Substituting fy = y f I c, defined above, yields F = a y f I c. Each partial force F Is the product of stress fy and the partial area a on which It acts, F = a fy. The Internal resisting moment Is the sum of all partial forces F rotating around the neutral axis with a lever arm of length y to balance the external moment. To satisfy equilibrium, the beam requires an Internal resisting moment that is equal and oppooi'e to the external bending moment. The bending stress fy at any distance y from the neutral axis Is found, considering tfimila' triangles, ncme!y fy relates to y as f relates to c f Is the maximum bending stress ai top cr bottom and c the distance from the Neutral Axis, namely f<, / y -11 c. Thus stress varies linearly over the depth of the beam and Is zero at the neutral axis (NA). Assuming stress varies linearly with strain, stress distribution over the beam depth Is proportional to strain deformation. As Illustrated by the hatched square, the top shortens and the bottom elongates, causing compressive stress on the top and tensile stress on the bottom. Referring to the diagram, a beam subject to positive bending assumes a concave curvature (circular under pure bending). It Is derived here for a rectangular beam but Is valid for any shape.Ģ Beam subject to bending with hatched square deformedģ Stress diagram of deformed beam subject to bending The flexure formula gives the Internal bending stress caused by an external moment on a beam or other bending member of homogeneous material.