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GATE 2025 CE (CE2) – Question 14

Structural Analysis · Influence lines and moving loads · 1 mark · Multiple choice

Consider the pin-jointed truss shown in the figure. Influence line is drawn for the axial force in the member G-I, when a unit load travels on the bottom chord of the truss. Identify the CORRECT influence line from the following options:
Note: Positive value corresponds to tension and negative value corresponds to compression in the member.

a truss with the bottom chord A-D-G-I-L-O-P, the top chord B-E-H-J-M and intermediate joints C, F, K and N, 6 panels of 6 m (36 m), height 6 m with the middle joints at 3 m. Options: (A) a triangle with the peak 1.33 at D, (B) a triangle with the peak 1.33 at G, (C) a triangle with the peak 1.33 at I, (D) a diagram with 1.33 at G that changes sign and reaches −1.33 at I.
  1. Option A in the figure
  2. Option B in the figure
  3. Option C in the figure
  4. Option D in the figure

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Show answer and explanation

Correct answer: (B) Option B in the figure

Explanation

Cut the truss between G and I. The cut members are E-H, F-H, F-I and G-I. At joint F the only non-vertical members are F-H and F-I, so their horizontal components must cancel: $T_{FI} = -T_{FH}$. For a load at I or to the right of it, take the left part, with the reaction $R_A = \frac{36 - x}{36}$. The vertical balance gives $T_{FI} = 1.118R_A$ and then the moment about H gives $-18R_A + 6T_{GI} + 6R_A = 0$, so $T_{GI} = 2R_A$ (tension). For a load at G or to the left, take the right part, with the reaction $R_P = \frac{x}{36}$: in the same way $T_{GI} = 4R_P$. At $x = 12$ this is $4 \times \frac{12}{36} = 1.33$ and at $x = 18$ it is $2 \times \frac{18}{36} = 1.0$. The influence line is therefore zero at A, 1.33 at G and falls in a straight line from G to zero at P, which is option B.