The flat roof of the steel-frame building in Fig. 2–16a is intended to support a total load of 2 kN/m2 over its surface. If the span of beams AD and BC is 5 m and the space between them (AB and DC) is 3 m, determine the roof load within region ABCD that is transmitted to beam BC.

Question

The flat roof of the steel-frame building in Fig. [latex] 2-16 (\mathrm{a})[/latex] is intended to support a total load of [latex]2 \mathrm{kN} / \mathrm{m}^{2}[/latex] over its surface. If the span of beams [latex]A D[/latex] and [latex]B C[/latex] is [latex]5 \mathrm{~m}[/latex] and the space between them [latex](A B[/latex] and [latex]D C)[/latex] is [latex]3 \mathrm{~m}[/latex], determine the roof load within region [latex]A B C D[/latex] that is transmitted to beam [latex]B C[/latex].

Accepted Answer

In this case [latex]L_{1}=5 \mathrm{~m}[/latex] and [latex]L_{2}=4 \mathrm{~m} .[/latex] Since [latex]L_{2} / L_{1}=1.25<1.5[/latex], we have two-way slab action. The tributary loading is shown in Fig. 2-16b, where the shaded trapezoidal area of loading is transmitted to member [latex]B C[/latex]. The peak intensity of this loading is [latex]\left(2 \mathrm{kN} / \mathrm{m}^{2}\right)(2 \mathrm{~m})=4 \mathrm{kN} / \mathrm{m}[/latex]. As a result, the distribution of load along [latex]B C[/latex] is shown in Fig. 2-16b. This process of tributary load transmission should also be calculated for the two square regions to the right of [latex]B C[/latex] in Fig. 2-16a, and this additional load should then be placed on [latex]B C[/latex].

Question 2.2: The flat roof of the steel-frame building in Fig. 2–16a is i...

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