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Mechanical CalculatorBending Stress & Deflection
Simply Supported Beam — Bending Stress & Deflection
Compute bending moment, section modulus, bending stress, and deflection for a simply supported beam with a central point load.
Inputs
Results
Max bending moment Mmax0.250 kN·m
Area moment of inertia I1.707e+3 mm⁴
Section modulus W4.267e+2 mm³
Bending stress σ586 MPa
Max deflection δ15.81 mm
Safety factor S0.41
Formulas assume a simply supported beam with a mid-span point load. Verify against applicable standards for critical designs.
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Formula
Mmax = F·L/4 | σ = M/W | I_rect = b·h^3/12 | I_circle = π·d^4/64 | δ = F·L^3/(48·E·I)
Assumptions
- Simply supported beam with a central point load.
- Linear elastic behavior and small deflection assumption.
References
- Roark's Formulas for Stress and Strain
- EN 1993-1-1 (Eurocode 3)
Design notes
S ≈ 0.41— Unsafe — yielding expected.
- Computed bending stress is about 586 MPa. Safety factor is based on yield strength.
- Deflection ratio is approximately L/δ ≈ 32. This is quite flexible (below L/150) and may cause alignment issues.
- If the design sees fatigue or dynamic loads, static safety alone is insufficient; check fatigue limits and stress concentrations.
- Connections, weld roots, and section changes can cause local stress peaks; this check uses nominal section values.
Bending Moment Diagram (schematic)
The diagram shows moment rising to Mmax ≈ 0.250 kN·m at midspan and dropping to zero at the supports.
Standard Documentation
Bending & DeflectionScope: What does this tool calculate?
Bending & Deflection performs the core engineering calculation for this tool type and presents results in a traceable format.
Assumptions and Units
- SI units are the baseline; input unit consistency must be verified by the user.
- The calculation path is deterministic (same inputs = same outputs).
- If default material/environment values are used, replace them with project-specific values.
Limits / Boundaries
- This tool is intended for preliminary sizing and technical checks, not final design approval.
- When inputs are outside expected ranges, validate input quality before interpreting outputs.
Reference Standard
- ISO / DIN / VDI references and common engineering handbooks
Validation Example
Validation example
| Input | Expected Output |
|---|---|
| Input set: Unit-consistent project values | Expected output: Tool result is in the same order as standard references |
Note: In real projects, run at least one manual check or reference-table comparison.
Version and Update
- Version
- v0.1.0
- Last updated
- 2026-03-04
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