Solved GATE Questions on Strain Energy Methods
Question 1. A stepped steel shaft shown below is subjected to 10 Nm torque. If the modulus of rigidity is 80 GPa, the strain energy in the shaft in N mm is
(A) 4.12
(B) 3.46
(C) 1.73
(D) 0.86
GATE-ME-2007
Hint 1. (Ans C)
Here,
Question 2. The strain energy stored in the beam with flexural rigidity EI and loaded as shown in the figure is
(A) 
(B) 
(C) 
(D) 
GATE-ME-2008
Hint 2. (Ans C)
Total strain energy stored is given by
Question 3. A frame of two arms of equal length L is shown in the figure. The flexural rigidity of each arm of the frame is EI. The vertical deflection at the point of application of load P is
(A) 
(B) 
(C) 
(D) 
GATE-ME-2009
Hint 3. (Ans D)
Integrating two time and putting x=L, we get
Alternately
For BC
Strain energy,
Total strain energy,
Question 4. Two threaded bolts A and B of same material and length are subjected to identical ensile load. If the elastic strain energy stored in bolt A is 4 times that of bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is
(A) 16
(B) 24
(C) 36
(D) 48
GATE-ME-2013
Hint 4. (Ans B)
Answer key
1. (C) 2. (C) 3. (D) 4. (B)