Free calculator

Beam Stress & Deflection

Analyse a simply supported or cantilever beam under a point load, a uniform load, or both. Enter the span, loads, and cross-section — the calculator returns reactions, maximum bending moment, maximum bending and shear stress, and maximum deflection using the standard handbook formulas.

σ_max = M_maxc / I τ_max = 3V_max/(2A) (rectangular) τ_max = 4V_max/(3A) (circular)

M_max	simply supported: PL/4 + wL²/8 at midspan · cantilever: PL + wL²/2 at the wall
δ_max	simply supported: PL³/(48EI) + 5wL⁴/(384EI) · cantilever: PL³/(3EI) + wL⁴/(8EI)
I, c, A	rectangle: I = bd³/12, c = d/2 · circle: I = πd⁴/64, c = d/2

Assumptions: the point load P acts at midspan (simply supported) or at the free end (cantilever); the uniform load w covers the full span; the beam stays elastic and deflections are small.

Unit system Beam type Span L (m) Point load P (kN, 0 if none) Uniform load w (kN/m, 0 if none) Modulus E (GPa) Cross-section Width b (mm) Depth d (mm) Diameter (mm)

For study and checking only. These calculators run entirely in your browser — nothing is sent anywhere. They are meant to verify your hand calculations while you study; on the exam you will work by hand with the NCEES reference handbook. See the theory behind every number on the Mechanics of Materials page.