KEVOS® MAKEOS · Strength
Overhanging Beam
What reactions, moments and deflections does this beam with overhanging ends have?
Reactions, maximum positive and negative bending moments, stress and deflections of a beam on two supports with one or two overhangs, under end point loads or a uniform load.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Arrangement | choice | Overhang arrangement and load type. |
| Span between supports | mm | Distance between the two supports. |
| Overhang length | mm | Length of each overhang beyond a support. |
| Point load (each), or uniform load per metre | N or N/m | Point load at each overhang tip (N), or uniform load intensity w (N per metre run) for the uniform cases. |
| Elastic modulus | GPa | Elastic modulus from the material data sheet (steel is typically about 200 GPa). |
| Second moment of area | mm⁴ | Second moment of area of the section about the bending axis. |
| Distance to extreme fibre | mm | Neutral axis to extreme fibre. |
| Allowable bending stress | MPa | Allowable bending stress from your design code. |
Method and formulas
- One overhang, tip load P: R₂ = P(L + a)/L, R₁ = −Pa/L; M = −Pa at the support; tip δ = Pa²(L + a) ÷ 3EI.
- Two overhangs, tip loads P: R = P each; M = −Pa between supports; tip δ = Pa²(3L + 2a) ÷ 6EI; mid-span rises Pa L² ÷ 8EI.
- Equal overhangs, uniform w: R = w(L + 2a)/2; M_support = −wa²/2; M_centre = wL²/8 − wa²/2; δ_centre = wL²(5L² − 24a²) ÷ 384EI; tip δ = wa(3a³ + 6a²L − L³) ÷ 24EI.
- One overhang, uniform w: R₁ = w(L² − a²)/2L; M_support = −wa²/2; M_span max = R₁²/2w; tip δ = wa(4a²L − L³ + 3a³) ÷ 24EI.
- Example: the default beam has a support moment of -1.28 kN·m and a mid-span moment of 3.22 kN·m.
Limitations
- Linear elastic, constant section; self-weight is part of the uniform load only if included.
- Deflection signs: positive downward; negative values are upward.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check platform, crane-runway and machine-bed beams with overhangs
- Choose support positions to balance moments
- Find tip deflection of an overhang
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Reactions
- Maximum negative (support) and positive (span) moments
- Stress
- Tip and mid-span deflections
Interpreting the result
- Overhangs of about 0.35 × span with uniform load roughly balance support and span moments.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 257–262. Topic reference; no source tables or recommended settings are reproduced.
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