Advances in Steel Structures - part 27 doc

240
A.T. Wheeler et al.
ferent end plate thicknesses (12 mm, 16 mm and 20 mm) were all within 3 percent, an average stress-
strain relationship was used for all plate thicknesses. This average stress-strain curve was based on a
yield stress of 351 MPa and an ultimate tensile strength of 492 MPa.
Bolts
In many cases, the ultimate strength of the connection was limited by tensile fracture of the bolts
rather than end plate or section failure. Therefore, to simulate the connection behaviour accurately,
each bolt was modelled as a separate entity using the nominal cross-sectional areas and measured
material properties. Reflecting the experimental behaviour of a bolt in tension, in the finite element
analyses the bolts were deemed to fracture when the strain reached 3 percent (Wheeler, 1998).
The interaction (i.e. contact and separation) between the bolt and the end plate was modelled using
the INTER4 cubic interface elements (HKS, 1995). These assemblages were positioned between the
underside of the bolt head and the end plate, and also between the bolt hole in the end plate and the
bolt shank. The interface elements between the underside of the bolt head and the end plate were im-
plemented as a "rough" interface to prevent slipping between the surfaces. The assemblages of inter-
face elements between the bolt shank and the bolt hole modelled a frictionless interface to prevent the
"penetration" of the bolt into the end plate at high rotations.
Weld
The connection between the tubular section and the end plate consisted of a combination butt-fillet
weld. The weld was modelled as an individual component using eight noded linear brick elements
(C3D8) and six noded linear triangular prism elements (C3D6) to encompass the butt and fillet por-
tions, respectively. The specified nominal material properties of the weld metal (fy = 428 MPa,
fu = 528 MPa) exceed those of the tubular section and the end plate.
Initial Stresses and End Plate Deformations
The cold-formed tubular sections used in the end plate connections contain residual stresses as a re-
sult of the manufacturing process. Welding the end plate to the tubular section induces residual
stresses and bowing deformations in the end plate. Bolt pre-tensioning introduces further initial
stresses in the connection. These heat induced distortions and the consequent initial stresses in the
end plate may have a significant effect on the stiffness of the connection as the subsequent bolt pre-
tensioning induces stresses into the end plate through the clamping action.

In the finite element analyses, the heat-induced deformations of the end plate were modelled by sim-
ply displacing the initial geometry as shown in Figure 4. The internal residual stress state resulting
from welding was not modelled. An initial transverse displacement of 80, the magnitude of which
depends on the end plate thickness and is based on measurements of test specimens, is applied to all
four edges of the end plate with a linear variation to zero initial displacement at the flanges and webs.
Although initial end plate deformations were incorporated in the finite element model, verification
studies have shown that the initial deformations have only a minor effect on the overall moment-
rotation response for the eight-bolt connections (Wheeler, 1998).
End Plate Thickness
tp (ram)
12
16
20
Initial Deformation
80 (mm)
2.0
1.0
0.75
Figure 4: Imposed initial end plate deformations
Finite Element Modelling of Bolted Moment End Plate Connections
241
Loading
To model the complete behaviour of the connection, the loading was carried out in five steps as
shown in Figure 5. In the first two steps, displacements are applied to close the nominal gap between
the solid elements and the appropriate rigid surfaces. In the third step, a concentrated load was ap-
plied to the end of the bolts to produce the pre-tension of 145 kN as specified in AS4100 for a fric-
tion grip connection employing high strength bolts (SA, 1998). In the fourth step, the bolts ends were
fixed in their pre-tensioned position and equilibrium re-established. In the fifth and final step, the
rigid end cap was rotated, thus applying a moment to the beam section and the connection.
Initial State

