Strain Energy Stored By A Beam Due To A Uniform Bending Moment
For this case, strain energy stored by the beam due to bending = Wi = ∫(M²/2EI).ds = M2l/2EI.
If the beam section is rectangular, with section width b and depth d and the beam is subjected to a uniform bending moment M. Now, M = (1/6)⨯fbd²
Where f is the extreme bending stress for each section.
And the moment of inertia for a rectangular beam section is = I = bd³/12. So, Wi = (given below).
So, The strain energy stored per unit volume of the beam due to a uniform bending moment is = f²/6E.