Cantilever Beam Bending 2D — Deflection & Stress Side View

Load

Force F 10 kN

Load position along beam 6.0 m

Geometry

Beam length L 6.0 m

Cross-section height h 0.45 m

Cross-section width b 0.35 m

Material

Stiffness E 70 GPa

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within limits

Tip deflection δ

—

Max stress σ

—

Moment at wall M

—

Moment of inertia I

—

How it works

A cantilever is fixed rigidly at one end and free at the other. A point load F applied a distance a from the wall bends the beam according to Euler-Bernoulli beam theory. For load at the very tip (a = L):

δ = F·L³ / (3·E·I)        (tip deflection)
M = F·L                    (moment at the wall)
σ = M·c / I                (max bending stress, c = h/2)
I = b·h³ / 12               (second moment of area, rectangle)

For a load applied partway along the beam (distance a from the wall), the deflection at the tip becomes δ = F·a²·(3L−a) / (6·E·I) and the moment at the wall is M = F·a. Switching to a distributed load spreads the same total force w·L evenly along the span, which produces a gentler curve and a lower peak stress than the same total force concentrated at one point.

Stiffer materials (higher E) deflect less under the same load but experience the same peak stress — stress depends only on the force and the cross-section's shape, not on stiffness. That's why a steel beam bends far less than an identical wooden one carrying the same load, even though both see the same stress at the wall.

Tension (top fiber) Compression (bottom fiber)