Step 1
Close bolt rigid surfaces
Step 2
Close end plate rigid surfaces
Step 3
Pre-tension bolts (load P)
IF
Step
4
Fix bolt ends in pre-tensioned position
Rotate end cap
Figure 5: Schematic representation of loading procedure
SIMULATION OF CONNECTIONS
The experimental and numerical results for the eight-bolt connections are given in Table 1. Graphical
comparisons for all tests are presented in Wheeler (1998). When comparing the results, it should be
noted that in the experimental study the tests were terminated when either a punching shear failure
had occurred (Wheeler et al., 1999), when the load cells indicated a drop in bolt load, or when the
section formed a plastic hinge. In the numerical analysis, the ultimate load was deemed to occur
when the bolts reached their predefined fracture strain (3 percent) or when the section failed plasti-
cally. Consequently, punching shear failure was not considered in the finite element model.
The agreement between the experimental (Mcu) and numerical (ABAQUS)
(mab)
ultimate moments is
excellent as indicated in Table 1, with the mean and standard deviation of the experimental-to-
numerical ratio
(mcu/Mab)
being 0.96 and 0.07, respectively. Furthermore, if the tests that failed as a
result of punching shear are ignored in the comparisons (Tests 2, 5, 8, 9, and 10), the mean and stan-
dard deviation are improved to 1.01 and 0.03, respectively. The comparison of experimental and nu-
merical overall moment-rotation responses was generally good for the RHS (see Figures 6 and 7), but

only fair for the SHS. The numerical predictions of the theoretical model (Mth) which considers yield
line analysis, the stub tee analogy, beam section plasticity and punching shear (Wheeler et al., 1999),
are also given in Table 1. With a mean theoretical-to-experimental ratio
(Mcu/Mth)
of 1.03 and a stan-
dard deviation of 0.05, the theoretical model is evidently very effective (Wheeler et al., 1999).
242
A.T. Wheeler et al.
TABLE 1
COMPARISON OF EXPERIMENTAL, NUMERICAL AND THEORETICAL ULTIMATE
MOMENTS
Test
1 (SHS)
2 (RHS)
3 (SHS)
4 (SHS)
5 (RHS)
6 (RHS)
7 (SHS)
8 (SHS)
9 (RHS)
10 (RHS)
Test
Mcu
(kNm)
116.0 (S)
124.5 (P)
93.9 (B)
116.0 (S)
92.7 (P)

136.7 (S)
113.2 (B)
97.6 (P)
133.0 (P)
119.3 (P)
ABAQUS
Mab
(kNm)
110.8
131.5
95.7
111.9
114.7
137.4
115.1
105.6
136.0
133.3
(P) = Punching shear failure
(S) = Section capacity failure
(B) = Failure by yield line formation
and bolt fracture
Theoretical
Mth
(~qrn)
116.3 (S)
116.8 (P)
92.8 (B)
116.3 (S)
87.6 (P)

128.4 (S)
116.3 (S)
104.9 (B)
123.2 (P)
110.0 (P)
Mean
S.D.
Mcu/Mab
1.05
0.95
0.98
1.04
0.81
0.99
0.98
0.92
0.98
0.89
0.96
0.07
MeulMth
1.00
1.07
1.01
1.00
1.06
1.06
0.97
0.93
1.08

