Combined Stresses

Most often, a structural member is subjected to different types of stresses that acts simultaneously. Such stresses are axial, shear, flexure, and torsion. Superposition method is used to determine the combined effect of two or more stresses acting over the cross-section of the member.
 

Axial stress
$$\sigma = \pm\dfrac{P}{A}$$
 

Shear stress
$$\tau = \dfrac{VQ}{Ib}$$
 

Flexural stress
$$\sigma_f = \dfrac{Mc}{I}$$
 

Torsional stress
$$\tau = \dfrac{T\rho}{J}$$