Determine the structural integrity of your design. This tool calculates the Max Deflection (δ) and Bending Stress (σ) based on the beam’s material, cross-section, and loading conditions.

1. Beam Configuration

Load Case

Length (L)

Load (P)

2. Cross Section & Material

Shape Profile

Width (b)

Height (h)

Young’s Modulus (E)

MPa

Diagram is representative only

Analysis Results

Max Deflection (δ)

—

Span / —

Max Bending Stress (σ)

—

Section Properties

Moment of Inertia (I) — mm⁴

Neutral Axis Dist (c) — mm

Calculated Moment (M) — N·mm

Formulas & Engineering Context

Bending Stress (σ)

σ = (M · c) / I

M = Bending Moment
c = Dist to Neutral Axis
I = Moment of Inertia

Deflection (δ)

Fn(Load, Length, E, I)

Depends on support type (see below). E = Young’s Modulus.

Simply Supported vs. Cantilever Beams

Simply Supported: A beam resting on two supports at its ends. Common in bridges and floor joists. The maximum deflection occurs at the center.
Cantilever: A beam fixed at one end and free at the other. Common in balconies and crane arms. Deflection is significantly higher for the same load compared to supported beams.

How is Moment of Inertia (I) calculated?

The Moment of Inertia measures a beam’s resistance to bending based on its shape.

Rectangle: I = (b × h³) / 12
Solid Circle: I = (π × D⁴) / 64
Hollow Tube: I = π × (D⁴ - d⁴) / 64

A higher “I” value means less deflection for the same load.

Common Deflection Formulas

SS Center Load: δ = (P × L³) / (48 × E × I)
SS Uniform Load: δ = (5 × w × L⁴) / (384 × E × I)
Cantilever End Load: δ = (P × L³) / (3 × E × I)