GATE CE 2025 Set 1 — Question 51
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Structural Engineering → Stress, Strain & Beams → Axial Deformation
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Question
Consider the rigid bar ABC supported by the pin-jointed links BD and CE and subjected to a load at the end A, as shown in the figure. The axial rigidities of BD and CE are 22500 kN and 15000 kN, respectively. If CE elongates by 5 mm due to the load , the magnitude of the downward deflection (in mm) of the end A would be ________________________ (rounded off to the nearest integer).
Correct answer
14 to 14
Solution
Let be the deflections of points A, B, and C respectively.1. Force in link CE:
Given elongation mm and axial rigidity kN, length mm.
kN.2. Equilibrium of the rigid bar ABC:
Taking moments about point B:
kN.
Sum of vertical forces:
kN.3. Deflection at B:
Given kN and mm.
mm.4. Deflection at A:
Assuming link CE elongates such that C moves up ( mm) and link BD elongates such that B moves down ( mm), the linear deflection profile of the rigid bar is:
mm.Rounding to the nearest integer, the downward deflection of end A is 14 mm.
Given elongation mm and axial rigidity kN, length mm.
kN.2. Equilibrium of the rigid bar ABC:
Taking moments about point B:
kN.
Sum of vertical forces:
kN.3. Deflection at B:
Given kN and mm.
mm.4. Deflection at A:
Assuming link CE elongates such that C moves up ( mm) and link BD elongates such that B moves down ( mm), the linear deflection profile of the rigid bar is:
mm.Rounding to the nearest integer, the downward deflection of end A is 14 mm.
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