~ is the slope of the m o m e n t - r o t a t i o n curve at zero rotation and is represented by: /~ = tan ~(® - (b)/(M)
(4)
The average end restraint shown by type 1 connections is 86%, while for types 2 and 3 it is 91% and 88% respectively. Even though the end restraint shown by endplate joints is fairly large, it is lower than what is normally assumed in the analysis of frames with 'rigid' joints. It is seen that maximum end restraint is provided by type 2 joints and the minimum by type 1 (flush endplate)joints. Unexpectedly, the behaviour of type 3 joints is intermediate between type 2 and type 1 joints. The additional bolts and increased length of plate in type 3 joints did not improve their stiffness. To compare the m o m e n t rotation behaviour of three different types of test specimens, two sets of plots of moment versus cumulative rotation were obtained for specimens C1, C5 and C9 (Fig. 8(a)) and for specimens
A. K
66
,IHq(~rwal
100
E
8O
.....
ff
Ii
Z
I' J-I .
--
Mp of beam .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
E 6O 0
.~
,
20
0
20
'~0 6'0 80 ' Rotation of joint (®-(~) x 10-3 rad
I(]0
'
120
Fig. 7(a). Moment versus total cumulative rotation for type 1 joints 100.
-__!
80
co
...___
c8
g 4o-I /Y~
i It 2o~!
/
',
0
I
20
40
do
~o
i;o
12o
Rotation of joint (®-(~) x 10 -3 rad
Fig. 7(b). M o m e n t
versus total c u m u l a t i v e r o t a t i o n for type 2 oints.
100 t~
C10
-~ 80-] . . . . ,!
- L - - '-' . . . . . "~= 60
o~ o
,'
-
~ /
-
.
20
-
~
l
C9~
~
~
J
.
Ct2
~
,
- , , ~ - c11
- - T ............T . . . . . . . . I
40 60 80 Rotation of joint (®-(~) x 10 3 rad
.
.
.
.
.
.
] Mnofbeam
l
lOO
- -]
12o
Fig. 7(c). Moment versus total cumulative rotation for type 3 joints.
Comparatit~e tests
on
endplate beam-to-column connections
167
C3, C7 and C l l (Fig. 8(b)). Both these sets had 16 mm diameter bolts but the former had 16 mm endplates and the latter 20 mm plates. It is also seen from the plots that the curves are virtually linear in the beginning, and after the initial phase the connection stiffness reduces owing to softening in the connection. This behaviour could possibly result from yield in the column web/flange. Once the connection has softened, its stiffness again becomes approximately constant but at a lower value. At the junction where the stiffness of the joint changes, a 'knee' is formed and the moment at which this forms seems to vary with the type of joint. For
Ioo
80 E
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z
Mpofbeam
E 60
~.~._~
c~
40 o
I t I I
~ 20
I
0
L
20
0
' '
40 6 Rotation of joint ((~-0) x 10-3 rad
1 0
120
Fig. 8(a). Effect of joint type on m o m e n t r o t a t i o n b e h a v i o u r (specimens C1, C5 and C9).
lOO
E
C7
80
z
60 E 40-
:~ 20 o
I
o
'
2'o
.
. 40 . .
.
60
80 '
'
1o 0
120
Rotation of joint (~-~) x 10-3 rad
Fig. 8(b). Effect of joint type on m o m e n t r o t a t i o n behaviour (specimens C3, C7 and C11).
