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Journal of Constructional Steel Research 62 (2006) 240–249
www.elsevier.com/locate/jcsr
Stiffness of joints in bolted connected cold-formed steel trusses
Raul Zaharia, Dan Dubina∗
Department of Steel Structures and Structural Mechanics, Faculty of Civil Engineering and Architecture, “Politehnica” University of Timisoara,
I. Curea no.1, 1900 Timisoara, Romania
Received 10 January 2005; accepted 1 July 2005
Abstract
Web members in cold-formed steel trusses are usually assumed to have pinned connections at the ends, but the latest AISI Cold-FormedSteel Truss Design Standard allows for the joint stiffness to be considered in design. The paper summarizes experimental research performed
for several years at the University of Timisoara, Romania, aimed at evaluating the real behaviour of bolted joints in cold-formed steel trusses.
By means of tests on single lap joints and on truss sub-assemblies, a theoretical model for joint stiffness was proposed. The formula for the
joint stiffness, from which the buckling length of web members was further determined, was also validated through a test on a full-scale truss.
© 2005 Elsevier Ltd. All rights reserved.
Keywords: Cold-formed steel trusses; Bolted connections; Joint stiffness; Buckling length; Experimental tests; Numerical analysis
1. Introduction
Cold-formed steel framing demonstrates extensive
development, even if is a relatively new system, due to somegreat advantages, such as high strength-to-weight ratio,
reduced labor costs and fast erection due to the light weight
of cold-formed members. The cold-formed steel trusses rep-
resent an economical option to the classical wood trusses
used mainly in residential buildings, and to the hot-rolled
trusses used for industrial applications. Several proprietary
products have been developed, considering C, Z, hat, or
more particular sections for chords and webs. The con-
nections may be realized by welding, by using adhesives,
with mechanical connectors as bolts or screws, or by some
innovative mechanical connecting techniques such as press
joining or rosette joining. The mechanical connections areamong the most suitable, taking into account the production
costs and rapidity of execution.
Initiated by the more widespread use of the cold-formed
steel in the residential construction market, systematic
research to investigate the behaviour of cold-formed steel
trusses was carried out at the University of Missouri-Rolla.
∗ Corresponding author. Tel.: +40 56 192970; fax: +40 56 192970. E-mail address: dubina@constructii.west.ro (D. Dubina).
0143-974X/$ - see front matter © 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jcsr.2005.07.002
On the basis of full-scale tests on fink C-section truss
assemblies, Harper [10] studied the buckling lengths for
the top chord members, realized by a single C-section.
Riemann [22] developed a computer analysis model andconducted full-scale truss tests in order to determine the
capacity of compression web members, and suggested an
interaction equation for the design of compression webs
as beam–columns. Ibrahim et al. [11] made another series
of tests on full-scale truss assemblies, considering the
same system, i.e. single C-sections for chords and webs,
connected by self-drilling screws. The authors proposed an
interaction equation for checking unreinforced top chords
subjected to axial compression, bending and web crippling.
LaBoube and Yu [13] synthesized the above-presented
research conducted at the University of Missouri-Rolla,
which strongly influenced the design recommendationscontained in the Standard for Cold-Formed Steel Truss
Design issued recently by AISI [1]. This standard is intended
to be a response to the problems that these particular
systems raise for the designer, and applies to the design,
quality assurance, installation and testing of cold-formed
steel trusses used for load carrying purposes in buildings.
As shown in the Standard Commentary [2], even if the
structural analysis requirements are based on available
information concerning the behaviour of cold-formed steel
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single C-section truss assemblies [13], these requirements
do not preclude the use of more rigorous analysis or design
assumptions, as determined by rational analysis and/or
testing.
As regards innovative mechanical connection techniques,
two interesting research areas are worth mentioning here.
Pedreschi et al. [17] demonstrated the efficiency of press joining, by making tests on single lap joints or groups of
press joins and on full-scale pitched trusses made from cold-
formed Z-sections. Mäkeläinen and Kesti [15] studied the
behaviour of the rosette joining system and its possibilities
in roof-truss structures, by making tests on simple joints
in shear or in cross-tension, and also by making tests on
sub-assemblies. The authors concluded that the rosette joint
has very good capacity to resist tensile forces and that the
shear capacity seems to be sufficient for applications in
lightweight steel trusses.
