Beams & Columns — Bending & Buckling

Bending stress — the load fibre furthest out feels

continues from lesson 1 — values defined earlier in the course stay live here

ELI5: when a beam bends, the top squashes and the bottom stretches — and the outermost fibres feel the most. Bending stress σ = M·c / I, where M is the bending moment and c is the distance to that outer fibre. It's what actually breaks a beam.

P_{load} := 10 kN

= 10 kN a central point load

L_{span} := 3 m

= 3 m the span between supports

M_{max} = \frac{P_{load} \cdot L_{span}}{4}

= 7.5 kN m peak moment for a central load = 7.5 kN·m

c_{dist} = \frac{h_{sec}}{2}

= 50 mm distance from centre to outer fibre

\sigma _{bend} := M_{max} * c_{dist} / I_{rect} in MPa

= 90 MPa bending stress = 90 MPa

✓ pass

abs(\sigma _{bend} - 90 MPa) < 0.5 MPa

the stress the beam's edge must survive

A simply supported beam under a central load — supports react, the middle bends the most.

x * (3 - x)

bending moment along a 3 m beam under uniform load — zero at the supports, peak in the middle