GATE 2023 AE – Question 50

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

A cantilever beam of length 2a is loaded at the tip with force F as shown in the figure. The beam is supported in the middle by a roller with a pin. The magnitude of moment reaction at the built-in end of the beam is αFa, where αis ______ . (round off to one decimal place)

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

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Correct answer: 0.49 to 0.51

Explanation

Zero deflection at x=a gives roller reaction $R=5F/2$. The built-in moment magnitude is $|2Fa-Ra|=0.5Fa$.