Science & Engineering

Beam deflection.

Estimate the elastic centre deflection of a simply supported beam under one point load at mid-span.

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Beam deflection formula

For a simply supported beam with a central point load, maximum deflection is δ = PL³ ÷ (48EI). The same model gives equal support reactions of P ÷ 2 and maximum bending moment of PL ÷ 4. The calculation converts the entered kN, GPa, and mm⁴ values into consistent SI units first.

Reference: Missouri S&T beam formula sheet and Neutron STEM Lab standard cases.

Structural note

This is a preliminary Euler–Bernoulli estimate for a prismatic, linear-elastic beam. It does not check strength, buckling, shear deformation, connections, or code limits.