Mechanics of Materials

Principal Stress

The largest and smallest normal stresses at a point, which act on planes carrying no shear.

At any point in a stressed body, the normal and shear stresses depend on the orientation of the plane considered. Two perpendicular orientations carry no shear at all, and the normal stresses on them are the principal stresses: the maximum and minimum normal stress at that point.

In plane stress they are found from Mohr’s circle as the centre plus or minus the radius, σ₁,₂ = (σₓ + σ_y)/2 ± √[((σₓ − σ_y)/2)² + τₓᵧ²]. The radius itself is the maximum in-plane shear stress, acting on planes 45° from the principal planes.

How much of the FE Civil exam is Mechanics of Materials?