Advances in Steel Structures - part 30 pdf

270 K.H. Ip and K.F. Chung
design codes 1-3, however, may be inappropriate for CFS sections with high yield
strength but low ductility (< 5%). Consequently, a close examination on the
resistance and the associated failure modes of bolted connections with high strength
low ductility CFS strip is essential before the established design codes can be applied
with confidence.
With the advent of computer hardware and software, numerical simulation has drawn
the attention of researchers in many areas of engineering and science. In the field of
solid mechanics, finite element (FE) method is perhaps the one having the greatest
impact. The method is particularly useful in solving boundary value problems where
large strains, nonlinear materials and contact surfaces are involved. Results from FE
analysis provide a clear picture on the stress and the strain distributions in a structure,
which is not easily obtained from physical tests. Besides, extensive parametric studies
can be carried out to reveal the effects of geometrical and material properties on the
performance of a structure.
The present study 4 concerns with finite element simulation on bolted connections
between CFS strips and HRS plates under static shear loading. Emphasis is given to
predict the possible failure modes, namely, (i) the bearing failure, (ii) the shear-out
failure and (iii) the net-section failure aider calibration. Parametric runs will be
carried out to reveal the effects of geometrical and material properties on the
resistances of different failure modes. The results are then compared with design
values to reveal the applicability of codified design rules 5.
FINITE ELEMENT ANALYSIS
The ANSYS (ver 4.3) finite element package is used to predict the load-extension
curves of bolted connections between cold-formed steel strips and hot rolled steel
plates under static shear loading. As the connection contains a plane of symmetry, the
half model shown in Figure 1 is sufficient, where the edge distance Se and the
specimen width W are indicated. The CFS strip, the HRS plate and the bolt-washer
assembly are represented three-dimensionally by eight-node iso-parametic solid
elements SOLID45, as they allow both geometric and material nonlinearities. Contact
between the various components is accomplished by employing contact elements

CONTACT49. The contact stiffness and the friction coefficient for all interfaces are
assigned the values of 2 x 103 N/mm and 0.2, respectively. In a typical FE model,
there are 1878 nodes, 1197 solid elements and 981 contact elements.
Plasticity in the CFS strip is considered by incorporating the von Mises yield criterion,
the Prandtl-Reuss flow rule together with isotropic hardening rule. However, for
simplicity, the bolt-washer assembly is linear elastic with Young's modulus, E, at
205 kN/mm 2 and Poisson's ratio v at 0.3.
Shear load is applied to the FE model by imposing incremental displacements to the
end of the CFS strip, along the longitudinal direction of the specimen. Throughout the
course of loading, the HRS plate and the root of the bolt are fixed in space. As the
model is highly nonlinear, the full Newton-Raphson (N-R) procedure is employed to
obtain the solution atter each displacement increment.
Failure M octes oj t~olted Cold-Formed Steel Connections
271
Figure 1 Finite element model of a bolted connection
between CFS strip and HRS plate
Figure 2
True Strain (%)
Proposed stress-strain curves for cold-formed steel strips
RESULTS AND DISCUSSIONS
The FE model is first calibrated with the results from lap shear tests. Both
G300 and
G550
cold-formed steel strips of different yield strengths
py
and thicknesses t are
considered. Their material curves as deduced from standard coupon tests and they are
presented in Figure 2. A negative slope is appended to each curve to simulate the
effect of strength degradation at high tensile or compressive strains. The CFS strip is
bolted to the HRS plate by a grade 8.8 bolt of 12mm diameter. Comparison between

