Advances in Steel Structures - part 28 pdf

250
K.F. Chung and K.H. Ip
Double bolted connection : 100-G550-B2- 48 • 95 -M12 (page 38 of Reference 7).
Thickness, t = 0.99mm; Bolt diameter, d = 12mm, and Bolt spacing, Sp = 36mm.
Figure 1 Geometry of a double bolted connection
Figure 2
Proposed stress-strain curves for high strength low ductility cold-formed steel
strips,
FEA-pr and FEA-pr
Finite Element Modelling of Double Bolted Connections
35
30
25
Z
9 -~ 20
"o
m
15
O
-J 10
5
0
J
. oo ~
;~~-'
/
FEA-pr L
FEA-py I
/ i
0 0.5 1 1.5 2 2.5 3
Extension

(mm)
Figure 4(a) Load-extension curves for double bolted connections
with different stress-strain curves
(Bolts 1 and 2 in contact with CFS at the same time)
31.10kN
28.08kN
251
35- L
30
2 mm gap
25
Z
20
"O
m
15
O
_! 10 i r ~ Bolt 1 first in contact
5 ~ Bolt 2 first in contact
Single bolt
0 i J
0 0.5 1 1.5 2 2.5
Extension
(mm)
Figure 4(b) Load-extension curves for double bolted connection
with different deformation sequences
1 mm gap~ ~
FEA-pr
28.08kN
26.69kN

24.10kN
15.90kN
35
30
A 25
z
20
-o
m
15
0
,_1 10
5
0
j
] Sp=36m m
Sp=48mm
, 1
0 0.5 1 1.5 2 2.5
Extension
(mm)
Load-extension curves for double bolted connection
with different bolt spacing, Sp
(Bolts 1 and 2 in contact with CFS at the same time)
o 31.82kN
_ ~
28.08kN
Figure 4(c)
252
Figure 5

K.F. Chung and K.H. Ip
Distribution of von Mises stress of the double bolted connection
Figure 6 Deformed mesh of double bolted connection at 3mm extension
(Failure mode - bearing failure of CFS strip)
ANALYTICAL MODEL FOR EIGHT-BOLT
RECTANGULAR HOLLOW SECTION
BOLTED MOMENT END PLATE CONNECTIONS
A. T. Wheeler l, M. J. Clarke 2 and G. J. Hancock 2
~Department of Civic Engineering and Environment, The University of Western Sydney Nepean
Kingswood, N.S.W., 2747, Australia
2Department of Civil Engineering, The University of Sydney,
Sydney, N.S.W., 2006, Australia
ABSTRACT
The increase in the use of rectangular hollow sections in mainstream structures has highlighted the need
for simple design methods for the production of economical connections. This paper presents a new
model for the determination of the serviceability limit moment and the ultimate moment capacity of
bolted moment end plate connections utilising rectangular hollow sections and eight bolts positioned in
an approximately equidistant sense around the perimeter of the section. The model considers the
combined effects of prying action due to flexible end plates, and the formation of yield lines in the end
plate. Failure modes involving plate yielding, bolt fracture, punching shear and beam section capacity are
considered.
The model has been calibrated and validated using experimental data from an associated test program.
The model constitutes a relatively simple method for predicting the serviceability limit moment and
ultimate moment capacity of moment end plate connections utilising square and rectangular hollow
sections and eight bolts.
KEYWORDS
Tubular, connections, moment end plate, structural design, prying, yield line.
INTRODUCTION
The use of moment end plate connections joining I-section members and their corresponding structural
behaviour has been well documented (Murray, 1990). Contrastingly, research on end plate connections

