Journal ASCE Splice Plate Tube Moment Connection
Journal ASCE Splice Plate Tube Moment Connection
Journal ASCE Splice Plate Tube Moment Connection
ABSTRACT: This paper presents a model for the determination of the serviceability and ultimate moment
capacities of bolted moment end plate connections utilizing rectangular hollow sections and two rows of bolts.
One row of bolts is positioned above the top flange, and the other is positioned symmetrically below the bottom
flange. The model considers the combined effects of prying action caused by flexible end plates and the formation
of yield lines in the end plates. The model is calibrated and validated using experimental data from an associated
test program. The design model constitutes a relatively simple method for predicting the serviceability and
ultimate moment capacities for the particular type of bolted moment end plate connection described here. An
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example is given to illustrate how the design model can be applied to practical connection designs.
INTRODUCTION the end plate is said to be "rigid," but in the latter case, the
The increase in the use of rectangular hollow sections in end plate is said to be "flexible." The design of rigid end
mainstream structures, coupled with the economics of prefab- plate connections may be less difficult than design of flexible
rication, has highlighted the need for simple design methods end plate connections due to the need to consider prying ef-
that produce economical connections for tubular members. In fects in the latter, but the flexible end plate provides a sub-
an effort to address this need, the Australian Institute of Steel stantially more economical and ductile connection.
Construction (AISC) has published the document Design of The effects of prying have been studied extensively, and
Structural Steel Hollow Section Connections (Syam and Chap- various methods, such as the stub-tee (split-tee) analogy
man 1996), in which design models are presented for com- (Agerskov 1976; Kato and McGuire 1973; Nair et al. 1974;
monly used tubular connections. The moment end plate con- Kennedy et al. 1981), have been developed to predict the ef-
nection described in this paper is not included in the AISC fects of prying on the connection strengths. These methods
document because an appropriate design model did not exist have primarily been associated with moment end plate con-
at the time of its publication. Some typical applications of the nections in I-sections. Although the behavior of the end plate
moment end plate connection using rectangular hollow sec- connection utilizing rectangular hollow sections differs from
tions are shown in Fig. 1. that in I-sections, it can be modeled through adaptation of the
The moment end plate connection joining I-section mem- stub-tee analogy.
bers has been used extensively and considerable documenta- As suggested by Kennedy et al. (1981), the behavior of the
tion on its behavior exists in the literature [for example, end plate can be divided into three distinct categories based
Grundy et al. (1980); Murray (1988, 1990); Kukreti et al. on the plate thickness and magnitude of loading. The first
(1990)]. In contrast, research on end plate connections joining mode is termed thick plate behavior and is characterized by
rectangular and square hollow sections has been limited. Fur- the absence of prying effects and yield lines, resulting in a
thermore, the research on tubular end plate connections that direct relationship between the bolt loads and the applied mo-
has been conducted has concentrated primarily on pure tensile ment. At the other extreme, the third mode is termed thin plate
loading (Kato and Hirose 1985; Packer et al. 1989), or on behavior and is characterized by yield lines through the bolt
combined compression and bending (Kato and Mukai 1991) positions and a maximum value of the prying force. The re-
as in a column-to-column bolted flange splice connection, sulting bolt loads are the superposition of the bolt pretension,
rather than the pure flexural loading considered here. Although the prying forces, and the forces induced in the bolts from the
some test programs on tubular end plate connections subject applied moment. The second mode, termed intermediate plate
to flexural loading have been conducted (Mang 1980; Petit et behavior, falls between the thick and thin plate behavior and
al. 1986), associated theoretical or design models were not is characterized by the prying force ranging from zero to the
presented. maximum attainable value.
