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Beam and frame playground

Supports, span and loads on a steel beam or portal frame, with live bending moment, shear and deflection.

Parameters

6
m
4
m
10
kN/m
0
kN
0.5
× L
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Results

Largest bending moment 45 kN·m Reference wL²/8 = 45 kN·m · difference 2.2 × 10−14 %
Largest shear 30 kN
Largest deflection 10.098 mm Reference 5wL⁴/384EI = 10.098 mm · difference 2.2 × 10−14 %

Certified (linear solve)· relative error bound ≤ 5.8 × 10−15

Bending moment (sagging positive) (kN·m)

kN·m010203040500246x (m)

Shear (kN)

kN−40−20020400246x (m)

Deflection (upward positive) (mm)

mm−12.5−10.0−7.5−5.0−2.50.02.50246x (m)

A steel member (E = 200 GPa, I = 8356 cm⁴, an IPE 300) carries a uniform load on the beam and a point load: downward on the beam, horizontal at the top of the portal. When a beam carries a single load, the result is shown beside its closed form.

Verified by: Tools: simply supported beam, checked against closed forms

A teaching example, not a design check. SI units: m, kN, MPa. Published by Ergodic Group.