Classify each of the structures in Fig. 2–24a through 2–24e as stable or unstable. The structures are subjected to arbitrary external loads that are assumed to be known.

Question

Classify each of the structures in Fig. [latex] 2-24 (\mathrm{a})[/latex] through [latex] 2-24 (\mathrm{e})[/latex] as stable or unstable. The structures are subjected to arbitrary external loads that are assumed to be known.

Accepted Answer

The structures are classified as indicated.

The member is stable since the reactions are nonconcurrent and nonparallel. It is also statically determinate.

The compound beam is stable. It is also indeterminate to the second degree.

The member is unstable since the three reactions are concurrent at [latex]B[/latex].

The beam is unstable since the three reactions are all parallel.

The structure is unstable since [latex]r=7, n=3[/latex], so that, by Eq. 2-4, [latex]r<3 n, 7<9 .[/latex] Also, this can be seen by inspection, since [latex]A B[/latex] can move horizontally without restraint.

[latex] \begin{array}{ll} r<3 n & ext { unstable } \ r \geq 3 n & ext { unstable if member reactions are } \ & ext { concurrent or parallel or some of the } \ & ext { components form a collapsible mechanism } \end{array} [/latex] (2-4)

Question 2.6: Classify each of the structures in Fig. 2–24a through 2–24e ...

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