Beam shear, bending moment & deflection (single span)

Advanced calculator for single-span simply-supported and cantilever beams: reactions, SFD/BMD and qualitative deflection. Statically determinate only.

1. Geometry & loading

Units

Beam type

Load case

Span / length L Use consistent length units.

2. Section & material (optional)

Allowable bending stress σ_allow Z_req = |M_max| / σ_allow.

Section modulus Z_provided Used to check bending utilisation (Z_provided/Z_req).

Elastic modulus E Force/length² (e.g. kN/m², kip/ft²).

Second moment of area I Same length units as L (e.g. m⁴, ft⁴). δ will be in same length units.

Section helper (optional)

Section type Dimensions in same length units as L.

3. Results summary

Left reaction R_A

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Right reaction R_B / end reaction

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Fixed‑end moment M_fixed (cantilever)

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Max shear |V|_max

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Max bending moment |M|_max

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Location of M_max

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Max deflection δ_max

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Required Z_req

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Bending utilisation

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Select beam type & load case, enter inputs, then click Calculate.

4. Load & support sketch

Loading diagram Shows supports and applied loads for the selected case.

5. Diagrams

Shear force diagram (SFD) Shear V(x)

Bending moment diagram (BMD) Bending moment M(x)

Deflection diagram (qualitative) If E & I are provided, shape is proportional to δ(x); otherwise scaled from M(x).

6. Export & downloads

Assumptions: prismatic, linearly elastic, statically determinate only. Sagging moments positive for simply-supported beams; cantilever fixed-end moments hogging (negative). Deflection from numerical integration of M/EI if E and I are given, otherwise a qualitative shape.