1.08
1.03
0.05
Figure 6: Effect of variation in end plate thickness for RHS connections
The numerical analyses demonstrate that the flexibility and strength of the connection depends on the
flexibility of the end plate. This flexibility is a function of the thickness of the end plate and the posi-
tion of the bolts relative to the section perimeter.
The effect of varying the end plate thickness is shown in Figure 6, in which the connection moment-
rotation behaviour is presented for Tests 5, 2 and 6 which comprise end plate thicknesses of 12 mm,
16 mm and 20 mm, respectively. These three tests differ only in end plate thickness. A significant
increase in the overall stiffness and strength is observed with an increase in the end plate thickness.
In both the physical test and the ABAQUS model, the 20 mm end plate connection (Test 6) failed
through the attainment of full plasticity in the beam section rather than the failure occurring in the
connection itself. Conversely, the 16 mm and 12 mm end plate connections (Tests 2 and 5) failed
through punching shear in the physical experiments, but are predicted to fail as a result of the bolts
attaining their assumed fracture strain of 3 percent in the ABAQUS model. The ramifications of the
inability of the ABAQUS model to consider the punching shear failure mode are particularly appar-
ent for Test 5 (12 mm end plate) as indicated in Figure 6.
Finite Element Modelling of Bolted Moment End Plate Connections
243
Figure 7: Effect of bolt position on moment-rotation behaviour for RHS connections
The stiffening effect of the position of the bolts relative to the section perimeter is illustrated in Fig-
ure 7. The three simulations presented in this figure have a constant end plate thickness of 16 mm,
with the distance to the perimeter of the section (So) being varied. Increasing the value of So reduces
the stiffness of the end plate, thus resulting in a more flexible moment-rotation response and lower
ultimate strength (compare Tests 10 and 2 for which So = 45 mm and 35 mm, respectively).
As can be seen in Figures 6 and 7, the finite element analysis is reasonably effective in simulating the
experimental moment-rotation response for the RHS connections. Generally the computed response
is marginally stiffer than the experimentally measured one. However, the SHS connections (Tests 1,
3, 4, 7 and 8) are generally significantly stiffer in the finite element simulations than in the tests

(Wheeler, 1998). It is believed that the additional stiffness in the SHS connections is associated with
inadequate modelling of the bolts and their interaction with the end plate. The bolts in the SHS con-
nection are positioned such that they restrain the comers of the section (i.e. the line of restraint be-
tween adjacent bolts passes through the comer of the section). Conversely, the positioning of the
bolts in the RHS connections offers less restraint to the comers of the section, thus enabling a greater
degree of flexibility within the end plate.
As can be seen in Figure 8, the yield mechanisms in the end plates vary depending on the shape of
the beam section (SHS or RHS), which defines the positions of the bolts. For both the SHS and RHS,
the pitch of the four bolts above and below the axis of bending is approximately constant. The dis-
tance between the bolts adjacent to the section webs varies according to the depth of the section. This
distance was generally either 90 mm for the SHS or 170 mm for the RHS. The close proximity of the
bolts in the SHS models causes high concentrations of stresses to form around the perimeter of the
section and between the tensile bolts (Figure 8a). On the other hand, the additional spacing between
the bolts in the RHS allows the formation of a horizontal yielded zone in the end plate at mid-depth
(Figure 8b). These areas of high stress concentration observed in the finite element results are con-
sistent with the yield line patterns observed experimentally and determined theoretically (Wheeler,
1998).
CONCLUSIONS
A numerical study of the behaviour of tubular bolted moment end plate connections has been de-
scribed in this paper. The analyses were conducted using the commercially available finite element
package ABAQUS. Brick elements were chosen to form the basis of the models used for this study as
244
A.T. Wheeler et al.
Figure 8: Von Mises stresses (MPa) illustrating end plate yield line patterns
this type of element is easily adapted to model the interfaces between the connecting surface and the
end plates and bolts.
Overall, the models simulated the behaviour of the eight-bolt connections well, with the mean and
standard deviation of the ratio of the experimental and numerical ultimate moments being 0.96 and
0.07. Comparisons of the experimental and numerical moment-rotation responses of the connections
were excellent for the eight-bolt connections comprising the RHS. The eight-bolt connections utilis-