The research on cold-formed steel trusses is generally
focused on systems for residential roofs, having relatively
reduced spans. For larger spans, efficient solutions can be
achieved with higher resistance members, made for example
with optimized cross-sections, like “pentagon” sections,
studied by Blumel and Fontana [3]. The authors showed that
the use of this particular cross-section with a large radius
of gyration for both axes offers statical and constructional
advantages for the chords. However, the low-cost design of
the truss joints using a gusset plate welded onto the ridge of
the cross-section can lead to important section deformations.
The authors developed a calculation model for the local load-
bearing behaviour of this particular type of cold-formedtruss
joint, and validated this model by means of numerical and
experimental analysis on truss segments.The trusses built of cold-formed steel sections with bolted
connections, made from built-up C-sections for chords
and single C-sections for webs, represent another possible
constructive system for residential buildings, also reliable
for larger spans. In this system, the webs are connected
to the chords by means of bolts placed on both flanges
of the C-section of the web member. Fig. 1 shows two
applications using such trusses. Fig. 1(a) shows the structure
of a supplementary storey built for the Alcatel Company
building in Timisoara, Romania, while Fig. 1(b) shows the
trusses used to build the roof of a church in Bucharest,
Romania.As regards the design of this type of cold-formed truss
system, two problems arise: the stability behaviour of the
compressed chord, taking into account that for these kinds
of built-up members no design recommendations exists in
the norms, and the real behaviour of the joints.
Studies concerning the stability behaviour of the built-up
C-profiles connected by bolted C-stitches were performed by
Niazi [16]: based on the results obtained by Johnston [12],
for hot-rolled columns in which the battens are attached
to the chords by hinged connections, the compressed built-
up C-section is supposed to work on an elastic foundation,
provided by the roof purlins. The authors of the present
Fig. 1. Cold formed steel trusses.
paper calibrated a finite element model suitable for
predicting the ultimate load for such built-up elements, used
for the compressed chords of cold-formed steel trusses,
but also as columns in cold-formed steel framing [7]. The
numerical model showed good results compared with the
above procedure and experimental results.
As regards the analysis of the web members, it must be
emphasized that the use of two or more bolts for each flange
of the C-section, in relation with the element slenderness,
is supposed to modify the classical assumption of pinned
connections, used in case of truss structures. Moreover, the
eccentricity of joints could not be avoided, and this factshould also be considered into a global analysis, because
it may require additional efforts. For these reasons, the
analysis of trusses built of cold-formed steel sections with
bolted connections should consider the real behaviour of the
joints. This may lead to reduced buckling lengths of the web
members, but at the same time, to supplementary bending
moments in these elements.
In chapter D3 “Analysis” of the latest AISI Cold-Formed
Steel Truss Design Standard [1] it is shown that: “in lieu of
a rigorous analysis to define joint flexibility, the following
analysis model assumptions should be assumed: . . . (b)
web members are assumed to have pinned connections at
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each end. Use of a specific joint stiffness other than the
complete rotational freedom of a pin for a connection shall
be permitted if the connection is designed for the forces
resulting from a structural analysis with this specific joint
stiffness”.
This means that the Standard allows for joint stiffness
to be considered in the design of a truss, even if nospecific equations for calculating this parameter are given.
This should be in fact difficult, considering the number of
different cold-formed steel truss systems. In the case of cold-
formed trusses with bolted connections, a rigid behaviour
of the joints is also not realistic, taking into account the
deformability of the joint due to the bearing deformation
produced by the bolt in the thin plate, associated with the
hole elongation, bolt tilting and slippage due to the hole
clearance.