the predicted and the measured load-extension curves associated with bearing failure
is given in Figure 3. Close agreement between the experimental and simulation
results indicates the accuracy of the finite element model as well as the proposed
material curves.
272
K.H. Ip and K.F. Chung
Figure 3 Theoretical and experimental load-extension curves
for bolted connections with 12mm diameter bolts
By changing the dimensions of the CFS model, i.e. the edge distance
Se and the
specimen width W, three distinct failure modes are identified:
(i) Bearing failure
It prevails for strips having sufficiently large Se and W, as shown in Figure
4(a). The yield zone emerges from the bearing edge of the CFS strip owing to
highly localized compressive stresses.
O0
Shear-out failure
It occurs when the edge distance Se of the specimen is small, as shown in
Figures 4(b). Such failure is characterized by large shear stresses between the
hole and the edge of the strip. Protrusion of the edge of the strip can be
observed.
(iii) Net-section failure
It takes place for narrow specimens as shown in Figure 4(c). In contrast to
bearing failure, the yield zone is developed from the tensile edges of the hole,
accompanied by necking of the net-section.
The deformed meshes of each failure mode are also presented in Figure 5 for
comparison.
Failure Modes of Bolted Cold-Formed Steel Connections
273
Figure 4 Failure modes of

G550
CFS strip at 3ram extension
(t - 1.60 mm with 12mm diameter bolts)
274
K.H. Ip and K.F. Chung
Figure 5
Deformed meshes of
G550
CFS strip at 3mm extension
(t = 1.60 mm with 12mm diameter bolts)
Failure Modes of Bolted Cold-Formed Steel Connections
275
A strength coefficient is established to compare the resistances of a bolted connections
from finite element models to basic resistances of the connections, and the strength
coefficient is defined as follows:
Resis tan ce at 3ram
Strength coefficient = (1)
tdU s
Through parametric runs, the effects of Se and W on the normalized resistance of the
FE model are summarized in Figures 6 and 7 for the G300 and G550 strips,
respectively. These figures also present the capacities of the connections based on the
design formulae in Section 8.2 in BS5950: Part 5 [1 ]. A glance at these plots reveals
that the FE predictions exhibit a similar trend with the design values. Maximum
connection resistance is found to occur in the bearing mode. The results also
demonstrate the independence of bearing resistance to
Se and W when the bolt hole is
sufficiently far from the sides of the strip. Inspection of Figure 6 shows that the
design rules is conservative for predicting the resistance of G300 strips under net-
section and bearing failures. In the FE model, transitions from the shear-out and the
net-section failures to the bearing failure are found to occur at larger Se / d and W/d.

In other words, sufficient distances, say
Se / d > 4 and W/d > 5, should be provided
for the CFS strip in order to secure the maximum connection resistance. Refer to
Figure 7 for
G550 strips, the design formulae are unsafe when applying to high
strength steels.
Figure 6 Strength coefficient of bolted connection with
G300 CFS strip ( t = 1.50 mm and d = 12 mm )
Figure 7 Strength coefficient of bolted connection with
G550 CFS strip ( t = 1.60 mm and d = 12 mm )
276
CONCLUSIONS
K.H. Ip and K.F. Chung
A finite element model was employed to determine the resistance of bolted
connections between cold-formed steel (CFS) strips and hot rolled steel (HRS) plates
subject to static shear loading. By incorporating both solid and contact elements, the
model is able to capture nonlinearities associated with geometry, materials and
boundary conditions. The von Mises stress distributions in the CFS strips under
different types of connection failure are also predicted. Results from parametric runs
indicate that the existing design formulae are sufficient only for bolted connections
with low strength steels, such as 280N/mm 2 and 350N/mm 2. However, the existing
codified design rules may not to conservative when applying to high strength low
ductility steel.
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. BS5950: Structural use of steelwork in buildings: Part 5 Code of practice for the
design of cold-formed sections, British Standards Institution, London, 1998.
2. Cold-formed steel structure code AS/NZ 4600: 1996, Standard Australia/Standards

