Formula and input notes
Midspan deflection = 5wL⁴ ÷ (384EI) for a simply supported beam under full-span uniform load
| Input | Practical note |
|---|---|
| Beam span | Use the clear or effective simply supported span intended by the analysis model; support and bearing geometry can change that definition. |
| Uniform load | Enter a line load distributed over the full span in pounds per foot, including self-weight if the load case requires it. |
| Modulus of elasticity | Enter the elastic modulus for the actual material and units shown; this stiffness term appears in the denominator of the deflection equation. |
| Moment of inertia | Use the section's moment of inertia about the bending axis. Rotating an asymmetric member can change this value substantially. |
Worked beam deflection example
Beam Deflection Calculator example: The code converts 10.3 ft to 123.6 in and 40 lb/ft to 3.3333 lb/in. Then 5wL⁴ ÷ 384EI = 0.084 in; the displayed L/360 comparison is 0.343 in.
Compare deflection with the displayed span reference
Compare the elastic estimate with the serviceability criterion specified for the member and load combination, not with Span/360 by default in every situation.
Support, loading, and stiffness details outside the model
Support fixity, shear deformation, creep, load duration, composite action, holes, notches, point loads, partial loads, and actual section properties alter deflection.
Questions specific to this calculation
Why do modulus of elasticity and moment of inertia both matter?
Elastic modulus describes material stiffness, while moment of inertia describes section stiffness about the bending axis. Deflection is inversely proportional to their product, EI.
Which beam case is represented by 5wL⁴/(384EI)?
The displayed equation is for a simply supported beam under a uniform load over the full span. Cantilevers, continuous spans, partial loads, point loads, shear deformation, and composite action require different models.