Generally, the research in the field of bolted connections
in cold-formed steel framing is focused on determining
their bearing resistance. For the first time, Zadanfarrokh andBryan [25] analysed both experimentally and theoretically
the flexibility of bolted connections in cold-formed steel
sections, and gave a formula for the flexibility of a single
lap bolted joint, but this approach was not included in any
design recommendation. More recently, [24] investigated
experimentally some particular column base connections
and beam–column sub-frames, made from cold-formed steel
sections, in different bolted connection configurations, in
order to assess their strength and stiffness. The study
identified different failure modes and concluded that the
bolted moment connections were effective in transmitting
moment between the connected sections, enabling effectivemoment framing in cold-formed steel structures. Another
recent study concerning the stiffness of bolted connections
in a steel portal framing system was made by Lim and
Nethercot [14]. The authors described a finite element model
that can be used to determine the stiffness of the individual
bolt joint. Using this stiffness, a beam idealization of a cold-
formed steel bolted moment connection was determined, in
order to predict the initial stiffness of the apex joints. The
numerical and theoretical study was validated through tests
on full-scale joints.
The research presented in this paper summarizes the
work performed for several years at the University of Timisoara, Romania, aimed at evaluating the real behaviour
of joints in cold-formed steel trusses connected by bolts,
and at proposing a theoretical model for the joint stiffness.
The experimental programme was developed in three steps.
First, the rotational rigidity of some truss connections was
evaluated, by means of tests on typical T-joints. In the
second step, a formula for the stiffness of a single lap bolted
joint was determined, together with a theoretical model for
the rotational stiffness of cold-formed steel truss bolted
joints. Based on this model, an equation for determining
the reduced buckling length of the web members was also
proposed. The third step of the experimental programme
included a full-scale test of a cold-formed steel truss, in order
to validate the theoretical formulations at structural level.
2. Experimental programme step 1: Tests on T-joint
specimens
This first step of the experimental programme has alreadybeen described in detail [5,6], and the results were included
in the Database for Research on Cold-formed Steel Structure
from University of Missouri-Rolla, USA [4]. From the
experimental moment–rotation characteristic of the ten T-
joint specimens tested, it was concluded that all tested joints
were of semi-rigid type with partial resistance, according to
Eurocode 3 [21] criteria of joint classification. An important
initial rotational slippage was observed for all specimens
tested, but it was not considered in the evaluation of the joint
rigidity, because the triangulated shape of the truss, which
is geometrically and kinetically stable, and the presence of
the axial forces in connected members prevent, or limit, at
least, this phenomenon at structural level. The test of the
cold-formed steel truss, in the third step of the experimental
programme, was aimed also at validating this assumption.
From this first part of the experimental programme it was
also concluded that the rotational deformability is mainly
due to the bearing work of the bolts in the thin plates, i.e. the
elastic and plastic deformation of the bolt holes and bolt
tilting. Consequently, the rotational rigidity of the joints may
be determined by analysing the single lap bolted joint.
3. Experimental programme step 2: Tests on single lap
joints
Experimental studies carried out in order to calibrate
a formula for the flexibility of single lap bolted joint for
thin-walled cold-formed elements were already performed
by Zadanfarrokh and Bryan [25]. The formula proposed by
these authors gives the flexibility of a single lap joint, as
a function of the thickness of the plates and the presence
of the threaded portion of the bolt in the connection. The
formula does not include the effect of bolt diameter, being
determined for lap joints using M16 bolts, but makes a
distinction between perfect fit and 2 mm clearance of the
bolt hole.
For the case of T-joints tested at Timisoara, for all tenspecimens, M12 bolts with 1 mm clearance of the bolt hole,
as specified in the Romanian code, were considered. Conse-
quently, the second step of the experimental programme was
aimed at calibrating a formula for the stiffness of single lap
joints, considering the plate thickness as in the Zadanfarrokh
and Bryan study, but also the bolt diameter, for the practical
case of a threaded portion of the bolt in the connection and
1 mm hole clearance.
The experimental programme considered three different
thicknesses for the plates, between 1.85 and 3.75 mm, and
five bolt diameters, between 8 and 16 mm. The mechanical
characteristics of the steel plates are given in Table 1.
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Table 1
Mechanical characteristics (N, mm)
t f y f u
1.85 279.8 402.1
3.15 276.8 392
3.75 258.5 375.5
Fig. 2. Test set-up.
The test set-up is shown in Fig. 2. The specimens were
tested in a ZWICK universal testing machine, using an
angular displacement transducer to record the extension
readings. The loading rate of 1 kN/min and the platedimensions were in accordance with the ones used in
the Zadanfarrokh and Bryan experimental programme.
