KEVOS® MAKEOS · Strength
Beam Cases: Off-Centre, Fixed and Propped
What reactions, moment, stress and deflection does this beam case give?
Reactions, maximum bending moment, bending stress and deflection for an off-centre point load, cantilever with uniform load, fixed–fixed beams and a propped cantilever.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Beam case | choice | The support and load arrangement. |
| Load (point load, or total uniform load) | N | Point load, or the total of a uniformly distributed load (w × L). |
| Span | mm | Distance between supports, or the cantilever length. |
| Load position from left support (off-centre case) | mm | Distance of the point load from the left support (off-centre case only). |
| Elastic modulus | GPa | Elastic modulus from the material data sheet or an approved materials database (steel is typically about 200 GPa). |
| Second moment of area | mm⁴ | Second moment of area about the bending axis, from a section table or the section properties calculator. |
| Distance to extreme fibre | mm | Distance from the neutral axis to the outermost fibre (half the depth for symmetrical sections). |
| Allowable bending stress | MPa | Allowable bending stress from your design code or company standard. |
Method and formulas
- Off-centre: R₁ = Pb ÷ L, M = Pab ÷ L; δmax = Pb(L² − b²)^1.5 ÷ (9√3 EIL) for the shorter segment b.
- Cantilever UDL: M = WL ÷ 2, δ = WL³ ÷ 8EI. Fixed–fixed point: M = PL ÷ 8, δ = PL³ ÷ 192EI. Fixed–fixed UDL: M = WL ÷ 12, δ = WL³ ÷ 384EI.
- Propped UDL: R = 5W/8 and 3W/8, M = WL ÷ 8 at the fixed end, δmax at 0.4215L from the support.
- Stress σ = M c ÷ I.
- Example: 5000 N at 600 mm on a 2000 mm span gives M = 2,100 N·m, σ = 13.125 MPa and δ = 0.41766 mm.
Limitations
- Linear elastic, small-deflection beams of constant section; self-weight is not added automatically.
- Lateral-torsional buckling, shear deflection and local bearing are not checked.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check frames, rails and support beams
- Compare support conditions
- Size a section for stress and stiffness
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Reactions
- Maximum bending moment
- Bending stress and its ratio to the allowable
- Maximum deflection and span-to-deflection ratio
Interpreting the result
- Typical deflection limits are span/250 to span/1000 depending on use; take yours from the design brief.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 257–277. Topic reference; no source tables or recommended settings are reproduced.
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Open the Beam Cases: Off-Centre, Fixed and Propped calculator
