Beam Deflection Studio

Beam & Loading

input

Beam type

Uniformly distributed load over the full span.

Span length L

m — distance between supports (cantilever: fixed → free)

Material · elastic modulus E

GPa

Second moment of area I

≈ 8.36×10⁷ mm⁴

Point load P · position a

kN (↓ positive)

m from left

Distributed load w

kN/m — over full span (↓ positive)

Examples

Max deflection δ

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Max bending moment

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Max shear force

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Span / deflection

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Beam · Supports · Loads

schematic

beam applied load support reaction

Shear Force Diagram

V(x) · kN

Bending Moment Diagram

M(x) · kN·m · +sagging

Deflected Shape

×1

undeformed deflected (exaggerated) max deflection

Governing relations & sign convention Euler–Bernoulli: EI·v'''' = w(x), V = dM/dx, M = −EI·v''. x measured from the left end; downward load & downward deflection positive; +M = sagging (tension on the bottom fibre). Maxima are taken from the analytic curves sampled along the span; combined loading is exact superposition of the point and uniform cases. Closed-form maxima used as checks SS point (central) δ = PL³/48EI · SS uniform δ = 5wL⁴/384EI, M = wL²/8 · cantilever tip load δ = PL³/3EI · cantilever uniform δ = wL⁴/8EI, M = wL²/2. Assumptions Prismatic, linear-elastic, homogeneous member · small deflections · shear deformation neglected · loads in the plane of bending. Move the cursor across any diagram to read V, M and δ at that section.