This value of loading rate is also given in the European
Recommendations [8]. Table 2 gives the experimental values
of the specimens’ stiffnesses. For each thickness of plate,
three different bolt diameters were used, and for each
combination of plate thickness and bolt diameter, three tests
were performed (a–c). Thus, a total of 27 experimental
results are available. Typical load–extension characteristics
for determining the initial stiffness of the lap joint,
considering an identical set of parameters, are presented
in Fig. 3.The formula for the stiffness of a single lap bolted joint
was calibrated using Annex D of Eurocode 0: Basis of
Structural Design [18]. This appendix describes a standard
procedure for the determination of the characteristic values,
design values and partial factor values for strength from
tests that is in compliance with the basic safety assumptions
outlined in Eurocode 1: Actions on Structures [19].
As shown by Tomà [23], in a pioneering study
concerning the rigidity of screw connections in cold-formed
elements, underestimating the rigidity of the connection
in the elastic range will relieve the connection, but will
put a supplementary bending moment into the element.
Fig. 3. Typical load–extension characteristics.
Overestimating the rigidity, on another hand, leads to a
supplementary moment into the joint, but this can be
resolved by an appropriate design of the connection.
It is safe, for the stability and displacement analysis,
to underestimate the rigidity. Therefore, the Annex D
procedure for calibration of the formula for the stiffness of a
single lap bolted joint, will follow the same steps as for the
determination of the characteristic values, design values and
partial factor values for a strength-type formula. The final
characteristic value, obtained after the application of the
standard procedure of Annex D, for the stiffness of a single
lap bolted joint, is given by the following formula [27]:
K = 6.8
√ D
5t 1
+ 5t 2
−1 (kN/mm) (1)
with a partial safety factor γ R = 1.25. In the above equation,
D is the nominal diameter of the bolt while t 1, t 2 represent
the thicknesses of joined plates. The range of validity of this
formula is for bolts between 8 and 16 mm nominal diameter
and thickness of plates between 2 and 4 mm, using 1 mm
hole clearance and considering the threaded portion of the
bolt in the connection. It can be noted that the partial safety
factor for this formula is identical to the partial safety factor
used in Eurocode 3 Part 1.3 [20] for the resistance of bolted
connections.
On the basis of Eq. (1), the stiffness of truss joints may
be determined. For the displacement analysis, and for the
computation of the buckling lengths of the web members,the design value must be applied, while for the connection
design the characteristic one is suitable.
4. Computation models for rotational stiffness of truss
joints
The computation scheme for the rotational stiffness of a
truss joint with two bolts on each flange of the C-section of
the web member (four bolts in total) is presented in Fig. 4.
The rotational stiffness of the joint, K node,t , can be
expressed in terms of total bending moment, M tot, and
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Fig. 4. Computation model for a four bolt joint.
Table 2Experimental values for single lap joint stiffness (kN/mm)
Bolt Plate thickness t (mm)
1.85 3.15 3.75
a b c a b c a b c
M8 4.237 4.695 4.348 – – – – – –
M10 5.102 6.211 5.025 10.000 10.417 10.204 – – –
M12 7.353 5.263 5.236 10.869 10.753 10.526 9.259 13.333 13.699
M14 – – – 11.111 11.628 11.765 14.286 14.493 14.925
M16 – – – – – – 16.667 16.393 15.385
Table 3
Comparison between experimental and theoretical values of joint stiffness
Node t 1 (mm) t 2 (mm) K node,exp (kN mm/rad) K node,t (kN mm/rad) K node,t /K node,exp K d node,t
/K node,exp
1 3 2.05 10 130 9 830 0.971 0.777
3 10 270 0.958 0.766
2 3 3 12 480 13 083 1.047 0.838
4 11 110 1.177 0.942
5 4.05 2.05 10 560 11 418 1.080 0.864
8 10 968 1.041 0.833
6 4.05 3 15 320 16 057 1.048 0.838
9 15 490 1.037 0.830
7 4.05 4.05 21 189 20 779 0.981 0.785
10 20 361 1.021 0.817
corresponding rotation, θ , as [27]
K node,t = M tot
θ = 2(Fa)
tan θ = 2K da
d 0.5a
= K a2
= 6.8a2√
D 5t 1+ 5
t 2− 1
(kN mm/rad) (2)
with the same partial safety factor as in Eq. (1), γ R = 1.25.
