Cantilever Beam Calculator

Analyze cantilever beams fixed at one end and free at the other. Calculate deflection, bending moment, shear force, and slope for point loads and distributed loads.

MAX DEFLECTION (at free end)
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Max Bending Moment
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Max Shear Force
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Slope at Free End
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Reaction at Support
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What is a Cantilever Beam?

A cantilever beam is a structural element fixed (or clamped) at one end and free at the other. The fixed end resists both vertical forces and moments, making the cantilever a statically determinate structure. Cantilevers are widely used in balconies, overhangs, airplane wings, diving boards, and sign structures.

Cantilever beams experience maximum bending moment and shear force at the fixed support. The maximum deflection occurs at the free end. These characteristics make the cantilever one of the most important beam configurations in engineering analysis.

Cantilever Beam Formulas

Point Load at End: δ = PL³ / (3EI)
UDL: δ = wL&sup4; / (8EI)
Point Load at End: M_max = P × L (at fixed end)
UDL: M_max = wL² / 2 (at fixed end)

Cantilever vs Simply Supported

PropertyCantileverSimply Supported
Point Load DeflectionPL³/(3EI)PL³/(48EI)
UDL DeflectionwL&sup4;/(8EI)5wL&sup4;/(384EI)
Support ConditionsFixed + FreePin + Roller
Max Moment LocationFixed endMidspan
Deflection LocationFree endMidspan

Frequently Asked Questions

Why does a cantilever deflect more than a simply supported beam?

A cantilever with a point load at the free end deflects PL^3/(3EI), which is 16 times more than a simply supported beam with the same load at midspan (PL^3/(48EI)). This is because the cantilever has only one support point and cannot distribute the load between two supports.

Where does maximum stress occur in a cantilever?

Maximum bending stress occurs at the fixed end where the bending moment is greatest. The stress is highest at the top and bottom fibers of the cross-section, furthest from the neutral axis. This is why cantilever connections must be carefully designed.

What is the moment connection at the fixed end?

The fixed end of a cantilever must resist both vertical shear force and bending moment. In steel construction, this requires welded or bolted moment connections. In concrete, sufficient reinforcement and anchorage must be provided at the support.