GATE ME 2020 Set 1 — Question 40
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Engineering Mechanics → Beams & Columns → Euler's Theory of Columns
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Question
The truss shown in the figure has four members of length and flexural rigidity , and one member of length and flexural rigidity . The truss is loaded by a pair of forces of magnitude , as shown in the figure.
The smallest value of , at which any of the truss members will buckle is
Correct answer
(C) (2π² EI)/(l²)
Solution
The two forces act outward along the diagonal that has no member (top-left to bottom-right corner).Joint at a loaded corner (e.g. top-left): the force at is resisted by the horizontal and vertical sides meeting there. Resolving, each side carries in tension.Joint at an unloaded corner (e.g. top-right): the two sides, each in tension , pull the joint towards the two loaded corners. Their resultant, , points along the member diagonal towards the centre, so the diagonal member is in compression with force .Only compressive members can buckle, so only the diagonal (length , rigidity , pin-ended) matters:Buckling starts when the diagonal force reaches this value. The sides are in tension and cannot buckle.
- (A) treats a side as compressed with force , but the sides are in tension.
- (B) and (D) use the wrong length or rigidity.
- (C) is correct.
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