Beam Stress Calculator (Bending Stress)
Estimate maximum bending stress for common beam/loading cases using:
What this beam stress calculator does
This tool calculates the maximum bending stress in a beam for several common loading cases. It is designed for quick checks during concept design, homework, estimating, and preliminary sizing. You enter the beam length, load, and section shape; the calculator then computes the peak bending moment and the corresponding stress.
The output stress is shown in MPa (N/mm²), which is convenient for most structural steel, aluminum, and timber comparison data. If you enter a material yield strength, it also reports a simple factor of safety estimate.
Equations used in the calculator
1) Maximum bending moment, M
- Simply supported beam, center point load:
M = P × L / 4 - Simply supported beam, uniform load:
M = w × L² / 8 - Cantilever beam, end point load:
M = P × L - Cantilever beam, uniform load:
M = w × L² / 2
2) Bending stress, σ
Once the maximum moment is known, the calculator applies:
where S is the section modulus. In this page, moment is converted to N·mm and section modulus is in mm³, so stress comes out as MPa.
3) Section modulus formulas used
- Rectangular section:
S = b × h² / 6 - Solid circular section:
S = π × d³ / 32 - Custom section: user-entered directly
How to use it correctly
- Select the beam/load case that matches your structure.
- Enter beam length in meters.
- Enter load as kN (point load) or kN/m (uniform load), depending on selected case.
- Choose a cross-section type and provide dimensions in millimeters.
- Optionally add yield strength to get a basic safety indicator.
- Click Calculate Stress.
Worked example
Suppose you have a simply supported beam with a center point load:
- L = 4 m
- P = 10 kN
- Rectangular section, b = 100 mm, h = 200 mm
First, moment:
M = P × L / 4 = 10 × 4 / 4 = 10 kN·m.
Convert to N·mm: 10 × 10⁶ N·mm.
Section modulus:
S = b × h² / 6 = 100 × 200² / 6 = 666,667 mm³ (approx).
Stress:
σ = M / S = 10,000,000 / 666,667 ≈ 15 MPa.
That is comfortably below many structural steel yield strengths, but design should still consider code factors and serviceability.
How to interpret results
- Maximum moment (kN·m): peak internal bending demand.
- Section modulus (mm³): geometric resistance to bending.
- Bending stress (MPa): estimated extreme-fiber stress.
- Factor of safety (if provided): yield strength / computed stress.
A higher section modulus gives lower stress for the same load and span. Increasing depth is usually the most effective way to increase section modulus for rectangular members.
Common mistakes to avoid
- Mixing units (for example entering mm as meters or vice versa).
- Using the wrong load case formula for your boundary condition.
- Ignoring self-weight for long or heavy beams.
- Assuming stress is the only criterion—deflection can govern design.
- Using yield strength alone without code-required load factors and limits.
When this simple calculator is not enough
Real beams may have multiple loads, partial distributed loads, varying cross-sections, holes, notches, local buckling, lateral-torsional buckling, and dynamic effects. In those situations, move to detailed hand analysis, structural software, or finite element analysis and follow the applicable design code.
FAQ
Does this include shear stress?
No. This page calculates bending stress only.
Can I use imperial units?
The calculator is set up for m, kN, and mm. You can still use it if you convert inputs beforehand.
Is this valid for final stamped design?
No. It is a preliminary tool for education and early design checks. Final design should be performed and reviewed by a qualified engineer using governing codes.