GATE 2024 AE – Question 53

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

In the figure shown below, the magnitude of internal force in member BC is ___________ N (rounded off to 1 decimal place).

A vertical bar AD hangs from a pin at A on the ceiling. A point C on it is 0.5 m below A, and D is 1.0 m below A. A pinned link BC joins C to the ceiling point B, which is 0.5 m to the right of A. A force of 100 N acts at D, pointing down and to the right at $30^\circ$ to the vertical.

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Correct answer: 140.69 to 142.11

Explanation

Take A as the origin. The link BC is a two-force member along the line from C(0, -0.5) to B(0.5, 0), at $45^\circ$. The 100 N load at D(0, -1) has the components (50, -86.6). Moments about A: the load gives $0 \cdot(-86.6) - (-1)(50) = +50$ N-m, and a force $F$ in BC (tension positive) gives $+0.5 \times 0.7071F$. Setting the sum to zero gives $F = -\frac{50}{0.3536} = -141.4$ N, so BC carries 141.4 N in compression.