ing the SHS were generally predicted to be stiffer than the corresponding test results. Although not
fully investigated in this paper due to time constraints, it is thought that this additional stiffness may
be due to the inadequate modelling of the bolts.
Although the predicted ultimate loads generally corresponded well with the experimental results, the
numerical analyses did not specifically model the effects of punching shear (although the effects of
shear yielding were of course modelled in the nonlinear material behaviour). The deformation and
yielding patterns developed in the models correlated well with the experimental results and the yield
line analyses developed in the corresponding theoretical models (Wheeler et al., 1999).
REFERENCES
AISC (1997).
Hollow Structural Sections Connections Manual,
American Institute of Steel Construction, Inc.
Bursi, O. S. and Jaspart, J. P. (1997a). Benchmarks for Finite Element Modelling of Bolted Steel Connections.
Journal of
Constructional Steel Research,
Elsevier, 43:1, 17-42.
Bursi, O. S. and Jaspart, J. P. (1997b). Calibration of a Finite Element Model for Isolated Bolted End Plate Steel Connec-
tions.
Journal of Constructional Steel Research,
Elsevier, 44:3, 225-262.
HKS (1995).
ABAQUS/Standard Users Manual,
Version 5.5, Hibbitt, Karlsson and Sorensen, Inc.
PDA Engineering (1994).
PATRAN 3,
PDA Engineering, Costa Mesa, California.
SA (1998).
AS 4100-1998: Steel Structures,
Standards Australia, Sydney.
Syam, A. A. and Chapman, B. G., (1996).

Design of Structural Steel Hollow Section Connections. Volume 1: Design
Models,
1 st Edition, Australian Institute of Steel Construction, Sydney.
Wheeler, A. T. (1998). The Behaviour of Bolted Moment End Plate Connections in Rectangular Hollow Sections Sub-
jected to Flexure.
PhD Thesis,
Department of Civil Engineering, The University of Sydney.
Wheeler, A. T., Clarke, M.J. and Hancock, G.J. (1995). Tests of Bolted Flange Plate Connections Joining Square and
Rectangular Hollow Sections.
Proceedings, Fourth Pacific Structural Steel Conference,
Singapore, 97-104.
Wheeler A. T., Clarke M. J. and Hancock G. J. (1999). Analytical Model for Eight-Bolt Rectangular Hollow Section
Bolted Moment End Plate Connections.
Proceedings, Second International Conference on Advances in Steel Structures,
Hong Kong, December.
FINITE ELEMENT MODELLING OF DOUBLE BOLTED
CONNECTIONS BETWEEN COLD-FORMED STEEL STRIPS UNDER
STATIC SHEAR LOADING
K.F.Chung 1 and K.H.Ip 2
t Department of Civil and Structural Engineering; 2 Department of Mechanical Engineering,
the Hong Kong Polytechnic University, Hung Horn, Hong Kong.
ABSTRACT
In a complementary paper 1, it was reported that a finite element model with three-
dimensional solid elements was successfully established to investigate the bearing failure of
bolted connections between cold-formed steel strips and hot rolled steel plates under static
shear loading. Non-linear material geometrical and contact analysis was carried out to
predict the load-extension curves of bolted connections with cold-formed steel strips of high
yield strength and low ductility. The predicted load-extension curves were found to follow
closely the measured load-extension curves, and both the maximum load carrying capacities
and the initial extensional stiffness were satisfactorily predicted

In this paper, the finite element model is further extended to examine the structural behaviour
of bolted connections with two bolts, or double bolted connections between cold-formed steel
strips and hot rolled steel plates under static shear loading. The effects of strength
degradation, hole clearance and bolt spacing on the load carrying capacity of double bolted
connections are discussed. Comparison on the predicted load carrying capacity of the finite
element model with the bearing resistances given by the design rules from both BS5950: Part
5 2 and Eurocode 3: Part 1.3 3 is also presented.
KEYWORDS
Cold-formed steel, bearing failure, double bolted connections, high strength steel with low
ductility.
INTRODUCTION
Galvanized cold-formed steel strips are commonly used in building construction, such as
sections for secondary steel frames and purlins, and sheetings for roof cladding and floor
decking. Cold-formed steel sections and sheetings are effective construction materials due to
their high strength to weight ratio, high buildability during construction and also long-term
durability against environmental attack. In building construction, cold-formed steel sections
are usually bolted to hot rolled steel plates or members to form simple and moment
connections.
With the development of material technology, high strength cold-formed steel products are
available for building applications, but concern has been raised on the reduced ductility of the
high strength steel (< 5%). Existing codified design rules 2-5 may not be necessarily
245
246
K.F. Chung and K.H. Ip
applicable for high strength low ductility steel, as the design rules are developed with low
strength high ductility steel 6,7. Consequently, a close examination s on the resistance and the
associated failure modes of bolted connections with high strength low ductility steel strip was
carded out.
Three distinct failure modes were identified 1 from the finite element modelling, namely, (i)
the bearing failure, (ii) the shear-out failure, and (iii) the net-section failure. Parametric

