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GATE CE 2022 Set 2 — Question 50

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NAT+2 / -0MediumAxial DeformationStress, Strain & BeamsStructural EngineeringThermal Stress

Structural Engineering → Stress, Strain & Beams → Axial Deformation

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Question

Consider two linearly elastic rods HIHI and IJIJ, each of length bb, as shown in the figure. The rods are co-linear, and confined between two fixed supports at HH and JJ. Both the rods are initially stress free. The coefficient of linear thermal expansion is α\alpha for both the rods. The temperature of the rod IJIJ is raised by ΔT\Delta T, whereas the temperature of rod HIHI remains unchanged. An external horizontal force PP is now applied at node II. It is given that α=10−6 ∘C−1\alpha = \mathbf{10^{-6} \text{ } ^\circ\text{C}^{-1}}, ΔT=50 ∘C\Delta T = \mathbf{50 \text{ } ^\circ\text{C}}, b=2 mb = \mathbf{2 \text{ m}}, AE=106 NAE = \mathbf{10^6 \text{ N}}. The axial rigidities of the rods HIHI and IJIJ are 2AE2AE and AEAE, respectively.
Diagram showing two co-linear rods HI and IJ between fixed supports H and J, with a force P applied at node I.
To make the axial force in rod HIHI equal to zero, the value of the external force PP (in N) is _________. (round off to the nearest integer)
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