GATE ME 2022 Set 1 — Question 37
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Strength of Materials → Beams & Columns → Deflection of Beams
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Question
An L-shaped elastic member ABC with slender arms AB and BC of uniform cross-section is clamped at end A and connected to a pin at end C. The pin remains in continuous contact with and is constrained to move in a smooth horizontal slot. The section modulus of the member is same in both the arms. The end C is subjected to a horizontal force and all the deflections are in the plane of the figure. Given the length AB is and length BC is , the magnitude and direction of the normal force on the pin from the slot, respectively, are
Correct answer
(A) 3P/8, and downwards
Solution
To find the normal force on the pin from the slot, we use Castigliano's theorem. The vertical displacement at point C is zero due to the horizontal slot constraint.Let be the vertical reaction force at C, assumed to be acting upwards.
Bending moment
Partial derivative
Bending moment
Partial derivative
1.Segment BC (vertical, length ):
Taking as the coordinate from C ():Bending moment
Partial derivative
2.Segment AB (horizontal, length ):
Taking as the coordinate from B ():Bending moment
Partial derivative
3.Applying Castigliano's Theorem ():
The negative sign indicates that the reaction force acts in the opposite direction to our assumption, i.e., it acts downwards. Thus, the magnitude is and the direction is downwards.Continue learning with Success Tracker
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