runs 9 were also carded out to reveal the effects of geometrical and material properties on the
resistances of different failure modes. It is found that while the existing design rules are
sufficient for bolted connections with low strength steels, such as steel with yield strength at
280 N/mm 2 and 350 N/ram 2, they may not be conservative when applying to high strength
low ductility steel.
In this paper, the finite element model is further extended to examine the structural behaviour
of bolted connections with two bolts, i.e. double bolted connections between cold-formed
steel strips and hot rolled steel plates under static shear loading as shown in Figure 1. The
effects of strength degradation, hole clearance and bolt spacing on the load carrying capacity
of typical double bolted connections are presented. The predicted load carrying capacity of
the finite element model is also compared with the bearing resistances given by the design
rules from both BS5950: Part 5 and Eurocode 3: Part 1.3; comparison with test data 10 is also
presented.
FINITE ELEMENT MODELLING
The finite element package ANSYS (Verison 5.3) is used to predict the bearing behaviour in
double bolted connections between cold-formed steel strips and hot rolled steel plates under
static shear loading, and the following areas of interest are examined in detail:
a) Stress-strain curves
Two different stress-strain curves are proposed for the model as illustrated in Figure 2:
9 bi-linear elastro-plastic curve for low strength high ductility steel, designated as FEA-
Pr,
9 multi-linear elastro-plastic curve with strength degradation at large strain for high
strength low ductility steel, designated as FEA-pr.
b) Deformation Sequences
Due to the presence of clearance in bolt holes for easy installation, it is possible that the
two bolts may not always come into contact with the cold-formed steel strips at the same
time. The bolts may have a hole clearance of 1 mm to 2 mm typically. In order to
examine the effect of hole clearance to the structural performance of the double bolted
connection, three deformation sequences are considered as follows:
9 Deformation sequence IA where Bolt 1 is always in direct contact with the cold-

formed steel strip while Bolt 2 only comes into contact with the cold-formed steel strip
aRer I mm (or 2 mm) extension.
9 Deformation sequence IB which is similar to that of Deformation sequence 1,4 but with
reverse order of bolts in contact, i.e. where Bolt 2 is always in direct contact with the
cold-formed steel strip while Bolt 1 only comes into contact with the cold-formed steel
strip after 1 mm (or 2 mm ) extension.
Finite Element Modelling of Double Bolted Connections 247
9 Deformation sequence 11where both Bolts 1 and 2 always come into contact with the
cold-formed steel strip together.
c) Bolt spacing
In BS5950: Part 5, the minimum bolt spacing Sp is recommended to be not less than 3 d,
and the total load carrying capacity of a connection with multiple bolts may be obtained
directly as the sum of the bearing resistances of all the bolts. No adverse interaction
between bolts should be allowed for and this design method seems satisfactory for low
strength high ductility steel. However, for high strength low ductility steel, it is necessary
to investigate the minimum bolt spacing to avoid any adverse interaction of yield zones
of the two bolts.
As the connection contains a plane of symmetry, the half model shown in Figure 3 is
incorporated. The cold-formed steel strip, the hot rolled steel plate and the two bolt-washer
assemblies are represented three-dimensionally by eight-node iso-parametic solid elements
SOLID45, as they allow both geometric and material non-linearities. Contact between the
various components is accomplished by employing contact elements CONTACT49. Shear
load is applied to the finite element model by imposing incremental displacement to the end
of the cold-formed steel strip, along the longitudinal direction of the model. Throughout the
entire deformation range, the hot rolled steel plate and the root of the bolt are fixed in space.
At present, only the bearing failure of double bolted connections is considered.
In typical fmite element models, there are over 3724 nodes, 2422 solid elements and 2022
contact elements. As the model is highly non-linear, the full Newton-Raphson procedure is
employed to obtain solution after each displacement increment. For detail of the finite
element model, see Reference 8.

