KEVOS® MAKEOS · Engineering
Beam Stress and Deflection
What stress and deflection does this ideal beam model predict?
Screen a prismatic beam under one defined load case using supplied section properties and elastic modulus.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Load case | choice | Match the actual support and load arrangement to one of these ideal cases. |
| Total applied load | N | Point force, or TOTAL uniformly distributed load over the entire span. |
| Span | mm | Support span, or fixed face to load for a cantilever. |
| Young’s modulus | MPa | Verified elastic modulus at the operating temperature. |
| Second moment of area | mm⁴ | Section property about the actual bending axis; do not use polar moment. |
| Extreme fibre distance | mm | Distance from the neutral axis to the most distant fibre. |
Method and formulas
- Simply supported central point: Mmax = F × L / 4; δmax = F × L³ / (48 × E × I).
- Cantilever tip point: Mmax = F × L; δmax = F × L³ / (3 × E × I).
- Simply supported uniform TOTAL load: Mmax = F × L / 8; δmax = 5 × F × L³ / (384 × E × I).
- Bending stress = Mmax × fibre distance / I. Example central point case: 1000 N, 1000 mm, E = 200000 MPa, I = 1000000 mm⁴, c = 50 mm gives 12.5 MPa and 0.104167 mm.
Limitations
- Linear elastic, small-deflection Euler–Bernoulli model; shear deflection and support flexibility excluded.
- No strength rating, buckling, fatigue, connection, impact or code-compliance assessment.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- beam bending
- stiffness
- deflection
Who it is for
- Mechanical designers
- Fixture designers
What you get
- Maximum bending moment
- Maximum nominal bending stress
- Maximum deflection
- Deflection / span
Interpreting the result
- Compare against project-specific allowables and verify that the ideal supports match the real load path.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 232–244, 256–273. Topic reference; no source tables or recommended settings are reproduced.
- MIT OpenCourseWare, David Roylance: Beam Displacements — https://ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/resources/mit3_11f99_bdisp/
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