CGCADGuide.tools
Free Structural Design Tool

Steel Beam Deflection & Stress Calculator

Instantly calculate section modulus, moment of inertia, maximum bending stress, and deflection for I-beams, box sections, pipe, and solid rectangular beams.

Beam Bending & Load Curve

Exaggerated deflection line based on Euler-Bernoulli beam theory

P = 10 kNL = 4 m
Structural Assessment: SAFE (structural safety)

Bending stress (56.0 MPa) and deflection (3.73 mm) are within the material limits for Structural Steel (Structural steel).

Beam Profile Cross-Section

Real-time scaled cross section visualizer with key variables

B = 100 mmH = 200 mm
Cross Section Properties:
Section Area (A):2704.0 mm²
Moment of Inertia (Ix):1.7869e+7 mm⁴
Section Modulus (Wx):1.7869e+5 mm³

Beam Setup Parameters

Select support structure and profile geometries

3. Cross Section Dimensions (mm)

Physical Loads & Materials

Define structural parameters and forces

Bending deflection & stress report
Max Moment
10.000kN·m
Max Deflection
3.73mm
Bending Stress
56.0MPa
Safety Factor
4.47
Standard building code deflection limit for this configuration is L/240 = 16.67 mm.

Beam Deflection Engineering Guidelines

1. Bending Stresses & Moment of Inertia

Moment of Inertia (Ix) measures a profile's resistance to bending based purely on its geometric shape. An I-beam concentrates material in the top and bottom flanges away from the neutral axis, maximizing Ix while minimizing weight.

Maximum Bending Stress (σmax) occurs at the extreme outer fibers of the beam (furthest from the neutral axis). It is calculated as:

σ_max = M_max / W_x

Where Mmax is the peak bending moment and Wx is the elastic section modulus (Wx = Ix / ymax). To prevent permanent structural deformation, this bending stress must not exceed the material's yield strength.

2. Standard Deflection Serviceability Limits

In structural engineering, beam deflection is governed by serviceability limits to prevent unsightly sagging, cracking of plaster, or vibration. Deflection limits are defined as a fraction of the span length L:

  • L/360: Strictest limit. Commonly used for floor joists supporting plaster ceilings to prevent cracking under live loads.
  • L/240: Standard limit for roof beams, rafters, and members supporting non-plaster ceilings under combined loads.
  • L/180: Frequently applied to cantilever beams or steel roof purlins where sagging has fewer cosmetic impacts.

If your beam deflection exceeds these thresholds, the structure may be safe from structural failure but will violate building codes or trigger serviceability issues.

AISC Steel Selection Tip: When designing structural members using AISC standards, beam self-weight should be added to the uniformly distributed dead load. The self-weight can be computed by multiplying the cross-sectional area (A) by the density of steel (7850 kg/m³ or 0.00000785 g/mm³).

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