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
$$\sigma = \dfrac{P}{A}$$

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

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

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

Possible combinations are as follows:

  1.   axial and shear
  2.   axial and flexural
  3.   axial and torsional
  4.   torsional and flexural
  5.   torsional and shear
  6.   flexural and shear
  7.   axial, torsional, and flexural
  8.   axial, torsional, and shear
  9.   axial, flexural, and shear
  10.   torsional, flexural, and shear
  11.   axial, torsional, shear, and flexural