Beam Bending Stress Calculator

This beam bending stress calculator works out the maximum bending or flexural stress in a loaded beam using the classic flexure formula from engineering mechanics. The stress, written as sigma, equals the bending moment M multiplied by the distance c from the neutral axis to the point of interest, divided by the second moment of area I of the cross section, written as sigma equals M times c over I. You enter the bending moment in newton metres, the distance c in metres, usually the distance to the outer fibre where stress is greatest, and the second moment of area in metres to the fourth power, and the tool returns the bending stress in pascals and megapascals. Structural, mechanical and civil engineers, along with engineering students, use this to size beams, check that a member stays below the yield strength of its material, and understand how shape drives stiffness. The formula shows why depth matters so much, since the second moment of area grows rapidly with depth, which is why I beams place most material far from the neutral axis. To get a sound result, work in consistent SI units, taking care with the second moment of area because it carries units of length to the fourth power and small errors there change the answer a lot. Use the distance to the extreme fibre for the maximum stress, since that is where failure begins. Finally, compare your calculated stress against the allowable stress for your material with a sensible safety factor, because this formula assumes elastic behaviour, a straight beam and pure bending, and it does not by itself account for shear, buckling or stress concentrations that a full design check would include.

Sigma = M c / I. Use newton metres, metres and metres to the fourth power. Assumes elastic pure bending.