168
A, K. Aggarwal
flush endplate joints, the knee formed around 28 kN m (0'43 My), but for extended endplate joints this behaviour was observed approximately at 42 kN m (0-65 Mp) for type 3 joints and 52 kN m (0"8 Mp) for type 2 joints. The effect of endplate thickness on the behaviour of joints was also considered and plots of moment versus cumulative rotation were obtained for specimens C2 and C4 (Fig. 9(a)) (type 1 joints), specimens C5 and C7 (Fig. 9(b)) (type 2 joints) and specimens C10 and CI 2 (Fig. 9(c))(type 3 joints). It is observed from Fig. 9(a) that both specimens have identical behaviour over almost the entire range of loading. In the initial stages, specimen C2 with a 16 mm endplate shows a higher stiffness than specimen C4 with a 20 mm endplate, but around a moment of 30 kN m its behaviour changes and it has bigger joint rotations for identical moments on the joints. In the case of type 2 joints, specimen C5 shows better ductility than C7 up to a moment of 65-0 kN m, and beyond this the curves for the two specimens almost overlap. In the case of type 3 joints, both specimens have similar moment-rotation curves for amost the entire range of loading. However, the maximum in-plane rotation of joint C12 is higher than that of C10. The effect of bolt diameter on the moment rotation behaviour of joints was also evaluated for a constant plate thickness and a constant beam and column cross-section using two different diameter bolts. Plots showing the variation of moment with cumulative rotation are shown in Figs 10(a) for specimens C3 and C4, Fig. 10(b) for specimens C5 and C6 and Fig. 10(c) for specimens C9 and C10. It is observed from Fig. 10(a) that both specimens (C3 and C4) have identical behaviour over almost the entire range of loading. For the same m o m e n t on the joints, test specimen C3 with 16 mm bolts shows marginally higher rotations that specimen C4 with 20 mm diameter bolts. An almost similar pattern is seen in the other two sets. However, in the case of specimens C9 and C10 (Fig. 10(c)), the joint with 16 mm diameter bolts is comparatively more flexible.
9 CONCLUSIONS From the comparative tests done on endplate beam-to-column joints, the following conclusions can be drawn: (1) The flush endplate joints have lower load and moment carrying capacities than similar specimens having extended endplates. The results of the tests indicate that on average 81% of the nominal moment of the beam is transferred across the joint. However, the experimental evidence is small. (2) Unexpectedly, the moment resisted by joints having an extension of endplate on one side (type 2) is higher than similar specimens having an extension of endplate on both sides. Statical considerations alone might
Comparative tests on endplate beam-to-column connections
E
'°°80ql C4 C2
g E 40-
~ 20 i i t
0 0
i
'1
20
i
40
i
1
60
i
I
I
80
100
120
Rotation of joint (®-¢) x 10 .3 rad
Fig. 9(a). Effect of endplate on moment rotation behaviour for type I joints. 100
~
A 80 E
Z v E
6O
C7
E 40
o :~ 20 p i
0
2C
40
60
i
i
80
Rotation o f joint (®-$) x 10 -3
1O0
120
rad
Fig. 9(b). Ffie,:t of endp;ate on moment rotation behaviour for type 2 joit~.ts. 1(10 F
.....
i
8:)-~ ~-
i
CIO
_~_____6 C 12
L r:.
/)w
f° :~ 20
J? n
~0
4;
6;
8'0
10'0
120
Rotation of joint ((3-$) x 10 .3 rad
Fig. 9(c). Effect of endp!ate on moment rotation behaviour for type 3 joints.
t69
.4. K. Ag,qarwal
70 100.
E
--
8O
Z
] I
E 60 5
C4
g 40
c
E o
:~ 20
l
T
20
O
i
l
I
i
I
i
i
40 60 80 Rotation of joint (0-0) x I0 -3 rad
T
T -
100
120
Fig. lO(a). Effect of bolt d i a m e t e r on m o m e n t - r o t a t i o n b e h a v i o u r for type 1 joints.
-!
100
E
]
_.,r-~'j' C6
80
~
c
5
!
Z
60
'5
8 c
40
o
20
i I i
0
t
t
20
~
......
T
T"
I
7-
....
--r
40 60 80 Rotation of joint (®-~) x 10-3 rad
T
100
I
120
Fig. 10(b). Effect of bolt d i a m e t e r o n m o m e n t - r o t a t i o n b e h a v i o u r for type 2 joints. 100
E
--
80C
l
O
~ C 9
"5
g E 40-
20
4;
80
80
lOO
Rotation of joint (0-(~) x 10-3 rad
Fig. lO(c). Effect o f bolt d i a m e t e r o n m o m e n t r o t a t i o n b e h a v i o u r for type 3 joints.
