Ideal Cantilever Beam Deflection Calculator

How the ideal cantilever beam deflection calculator works

The only modeled load/support case is a perfectly fixed cantilever with one concentrated end load and constant E and I. Ideal tip deflection = P × L³ ÷ (3EI). Convert kN to N, GPa to Pa and cm⁴ to m⁴ by multiplying inertia by 1e−8. Output deflection converts metres to millimetres. Fixed-end moment magnitude is P × L.

Small-deformation linear-elastic Euler-Bernoulli assumptions apply. Real support flexibility, shear deformation, varying section, buckling, lateral stability and other loads are omitted. The tool does not select a safe span, section, load, allowable deflection, connection or code-compliant structure. All properties and the idealization must be reviewed independently.

Quantities use the stated units and finite bounded inputs. Whole purchases round up under the documented model; cost components round half-up to cents before totals are summed. Undefined ratios stay unavailable. π and logarithms use normal numeric precision. Display rounding does not alter the entered assumptions.

Worked example

An illustrative 10 kN end load on a 3 m ideal cantilever with E = 200 GPa and I = 8,000 cm⁴ gives 5.625 mm tip deflection and 30 kN·m fixed-end moment. Doubling the end load gives 11.25 mm.

Sources and assumptions

The source material explains the underlying calculation or pricing structure. Entered prices, costs, schedules and scenario choices are your assumptions; this tool does not obtain supplier quotes or predict actual results.

• MIT OCW Unified Engineering materials/structures Pset12 solutions