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StructuralEngineerLab · TOOL-005

Simply Supported Beam Calculator

Analyze a simply supported beam with point loads and full-span or partial UDLs using the verified TOOL-001 beam mechanics.

Beam & loads

Point Loads

Downward load magnitude is entered as positive.

Uniform Distributed Loads

Use start = 0 and end = L for a full-span UDL.

Ready.

Results

Calculate to view verified simply supported beam results.

Example

A 6 m simply supported beam with a 12 kN point load at midspan gives equal 6 kN reactions and a maximum sagging moment of 18 kN·m at midspan.

Assumptions

  • Simply supported beam only.
  • Point loads and uniform distributed loads only.
  • Linear superposition follows the frozen TOOL-001 mechanics.
  • E and I are required only when deflection is requested.

Warnings

  • No cantilever, multi-span, triangular, or trapezoidal load analysis.
  • No material-strength, utilization, or code-design conclusion.
  • Critical locations are a practical review set, not an exhaustive analytical root set.

Method & assumptions

TOOL-005 is a focused simply supported beam interface that reuses the verified TOOL-001 beam mechanics. Inputs are normalized to canonical SI before calculation.

  • The beam is simply supported.
  • Supported loads are point loads and uniform distributed loads only.
  • All supported loads are treated with the frozen linear TOOL-001 beam mechanics.
  • The TOOL-001 sign convention is inherited unchanged.
  • E and I are required only when deflection is requested.
  • The calculation uses one consistent canonical SI model internally.

Sign convention

  • x = 0 at the left support and x = L at the right support.
  • Downward applied load magnitude is entered as positive.
  • Upward support reaction is positive.
  • Sagging bending moment is positive.
  • Downward deflection is negative.

Critical locations

criticalLocationsM is intentionally non-exhaustive. It includes inherited TOOL-001 extrema, TOOL-005 point-load positions, UDL start/end breakpoints, and required beam boundaries. It is not every analytical root or every one-sided discontinuity limit.

Limitations

  • No cantilever or multi-span analysis.
  • No triangular or trapezoidal distributed loads.
  • No applied concentrated moments.
  • No material-strength or allowable-stress calculation.
  • No code-based design verification.
  • No utilization ratio or PASS/FAIL conclusion.
  • criticalLocationsM is non-exhaustive and should not be interpreted as every analytical root or one-sided limit.

Worked examples

Midspan point load

Inputs: L = 6 m, P = 12 kN at x = 3 m

The simply supported reactions are 6 kN left and 6 kN right, and the maximum sagging moment is 18 kN·m at midspan.

Full-span UDL

Inputs: L = 10 m, w = 4 kN/m over the full span

The total distributed load is 40 kN, the support reactions are 20 kN each, and the maximum sagging moment is 50 kN·m at midspan.

Partial UDL

Inputs: L = 10 m, w = 5 kN/m from x = 2 m to x = 6 m

The UDL resultant is 20 kN acting at x = 4 m, giving 12 kN left reaction and 8 kN right reaction.

Frequently asked questions

What beam support condition does this calculator support?

TOOL-005 supports a simply supported beam only, using the frozen TOOL-001 beam mechanics and sign convention.

What loads are supported?

The calculator supports one or more downward point loads and one or more uniform distributed loads, including full-span and partial-span UDLs.

When is beam deflection calculated?

Deflection is calculated only when both Young's modulus E and second moment of area I are supplied. Without E and I, reactions, shear, and moment remain available.

What sign convention is used?

x = 0 is the left support, downward applied load magnitude is entered as positive, upward support reaction is positive, sagging bending moment is positive, and downward deflection is negative.

Are criticalLocationsM exhaustive?

No. criticalLocationsM is a practical review set containing inherited TOOL-001 extrema plus TOOL-005 point-load positions, UDL breakpoints, and required beam boundaries. It is not every analytical root or every one-sided discontinuity limit.

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