Engineering lab · Interactive tool
Beam Deflection + Stress Calculator
Screen a solid rectangular beam under a cantilever end load, simply supported center load, or simply supported uniform line load.
Elastic beam screening / rectangular section
Live calculationI = b·h³ / 12Beam results updated. Maximum deflection 0.9662 millimeters. Maximum stress 20 megapascals. Yield factor of safety 13.8.
Model, assumptions, and a reproducible reference case
I = bh³/12; δ = PL³/(3EI); σ = PLh/(2I)
Reference inputs
Cantilever, 100 N end load, length 500 mm, width 20 mm, bending height 10 mm, E = 160 GPa, yield strength 250 MPa.
- Expected elastic tip deflection
- 15.625 mm
- Calculated by this tool
- 15.625 mm
The corresponding bending stress is 150 MPa. This deliberately flexible example checks arithmetic; its 3.125% span deflection triggers review of the small-deflection assumption.
Check the material basis, load cases, and applicable design criteria before using a result. Warning thresholds are prompts for review, not acceptance criteria.
Use first-order response to guide the next model
The calculator applies closed-form Euler–Bernoulli beam equations in an N-mm-MPa unit system. It reports the extreme-fiber bending stress, maximum elastic deflection, maximum moment, and arithmetic yield factor of safety.
A result that appears acceptable is not proof that the real part is acceptable. Connections, cutouts, load introduction, stability, geometry changes, and multidirectional loading often control the design.
Escalate beyond this model when
- Deflection is not small relative to the span or section depth
- The section changes, contains openings, or is not rectangular
- Shear deformation may be important
- Buckling or lateral-torsional stability can control
- Loads are dynamic, cyclic, thermal, or multidirectional
- Supports and joints are not reasonably idealized
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