New Zealand, Sydney, 1996.
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. 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).
5. 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.
DESIGN MOMENT RESISTANCE OF END PLATE CONNECTIONS*
Yongjiu Shi Jun Jing
Department of Civil Engineering, Tsinghua University,
Beijing 100084, China
ABSTRACT
The end plate connection, either flush end plate or extended end plate, bolted with high strength friction
fasteners, is one of the moment resistant connections recommended for steel portal frame design, and
can be used for rafter to column connection or rafter splice. Current design rules specify that the tension
force produced by the bending moment is triangularly distributed among the bolt rows in tension zone,
if the end plate is stiff enough and its deformation is negligible. The engineering practice demonstrates
that the end plate thickness usually varies from 12 to 36mm and its flexible deformation can not be
neglected. In this paper, a finite element model is constructed to analyze connection behaviour under the
applied bending moment and the model is verified by the available test results. The bolt tension force
distribution and end plate deformation for connections with different configurations are compared.
Finally, a modified design method is proposed.
KEY WORDS
Steel structures, End plate connection, High strength fastener, Portal frame design
INTRODUCTION
In design of steel portal frame, end plate connection is the most widely recommended economic
moment-resistant joint with the advantage of fast erection and no field welding(Fig 1). The bolted end

plate connection can be used for beam splice or beam to column connection and can be detailed as either
flush or extended with or without stiffeners(CECS102:98, 1998). The moment resistance of end plate
connections largely depends on the component behaviour in the tension zone, compression zone and
shears zone, such as the bolt tension resistance, end plate yielding resistance and column web buckling
resistance, etc. The traditional design guides(JGJ82 91,1992) suggest that the tension force produced
by the bending moment is triangularly distributed among the bolt rows in tension zone under the
assumption that both the flush and extended end plate is adequately stiff and its flexible deformation and
prying force can be neglected(Fig. 2). The outermost row of bolts are assigned with the maximum
"Supported by National Natural Science Foundation of China
277
278
Y. Shi and J. Jing
tension and the forces resisted by any row of bolts can be given by
Nti =
Myi / E
yi2 ( 1 )
It is required in Chinese code of practice that Nt~ should be limited to
Na<~O.8P,
where P is the bolt
pretension.
f(3 tit
Figure 1: End plate connections for portal frame
Ntl .
v
Figure 2: Traditional design model
However, the end plate applied in the steel portal frame design may be just 20mm or less in thickness
and the assumption described above may not be applicable. It is necessary to further investigate the
design model that would be appropriate for connections in steel portal frame. In this paper, a finite
element model is established to analyze the bolt force distribution for the beam to column connections.
The contact pressure between end plate and column flange under different bending moment is also

investigated. A revised design model is proposed for portal frame end plate connections.
ANALYTICAL MODELING
Traditionally, the T-stub or yielding line theory is used for analyzing the end plate deformation (Brown
et al,
1996), and later, the 2D/3D finite element model was introduced(Sherbourne and Bahaari, 1994,
Gebbeken
et al,
1994). In this paper, a hybrid 2D/3D model was developed. The beam web and flange
were modeled with plate element, while the end plate, bolt heads and nuts were represented by 3D block
elements. A number of bar elements were adopted to simulate the bolt shank. The contact elements,
which could resist compression but not tension, were used to simulate the interface between the end
plate and the column flange. In establishing the finite element model, the bolt pretension were well
simulated by temperature action, that is, a temperature stress were applied to the bolt shank, leading to
the bolt to contract and subject to pretension. The established finite element model is shown in Fig. 3.
The connection model is analyzed by loading increment method and the material properties are assumed
remaining elastic.
Figure 3. Finite element model
Figure 4: Tested connection and result comparison
To verify the finite element model, an end plate connection tested by Jenkins
et al(1986)
were analyzed
again. The bolt tension force produced by the applied bending moment is compared in Fig. 4. It is noted
that the finite element model simulates the tension force development very well, but gives higher value.
Since calculated results are obtained in the elastic range of material properties, while partial plasticity
Design Moment Res&tance of End Plate Connections
279
may be developed under large bending moment during the tests, it is understandable that the calculated
tension is larger than the measured tension. Both the experiment and calculation reveal that the tension
force on the first row of bolts is well below that on the second row of bolts. The traditional design
model(Fig 2) is inappropriate to the extended end plate connection.

PARAMETRIC STUDY
Based on the establishedmodel, some typical joints with flush or extended end plates(Fig. 5a) were
investigated. The end plate thickness varies from t = 10mm to t = 40mm, and the high strength bolts are
M20, Grade 8.8 with pretension P = 110kN. The extended part can be stiffened or unstiffened.
Figure 5: Bolt force versus applied bending moment