Comparative tests on endplate beam-to-column connections
171
indicate the merits of type 2 joints but further work under varying loads may show contradictory disadvantages. (3) The disign criteria make a conservative assessment of the plate strength in bending, thus resulting in a high factor of safety for the joints. The reserve strength in the plate could not be related to any other factor except the joint modelling technique. (4) Maximum end restraint (91%) is shown by type 2 joints and the minimum (86%) by flush endplate joints. Unexpectedly, the end restraint shown by type 3 joints (88%) is lower than for type 2 connections. (5) The moment rotation curves for all three types of joints indicate an almost similar pattern with an almost linear initial phase, followed by another portion with a substantially reduced stiffness. The change-over from high stiffness to a lower value seems to depend on the geometry of the joint. For the flush endplate joints the stiffness was reduced around 28 kN m, but for type 2 joints the transition occurred around 52 kN m. (6) Strength-ductility characteristics of joints reveal that flush endplate joints have an average in-plane rotation of 88-2 × 10 3 tad while type 2 and 3 joints have an average rotation of 86-5 x 10 -3 and 78'4 × 10 -3 rad respectively. The ductility shown by all three types of joints is sufficient to permit the use of a plastic method for their design. (7) For a constant endplate thickness, smaller diameter bolts reveal better ductility because of the small initial clamping force between the endplate and the column flange. Finally, the need to formulate an improved design criterion for flush endplate joints is necessary because of the popularity of the joint in structural steelwork. The areas requiring modification for extending the existing guidelines have been identified.
ACKNOWLEDGEMENTS The financial support given by the Papua New Guinea University of Technology for this project is gratefully acknowledged. Words of appreciation are also extended to the technical and secretarial staff in the Department of Civil Engineering.
REFERENCES 1. Pask, J. W., M a n u a l on Connections [i~r B e a m and Column
Construction.
Publication No. 9/82, British Constructional Steelwork Association~ London. 1982.
A. K. Aggarwal
172
2. Standards Association of Australia, AS 1204, Weldable Structural Steels-Ordinary Weldable Grades. SAA, Sydney, Australia, 1980. 3. Standards Association of Australia, AS 1227, General Requirements for the Supply of Hot-Rolled Steel Plates, Sections, Piling and Bars ,fi)r Structural Purposes. SAA, Sydney, Australia, 1980. 4. Hogan, T. J. & Thomas, I. R., Design o[ Structural Connections, 3rd edn (first published 1978). Australian Institute of Steel Construction, Sydney, Australia, 1988. 5. Standards Association of Australia, AS 1252, General Grade High Strength Steel Bolts with Associated Nuts and Washers.lor Structural En,qineerin,q. SAA, Sydney, Australia, 1973. 6. British Standards Institution, BS 4395, High-Strength Friction-Grip Bolts and Associated Nuts and Washers [or Structural Engineering, Part 1: General Grade. BSI, London, 1969. 7. European Committee for Standardisation, EC 3, Design q/'Steel Structures, Part 1.1: General Rules and RulesJbr Buildings. ENV 1993-1-1, Brussels, Feb. 1992. 8. Standards Association of Australia, AS 1511, High Stren.qth Structural Boltin.q Code. SAA, Sydney, Australia, 1984. 9. Aggarwal, A. K. & Coates, R. C., Moment-rotation characteristics of bolted beam-column connections. J. Construct. Steel Res., 6(4) (1986) 303 18. 10. Aggarwal, A. K., Behaviour of flexible beam-to-column connections. Proceedings q[" the Second National Structural Engineering Confi, rence, Adelaide, Australia. National Conference Publication No. 90/10, 1990, pp. 462 7. 11. Packer, J. A. & Morris, L. J., A limit state design method for the tension region of bolted beam column connections. Struct. Engr, 5(10) (1977). 12. Kennedy, A. N., Vinnakota, S. & Sherbourne, A. N., The split-tee analogy in bolted splices and beam-column connections. Proceedimts of the International Conlerence on Joints in Structural Steelwork, Teesside Polytechnic, U K, 1981. 13. Grundy, P., Thomas, 1. R. & Bennett, I. D., Beam-to-column moment connections. J. Struct. Div. ASCE, STI (1980) 313-30. 14. Horne, M. R. & Morris, L. J., Plastic Desi.qn qflJ~w-Rise Frames. Constrado Monograph, Granada, London, 1981. 15. Packer, J. A. & Morris, L. J., A limit state design method for thc tension region of bolted beam-to-column connections (Discussion by Suttees). Struct. Enqr, 56 (1978).
