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PRELIMINARY DESIGN
Fig. 3.4 Plastic analysis: (a) frame load and hinges; (b) plastic bending moments; (c) analysis chart.
It is more economical to use a lighter section for the rafter than for the column, rather than a uniform section throughout. The rafter is haunched at the eaves. This permits use of a bolted joint at the eaves and ensures that the hinge there forms in the column. Let Mp be the plastic moment of resistance of the column and qMp be the plastic moment of resistance of the rafter, where q=0.75 for chart. Then
where w=roof load per unit length; L=span; H=horizontal reaction; h=eaves height; g=depth of column hinge below intersection of column and rafter centrelines (0.3–0.5 m for chart); Φ=roof slope (15° for chart); x=distance of rafter hinge from support. Equate dH/dx=0, solve for x and obtain H and Mp. A chart is given in Figure 3.4(c) to show values of the column plastic moment Mp for various values of span L and eaves height h.