Mechanics

Beam Bending from Section Properties

Enter values in the stated units. Example inputs are provided to help you explore the method.

Results

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Uniform homogeneous linear-elastic slender beam, constant EI, small deflection and principal-axis bending. Loads act in the bending plane without torsion. I is the area second moment about that axis, not polar or mass inertia; c is the farthest material fibre from the neutral axis.
S = I/c; stress magnitude = Mmax/S. Use the larger extreme distance for an asymmetric section. The tool cannot validate a supplied I and c against a real section. Shear force is reported; no shape-independent shear stress is inferred.
Simply supported: Rleft = Rright = (P + wL)/2; Mmax = PL/4 + wL²/8; δmax = PL³/(48EI) + 5wL⁴/(384EI), both at midspan.
Cantilever: Rleft = P + wL, Rright = 0; reaction moment magnitude = PL + wL²/2; δmax = PL³/(3EI) + wL⁴/(8EI). Moment is largest at the root, deflection at the tip.
Include self-weight in w if relevant. No shear deformation, torsion, yielding, fatigue, local/lateral buckling, connection or design-code assessment. Transferred geometry does not establish a material grade, load or safe capacity.