APPENDIX SAMPLE
CALCULATION FOR VALUES TYPE 2 JOINTS
GIVEN
I N T A B L E 4:
Bolt strength (i) Strength of the bolt g r o u p in shear
= N ' B ~ where Bv = 1/0-6 x (strength of bolt in shear) = 1/0.6 × ( 3 5 ) - 5 8 . 3 for 1 6 r a m bolts
(_'otttptlralit'e tests or1 fildplafe [~t'tlm-lo-COlllt~'ltl connections
or 6 x 583 = 349.8 k N for 6 bolts/'joint = 1/'0-6 x (55)=91"6 for 20 mm bolts or 6 × 9 1 . 6 = 5 4 9 . 6 k N for 6 bolts/joint (ii) Strength of the bolt g r o u p in tension Bt. = Bt,~./1
(bvj/(Bv) 2
where (b,.),v = 117/'6= t9'5 k N
B t, =
(19-5) 2 - - 57 x 0"942 = 53"7 k N for 16 mm bolts (58'3)
57 x ~/1
Bt,=88 x
•/
(19"5)2 1-- ( 9 1 . 6 ~ = 8 8 x 0"977=86-0 k N for 2 0 m m bolts
1 ( 4 x 53.7"] Put =O'6k, i + 0 ' 2 ] = 2 9 8 ' 3 kN for 16 mm bolts
1 ( 4 x 86-0"] Pb, = 0-6k i +~7~ j = 477-8 k N for 20 mm bolts
Plate strength (i) Bending Fv x PP' -
!4' i
X t~
b 250 x 200 x t 2 65"0
= 769-2 × ti2
where t~ is the thickness of plate. For plate thickness 16 mm, Pp, = 196"9 k N 20 mm, Pp, = 307.7 k N
173
A.K. Aggarwal
174
(ii) P l a t e s t r e n g t h in s h e a r Ppv = 2 x 0"55 x fly x w i x fi = 2 x 0"55 x 250 x 200 x ti
= 55 x ti k N F o r p l a t e t h i c k n e s s 16 mm, Ppv = 8 8 0 k N 20 m m , Ppv = 1100 k N
Weld strength
(i)
F l a n g e weld
Pwt -
2xPt
x l,
0.6
w h e r e lv = l - 2tw
Iv = ( 1 3 3 " 4 x 2 - 5 " 8 4 ) - 2 = 248"96 m m
x 6
2x0-7 Pwt - - x 248"96 0"6 = 580-9 k N (for 6 m m welds) (ii) W e b w e l d
Pwv --
2xPt 0"6
where
x lv 1,. = l - 2 t w •=(203"2--2
x 7"82) x 2 = 3 7 5 " 1 2 m m
1 , = 3 7 5 " 1 2 - - 2 x 6"0 = 363-12 m m Pwv --
2 x 363.12 0.60
x 0"57 = 689"9 k N
(for 6 m m welds)
C o l u m n strength C a p a c i t y o f unstiffened c o l u m n s e c t i o n in t e n s i o n / c o m p r e s s i o n Qmc = Fy~r" T~ [ 3 ' 1 4 + 2 ( e c + p - ~bl)/f]
Comparative tests on endplate beam-to-column connections
175
where
f =(,q-tc- 2"r~)/2 OF
f = ( 1 4 0 - 8 - 0 2 - 2 x 10.2)/2.0 = 111-58/2 = 55.79 Qmc = 283 x 10-922 [3.14 + 2(30 + 130 - 22)/55.79] = 272.9 k N W h e n the c o l u m n is stiffened b y t w o full d e p t h 6 m m thick stiffeners, the a d d i t i o n a l force o n a c c o u n t o f stiffeners P~s = (0-6" Fyw" t~" d~)2 PTs = 0 " 6 x 315 x 6 x
(206 - 8"02) x 2 2
= 224"5 k N T o t a l c a p a c i t y o f c o l u m n flange w i t h stiffeners = 272-9 + 224.5 = 497.4 k N
Column web shear capacity V:,.x = 0 ' 5 5 " Fyw" De" tc
= 0 ' 5 5 x 315 x 206 x 8"02 = 286"2 k N