Beam Bending Stress Calculator
Calculate the maximum bending stress in a simply supported beam under point or distributed loads.
Essential for structural engineering.
Beam Bending Theory When a beam is loaded, it bends. The material on the outside of the bend is in tension, and the material on the inside is in compression. The maximum stress occurs at the surface farthest from the neutral axis.
The Bending Stress Formula sigma = M * y / I. Where sigma is the bending stress (Pa or psi), M is the bending moment (Nm or lbft), y is the distance from the neutral axis to the extreme fiber (half the beam depth for symmetric sections), and I is the moment of inertia of the cross-section (m^4 or in^4).
Simply Supported Beam A simply supported beam rests on two supports at its ends. Under a concentrated load P at the center: Maximum moment M = PL/4 (at midspan). Under a uniform distributed load w (per unit length): Maximum moment M = wL^2/8 (at midspan). Where L is the beam span.
Moment of Inertia for Common Sections Rectangular: I = bh^3/12 (b = width, h = height). Circular: I = pid^4/64 (d = diameter). I-beam: I = (bH^3 - (b-t_w)(H-2*t_f)^3) / 12 (flanges + web).
Safety Factors In structural design, the calculated stress must be well below the material’s yield strength. Typical safety factors: steel structures 1.5-2.0, wood structures 2.0-3.0, concrete 2.5-3.5. Building codes specify the required factors for different applications.
Units In SI: stress in Pascals (Pa) or Megapascals (MPa), force in Newtons, distance in meters. In US customary: stress in psi, force in pounds, distance in inches.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.