Beam deflection

Enter section dimensions in the bending direction

For a rectangular section, depth in the bending direction has a much larger effect on stiffness than width. Check the section orientation and elastic modulus. Where the tool asks for a total distributed load, enter the force over the whole span, not force per unit length. Add self-weight to the load where relevant.

Separate stiffness from strength

A beam can remain below an entered stress allowance but deflect too far for its purpose. This linear, small-deflection model does not check buckling, connection behavior, local failure, or every shear-deformation effect. Use the result for the represented support and load case only.

Reading the effect of span and section depth

For a simply supported beam with a center point load, the small-deflection expression contains span cubed divided by elastic modulus and second moment of area. Doubling span with the same point load and section increases modeled deflection eightfold. This comparison does not apply unchanged when a load is specified per unit length, because doubling the span then also doubles total force.

For a rectangular section, second moment of area is width times depth cubed divided by twelve. Rotating a rectangular beam changes which dimension is depth and can greatly alter stiffness without changing mass. Check the load direction before entering width and height. The stress and deflection results answer different questions, and both depend on the chosen support case. A real connection that partially restrains rotation may not match either ideal support exactly. Consider support movement, load distribution, self-weight, and the actual structural requirements before relying on the model for a built beam or shelf.

Formula

Euler–Bernoulli closed forms for prismatic beams. Stress = M/Z; deflection scales with load × span³/(EI).