Test: Strain Energy

QUESTION: 1

Total strain energy stored in a simply supported beam of span ‘L' and flexural rigidity ‘El’ subjected to a concentrated load ‘W at the centre is equal to

A.
W²L³/40EI
B.
W²L³/60EI
C.
W²L²/240EI
D.
W²L³/96EI

Solution:

QUESTION: 2

Which one of the following gives the correct expression for strain energy stored in a beam of length L and of uniform cross-section having moment of inertia I and subjected to constant bending moment M?

A.
ML/EI
B.
ML/2EI
C.
M²L/EI
D.
M²L/2EI

Solution:

QUESTION: 3

A square bar of side 40 mm and length 1 m is subjected to an axial load P. The same bar is then used as a cantilever beam and subjected to an end load P. The ratio of the strain energies, stored in the bar in the second case to that stored in the first case, is

A.
16
B.
400
C.
1000
D.
2500

Solution:

QUESTION: 4

A bar of length L and of uniform cross-sectional area A. and second moment of area I is subjected to a pull P. If young’s modulus of elasticity of the bar material is E, the expression for strain energy stored in the bar will be

A.
P²L/2AE
B.
PL²/2AE
C.
PL²/AE
D.
P²L/AE

Solution:

QUESTION: 5

Strain energy stored in a body of volume V subjected to uniform stress σ is

A.
σE/V
B.
σE²/V
C.
σV²/E
D.
σ²V/2E

Solution:

QUESTION: 6

A bar having length L and uniform cross-section with area A is subjected to both tensile force P and torque T. If G is the shear modulus and E is the Young’s modulus, the internal strain energy stored in the bar is

Solution:

Total strain energy,

QUESTION: 7

What is the strain energy stored in a body volume V with stress σ due to gradually applied load?

A.
σE/V
B.
σE²/V
C.
σV²/E
D.
σ²V/2E

Solution:

U = σ²V/2E

QUESTION: 8

Strain energy in a member is

A.
directly proportional to strains
B.
directly proportional to changes in strain
C.
a function of strains as well as stresses
D.
a function of loads only

Solution:

QUESTION: 9

For the state of stress of pure shear τ, the strain energy stored per unit volume in the elastic, homogeneous isotropic material having elastic constants E and v will be

A.
τ²(1 + v )/E
B.
τ²(1 + v )/2E
C.
2τ²(1 + v )/E
D.
τ²(2 + v )/2E

Solution:

QUESTION: 10

A beam of length L, simply supported at ends, carries a load W at a distance of a from one end and at a distance of b from other end such that a + b = L. If El is flexural rigidity of the beam, how much strain energy is absorbed in beam?