Zaharia Dubin A

8/10/2019 Zaharia Dubin A

http://slidepdf.com/reader/full/zaharia-dubin-a 1/10

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: [email protected] (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

http://www.elsevier.com/locate/jcsr

http://www.elsevier.com/locate/jcsr



R. Zaharia, D. Dubina / Journal of Constructional Steel Research 62 (2006) 240–249 241

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



242 R. Zaharia, D. Dubina / Journal of Constructional Steel Research 62 (2006) 240–249

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.




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




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




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




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




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




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




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.

References

[1] AISI/COFS. Standard for cold-formed steel framing — Truss design,

Revision of AISI/COFS/TRUSS 2000. American Iron and Steel

Institute, Committee on Framing Standards (COFS); 2001 [1stprinting June 2002].

[2] AISI. Commentary on the standard for cold-formed steel framing

— Truss design. American Iron and Steel Institute. Committee on

Framing Standards (COFS); 2001 [1st printing June 2002].

[3] Blumel S, Fontana M. Load-bearing and deformation behaviour of

truss joints using thin-walled pentagon cross-sections. Thin Wall

Struct 2004;42(2):295–307.

[4] Database. Database for research on cold-formed steel structures

project title: Behaviour of bolted connections in cold-formed steel

plane trusses — Center for Cold-formed Steel Structures. University

of Missouri-Rolla M 065401-0249 USA; 1996.

[5] Dubina D, Zaharia R. Experimental evidence of semi-rigid behaviour

of some cold-formed steel truss bolted joints. In: International

conference on experimental model research and testing of thin-walled

steel structures. 1997.[6] Dubina D, Zaharia R. Cold-formed steel trusses with semi-rigid joints.

Thin Wall Struct 1998;29(1–4):237–87.

[7] Dubina D, Zaharia R, Ungureanu V. Behaviour of built-up columns

made of C sections connected with bolted stitches. In: International

colloquium on stability and ductility of steel structures. 2002.

[8] ECCS. TC7 European recommendations for steel construction: The

design and testing of connections in steel sheeting and sections,

Publication No. 21; 1983.

[9] Galea Y, Bureau A. PEP–micro: Analyse plastique au second ordre

de structures plannes a barres. Paris (France): Centre Technique

Industriel de la Construction Metallique; 1992.

[10] Harper MM. Cold-formed steel in residential roof trusses. Thesis

presented to the Faculty of the University of Missouri-Rolla in

partial fulfillment for the degree master of Science. Missouri-Rolla,

USA; 1995.

[11] Ibrahim TM, LaBoube RA, Yu WW. Behaviour of cold-formed steel

roof trusses under concentrated loads. J Constr Steel Res 1998;

46(1–3):176–7.

[12] Johnston BG. Spaced steel columns. J Struct Div, ASCE 1971;

97(ST5):1465–79.

[13] LaBoube RA, Yu WW. Recent research and developments in cold-

formed steel framing. Thin Wall Struct 1998;32(1–3):19–39.

[14] Lim JPB, Nethercot DA. Stiffness prediction for bolted moment-

connections between cold-formed steel members. J Constr Steel Res

2004;60(1):85–107.

[15] Mäkeläinen P, Kesti J. Advanced method for light-weight steel

joining. J Constr Steel Res 1999;49(2):107–16.

[16] Niazi A. Contribution a l’etude de la stabilite des structures composeesde profils a parois minces et section ouverte de type C. These presentee

en vue de l’obtention du grade scientifique de Docteur en Sciences

Appliquees. Universite de Liege; 1993.

[17] Pedreschi RF, Sinha BP, Davies R. Advanced connection technique

for cold-formed steel structures. J Struct Eng 1997;123(2):138–44.

[18] prEN1990. Eurocode 0, Basis of structural design. Brussels

(Belgium): European Committee for Standardisation; 2001.

[19] prEN1991. Eurocode 1: Actions on structures. Brussels (Belgium):

European Committee for Standardisation; 2001.

[20] prEN1993-1-3. Eurocode 3, Design of steel structures, Part 1.3

General rules, Supplementary rules for cold formed thin gauge

members and sheeting. Brussels (Belgium): European Committee for

Standardisation; 2003.

[21] prEN1993-1-8. Eurocode 3, Design of steel structures, Part 1.8,

‘Design of steel joints’. Brussels (Belgium): European Committee forStandardisation; 2003.

[22] Riemann JA. The behaviour of compression web members in cold-

formed steel truss assemblies. Thesis presented to the Faculty of

the University of Missouri-Rolla in partial fulfillment for the degree

master of Science. Missouri-Rolla, USA; 1996.

[23] Tomà AW. Connections in cold-rolled sections. Research report BI-

76-78, TNO Delft; 1976.

[24] Wong MF, Chung KF. Structural behaviour of bolted moment

connections in cold-formed steel beam–column sub-frames. J Constr

Steel Res 2002;58(2):253–74.

[25] Zadanfarrokh F, Bryan ER. Testing and design of bolted connections

in cold-formed steel sections. In: Eleventh international specialty

conference on cold-formed steel structures, University of Missouri-

Rolla, St. Louis, Missouri, U.S.A, 1992.

[26] Zaharia R. Cold-formed steel trusses with bolted connections. Ph.D.thesis. Romania: The ‘Politehnica’ University of Timisoara; 2000 [in

Romanian].

[27] Zaharia R, Dubina D. Behaviour of cold-formed steel truss bolted

joints. In: The IV’th international workshop on connections in steel

structures. 2000.

Documents

Zaharia Dubin A