Beam Deflection Calculator

About the Beam Deflection Calculator

The Beam Deflection Calculator is a free, browser-based structural engineering tool that computes beam deflection, slope, support reactions, bending moment, and shear force using Euler–Bernoulli beam theory. It supports simply supported, cantilever, fixed-end, and overhanging beams under point loads, uniformly distributed loads (UDL), and applied moments.

Key Formulas Used

• Simply Supported – Center Point Load: δ_max = PL³ / (48EI)
• Simply Supported – UDL: δ_max = 5wL⁴ / (384EI)
• Cantilever – End Point Load: δ_max = PL³ / (3EI)
• Cantilever – UDL: δ_max = wL⁴ / (8EI)
• Fixed Beam – Center Point Load: δ_max = PL³ / (192EI)
• Fixed Beam – UDL: δ_max = wL⁴ / (384EI)

What is Beam Deflection?

Beam deflection is the displacement of a structural beam from its original position when subjected to external loads. Engineers must calculate deflection to ensure beams remain within acceptable serviceability limits — typically L/360 for floor beams and L/240 for roof beams per AISC and building codes. Excessive deflection can cause cracking, misalignment, and structural failure.

Supported Beam Types

• Simply Supported Beam: Pinned at both ends, free to rotate. Most common in bridges and floor systems.
• Cantilever Beam: Fixed at one end, free at the other. Used in balconies, overhangs, and brackets.
• Fixed Beam: Both ends are fully restrained. Stiffer than simply supported — deflects less under the same load.
• Overhanging Beam: Extends beyond one or both supports. Common in crane girders and continuous structures.

Material Properties

The calculator includes preset elastic moduli for common engineering materials: Steel (200 GPa), Aluminum (69 GPa), Concrete (30 GPa), and Wood (12 GPa). A custom material option lets you enter any elastic modulus in GPa or ksi for specialized applications.

Who Uses This Tool?

Mechanical engineers, civil engineers, structural engineers, architecture students, industrial fabricators, and machine designers use beam deflection calculators daily to verify structural designs, check code compliance, and estimate material requirements without specialized software.