Numerical - Strain energy, given shear stress & length of cube

Q.  What is the strain energy stored in a cube of 50 mm, when it is subjected to shear stress of 200 Mpa. (G = 100 Gpa)   
- Published on 23 Sep 15

a. 25 Nm
b. 75 Nm
c. 125 Nm
d. 150 Nm

ANSWER: 25 Nm

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    Discussion

  • Sravanthi   -Posted on 24 Nov 15
    - Strain energy is defined as the energy stored by a system which undergoes deformation under the application of load.

    Given: Side of cube = 50 mm, shear stress = 200 Mpa

    Formula: 1) Strain energy in a block = (τ2 V) / ( 2 G)

    G is the modulus of rigidity, τ is the shear stress, V is the volume

    2) Strain energy in a solid shaft = (τ2 V) / ( 4 G)

    Solution:

    Volume of cube = 503 = 125000 mm3

    Strain energy = (τ2 V) / ( 4 G)

    Substituting the given values, we get

    = (2002 x 125000) / (4 x 100 x 103)

    = 25000 N.m

    = 250 N.mm

    Strain energy stored in a cube is 250 N.mm

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