RESULTS AND DISCUSSIONS
The load-extension curves for the double bolted connection with different stress-strain curves,
deformation sequences and bolt spacings are presented in Figure 4. The von Mises stress
distribution of the double bolted connections at various extensions are presented in Figure 5
while the deformed mesh of the double bolted connection is presented in Figure 6.
a) Stress-strain curves
With Sp = 3 d and Deformation sequence 11, the load carrying capacity of the connection is
estimated to be 31.10 kN with material curve FEA-py, and 28.08 kN with material curve
FEA-pr, as illustrated in Figure 4a. It is thus shown that the strength of the connection
may be reduced by 10% when strength degradation is considered in high strength low
ductility steel.
b) Deformation sequences
In Figure 4b, it is shown that the load-extension curves derived from both Deformation
sequences IA and 1B follow each other fairly closely along the entire deformation range.
By plotting the load-extension curve derived from Deformation sequence 11 on the same
graph for direct comparison, it is shown that both the load carrying capacity and the
extensional stiffness of the connection will be reduced approximately by half if only one
bolt is in contact with the cold-formed steel strip. However, at 3 mm extension, the load
248
K.F. Chung and K.H. Ip
carrying capacity with
Deformation sequences IA and IB
are found to be
26.69 kN with
1 mm gap and
24.10 kN with a 2 mm
gap, corresponding to a strength reduction of
0.95
and 0.85
respectively.

c) Bolt spacing
In Figure 4c, it is shown that with
Deformation sequence 11, the
load carrying capacity of
the double bolted connection is found to be increased from
28.08 kN
at Sp = 3 d or
36 mm
to
31.82 kN
at
Sp = 4 d
or
48 mm,
i.e. an increase of
13% in
strength. A close
examination on the von Mises stress distribution of the cold-formed steel strip in Figure 5
reveals that under low applied loads, the yield zones in the cold-formed steel for both
bolts are fairly localized around the bolt holes. However, under large applied load at 3
mm extension, it is evident that the yield zones of both bolts overlap, leading to significant
reduction to the total load carrying capacity of the connection. Consequently, in bolted
connections with high strength low ductility steel, it is recommended that the minimum
bolt spacing should be 4 d.
COMPARISON WITH DESIGN RULES
In order to provide simple design rules in assessing the bearing resistance, Pb, of double
bolted connections with high strength low ductility steel, a number of existing design rules are
examined as follows:
Pb = (1.64 + 0.45 t) t dpy
= 2.5tdpy

= (4-0.1 d/t) tdpy
from clause
8.2.5.2
of
BS5950:Part 5
(A)
from clause
8.4(4)
with Table
8.4, EC3: Part 1.3 03)
from page 133 & Table 4.12, Volume 1 of Reference 10 (C)
Substituting the numerical values of t =
0.99 mm, d = 12
mm and replacing
py with f~ =
592
N/mm" (where
py
and f~ are the yield strength and the tensile strength respectively) into
the above design rules, the beating resistances are summarized in Table 1 together with the
f'mite element results. Based on the results from the present research project, it is shown that
a) Existing design rules tend to over-estimate the bearing resistances of bolted connections
with high strength low ductility steel up to
30 %
for both single and double bored
connections when compared with test results.
b) The results from the finite element models are found to be conservative when compared
with test results.
c) R is necessary to allow for adverse interaction of yield zones around boR holes indouble
bored connections. At a boR spacing of 3 d, the reduction factor is estimated to be 27.13