When the end plate connection is subjected to pure flexure,
In this paper, an analytical model to determine the moment
tensile loads are applied to the bolts on the tensile side of the
capacity of end plate connections joining rectangular hollow
neutral axis through the bending of the plate. Failure of the
sections is presented. The model is based on the modified stub-
connection generally occurs when these bolts reach their ten-
sile capacity. As outlined by Nair et al. (1974), the ultimate tee analogy, which enables the effects of bolt prying forces to
strength of the connection may be reached either before or be incorporated. The model is further refined using yield line
after yielding has occurred in the end plate. In the former case, analysis to include the effect of the bolt positions along the
tensile face of the end plate. The model described in this paper
'Postgrad. Student, Dept. of Civ. Engrg., Univ. of Sydney, N.S.W. is limited to the end plate connection containing two rows of
2006, Australia. bolts, as shown in Fig. 1. The predictions of the model are
'Sr. Lect., Dept. of Civ. Engrg., Univ. of Sydney. compared with the results obtained from an associated ex-
'BHP Steel Prof. of Steel Struct., Dept. of Civ. Engrg., Univ. of Syd- perimental program conducted at the University of Sydney
ney.
'Montague-Betts Prof. of Struct. Steel Des., Dept. of Civ. Engrg., Vir-
(Wheeler et al. 1995, 1997a). At the end of the paper, a design
ginia Polytechnic Inst. and State Univ., Blacksburg, VA 24061. example illustrating the practical application of the model is
Note. Associate Editor: W. Samuel Easterling. Discussion open until presented.
July I, 1998. To extend the closing date one month, a written request A model of this type has not been presented in the literature
must be filed with the ASCE Manager of Journals. The manuscript for previously and is of immediate practical use to the structural
this paper was submitted for review and possible publication on June 23,
1997. This paper is part of the JourlUll of Structural Engineering, Vol.
engineering profession. The model is largely based on funda-
124, No.2, February, 1998. ©ASCE, ISSN 0733-9445/98/0002-0164- mental concepts of mechanics and includes very few empirical
0173/$4.00 + $.50 per page. Paper No. 16059. adjustments.
164/ JOURNAL OF STRUCTURAL ENGINEERING / FEBRUARY 1998
For the flexible end plate, the failure load (Pu) is defined as
the ultimate tensile load in the bolts (B.) minus the prying
force at ultimate load (Qu).
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p. = B. - Q. (2)
EXPERIMENTAL STUDY
An experimental program on moment end-plate connections
for tubular members has been conducted at the University of
Sydney (Wheeler et al. 1995, 1997a). Two basic connection
configurations, termed type A and type B, were investigated.
(a) Rigid End Plate (b) Flexible End Plate The type A connections utilized eight bolts, and the type B
FIG. 2. Basic End Plate Behavior connections employed four bolts. This report deals only with
the type B (four-bolt) connections, the general configuration
of which is shown in Fig. 3. The connections were tested in
PRYING ACTION
pure bending by subjecting a beam, containing a beam splice
The behavior of a connection where tensile loads are trans- connection [of the type shown in Fig. l(a)] at midspan, to four-
ferred to fasteners through an end plate depends on the rigidity point bending.
of this plate. This is demonstrated in Fig. 2, where two stub- The parameters varied in the experimental program include
tee connections are shown. In the first connection, which com- the plate size (Wp , Dp ), the plate thickness (tp ), the section
prises a rigid end plate, minimal deformation occurs when the shape (square or rectangular), and the position of the bolts with
tensile load (P) is applied; the plate remains virtually parallel respect to the section flange (so) and to the section web (c).
to the connecting surface. The second connection, which con- Each test contained two rows of bolts, one above the section
tains a flexible end plate, deforms as shown when loaded, gen- compression flange and the other below the section tensile
erating compressive (prying) forces between the contacting flange. The dimensions of the end plates and the type of sec-
surfaces, which raise the tensile bolt forces correspondingly. tions [square (SHS) or rectangular (RHS)] used for all type B
The study by Nair et al. (1974) on the effect of tension and specimens in the experimental program are given in Table 1.
w;p
Compression
~ ~
f-- 0 0
So
tp = end plate thickness
s = weld leg length
D~'
n = number of tensile bolts
(= 2 in all tests)
d
a p = min(2tp• a.)
d' = d+ s..J2
dr so' = So - s/..J2
So
- 0 .-.
