Identify all zero-force members in the Fink roof truss subjected to an unbalanced snow load, as shown in Fig. 4.18.

Question

Identify all zero-force members in the Fink roof truss subjected to an unbalanced snow load, as shown in Fig. [latex]4.18 [/latex].

Accepted Answer

It can be seen from the figure that at joint [latex]B[/latex], three members, [latex]A B, B C[/latex], and [latex]B J[/latex], are connected, of which [latex]A B[/latex] and [latex]B C[/latex] are collinear and [latex]B J[/latex] is not. Since no external loads are applied at joint [latex]B[/latex], member [latex]B J[/latex] is a zero-force member. A similar reasoning can be used for joint [latex]D[/latex] to identify member [latex]D N[/latex] as a zero-force member. Next, we focus our attention on joint [latex]J[/latex], where four members, [latex]A J[/latex],

[latex]B J, C J[/latex], and [latex]J K[/latex], are connected and no external loads are applied. We have already identified [latex]B J[/latex] as a zero-force member. Of the three remaining members, [latex]A J[/latex] and [latex]J K[/latex] are collinear; therefore, [latex]C J[/latex] must be a zero-force member. Similarly, at joint [latex]N[/latex], member [latex]C N[/latex] is identified as a zero-force member; the same type of arguments can be used for joint [latex]C[/latex] to identify member [latex]C K[/latex] as a zero-force member and for joint [latex]K[/latex] to identify member [latex]K N[/latex] as a zero-force member. Finally, we consider joint [latex]N[/latex], where four members, [latex]C N[/latex], [latex]D N, E N[/latex], and [latex]K N[/latex], are connected, of which three members, [latex]C N, D N[/latex], and [latex]K N[/latex], have already been identified as zero-force members. No external loads are applied at joint [latex]N[/latex], so the force in the remaining member, [latex]E N[/latex], must also be zero.

Question 4.3: Identify all zero-force members in the Fink roof truss subje...

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