joining rectangular and square hollow sections has been limited and consequently few design models are
available for routine use. Furthermore, documented studies have concentrated primarily upon pure tensile
loading, or combined compression and bending, as in a column-to-column bolted flange splice
connection (Packer et al., 1989; Kato and Mukai, 1991).
The eight-bolt moment end plate connection described in this paper and depicted in Figure I has a similar
layout to that used by Kato and Mukai (1991), and represents one of two fundamental bolting
arrangements studied by Wheeler (1998). The other bolting arrangement utilises four bolts, with the
corresponding design model described in Wheeler et al. (1998).
253
254
A.T. Wheeler et al.
Figure 1" Typical eight-bolt end plate application and layout
The theoretical model presented in this paper pertains to tubular eight-bolt end plate connections
subjected to flexural loading. The model determines the yield moment of the connection using yield line
analysis, and combines the yield line analysis with stub-tee analysis to predict the ultimate strength of the
connection. Two additional failure modes observed in the experimental program, namely section capacity
and punching shear, have also been included in the theoretical model. Full details of the derivation of the
model are given in Wheeler (1998). The predictions of the model are compared with the results obtained
from an associated experimental program (Wheeler et al., 1995).
EXPERIMENTAL PROGRAM
An experimental program in which ten eight-bolt connections were tested has been conducted at the
University of Sydney (Wheeler et al., 1995). The connections were loaded in pure flexure by subjecting a
beam, with a splice connection at mid-span, to four-point bending. As the sections were not susceptible
to local buckling, the ultimate load of the specimen was limited to connection failure, which occurred
due to tensile bolt fracture, excessive end plate deformations, section failure or punching shear failure.
The experimental ultimate moment (Mcu) and the failure mode for each test are listed in Table 1. The end
plate material properties of yield stress (fy) and ultimate tensile strength (fu), and the beam section
dimensional details and measured ultimate moment capacity (Mus) are given in Table 2.
The parameters varied in the experimental program are also given in Table 1 and include the plate size
(Wp, Dp), the plate thickness (tp), the section shape, and the positions of the bolts with respect to the

section flange and web (So and g). The bolt and nut assemblies were M20 structural grade 8.8 (Grade
TABLE 1
END PLATE CONNECTION DETAILS AND TEST RESULTS
Specimen
No.
Section
Type
SHS
2 RHS
3 SHS
4 SHS
5 RHS
6 RHS
7 SHS
8 SHS
9 RHS
10 RHS
Pla~ Dimensions(mm) Mcu
Wp
Dp So ~ (kNm)
16 280 280 35 30 116.0
16 230 330 35 15 124.5
12 280 280 35 30 93.9
20 280 280 35 30 116.0
12 230 330 35 15 92.7
20 230 330 35 15 136.7
16 260 260 25 35 113.2
16 300 300 45 25 97.6
16 210 310 25 20 133.0
16 250 350 45 10 119.3

Failure
Mode*
Bolt
Punching
Bolt
Bolt
Punching
Bolt
Bolt
Punching
Punching
Punching
* Punching = Failure by section tearing away from plate at toe of weld (punching shear).
Bolt = Failure by bolt fracture.
Analytical Model for Bolted Moment End Plate Connections
TABLE 2
END PLATE MATERIAL PROPERTIES AND BEAM SECTION DETAILS
255
End Plate Properties Beam Section Details
tp (mm) fy (MPa) fu (MPa) Section Depth d (mm) Width b (mm) Thickness ts (mm) Mus (kNm)
12 354 499 SHS 151.0 150.9 9.0 119
16 349 482 RHS 199.5 101.5 9.1 138
20 351 496
8.8/T), with a measured yield strength and ultimate tensile strength of 195 kN and 230 kN, respectively.
The connections were prefabricated using a combination fillet/butt weld joining the section to the end
plate, with a nominal fillet leg length of 8 mm.
YIELD LINE ANALYSIS
The yield line analysis serves primarily to determine the failure mode of the end plate, with prying action
of the bolts ignored. As a secondary function, the analysis provides an estimate of the yield moment of
the connection (Mcy). To determine the critical yield line pattern, numerous plastic mechanisms were