'._J 0 c = a. - a.
d :s; 400mm
Tension
b
FIG. 3. End Plate Layout and Model Parameters
~
o ~O ----0---
o
----0----
---- .---
----0----
---- ----
............. "
0
"
shown in Fig. 5. The variables used are defined in Fig. 3,
where n is the number of tensile bolts. In the yield line analysis
for mode 1, By/ is taken as the yield load per bolt, which was
',a --y~ 0" measured to be 195 kN. The position of the yield lines is
o 0 -0---------0-
I 1u,-"
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" assumed to be influenced by the size of the weld fillet; for this
reason the depth of the section (d) and distance from the line
FIG. 5. Yield Line Modes of Failure: (a) Mode 1; (b) Mode 2; (c) of bolts to the section flange (so) are corrected to d' :: d +
Mode 3 sy'2 and s; = So - s/y'2, respectively, where s is the leg
length (8 mm) of the fillet weld. It is also assumed that the
plastic mechanism [Fig. 5(c)] in which yield lines form diag- section is perfectly rectangular (neglecting the rounding of the
onally across the tensile corners of the end plate rather than corners).
in a purely one-dimensional fashion [modes 1 and 2 in Figs. As derived by Wheeler et al. (l997b), the yield moments
5(a) and (b), respectively]. for mode 1, mode 2, and mode 3 are
Mode 1
YIELD LINE ANALYSIS
The analysis of stub-tee end plate connections generally as- My/ = (d' + 2(s; + a.»W p
m + nBy,a.) d (3)
sumes that yield lines form transversely across the end plate (s; + a.)d' P s; + a.
(Agerskov 1976; Kato and McGuire 1973). In the experi- Mode 2
mental program described previously, such patterns of yield
lines were observed when the bolts were located sufficiently M
y/
= (2(d' +'d's;)W p _ '!!!L)
,
A
mp'"
(4)
closely to the section webs. However, other plastic mecha- So So
nisms involving inclined yield lines were also observed when
the bolts were moved farther away from the section webs. Mode 3
The three yield line mechanisms observed experimentally
are shown in Fig. 5. Mode 1 consists of yield lines forming vWp (b2 + 4l) + (y'r 2 + 4v 2l)d34 + 4U q V)
Wp b
at the top and bottom of the section, coupled with elongation My/ = ( 7 + --=------(-2q-c-+-s-:-:;b-)'"':d:-'- - - - - dmp
and yielding of the tensile bolts [Fig. 5(a)]. In mode 2, an
additional yield line forms through the line of bolts on the (5)
tension side of the connection [Fig. 5(b)]. Once the mode 2
mechanism has formed, no additional load is transferred to the where Wp :: b + 2a. + 2c; v :: d' + s;; q = at + s; - u;
tensile bolts as the end plate deforms. Mode 3 comprises a r = 2qc - bd'; and d34 = a.(2qv - r) d 34 :: a.(2qv -
more complex arrangement of yield lines, as shown in Fig. r)yr 2 + 4q 2v 2 ¢ (qvr) - 2df . For mode 3, the yield moment
5(c). As for mode 2, the yield lines pass through the tensile My, must be minimized with respect to the variable u to obtain
bolts and no additional loads are transferred to the bolts fol- the correct lower-bound solution.
Experimental
Plate Dimensions yield moment, Calculated Yield Moment, My! (kN . m)
tp c Mcy
Test (mm) (mm) (kN·m) Mode 1 Mode 2 Mode 3 Critical mode My,lMcy
(1 ) (2) (3) (4) (5) (6) (7) (8) (9)
11 12 0 31.0 38.0 29.1 34.4 2 0.94
12 16 0 49.7 49.5 51.8 61.1 1 1.00
13 20 0 57.2 61.1 80.9 95.5 1 1.07
14 12 0 39.2 45.6 27.5 40.7 2 0.70
15 16 0 53.5 57.3 48.9 72.3 2 0.91
16 20 0 52.2 67.9 76.4 113.0 1 1.30
17 12 35 22.0 42.1 39.8 28.1 3 1.28
18 16 35 39.2 56.3 70.7 50.0 3 1.28
19 20 35 52.2 71.8 110.5 78.1 1 1.38
20 12 35 30.7 50.5 41.2 30.0 3 0.98
21 16 35 50.2 65.5 73.3 53.3 3 1.06
22 20 35 56.2 80.8 114.5 83.2 1 1.44
23 16 0 42.5 43.6 40.9 50.4 2 0.96
24 16 0 48.4 57.7 74.1 92.5 1 1.19
25 16 0 46.7 50.0 38.2 65.0 2 0.82
26 16 0 63.9 67.5 70.7 99.6 1 1.06
Note: Mean of M,/Mev = 1.08. Standard deViation = 0.21.
