How to use the simple beam moment and stress calculator
A simple beam is pinned at one end and on a roller at the other, the baseline case behind most floor joists, lintels, and short-span girders. Enter the span, the load type and magnitude, the rectangular section size, and the allowable bending stress to get the maximum moment, the maximum shear, the actual bending stress, and the required section modulus.
Under a uniform load the maximum moment occurs at midspan as M = wL²/8, with maximum shear V = wL/2 at the supports. Under a point load at midspan the values become M = PL/4 and V = P/2. For the same total load, the point load produces twice the moment, so the load pattern matters as much as its size.
Bending stress is s = M/S, and a rectangular section has S = bh²/6. The required section modulus is simply the maximum moment divided by the allowable stress, which makes it easy to scan an AISC shape table and pick the lightest member that clears the number.
Bending alone does not finish a design. Shear stress, deflection serviceability, lateral torsional buckling, bearing at supports, and connection detailing all need checking, and long spans are usually governed by deflection rather than stress. Confirm the final member with a licensed structural engineer before fabrication.
Frequently asked questions
For the same total load, the center point load is worse. Uniform load gives wL squared over 8 while a center point load gives PL over 4, which is twice the moment.
It is the maximum moment divided by the allowable bending stress. Pick any shape from the AISC manual whose section modulus exceeds that number and the member passes the first bending check.
No. Shear stress, deflection serviceability, lateral torsional buckling, bearing, and connection design all matter. On long spans deflection usually controls the member size, not bending.