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GATE 2023 CE (CE1) – Question 54

Structural Analysis · Influence lines and moving loads · 2 marks · Numerical answer

An idealised bridge truss is shown in the figure. The force in Member U$_2$L$_3$ is __________________ kN (round off to one decimal place).

a Pratt-type bridge truss of 6 panels of 3 m (18 m) and height 3 m, with the top chord joints U0 to U6 and the bottom chord joints L1 to L5. A 20 kN downward load acts at each of U1 to U5. U0 is a hinge support and U6 a roller. The posts U1L1, U2L2, ... are vertical and the diagonals go down to the right in the left half (U0L1, U1L2, U2L3) and down to the left in the right half.

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Correct answer: 14.03 to 14.17

Explanation

The total load is $5 \times 20 = 100$ kN, so each support reaction is 50 kN by symmetry. Cut the truss through the panel between U2 and U3 (members U2U3, U2L3 and L2L3). For the left part, the vertical force available is $50 - 20 - 20 = 10$ kN upward (the loads at U1 and U2 are on the left). This must be balanced by the vertical component of the diagonal, which is at 45° (3 m by 3 m): $F\sin 45° = 10$, so $F = 10\sqrt{2} = 14.1$ kN. The diagonal runs downward to the right and pulls on the left part, so it is in tension.