JOURNAL OF STRUCTURAL ENGINEERING / FEBRUARY 1998/167
MJ: F~M2~M2i_R
ysis is given by
_FR:bMI
(6)
MODIFIED STUB-TEE ANALYSIS where F L is the shear force on the left and F R the shear force
on the right side of the flange, as shown in Fig. 7. These shear
General Model forces can be expressed in terms of the bolt loads (B), the
prying force (Q), and the internal moments at points 1 and 2
The stub-tee analysis method involves the application of (M lo M 2 ) using
simple rigid plastic (yield line) analysis to an analogous beam
that represents the one-dimensional behavior of the end plate (9)
with yield lines parallel to the axis of bending only. This sim-
ple representation of the connection is shown in Fig. 6, where (10)
the equivalent beam has a length equal to the plate depth (Dp )
and a depth equal to the plate thickness (tp ). The model as-
sumes that the plastic hinges that form at points, I, 2, and 3 By combining (7)-(10), the following general expression for
(Fig. 6) represent yield lines, that form transversely across the the connection moment is obtained:
Mb ,.,..,
s d
B'I the ultimate connection failure due to bolt fracture occurs sub-
sequent to the formation of a yield line at point 1 but prior to
rr-Tl "'"
-3
r
-2
rTIl
the formation of a yield line at points 2 or 3. Intermediate
plate behavior occurs when the bolts fracture after the for-
mation of yield lines at points 1 and 2 (mode 1 mechanism).
- 1 Thin plate behavior corresponds to the formation of yield lines
-rTT T T T T T at points I, 2, and 3 (mode 2 mechanism) in the end plate
an Sn' d' P without deformation of the bolts.
a. The plastic moment M ip for each "hinge" (i), shown in Fig.
Dp 6, is given by
Q
(12)
FIG. 6. Analytical Model Used in Modified Stub-Tee Analysis
~
the plastic moment capacity of the end plate is assumed to be Mb
intermediate in value between the yield stress (h) and the ul- (2)
wt'p
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Thick end plate behavior is considered to hold as long as the Substituting (18) into (11) and setting the prying force to zero
moment at point 2, as calculated using (15), is less than the allows the minimum moment for the connection for interme-
plastic moment (M 2 ~ M 2p ). diate behavior to be expressed as
p . (d - t,) (22)
FIG. 8. Thick Plate Behavior This exposition on intermediate behavior is valid from the
JOURNAL OF STRUCTURAL ENGINEERING / FEBRUARY 1998/169
(a)
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(b)
FIG. 10. Thin Plate Behavior
point when the moment at point 2, calculated from (15), ex- width Weq that fails by a mode 2 mechanism [Fig. 5(b») with the
ceeds the plastic moment, and while the moment at point 3 is one-dimensional patterns of yield lines. This equivalent width Weq
less than the plastic moment. The bolt load B must also be is determined using (4) and is expressed as
less than or equal to the ultimate bolt load (B u ). These con-
the same manner as a wide beam is appropriate. The connec- depth of the beam section (d) assumed to be no greater than
tions characterized by an end plate failure mode showed a less 400 mm.
