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StructuralEngineerLab · TOOL-006

Cantilever Beam Calculator

Fixed support at the left, free end at the right. Analyze supported point loads and full/partial UDLs using the verified TOOL-001 cantilever mechanics.

Support model: Fixed left · Free right · x = 0 at fixed support · x = L at free end

Beam & loads

Point Loads

Downward applied load is entered as a positive magnitude.

Uniform Distributed Loads

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

Ready.

Results

Calculate to view verified cantilever results.

Example

A 4 m fixed-left cantilever with a 10 kN downward point load at the free end gives a +10 kN fixed vertical reaction and a +40 kN·m fixed-end reaction moment. The internal fixed-end bending moment is −40 kN·m.

Assumptions

  • Fixed support at the left and free end at the right.
  • Point loads and uniform distributed loads only.
  • Linear mechanics and sign convention are inherited from frozen TOOL-001.
  • E and I are required only when deflection is requested.
  • Fixed-end zero slope is inherited but not separately output.

Warnings

  • No simply supported or multi-span analysis.
  • No triangular or trapezoidal loads.
  • No material-strength, utilization, or code-design conclusion.
  • No PASS/FAIL conclusion.
  • Critical locations are a practical review set, not an exhaustive analytical root set.

Method & assumptions

TOOL-006 is a focused fixed-left, free-right cantilever interface that reuses the verified TOOL-001 cantilever mechanics. Inputs are normalized to canonical SI before calculation.

  • The beam is fixed at the left and free at the right.
  • Supported loads are point loads and uniform distributed loads only.
  • The frozen TOOL-001 cantilever mechanics and sign convention are inherited unchanged.
  • E and I are required only when deflection is requested.
  • Fixed-End Zero Slope is an inherited boundary condition and is not added as a TOOL-006 output field.
  • Inputs are normalized into one canonical SI engineering model.

TOOL-001 sign convention

  • x = 0 at the fixed left support and x = L at the free right end.
  • Downward applied load magnitude is entered as positive.
  • Fixed vertical reaction upward is positive.
  • Fixed-End Reaction Moment is positive for the frozen representative downward-load case.
  • Internal Fixed-End Moment is negative for the frozen representative downward-load case.
  • Sagging internal bending moment is positive.
  • Downward deflection is negative.

Fixed-End Zero Slope

Fixed-End Zero Slope is inherited from the TOOL-001 cantilever_fixed_left boundary condition. TOOL-006 does not add slope as a separate output field.

Critical locations

criticalLocationsM is intentionally non-exhaustive. It contains inherited TOOL-001 extrema, TOOL-006 point-load positions, UDL start/end breakpoints, and beam boundaries. It is not every analytical root or every one-sided discontinuity limit.

Limitations

  • No simply supported beam mode.
  • No multi-span or continuous-beam 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 is not every analytical root or one-sided limit.

Worked examples

Free-end point load

Inputs: L = 4 m, P = 10 kN downward at x = 4 m

The fixed vertical reaction is +10 kN, the fixed-end reaction moment is +40 kN·m, and the internal fixed-end bending moment is −40 kN·m under the frozen TOOL-001 sign convention.

Full-span UDL

Inputs: L = 5 m, w = 4 kN/m over x = 0 to 5 m

The total distributed load is 20 kN acting at x = 2.5 m, giving a 20 kN fixed vertical reaction magnitude and a 50 kN·m fixed-end reaction-moment magnitude.

Partial UDL

Inputs: L = 8 m, w = 3 kN/m from x = 2 m to x = 6 m

The UDL resultant is 12 kN at x = 4 m, giving a 12 kN fixed vertical reaction magnitude and a 48 kN·m fixed-end reaction-moment magnitude.

Frequently asked questions

What support condition does this cantilever calculator use?

TOOL-006 uses a fixed support at the left and a free end at the right, inheriting the frozen TOOL-001 cantilever_fixed_left mechanics.

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 deflection calculated?

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

What sign convention is used?

x = 0 is the fixed left support and x = L is the free right end. Upward fixed reaction is positive, the frozen representative fixed-end reaction moment is positive, internal fixed-end bending moment is negative, sagging internal moment is positive, and downward deflection is negative.

Does TOOL-006 output beam slope?

No. Fixed-End Zero Slope is an inherited TOOL-001 cantilever boundary condition, but TOOL-006 does not add slope as a separate output field.

Are criticalLocationsM exhaustive?

No. criticalLocationsM is a practical review set containing inherited TOOL-001 extrema plus TOOL-006 point-load positions, UDL breakpoints, and beam boundaries. It is not every analytical root or every one-sided discontinuity limit.

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