Internal strain energy in torsion
Under torsion the torques make the work owing to the section twist to which they are applied to be. This work is used to store the strain energy which is numerically equal to the internal force work. The work of the statically applied torque is equal to half the product of the finite moment and the finite angle of the twist:
The internal force work of the negative sign is numerically equal to the strain energy
where T is the twisting moment, But according to the formula (4.17) we have
Hence
Integrating the expression of the elemental work along the bar length
To calculate the strain energy which is equal to the internal force work of the same magnitude but the inverse sign we have
|
(4.16)
(4.17)
is the twist angle of the element which has the length dz.
(4.18)
we receive the total internal force work:
.
(4.19)