The term a represents the distance between bolts.
Table 3 shows the comparison between the experimental
values of the rotational stiffness for the T-joints obtained
in the first step of the experimental programme ( K node,exp)
and the theoretical values obtained with the proposed
relation ( K node,t ).
It may be observed that there is a good correlation
between the experimental results and the characteristic
values of the joint rotational stiffness. The average reported
ratio between the theoretical characteristic values and the
experimental ones is 1.036 and the correlation coefficient
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is ρ = 0.982. Considering the design theoretical value of
the formula (K d node,t
), affected by the partial safety factor,
it may be observed that all the theoretical values are in the
safe range.
A similar model may be used for determining the
rotational stiffness for a six bolt truss joint. Considering that
the centre of rotation of the bolt group is in the axis of themiddle bolt, as shown in Fig. 5, the following equation may
be determined [26]:
K node,t = M tot
θ = 2(F × 2a)
tan θ = 4K da
d a
= 4K a2
= 27.2a2√
D 5t 1+ 5
t 2− 1
(kN mm/rad). (3)
5. Buckling length of truss web members
The rotational stiffness of joints may be used to determinethe buckling lengths of the web members. Trusses may be
classified as fixed-node-type structures. The computation
model for the buckling length of truss web members L b,web
is then as for an element with fixed nodes for lateral
displacement and elastic rotational springs on both ends.
For this model, the buckling length should be determined
considering the following equation:
Lb,web = µ Lweb (4)
where Lweb is the length of the web member measured
between centrelines of connections and µ is computed with
Eq. (5):
µ = 0.5+ 0.14(η1 + η2) + 0.055(η1 + η2)2. (5)
For the case of cold-formed steel trusses with bolted
joints, the coefficients η1 and η2 may be computed as
follows:
η1 =K web
K web + K node,1η2 =
K web
K web + K node,2
with K web = E I web
Lweb(6)
where I web is the second moment of area of the web member
and K node,1, K node,2 are the rotational rigidities of the two
joints connecting the web member on the chords, computedwith Eq. (2) or (3), a function of the number of bolts.
Note that for the computation of the buckling length, the
design values of the rotational rigidities K node,i should be
considered.
6. Experimental programme step 3: Test on the truss
structure
In order to demonstrate that the initial rotational
slippage from the moment–rotation characteristics of
T-joints determined in the first step of the experimental
programme is not present in the truss, and to validate at
Fig. 5. Computation model for a six bolt joint.
Fig. 6. Specimen dimensions.
Table 4
Cross-section characteristics (mm)
Profile h b1 b2 c t
C100/2 100 40 45 20 1.91
C120/2 120 40 45 20 1.91
structural level the theoretical formulas presented above,
a full-scale test of a truss was performed. The dimensions
of the experimental model are presented in Fig. 6. All joints
used six M12 8.8 grade bolts. The section characteristics
are presented in Table 4 (LINDAB® profiles) and the
mechanical proprieties of steel are presented in Table 5.
Fig. 7 presents the experimental arrangement. The load
was introduced by means of a 50 ton actuator, in
displacement control, imposing a rate of 2.5 mm/min.
Fig. 8 presents the instrumentation of the test. In order to
measure the joint rotations, two inclinometers ( R1– R2) were
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Table 5
Material characteristics (N, mm)
Profile f y f u εu (%)
C100/2 367.2 542 19
C120/2 354 493.4 14
Fig. 7. Experimental arrangement.
Fig. 8. Instrumentation.
placed on the web of the C-section of each web member,
in the axis of the lower chord joints. For determining the
slippage on the connections, along the axial forces in the
web members, four LVDT displacement transducers ( I 1– I 4)
were placed along the axis of web members, near the joints.
Four potentiometric displacement transducers ( P1–P4) were
also used for global structural displacement control.
