Stress Theory

When is σ=F/A Valid?

The equation σ=F/A is valid only if the stress is uniformly distributed over the cross-section of the bar. This condition is realized if the axial force F acts through the centroid of the cross-sectional area. Uniform stress exists throughout the length of the bar except near the ends. The stress distribution at the end of a bar depends upon how the load F is transmitted to the bar. If the load is distributed uniformly over the end, the stress pattern at the end is the same as everywhere else. However, it is more likely that the load is transmitted through a pin or a bolt, producing high localized stresses called stress concentrations. As a practical rule, the formula σ=F/A may be used with good accuracy at any point within a prismatic bar that is at least as far away from the stress concentration as the largest lateral dimension of the bar. Of course, even when the stress is not uniformly distributed, the equation σ=F/A may still be useful because it gives the average normal stress on the

cross section.