KEVOS® MAKEOS · Strength
Continuous Beam over Two Spans
What reactions, moments and deflections does this beam continuous over three supports have?
Reactions, the support moment (three-moment equation), maximum span moments, stress and deflections of a beam continuous over two equal or unequal spans with uniform or point loads.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Loading | choice | Uniform loads or one point load per span. |
| Span 1 | mm | Length of the first span. |
| Span 2 | mm | Length of the second span. |
| Load on span 1 (N/m, or N for a point load) | N/m or N | Uniform load on span 1 in N per metre, or the point load in N. |
| Load on span 2 (N/m, or N for a point load) | N/m or N | Uniform load on span 2, or its point load. |
| Point load position in span 1 (from end support) | mm | Point load distance from the end support in span 1. |
| Point load position in span 2 (from centre support) | mm | Point load distance from the centre support in span 2. |
| 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
- Three-moment equation with pinned ends: M_B = −(T₁ + T₂) ÷ 2(L₁ + L₂), with T = wL³/4 for a uniform load and P a(L² − a²)/L for a point load (a measured from the outer support).
- Reactions by statics: R_A = (simple-span reaction) + M_B ÷ L₁, similarly R_C; R_B = total load − R_A − R_C.
- Deflection of each span by superposition of the simple-span load and the end moment; maxima found by sampling.
- Example: two equal 3000 mm spans at 2000 N/m give a centre reaction of 7,500 N and a support moment of -2.25 kN·m.
Limitations
- Supports at the same level and rigid; constant section.
- Pattern loading (one span loaded) can govern; check it by setting one load to zero.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check purlins, rails and shafts over three supports
- Find the centre support load
- Compare continuous and simply supported spans
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- End and centre reactions
- Centre support moment
- Maximum span moments and stress
- Maximum deflection in each span
Interpreting the result
- The centre support carries about 5/4 of a span’s uniform load for equal spans.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 264–267. Topic reference; no source tables or recommended settings are reproduced.
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