Steel Buildings in Europe

Part 5: Detailed Design of Trusses 5 - 18 3.4 Simplified global analysis of the worked example A triangulated beam, with a constant depth, can be equated to an I-beam. This equivalence is possible and provides a good approximation, for example, for a truss with parallel chords. The global shear force V global and the global bending moment M global in the equivalent beam vary very little along a panel and can be equated with the mean values in the panel. Therefore the axial load can be assessed using the following expressions (see Figure 3.3 for the notations): N ch = ± M global / h in the chords N d = ± V global /cos θ in a diagonal h θ Figure 3.3 Truss with parallel chords - Notation An estimate can also be made for the deflection of the truss beam by calculating that for an equivalent beam, for the same loading. In order to do this, the classic approach is to use elementary beam theory, giving the equivalent beam a second moment of area equal to: 2 2 1 ch, i i i I A d    where: A ch, i is the section area of the chord i d i is the distance from the centroid of both chords to the centroid of the chord i . In order to take into account global shear deformations, not dealt with in elementary formulae, a reduced modulus of elasticity is used. Global shear deformations are not, in fact, negligible in the case of trusses, since they result from a variation in length of the diagonals and posts. The value of the reduced modulus of elasticity clearly varies depending on the geometry of the truss, the section of the members, etc. For a truss beam with “well proportioned” parallel chords, the reduced modulus of elasticity is about 160000 N/mm 2 (instead of 210000 N/mm 2 ).