A prismatic circular bar is situated in the x-y-z coordinate system with the length L measured in the x direction. We measure the shear stress at a radius ρ from the center and the shear modulus of elasticity is G. The polar moment of inertia of the bar is J. What is the strain energy for the member when subjected to torsion T ?
1
\(\int_L \frac{T^2}{2GJ}[\iint\rho^2dy \ dz]dx\)
2
\(\iiint\frac{T^2}{2GJ}dxdydz\)
3
\(\iiint\frac{T^2}{2GJ^2}dxdydz\)
4
\(\int_L\frac{T^2}{2GJ^2}[\iint\rho^2dy \ dz]dx\)