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GATE 2025 AE – Question 56

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

For a three-bar truss loaded as shown in the figure, the magnitude of the force in the horizontal member AB is ___N (answer in integer).

An equilateral triangular truss ABC with sides of 1 m. A is a pin support at the bottom left, B is a roller support at the bottom right, and C is the apex. A horizontal force of 50 N acts to the right at C.

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Correct answer: 25

Explanation

Take moments about A: the 50 N load acts at a height of $\frac{\sqrt 3}{2}$ m, so the roller reaction at B is $R_B = 50 \times \frac{\sqrt 3}{2} = 43.3$ N upward, and A has $R_{Ay} = -43.3$ N and $R_{Ax} = -50$ N. At joint A the vertical balance gives a force $F_{AC} = \frac{43.3}{\sin 60^\circ} = 50$ N (tension). The horizontal balance gives $-50 + 50\cos 60^\circ + F_{AB} = 0$, so $F_{AB} = 25$ N.