Stiffness prediction for bolted moment-connections between cold-formed steel members

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Abstract

The authors have recently described a cold-formed steel portal framing system in which simple bolted moment-connections, formed through brackets, were used for the eaves and apex joints. Such connections, however, cannot be considered as rigid because of localised in-plane elongation of the bolt-holes caused by bearing against the bolt-shanks. To therefore predict the initial stiffness of such connections, it is necessary to know the initial bolt-hole elongation stiffness kb. In this paper, a finite element solid idealisation of a bolted lap-joint in shear will be described that can be used to determine kb; the results obtained are validated against experimental data. A beam idealisation of a cold-formed steel bolted moment-connection is then described, in which spring elements are used to idealise the rotational flexibility of the bolt-groups resulting from bolt-hole elongation. Using the value of kb in the beam idealisation, the deflections predicted are shown to be similar to those measured experimentally in laboratory tests conducted on the apex joint of a cold-formed steel portal frame.

Introduction

Cold-formed steel sections are finding increasing uses as the primary members of load-bearing structures. Examples include: portal frames [1], racking systems [2] and multi-storey buildings [3]. Such structures require site joints which should not only possess the requisite structural properties of strength, stiffness and ductility, but must also be simple to fabricate and straightforward to erect. This argues for the use of mechanical fasteners and a limited number of simple components.

In previous papers [4], [5], the authors have described a cold-formed steel portal framing system in which the eaves and apex joints (Fig. 1) were formed from bolted moment-connections made through brackets. Because of the inherent flexibility of such joints, the proposed frame analysis procedure made explicit use of joint stiffness as one of the input parameters. It is therefore necessary to be able to predict the initial rotational stiffness of such connections from a knowledge of the component layout (Fig. 2, Fig. 3). A method for doing this is presented herein.

Full-scale tests on apex joints are used to demonstrate that the single most important contributory factor to joint flexibility is the elongation of the bolt-holes caused by bearing against the bolt-shanks. Tests on simple bolted lap-joints permit the load-extension characteristics of bolt-hole elongation to be measured; differences in the initial bolt-hole elongation stiffness kb when using plain or fully threaded bolt-shanks are identified.

The bolted lap-joint test results are used to validate a non-linear large-displacement elasto-plastic finite element solid idealisation in which contact is simulated between the bolt-shank and the bolt-hole; a remarkably close agreement between the experimental and numerical results is demonstrated. A beam idealisation of a cold-formed steel bolted moment-connection is then described, in which spring elements are used to idealise the rotational flexibility of the bolt-group that results from bolt-hole elongation.

Using the value of kb obtained from the finite element solid idealisation of the bolted lap-joint, the beam idealisation is used to predict the initial stiffness of the apex joints tested; close agreement between the experimental and numerical results is again demonstrated.

Availability of the beam idealisation therefore permits the ready determination of the initial rotational stiffness for a range of connection layouts. These data can then be used directly with the overall frame design procedure of [4].

Section snippets

Literature review

General information on the behaviour and design of connections in structural steelwork may be found in a number of specialist texts [6], [7] and design guides [8], [9], [10]. These do, however, deal almost exclusively with connections in heavy gauge construction. Design texts orientated specifically towards cold-formed steel construction [11], [12] provide relatively little information on connection design.

Whilst the research literature does contain numerous references to studies of joints in

Details of tests

Laboratory tests were conducted on two apex joints, with each having a different size of bracket (Fig. 3). The nominal thickness of each bracket was 4 mm, and the nominal diameters of the bolts and bolt-holes were 16 mm and 18 mm, respectively; all the bolts used had fully threaded bolt-shanks. Details of each specimen are summarised in Table 1. The average yield and ultimate strengths of the brackets, measured from three tensile coupons, were 341 N/mm2 and 511 N/mm2, respectively (Table 2).

The

Finite element idealisation of a double shear lap joint

The finite element program ABAQUS was used to model the plate and to simulate contact between the bolt-shank and the bolt-hole. The model was solved using non-linear large-displacement elasto-plastic analysis.

Details of the finite element idealisation of the plate with a bolt-hole are shown in Fig. 12. The plate was modelled using the 20-noded solid element C3D20R. Four elements were used through the thickness of the plate (so that yielding through the thickness can be simulated) and 40

Rotational stiffness of bolt-group

Fig. 19(a) shows a bolt-group of length aB and breadth bB formed from nine bolts. When the bolt-group resists an applied moment M, the bolt-group rotates about a point known as the centre of rotation [6], [14], [15], [19]. The resisting force Fi at each bolt-hole is proportional to its distance di from the centre of rotation and acts in a direction perpendicular to the line drawn from the bolt-hole to the centre of rotation (Fig. 19(b)).

From symmetry, the centre of rotation of the bolt-group is

Comparison of apex joint test results with beam idealisation

For the bracket and channel-sections, the variation of load against bolt-hole elongation for bearing of the bolt-hole against a threaded bolt-shank was determined using the finite element model described in Section 4 and shown in Fig. 25. From Fig. 25, the value of kb used for the beam idealisation of the apex joint is 18.63 kN/mm.

The parameters used for the beam idealisation are shown in Table 6. Details of the beam idealisation are shown in Fig. 26. It should be noted that the rotational

Concluding remarks

A method has been presented for determining the initial rotational stiffness of a shear-type bolted moment-connection between cold-formed members. The elongation of the bolt-holes as bolts bear into the material immediately behind each bolt is shown to be by far the most important structural phenomenon controlling stiffness. A finite element representation of the bolt/bolt-hole interaction is shown to represent behaviour well. Stiffness values for individual bolts obtained from this approach

Acknowledgements

The work reported herein was undertaken in association with Ayrshire Metal Products as a ‘Partners in Technology’ project with financial support from the DETR. The technical, financial and material contributions from Ayrshire are gratefully acknowledged.

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    It was shown that such frames provide competitive alternatives to conventional rigid jointed hot-rolled steel connections for certain combinations of frame geometry and imposed loading. In a follow-up study [124], a FE solid idealisation of a bolted lap-joint in shear was used to determine elongation stiffness. In the light of a beam idealisation of a CFS bolted-moment connection, spring elements were then used to idealise the rotational flexibility of the bolt-groups resulting from bolt-hole elongation.

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