Beam Load Calculator

How to Estimate Beam Bending Moment and Deflection

For a simply supported beam (resting on two end supports), the maximum bending moment and deflection depend on the beam's length, how the load is applied, and the beam's stiffness (its modulus of elasticity and moment of inertia). This calculator covers the two most common loading cases: a single point load at the center, and a uniformly distributed load across the full span.

Example

A 4 m simply supported beam with a 5,000 N point load at its center has a maximum bending moment of M = (5,000 × 4) ÷ 4 = 5,000 N·m. With a beam stiffness of E = 200 GPa and I = 8,000 cm⁴ (typical for a steel I-beam), the maximum deflection works out to a few millimeters at the center span.

Common Use Cases

FAQs

Is this suitable for real construction projects?

No. This calculator provides a simplified estimate for basic reference and educational purposes only, based on idealized simply-supported-beam formulas. Real structural design must account for material safety factors, load combinations, dynamic and lateral loads, connection details, and local building codes — always consult a licensed structural engineer for any real construction project.

What do E and I represent?

E is the modulus of elasticity (material stiffness, e.g. ~200 GPa for steel, ~10-13 GPa for typical structural timber), and I is the second moment of area (moment of inertia) of the beam's cross-section, which depends on its shape and dimensions. Both determine how much the beam deflects under load.

What's the difference between a point load and a uniformly distributed load?

A point load acts at a single location, like a column resting on the beam, while a uniformly distributed load (UDL) is spread evenly across the beam's full length, like the weight of a floor or roof pressing down along the span.