considered. Most of these entailed relatively complicated patterns and resulted in lengthy expressions for
the collapse moment (Myl). The derivations of the collapse moments for the different mechanisms
considered are given in Wheeler (1998). The three most critical end plate mechanisms are presented in
Figure 2. For each test, the experimental yield moment (Mcy) and the corresponding calculated yield
moments (My0 are presented in Table 3, with the critical mode highlighted. The yield mechanism termed
"Mode 8" in fact corresponds to beam yield capacity, determined using the measured yield stress of the
tubular section.
Figure 2: End plate yield line mechanisms
TABLE 3
THEORETICAL AND OBSERVED RESULTS FOR CONNECTION YIELD MOMENTS
256 A.T. Wheeler et al.
It can be seen in Table 3 that the majority of the tests were govemed by section yielding (Mode 8).
Additionally, the calculated yield moments for Modes 4 and 5 are virtually identical.
CUMULATIVE MODIFIED STUB-TEE METHOD
To consider both the combined effects of bolt prying and end plate yielding on the ultimate capacity of
the connection, a modified version of the stub-tee analogy is employed. Stub-tee analogies have been
used extensively to determine the strength of end plate connections in I-sections (Nair et al., 1974;
Kennedy et al., 1981). Generally the stub-tee utilises a simple rigid plastic analysis of an analogous beam
that represents the one-dimensional behaviour of the end plate, with yield lines parallel to the axis of
bending only. However, in the eight-bolt tubular end plate connections bending occurs about two axes,
with the yield lines not necessarily being parallel to either axis of bending. The model presented in this
paper is consequently termed the "cumulative modified stub-tee method", and is based on the analysis of
analogous beams in both orthogonal directions. The principle of superposition is then used to obtain the
resultant connection behaviour.
Figure 3: Analogous beams for cumulative stub-tee model
Simple representations of the analogous beams used in the cumulative modified stub-tee method are
shown in Figure 3. The beam referred to as "in-plane bending" models the effect of the bolts below the
flange of the section, with plastic hinges forming at points 1, 2 and 3 as shown in Figure 3a. The beam
referred to as "out-of-plane bending", models the effect of the bolts lying on either side of the section
webs. In this case, plastic hinges are assumed to form at points 4 and 5 on both sides of the hollow

section, as indicated in Figure 3b. To simplify the problem, the bolts above the neutral axis are assumed
to have a negligible effect on connection strength and are ignored.
As defined by Kennedy et. al, (1981) the behaviour of the end plate may be defined as
thick plate
behaviour, intermediate plate behaviour
and thin plate behaviour, depending on the thickness of the end
plate (tp) and the magnitude of the applied load. In the cumulative stub-tee model, these categories are
Analytical Model for Bolted Moment End Plate Connections
257
identified by the position and number of yield lines. Thick plate behaviour occurs when the connection
fails due to bolt fracture, with a yield line forming only at point 1. Intermediate plate behaviour occurs
when the bolts fracture after the formation of yield lines at points 1, 2 and 4 (i.e. plastic mechanism 5).
Thin plate behaviour corresponds to the formation of yield lines at points 1, 2, 3, 4 and 5 in the end plate
(i.e. plastic mechanism 2), without deformation of the bolts.
To determine the moment capacity for the thick, intermediate and thin modes of behaviour, the analogous
beams are analysed using statics as described by Wheeler (1998). The resulting capacities are given by
Equations 1-3 following, in which it is assumed that the moment generated by the bending of the bolts is
m b
=
~Td~b3fyb/32 (where db = bolt diameter, fyb = bolt yield stress), and
Mip
is the plastic moment for the
i th yield line. It is also assumed that the bolts below the flange reach their ultimate load, while those
beside the webs of the section only reach a proportion (h) of their ultimate load based on their distance
from the axis of rotation,
h = (d- g)/(d
+Soi).
/Mlp +2.B~
"(d +Soi
+h.d)l.(d_ts )