The load increased until the failure of the structure,
produced by the flexural instability of the compressed web
member, occurred in the plane of the truss, as shown
in Fig. 9(a). A local buckling of the lower chord C-section
webs, due to the shear of the panel between the joints,
was observed (Fig. 9(b)), before reaching the ultimate load.
This phenomenon increases the deformability of the joint.
Fig. 9(c) presents the bolt hole plastic deformations, for the
compressed web member. It may be observed that the hole
of the middle bolt suffers only elongations along the axis of the member, which confirms the computation model from
Fig. 5, in which the middle bolt was considered the centre of
rotation for the six bolt connection.
Fig. 10 presents the evolution of the displacements
reported by the LVDT transducers I 3 and I 4, along the
axis of the compressed web member. One may observe
the typical behaviour of a thin-walled bolted connection
subjected to shear. After reaching the slippage force
(corresponding, at bolt level, to approximately 200 daN) the
initial slippage extension is extended until the hole clearance
is reached; the size of this extension is a function of the
initial position of the elements in the structure.
Fig. 11 shows the evolution of the rotations in web
member connections. Corresponding to the load range in
which the axial slippage occurs, only small rotations are
observed. Until the structure ‘shakes down’, the presence
of the axial forces and the triangulated shape of the truss
prevent the development of significant rotational slippage
in connections. Consequently, the initial rotational slippage
observed for the T-joints is not present in the structure,
and the rotational stiffness evaluated without considering
the initial slippage represents the real initial stiffness of the
connection in the truss.
For quantitative validation of the proposed theoretical
formulas, the tested truss was numerically analysed bymeans of PEP-micro programme [9]. PEP-micro is a
specialized programme for the non-linear analysis of steel
structures with semi-rigid joints.
The static scheme of the structure is presented in Fig. 12.
For the stability verification of a structure, Eurocode 3
allows for a second order analysis with initial sinusoidal
imperfection of the elements. The amplitude of those
initial imperfections is a function of the buckling curve
for the corresponding cross-section of the element. For
lipped channels, according to Eurocode 3 Part 1.3, the
corresponding buckling curve is B, with an initial equivalent
imperfection e0 = l/380. The ultimate load of the element isthen the load corresponding to the reach of the yield stress in
the extreme fibre of the cross-section, taking into account the
second order effects. A step-by-step second order analysis
was performed, with a load step corresponding to 1% of the
ultimate load. The connection eccentricities were taken into
account by introducing supplementary rigid elements on the
edges of the diagonals, of length L exc in Fig. 12.
The structure was analysed considering the classical
pinned assumption for joint behaviour and also the rotational
stiffness, computed by means of Eq. (3), for a six bolt
joint. The effect of the axial stiffness of the connections
on the direction of the axial force in web members
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Fig. 9. Structure after test.
Fig. 10. Axial displacements of the web member.
Fig. 11. Web member joint rotations.
was also considered. The PEP-micro programme is not
able to model this axial stiffness, and consequently an
equivalent finite element to simulate this behaviour of the
connections was considered. The equivalent cross-section
area of this finite element may be determined by equalizing
the expression for the axial stiffness of the bar element
having a length L ech equal to the distance between the centre
of rotation of the bolts group and the last bolt, with the axial
stiffness of the connection, K axial, determined using Eq. (1)
Fig. 12. Static scheme of the experimental model.
for the corresponding number of bolts in the connection,
i.e. multiplied by six:
K axial = 6× 6.8
√ D
10t − 1
= E Aech
Lech(7)
Fig. 13 presents the comparison between the experimen-
tal load–displacement characteristic and the results of thenumerical analysis. In Fig. 13(a) are represented the nu-
merical load–displacement characteristics, considering the
rotational stiffness (K node), together or not with the
axial stiffness of the joint ( K axial). Fig. 13(b) shows also the
response of the numerical model for the complete rotational
freedom of web member connections (pinned), considering
the axial stiffness of the joints.