accurate correlation to the experimental results, having a mean A major recommendation of this paper is that the end plate
ratio of predicted to experimental moments of 0.89 and a stan- should behave in an intermediate manner to achieve an eco-
dard deviation of 0.09. The low average predicted strength of nomical and ductile design. The disadvantage of a thin end
the connections with a thin end plate is thought to be a result plate is that it exhibits low stiffness, causing large deforma-
of the fact that the model does not incorporate the tension tions that reduce the serviceability limit moment of the con-
stiffening effects that occur in practice when the end plates nection relative to the connection ultimate moment. On the
deform significantly. other hand, a connection with an end plate classified as thick
The correlation between the actual and predicted failure can fail in a brittle manner due to bolt fracture and may also
modes can be gauged by comparing the last column of Table be unnecessarily expensive. Therefore, the "ideal" failure
1 with the penultimate column of Table 5. In almost all cases, mode should involve bolt capacity combined with intermediate
the actual failure mode labeled "deformation" in Table 1 plate behavior.
matches a predicted end plate failure mode in Table 5. Simi- Based on Murray's (1990) philosophy, it is assumed that the
larly, the theoretical model appears to be quite adept at pre- bolts in the compressive region resist all the shear loads. It is
dicting the bolt failure mode. In some instances where the recommended that the tensile bolts be positioned such that two
actual and predicted failure modes do not coincide, this is sim- or more bolts fall between the line of the webs (c = as - a.
ply a reflection of the fact that there is no clear-cut distinction :$ 0) (see Fig. 3). If this condition is not met, yield line anal-
between the ultimate moments premised on bolt capacity and ysis is necessary to calculate the equivalent end plate width
plate capacity in the theoretical model. (weq ).
The equivalent width is calculated assuming the section is The strength limit state moment capacity of the connection
square or rectangular and ignores the rounded nature of the (Me.) is the lower value of the ultimate moments computed on
corners. The consequence of this assumption is that the yield the basis of bolt capacity (Meb ) and plate capacity (Mep ). The
moments for mode 3 calculated using (5) are larger than results connection serviceability moment (Mes ) is the lower of the mo-
obtained by a more precise yield line analysis. As a result, in ments that cause yielding of the bolts (Mebs ) or yielding of the
the tests where the equivalent width concept was used (#17 to end plate (Mcp.).
#22), the predicted to experimental moment ratios are gener- The resisting moment generated by the bolts (Mb ) and the
ally higher than in the other tests. plate design stress in the end plate (ft,) are defined by (17) and
As described in this paper, the calibration of the connection (14), respectively. The corresponding material properties
model is based on tests for which the sections are relatively should be the nominal values obtained from the appropriate
shallow (d = 150 or 200 mm) relative to I-sections often used standards.
in moment end plate connections. It is recognized, however,
that for deeper sections the yield lines through point 1 (Fig.
6) may not form, due to insufficient rotations at this point STRENGTH LIMIT STATE DESIGN
(Murray 1988). For this reason, an upper limit of 400 mm on The moment capacity of the connection is determined using
the depth of the section has been applied to the design model the modified stub-tee method, which includes the effects of
described in this paper. prying forces. Equations to calculate the connection capacity
In addition to the verification discussed previously, it would based on bolt failure and end plate failure are presented. The
be ideal to further evaluate the effectiveness of the model by moment capacity of the connection is the lower of these two
applying it to Mang's (1980) test data on tubular moment end values.
plate connections subjected to flexure. This has not been at-
tempted, however, since the measured material properties of
the end plates were not reported by Mang (1980). Connection Capacity Limited by Bolt Failure
. (d - ts ) (29) (37)
To avoid thick plate behavior, the limit on the plate thickness for tions governed by bolt capacity. Connections governed by
capacity limited by bolt failure is plate capacity are also more influenced by membrane stiffen-
ing effects in the end plate, a phenomenon that is not consid-
ered in the design model described in this paper.
(31)
The recommended procedure for the design of an end plate
connection of the type shown in Fig. 3 is as follows:
Connection Capacity Limited by End Plate Failure 1. Estimate the end plate dimensions for initial design based
on section size, bolt size, and number of bolts.
