GATE CE 2016 Set 2 — Question 44
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Structural Engineering → Determinate Structures & Energy Methods → Axial Deformation
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Question
Consider the structural system shown in the figure under the action of weight . All the joints are hinged. The properties of the members in terms of length (), area () and the modulus of elasticity () are also given in the figure. Let and be and , respectively, and be .
Which one of the following sets gives the correct values of the force, stress and change in length of the horizontal member ?
Correct answer
(C) Compressive force = 100 kN; Stress = 1000 kN/m²; Shortening = 0.0417 m
Solution
1.Force Analysis: By symmetry, the vertical reaction at support is . At joint , the tension in members and is . At joint , the horizontal equilibrium gives , where is the compression in . Vertical equilibrium at gives . Thus, . The force in is (Compression).
2.Stress Analysis: Stress .
3.Deformation: Since the member is in compression, it will undergo shortening. Comparing options, (C) is the only one with compression and shortening.
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