GATE CE 2024 Set 2 — Question 16
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Structural Engineering → Statics & Rigid Bodies → Equilibrium Equations
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Question
A long, horizontal, rigid, uniform beam has negligible mass. The beam is subjected to a concentrated vertically downward force at from , as shown in the figure. The beam is resting on vertical linear springs at the ends and . For the spring at the end , the spring constant .
(Figure NOT to scale)If the beam DOES NOT rotate under the application of the force and displaces only vertically, the value of the spring constant (in ) for the spring at the end is
Correct answer
(C) 50
Solution
For the beam to displace only vertically without rotation, the vertical displacement at both ends must be equal ().
Let and be the reaction forces from the springs at and respectively.
and .
Taking moments about the point of application of the load:
Substituting the spring force expressions:
Given :
.
Let and be the reaction forces from the springs at and respectively.
and .
Taking moments about the point of application of the load:
Substituting the spring force expressions:
Given :
.
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