One may observe, in the experimental load–displace-
ment curve, an initial structural slippage, at the level of the
force corresponding to the connection slippage along the
axis of the web members. Neglecting this phenomenon, not
considered in the numerical analysis, the structural rigidity
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Table 6
Results of the numerical and experimental analysis
K node without K axial (1) K node with K axial (2) Pinned with K axial (3) Experiment (4) (1)/(4) (2)/(4) (3)/(4)
Ultimate load (daN)
6650 7665 5790 7820 0.85 0.98 0.74
Displacement (mm)
3.3 9.9 7.5 15.8 0.21 0.63 0.47
Structural rigidity (daN/mm)
2015 774 772 734 2.74 1.05 0.99
Fig. 13. Comparison between experimental and numerical analysis.
obtained numerically, taking into account both axial ( K axial)
and rotational (K node) stiffness of the connections, is very
close to the experimental one. Table 6 presents the results of
the numerical analysis, in comparison with the experimental
values.
It may be observed that the analysis considering bothaxial and rotational stiffness of the connections gives
differences around only 2% for the ultimate load and
37% for the corresponding displacement. The difference
at displacement level is due to the initial axial slippage
in the joints and to the bolt plastic bearing appearing
at high force levels, phenomena not considered in the
numerical analysis. However, the comparison between the
initial numerical and experimental structural rigidities, after
the consumption of the slippage, gives differences of only
5%. It may be observed that the axial stiffness of the joints
plays an important role in the structural rigidity, and it
affects also, but to a lower extent, the ultimate load. On
the other hand, the rotational stiffnesses of the joints have
a very slight influence on the structural rigidity compared
with the classical assumption of pinned joints, due to the
triangulated shape of the truss, but affect in a significant way
the resistance of the structure.
Considering the results of the numerical and experimental
analysis at structural level, it may be concluded that the
theoretical formulas proposed may be successfully appliedto represent the joint stiffness in cold-formed steel trusses
with bolted joints.
7. Conclusions
Cold-formed steel trusses are much used, especially in
residential construction, but such systems are also reliable
for larger span applications. Trusses made from built-up C-
sections for chords and single C-sections for webs, with
bolted joints, represent a suitable solution for both situations,
taking into account the production costs and the rapidity of
execution.Despite the extensive use of cold-formed steel truss
systems and of cold-formed steel framing in general, and
despite the fact that new standards appeared in recent years
to cover this domain, there is still a lack of information
considering different behavioural aspects of this particular
type of structural system. In the case of steel trusses, current
design practice assumes that web members have pinned
connections, but the latest revision of the AISI Cold-Formed
Steel Truss Design Standard allows for joint stiffness to be
considered in the design of a truss. However, the standard
did not offer formulas for calculating this parameter.
In order to determine a theoretical model for the jointstiffness of bolt connected cold-formed steel trusses, the
authors developed an experimental programme. In the
first step, the stiffness of some cold-formed steel truss
bolted joints was evaluated, by means of tests on typical
T-joints. It was emphasized that the joint deformability
is mainly due to the bearing work of the bolts, and
consequently the rotational rigidity of the connection may
be determined by analysing the single lap bolted joint.
In order to determine the stiffness of a single lap bolted
joint, a second experimental programme was performed,
and a formula for the characteristic and design stiffness
was calibrated. Using this formula, a computational model
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for the rotational stiffness of truss joints was established.
The theoretical model for a four bolt joint demonstrates
a good correlation in comparison with the experimental
results on T-joints. Considering this model, a formula
for the buckling length of truss diagonals was further
determined.
In the last part of the experimental programme, onetest on a full-scale truss demonstrated that the initial
rotational slippages observed in the T-joint tests are not
present at structural level, so these slippages are not
influencing the initial rotational stiffness of the truss joints.
The numerical analysis of the truss tested, considering
the axial and rotational stiffness of the joints, computed
with the corresponding formulas for a six bolt joint,
demonstrates a good correlation with the experimental
results. Consequently, the formulas proposed by the authors
may be successfully applied to represent the joint stiffness
in cold-formed steel trusses with bolted joints. For design
purposes, when computing the displacements of the truss or
the buckling lengths of the web members, the design valuesof the joint stiffness computed with the formulas proposed in
this paper have to be applied, while for the connection design
the characteristic values are suitable. The study revealed
that the response of the truss is influenced not only by the
rotational stiffness, but also by the axial stiffness of joints,
in the direction of the axial forces of web members.
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