(l)
M Cthick = d
Mcint =
(ap + Soi) +2.
(ap+Soo) Jr d .(d-t~)
(2)
Mlp +M2p Msp +M2p +M b M3p +M2p +2.M b /
Mcthi" = d +2. Soo + ~:So:
.(d-t,)
(3)
/
Since the yield lines invariably undergo significant rotations prior to the ultimate strength being reached,
much of the material is stressed into the strain-hardening range. Consequently, the plastic moment
Mip
is
defined in terms of a "design stress" (fp) rather than the yield stress (Packer et al., 1989).
1 2 fy + 2" fu (4)
Mip = 4" tp " fp " I i f P : 3
The stub-tee analogy assumes that the yield lines form in a linear fashion, transversely across the end
plate. However, the yield line analysis for the eight bolt end plates indicates that such patterns rarely
occur in practice. To compensate for this inconsistency, "equivalent lengths" (for in-plane and out-of-
plane bending) are determined for the yield lines such that the total amount of internal work involved in
the mechanism remains unchanged. The equivalent lengths of the yield lines used for the cumulative
stub-tee analysis depend on the assumed plastic collapse mechanism. Furthermore, these yield line
lengths represent the cumulative length of the x or y components of several yield lines. Full details are
given in Wheeler (1998). The theoretical connection capacities based on the cumulative modified stub-
tee method are listed in Table 4 (presented later).
PLASTIC SECTION CAPACITY
The plastic section capacity of the tubular member may also govem the ultimate moment that the
connection can attain. For compact cross-sections, design specifications generally define the plastic

section capacity as the yield stress (fy) times the plastic section modulus (S). Although appropriate for
design, this method of calculating the section plastic capacity does not usually reflect the experimentally
measured ultimate moment as the cold working of the section produces significant strain hardening of the
material. A more accurate method to predict the experimental plastic section capacity is to use the design
stress (fp) as defined in Equation 4, fumishing
M s = S.fp
(5)
258 A.T. Wheeler et al.
PUNCHING SHEAR
Punching shear failure (tearing of the end plate) occurs when the concentrated loads transferred from the
section to the end plate exceed the shear capacity of the end plate over a localised region. To model
punching shear failure, a simple approach is used in which it is assumed that shear failure planes are
defined by the geometry of the connection. It is also assumed that the punching shear capacity of the end
plate is not affected by any concomitant bending moment. The connection is considered to have failed in
punching shear when the load in the tensile flange and adjacent regions of the section (Figure 4) exceed
the shear capacity of a predefined "nominal shear length" of the end plate. The nominal shear length is
the length around the perimeter of the section that is assumed to fail as a result of the section pulling out
from the end plate. As shown in Figure 4, the nominal shear length is divided into two regions,
corresponding to flange failure (/sf) and web failure (lsw).
Figure 4: Punching shear failure regions
In Figure 4, s denotes the fillet weld leg length, dbh is the diameter of the bolt head, and it is assumed that
the tubular section has an extemal comer radius of 2.5 times the wall thickness. Using the von Mises
yield criterion, the moment capacity of the connection with respect to punching shear failure is given by
Mp s
:~3.tp.(Isf.(d-ts)+Isw.(d-g))
(6)
The theoretical capacities of the connections tested in the experimental program with respect to the
punching shear are shown in Table 4.
GENERALISED CONNECTION MODEL
The model described in this paper identifies three modes of failure, namely connection capacity

(cumulative modified stub tee model), plastic section capacity, and punching shear. The computed
capacities for each mode of failure are presented in Table 4, with the critical one highlighted.
Failure modes determined using the cumulative modified stub-tee model may be govemed by bolt
capacity or end plate capacity. Bolt capacity (fracture of bolts) is associated with either thick or
intermediate plate behaviour, while plate capacity occurs with thin plate behaviour and is independent of
the bolt loads.
The results shown in Table 4 indicate that for the ten experimental tests carried out, four of these were
limited in strength by punching shear and a further four were govemed by plastic section capacity. Only
two tests were govemed by failure of the bolts according to the stub tee model. While the ultimate failure
mode of the specimens was generally punching shear, bolt failure or section failure, substantial yielding
in the end plates was observed in the experimental program. The failure criteria and failure loads for the
standard SHS tests (Tests 1, 3, 4) and the RHS tests (Tests 2, 5, 6) are presented in Figures 4 and 5,
respectively.
Analytical Model for Bolted Moment End Plate Connections
TABLE 4
THEORETICAL AND OBSERVED ULTIMATE CONNECTION MOMENTS
259
Figure 5: Failure criteria for SHS connections (So = 35 mm)
Figure 6" Failure criteria for RHS connections (So = 35 mm)