GATE ME 2021 Set 2 — Question 41
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Strength of Materials → Beams & Columns → Energy Methods & Castigliano
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Question
A plane frame PQR (fixed at P and free at R) is shown in the figure. Both members (PQ and QR) have length, , and flexural rigidity, . Neglecting the effect of axial stress and transverse shear, the horizontal deflection at free end, R, is
Correct answer
(B) (4FL³)/(3EI)
Solution
Using Castigliano's theorem, the total strain energy is the sum of strain energies of members and .
For member (length ): , where is distance from . .
For member (length ): , where is distance from . .
Total strain energy .
The horizontal deflection at is .
For member (length ): , where is distance from . .
For member (length ): , where is distance from . .
Total strain energy .
The horizontal deflection at is .
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