# Combined Stresses

## Problem 903 | Combined Axial and Bending

**Problem 903**

A cast iron link is 40 mm wide by 200 mm high by 500 mm long. The allowable stresses are 40 MPa in tension and 80 MPa in compression. Compute the largest compressive load P that can be applied to the ends of the link along a longitudinal axis that is located 150 mm above the bottom of the link.

## 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

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

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