Project ForgeThe truss shown in the figure has four members of length l and flexural rigidity EI, and one member of length l√2 and flexural rigidity 4EI (the diagonal, pin-jointed at both ends). The truss is loaded by a pair of forces of magnitude P applied at 45° along the diagonal's own line of action, at its two end joints. The smallest value of P, at which any of the truss members will buckle, is
- A√2π²EI/l²
- Bπ²EI/l²
- 2π²EI/l²
- Dπ²EI/2l²
Explanation
The applied force pair acts exactly along the diagonal member's own axis at its two end joints, so the diagonal (length l√2, rigidity 4EI, pinned at both ends) carries an axial compressive force equal to P directly, while the four square-perimeter members carry comparatively little load. The diagonal governs buckling first: Pcr = π²(4EI)/(√2·l)² = π²·4EI/(2l²) = 2π²EI/l².
Source: GATE ME 2020 Session 1 (ME-1) (2020)
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