Cantilever Beam Calculator

How the Cantilever Beam Calculator works

The cantilever beam calculator performs structural analysis for beams fixed at one end and free at the other. It computes bending moment, shear force, and deflection at any point along the span for both point loads and uniformly distributed loads (UDL). Engineers use it for balconies, overhanging roofs, retaining wall stems, and machine brackets.

Point load vs uniformly distributed load

A point load P at the free tip produces a maximum bending moment of P × L at the fixed support and tip deflection of PL³/(3EI). A UDL of intensity w over the full span gives a fixed-end moment of wL²/2 and tip deflection of wL⁴/(8EI). Combining both load cases uses superposition — the calculator sums moments and deflections algebraically.

Material properties and moment of inertia

The deflection formula requires Young's modulus (E) and second moment of area (I). For steel E = 200 GPa, concrete E = 25–30 GPa, and timber E = 10–12 GPa. Section I values for rectangular, I-beam, or circular cross-sections are calculated automatically when you enter the cross-section dimensions alongside the span and load inputs.

Safety factor and deflection limits

IS 456 and IS 800 specify that deflection under service loads should not exceed span/250 for cantilevers, or span/350 where attached to brittle finishes. The calculator flags whether the computed deflection is within these limits and displays the maximum allowable value alongside the calculated one for a quick pass/fail assessment without manual lookup.

Bending moment diagram interpretation

The bending moment is maximum (hogging) at the fixed support and zero at the free tip. The shear force is constant under a single point load and linear under UDL. The visual BMD and SFD diagrams generated by the calculator identify critical sections that govern the design of the beam cross-section, connections, and any required reinforcement.

Frequently asked questions

What is a cantilever beam?

A cantilever beam is fixed rigidly at one end and completely free at the other. All applied loads are resisted by the fixed support, which develops both a vertical reaction force and a resisting moment. Common examples include balconies, overhanging roof eaves, diving boards, and bracket shelves attached to walls.

What is the maximum moment in a cantilever with UDL?

For a cantilever of span L carrying a uniform distributed load w (in kN/m), the maximum bending moment occurs at the fixed support and equals M = wL²/2. For example, a 3 m cantilever with a 10 kN/m UDL develops a maximum moment of 10 × 9/2 = 45 kN·m at the wall. This is where failure is most likely to initiate.

What is the tip deflection formula for a cantilever?

For a uniform distributed load (UDL) of w over the full span L, the maximum deflection at the free tip is δ_max = wL⁴ / (8EI). For a point load P applied at the free end, δ_max = PL³ / (3EI). Both formulas assume small deflections, linear elastic material behaviour, and a prismatic (constant cross-section) beam.