The equations for end plate capacity are based on thin plate 2. If two or more bolts are not positioned within the webs
behavior using the plate design stress (jp). Since the capacity of the section (c :s 0), yield line analysis is required to
of the plate is assumed to govern, with no significant contri- determine the equivalent width (Weq). Otherwise, the
bution from the bolts, it is appropriate that the resistance factor equivalent width is equal to the end plate width (Wp ). If
for the plate in bending (<p p) be used. the plate thickness is already known, go to step 6.
From an adaptation of (27), the connection design moment 3. Solve for the strength limit state design thicknesses tb•
capacity is given by and f pa using (30) and (33). For appropriate ultimate
strength limit state design, the required plate thickness
<j>pMcp == <j>p (t.) is equal to the maximum of the thickness based on
bolt and plate capacity.
. (t;!p(We<j(d' + 2s;) + (we<j - Mt)d') + n ~ d') t a == max(tba, fpa )
4d's; 4. Solve for the serviceability design thicknesses tbs and tps
using (36) and (37). For appropriate serviceability limit
. (d - f,) (32) state design, the required plate thickness (fs .) is equal to
the maximum of the serviceability thicknesses calculated.
Alternatively, for a given connection design moment M*, the
appropriate end plate thickness is given by
M*s; _ n 'IT'd~'!Ify) d' 5. The resulting thickness for the end plate (fp ) must exceed
( <!>id + f,) 32 both the serviceability and ultimate limit state thick-
tpa == 2 (33) nesses, but must be less than the maximum allowable
plate thickness (tm,x) given by (31). That is,
3. Substitution into (30) and (33) gives tbu = 17.2 mm and Agerskov, H. (1976). "High-strength bolted connections subject to pry-
tpu = 13.5 mm. Therefore, tu = 17.2 mm. ing." J. Struct. Div., ASCE, 102(1), 161-175.
4. Substitution into (36) and (37) gives tbs = 13.6 mm and Grundy, P., Thomas, I. R., and Bennetts, I. D. (1980). "Beam-to-column
tps = 12.3 mm. Therefore, ts = 13.6 mm. moment connections." J. Struct. Engrg., ASCE, 106(1),313-330.
"High-strength steel structural bolts with associated nuts and washers for
5. The maximum allowable end plate thickness (tm..) is 20.2 structural engineering." (198la). AS 1252-1981, Standards Australia,
mm [see (31)]. The required end plate thickness must Sydney, Australia.
therefore be in the range max(t" tu) :s; tp :s; tm... That is, Kato, B., and Hirose, R. (1985). "Bolted tension flanges joining square
17.2 mm :s; tp :s; 20.2 mm. Therefore, assume that tp = hollow section members." J. Struct. Engrg., ASCE, 111(5), 163-177.
18 mm. Kato, B., and McGuire, W. (1973). "Analysis of T-stub flange-to-column
6. The design ultimate strength limit state moment capaci- connections." J. Struct. Div., ASCE, 99(5), 865-888.
Kato, B., and Mukai, A. (1991). "High strength bolted flanges joints of
ties are <l>bMcb = 37.0 kN'm and <l>pMcp = 60.7 kN·m. SHS stainless steel columns." Proc., Int. Cont on Steel and Aluminum
[See (29) and (32).] Since M* < <l>bMcb < <l>pMcp , the Struct.
strength limit state is satisfactory. Kennedy, N. A., Vinnakota, S., and Sherbourne, A. N. (1981). "The split-
7. The serviceability limit state moments are <l>bMcbs = 29.8 tee analogy in bolted splices and beam-column connections." Joints in
kN/m and <l>pMcps = 45.8 kN· m. [See (34) and (35).] Structural Steelwork, John Wiley & Sons, Inc., New York, N.Y., 2.138-
Since M: < <l>bM'bst the serviceability limit state is sat- 2.157.
Kukreti, A. R., Ghassemieh, M., and Murray, T. M. (1990). "Behavior
isfactory. and design of large-capacity moment end plates." J. Struct. Engrg.,
8. The strength limit state design moment capacity for the ASCE, 116(3), 809-828.
connection is 37.0 kN· m, and the serviceability limit Mang, F. (1980). "Investigation of standard bolted flange connections for
state moment is 29.8 kN· m. circular and rectangular hollow sections," CIDECT Programme 8A Fi-
nal Rep. Steel Construction Inst., Ascot, U.K.
