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The column base of the portal frame should be pinned (worst case) for the moment gradient factor of the column to be 1.22. Since the unbraced length of the rafter is larger than the one for the column (1.245 m), the unbraced length of the rafter is therefore more critical than the column (Table 4). The factored lateral-torsional buckling moment of resistance (Mrb) and compression resistance of the rafter, determined based on the properties in Tables 2 and 3 are shown in Table 6.7.2. Cross-sectional strength Cross-sectional strength refers to the possibility of the
section yielding at the section of combined bending and axial stress. This is normally at the eaves connection.This case ensures that, despite the existence of other forms of buckling, the ultimate strength of the section may not be exceeded. The governing interaction equation for this case is given in Table 5. Nu and Mu are the axial compression and moment about the x-axis due to the ultimate design loads respectively, and are determined based on the load factors of 1.2 and 1.6 for dead plus imposed load. These loads are calculated for channel sections spanning 10 m to 12 m and a frame spacing of 4.5 m. In this interaction equation, the cross-sectional compressive resistance at yield Ny and moment of resistance at My are calculated using effective section properties, derived by taking the design stress as the yield stress and resistance factors of 0.75 and 0.9 respectively.
7.3. Overall buckling strength Overall buckling strength considers the possibility of failure of the entire member occurring. This is covered by the stability interaction equation in Table 6. The compressive buckling resistance (Nrb) and the lateral buckling moment of resistance (Mrb) are calculated using effective section
properties, derived by taking the design stress as the buckling stress and resistance factors of 0.75 and 0.9 respectively. These buckling resistances are calculated for
a range of channel sections and purlin spacing. SANS 10162-2 (2005) prescribes Cb as a function of the moment gradient for bending, but stipulates that Cb=1 where there is interaction of axial force and bending. This is done to avoid applying the moment gradient factor twice as the interaction equation contains an equivalent moment coefficient that takes account of the changing moment. A moment gradient factor of Cb=1.67 is used in buckling calculations. This is found to give better results than using Cb=1, as required by the code. A factor of 0.8 is applied to My and Mrb respectively, based on test results of Dundu and Kemp (2006a, b), to
take account of stress concentrations, shear lag and bearing deformations in the connections. The values of ω and α reflect the differing susceptibility to buckling of the shape of the bending moment distributions and the
moment amplification factors respectively. Unlike in the hot-rolled code, where there are separate equations for overall and lateral torsional buckling, lateral torsional buckling is taken into account in the overall buckling equation in the cold-formed code. 7.4. Shear and bending interaction The results of the interaction equation of combined shear and bending are shown in Table 7. Vu is the shear force due to ultimate loads and Vr is the factored shear resistance. Combined bending and shear is theoretically not critical, since it has the smallest value in each case.
There was also no evidence of combined bending and shear failure in the tests. Beams having thin webs may suffer buckling of the webs if high concentrated loads are
applied transverse to the beams (web crippling). High concentrated loads are commonly encountered at the end supports of beams. The design for crippling is not carried out, as the transverse loads are low.
8. Portal frame connections
8.1. Eaves connection
The bolts in Fig. 9 transfer a shear force, an axial force and a moment between the members. The moment is applied in the plane of the connection and the bolt group rotates about its centroid. The connections are designed based on the following assumptions: