GATE CE 2026 Set 1 — Question 51
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Structural Engineering → Stress, Strain & Beams → Axial Deformation
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Question
A homogenous, linearly elastic rod AB is connected to a linearly elastic spring BC in between the fixed supports at A and C, as shown in the figure. The cross-sectional area, modulus of elasticity, and the coefficient of thermal expansion of the rod AB are , , and , respectively. The stiffness (k) of spring BC is .
The internal force (in kN) that will develop in the spring BC when the temperature of rod AB is increased by is _________ (rounded off to one decimal place).
Correct answer
7 to 7.4
Solution
1.Calculate the free thermal expansion of rod AB:
The free expansion is given by:Given , , and .
2.Determine the compatibility equation:
Let be the internal force developed (compressive in the rod and tensile in the spring). The total expansion is restricted by the fixed supports, so the free thermal expansion must be equal to the sum of the elastic deformations of the rod and the spring:3.Substitute the given values:
4.Solve for P:
Converting to kN:The internal force developed is .
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