/
(2 x 14.43)
or
0.94
based on test results, or
26.72 / (2 x 14.54)
or
0.92
based on finite
element results. Thus, a value of
0.90
is recommended for design purpose. Alternatively,
the minimum boR spacing, Sp, for no adverse interaction should be increased and Sp = 4 d
is recommended as appropriate.
CONCLUSIONS
A finite element model is presented to examine the structural performance of the bearing
failure in double bolted connections between cold-formed steel strips and hot rolled steel
plates under static shear loading. By incorporating bolt solid and contact elements, the model
Finite Element Modelling of Double Bolted Connections
249
is demonstrated to able to capture non-linearities associated with geometry, material and
contact (boundary) conditions. It is shown that existing design rules may not be applicable
for high strength low ductility steel and new design rules are required to ensure structural
adequacy. The bearing resistances of double bolted connections may be reduced by 10 % to
30 % due to strength degradation, hole clearance, and also adverse interaction of yield zones.
ACKNOWLEDGEMENT
The research project leading to the publication of this paper is supported by the Hong Kong
Polytechnic University Research Committee (Project A/C code G-$565).
REFERENCES
1. Ip K.H. and Chung, K.F.: Failure modes of bolted cold-formed steel connections under static

shear loading, Proceeding of the Second International Conference on Advances in Steel
Structures, Hong Kong, December 1999.
2. BS5950: Structural use of steelwork in buildings: Part 5 Code of practice for the design of cold-
formed sections, British Standards Institution, London, 1998.
3. Eurocode 3: Design of steel structures: Part 1.3: General rules - Supplementary rules for cold-
formed thin gauge members and sheeting, ENV 1993-1-3, European Committee for
Standardization.
4. Cold-formed steel structure code AS/NZ 4600: 1996, Standard Australia/Standards New Zealand,
Sydney, 1996.
5. Toma, A.W., Sedlacek, G., and Weynand, K.: Connections in cold-formed steel, Thin Walled
Structures, Vol. 16, pp219-237, 1993.
6. Holcomb, B.D., LaBoube, R.A., and Yu, W.W.: Tensile and bearing capacities of bolted
connections, Final Summary Report, Civil Engineering Study 95-1, Cold Formed Steel Series,
Centre for Cold Formed Steel Structures, Department of Civil Engineering, University of
Missouri-Rolla, MO, U.S.A.
7. Rogers, C. A. and Hancock, G. J.: New bolted connection design formulae for G550 and G300
sheet steels less than 1.0 mm thick, Research Report No. R769, the Centre for Advanced Structural
Engineering, University of Sydney, Sydney, Australia, 1998.
8. Chung, K.F. and Ip, K.H.: Finite element modelling of bolted connections between cold-formed
steel strips and hot rolled steel plates under shear, Engineering Structures (to be published).
9. Chung K.F. and Ip, K.H.: Finite element modelling of cold-formed steel bolted connections,
Proceedings of the Second European Conference on Steel Structures, Praha, May 1999, pp503 to
506.
10. Rogers, C. A.: Structural behaviour of thin sheet steels, Ph.D. dissertation, Department of Civil
Engineering, the University of Sydney, Australia, 1998.
Table 1 Summary of bearing resistances - Design rules vs Finite element analysis
(A)
Single bolts
e~(w0
14.77

03) 17.58
(C) 19.61
Finite element model (15.90 1.36) = 14.54
+Test value, Pr I 14. 43
Pr/Pb
0.977
0.821
0.736
0.992
I -
Double bolts
Pb (ld~ Pr / Pb
29.54 0.918
35.16 0.772
39.21 0.692
(28.08-1.36) = 26.72 1.015
I 27.13 ] -
Note: * The model incorporates FEA-pr stress-strain curve, Deformation sequence 11 and Sp at 3d. A
frictional force of 1.36 kN at zero extension is deducted from the load carrying capacity of
the predicted resistance for direct comparison.
+ Averaged values from three test data in Table B55, Page 331 of Volume 2, Reference 10.