KEVOS® MAKEOS · Strength
Beam Cases: Fixed, Guided, Propped and Partial Loads
What moments and deflection does this less common beam case give?
Reactions, maximum bending moment, stress and maximum deflection for a fixed–fixed beam with an off-centre load, beams fixed at one end and guided at the other, a propped cantilever with a point load anywhere, two symmetrical loads, and a uniform load on part of a span.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Beam case | choice | Support and load arrangement. |
| Load (each point load, or total uniform load) | N | Each point load, or the total of a uniform load. |
| Span | mm | Span between supports. |
| Distance a | mm | Load position as described for the case. |
| Loaded length c (partial load) | mm | Length of a part-span uniform load. |
| 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
- Fixed–fixed, load at a: M_A = −Pab²/L², M_B = −Pa²b/L², M_load = 2Pa²b²/L³; δ_load = Pa³b³ ÷ 3EIL³.
- Fixed–guided, end load: M = PL/2 at both ends, δ = PL³/12EI. Uniform: M = WL/3 fixed, WL/6 guided, δ = WL³/24EI.
- Propped, load at a from fixed end: R_B = Pa²(3L − a)/2L³; deflection from cantilever superposition.
- Two symmetrical loads: M = Pa, δ_centre = Pa(3L² − 4a²)/24EI. Part-span load: moment from statics, deflection by numerical integration of M/EI.
- Example: 5000 N at 600 mm on a fixed–fixed 2000 mm beam gives an end moment of 1.47 kN·m.
Limitations
- Linear elastic, constant section, small deflections.
- Fixed ends are assumed perfectly rigid; real connections rotate and reduce end moments.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check beams with built-in or guided ends
- Check a simply supported beam with two loads or a part-length load
- Fill gaps in standard beam tables
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Reactions and maximum bending moment
- Bending stress
- Maximum deflection
Interpreting the result
- If the real end fixity is uncertain, check both the fixed and the simply supported cases.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 257–270. Topic reference; no source tables or recommended settings are reproduced.
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Open the Beam Cases: Fixed, Guided, Propped and Partial Loads calculator