The connection requires a 210 X 290 X 18 mm end plate with Murray, T. M. (1988). "Recent developments for the design of moment
end-plate connections." J. Constructional Steel Res., 10, 133-162.
four M16 grade 8.8 bolts. Additional design examples are Murray, T. M. (1990). "Design guide for extended end plate moment
given in a report by Wheeler et al. (l997b). connections." Steel Design Guide, No.4, Am. Inst. of Steel Constr.
Nair, R. S., Birkemoe, P. C., and Munse, W. H. (1974). "High strength
CONCLUSIONS bolts subject to tension and prying." J. Struct. Div., ASCE, 100(2),
351-372.
This paper presents a simple and accurate model for pre- Packer, J. A., Bruno, L., and Birkemoe, P. C. (1989). "Limit analysis of
dicting the strength of a moment end plate connection using bolted RHS flange plate joints." J. Struct. Engrg., ASCE, 115(9),
rectangular hollow sections. The model uses a modified stub- 2226-2241.
Petit, L., Plumier, A., and Rondal, J. (1986). "Tests on T type bolted
tee analogy coupled with yield line analysis to predict both
joints in hollow section intended to transmit a moment," CIDECT Pro-
the ultimate moment capacity and maximum serviceability gramme 6B Final Rep. Steel Construction Inst., Ascot, U.K.
moment for the connection. The modified stub-tee incorporates "Steel structures." (1990). AS 4100-1990. Standards Australia, Sydney,
the effects of the prying forces on the connection strength, Australia.
while the yield line analysis predicts the failure mechanism of "Structural steel hollow sections." (1991a). AS 1163-1981. Standards
the end plate to enable the calculation of an end plate "equiv- Australia, Sydney, Australia.
"Structural steel: Hot-rolled plates, floorplates and slabs." (1981b). AS
alent width" to be used in conjunction with the stub-tee
3678-1981. Standards Australia, Sydney, Australia.
model. "Structural steel welding. Part I: Welding of steel structures." (1991c).
The model is limited to square and rectangular sections with AS 1554.1-1991. Standards Australia, Sydney, Australia.
two rows of bolts, one above the top flange and the other Syam, A. A., and Chapman, B. G. (1996). Design of structural steel
below the bottom flange. While the connections tested exper- hollow section connections. Volume 1: Design models, 1st Ed., Austra-
imentally and used for model verification contained only two lian Inst. of Steel Constr., Sydney, Australia.
bolts in each row, the addition of extra bolts in the tensile (and Wheeler, A. T., Clarke, M. J., and Hancock, G. J. (1995). "Tests of bolted
moment end plate connections in tubular members." Proc., 14th Aus-
compressive) bolt rows does not invalidate the model. The tralasian Cont on Mechanics of Struct. and Mat., Univ. of Tasmania,
reason for this is that the use of additional bolts in the tensile Hobart, Tasmania, Australia, 331-336.
row tends to enforce a mode 2 end plate failure to which the Wheeler, A. T., Clarke, M. J., and Hancock, G. J. (1997a). "Bending tests
model presented in this paper is well suited. of bolted end plate connections in cold formed rectangular hollow sec-
Of the three types of plate behavior presented (thick, thin, tions." Res. Rep. No. R736, Dept. of Civ. Engrg., Univ. of Sydney,
Sydney, Australia.
and intermediate), it is recommended that the end plate con-
Wheeler, A. T., Clarke, M. J., Hancock, G. J., and Murray, T. M. (1997b).
nections be designed to behave in an intermediate fashion, "Design model for bolted moment end plate connections using rectan-
with connection strength being governed by bolt failure. Thin gular hollow sections." Res. Rep. No. R745, Dept. ofCiv. Engrg., Univ.
plate behavior results in connections that are very ductile and of Sydney, Sydney, Australia.