GATE ME 2022 Set 2 — Question 51
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Strength of Materials → Stress, Strain & Elastic Constants → Stress & Strain
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Question
A rigid beam AD of length m is hinged at frictionless pin joint A and supported by two strings as shown in the figure. String BC passes over two small frictionless pulleys of negligible radius. All the strings are made of the same material and have equal cross-sectional area. A force kN is applied at C and the resulting stresses in the strings are within linear elastic limit. The self-weight of the beam is negligible with respect to the applied load. Assuming small deflections, the tension developed in the string at C is _________ kN (round off to 2 decimal places).
Correct answer
1.48 to 1.52
Solution
Let be the small angular rotation of the rigid beam about the hinge A. The downward deflections at points B, C, and D are:
String 1 (BC):
This string is attached at B and C and passes over two pulleys. The total extension of this string is .
The length of string 1 is (two vertical segments of length and one horizontal segment of length ).
The tension in string 1 is:String 2 (at D):
This string is attached at D and has a length . Its extension is .
The tension in string 2 is:Thus, .Equilibrium of the beam:
Taking moments about hinge A ():Given kN:The tension in the string at C is kN.
String 1 (BC):
This string is attached at B and C and passes over two pulleys. The total extension of this string is .
The length of string 1 is (two vertical segments of length and one horizontal segment of length ).
The tension in string 1 is:String 2 (at D):
This string is attached at D and has a length . Its extension is .
The tension in string 2 is:Thus, .Equilibrium of the beam:
Taking moments about hinge A ():Given kN:The tension in the string at C is kN.
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