A rational approach to predicting the buckling length of compression chords in prefabricated timber truss roof structures braced by means of diagonal bracing

摘要

In South Africa, timber-trussed roofs supporting concrete tiles have for many years often been braced solely by means of diagonal braces. Failures have shown that the diagonal brace was inadequate for larger span roofs, and the use of diagonal bracing has subsequently been limited to spans of less or equal to 10 m. When designing the compression chords of a timber truss in a braced roof, SANS 10163:1 (2003) recommends a minimum effective length for out-of-plane buckling of not less than 15 x b, which is 540 mm for a 36 mm wide member. This effective or out-of-plane buckling length of the top chord was later assumed to be equal to the spacing of the trusses. With the availability of PC-based packages that are able to perform three-dimensional buckling analyses, it is perhaps useful to investigate the validity of using the effective length equal to the truss spacing, and then also the 10 m limit on span for roofs braced by means of diagonal braces. A common error made when analysing three-dimensional buckling problems is to assume connectivity on the centreline of the members, thereby neglecting eccentricity between the centreline of the bracing and the centreline of the member being braced (see Figure 1). In timber-trussed roofs, the diagonal brace is nailed to the underside of the top chord of a number of adjacent trusses. The brace runs at more or less 45° and triangulation appears to be complete when viewed on plan, as the battens form the other elements of the bracing system triangulation. Trusses some distance from the trusses that are connected to the diagonal brace can, however, only obtain lateral support via the battens that are connected to the top of the compression chords. The authors feel that a more correct way of analysing a timber-trussed roof, braced by means of a diagonal brace, requires that the eccentricity between the centreline of the battens on top of the compression chords and the centreline of the braced points on the underside of the compression chords be taken into account. Furthermore, the connections between the battens and the top chord are not infinitely stiff and this stiffness, together with the low torsional rigidity of the timber members, should be taken into account in the buckling analysis. The analysis can be further improved by taking the out-of-plane bending stiffness of the web members into account. All these factors will influence the buckling length of the compression chords to some degree. In this paper, the authors show how incorrect assumptions may mislead the designer into believing that the buckling length is equal to or less than the spacing of the trusses. They also show that, even though the bracing members have been placed on the correct sides of the top chord in the analysis, incorrect assumptions about the torsional stiffness of the top chords can lead to buckling lengths that are slightly less than when a more realistic torsional stiffness is used.