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GATE 2023 AE – Question 49

Structures · Strength of materials: stress and strain, stress-strain curves, trusses, bars, beams and shafts, determinate and indeterminate · 2 marks · Numerical answer

A rigid bar AB is subjected to a uniformly distributed load of 100 N/m as shown in the figure. The bar is supported by rod CD, with A, C, and D as pin joints. The rod CD has axial stiffness of 40 N/mm. The vertical deflection at point D is __________ mm. (round off to nearest integer)

source diagram and its labels are reproduced in the attached image.

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Correct answer: 10

Explanation

The 2 m bar carries 200 N at its midpoint D, so the rod vertical component is 200 N. At 45°, axial force is $200\sqrt2$ N; extension is $5\sqrt2$ mm and D moves 10 mm vertically.