Cantilever Beam Bending: Material Deflection & Stress Lab (2D)

Material

Material Steel

Load & Geometry

Tip load F 200 N

Beam length L 1.00 m

Section width b 40 mm

Section height h 20 mm

Live Readout

Tip deflection δ

0 mm

Second moment I

0 mm⁴

Max bending stress

0 MPa

Yield strength

0 MPa

Safety factor

0×

Status

Safe

How it works

A cantilever beam of length L is fixed at one end and loaded by a downward force F at the free tip. Euler-Bernoulli beam theory gives the tip deflection in closed form:

I  = b·h³ / 12                 (rectangular section)
δ  = F·L³ / (3·E·I)            (tip deflection)
M(x) = F·(L − x)                (bending moment, x from wall)
σ(x) = M(x)·(h/2) / I           (max fiber stress at x)
σmax = 6·F·L / (b·h²)           (at the fixed wall, x=0)

E is the material's Young's modulus and I is the second moment of area of the rectangular cross-section (width b, height h). The top fiber is in tension and the bottom fiber in compression for a downward tip load; stress is largest at the wall (x=0, where the bending moment M is largest) and falls linearly to zero at the free tip. If σmax exceeds the material's yield strength, the beam is flagged as yielding/failing — real engineering designs keep a safety factor (yield ÷ σmax) well above 1.

Color gradient — red (tension) on top, blue (compression) on bottom, intensity scaled to local stress ÷ yield strength.
Bend shape — traces the real deflection curve y(x) = F/(6EI)·(3Lx² − x³), not a cosmetic bow.
Failure flag — appears once σmax ≥ yield strength for the selected material.

⚠ YIELD / FAILURE

Compression (bottom fiber) Tension (top fiber) Neutral axis