Beam Deflection Calculator computes beam deflection, bending moment, and shear force using Euler-Bernoulli beam theory. Use the formula delta = (q x L^3) / (48 x E x I) where q = distributed load, L = span length, E = modulus of elasticity, I = moment of inertia. This calculator implements AISC / Roark's formulas.
Beam Deflection Calculator
Calculate maximum deflection and bending stress for simply supported, cantilever, fixed-fixed, and fixed-pinned beams under common load configurations. Based on Roark's Formulas for Stress and Strain.
Domain of Validity
Valid for slender beams (length-to-depth ratio > 10) with linear elastic material behavior. Assumes small deflections and plane sections remain plane. Not valid for composite beams or significant shear deformation.
Worked Example
Simply supported steel beam, 4 m span, UDL 10 kN/m, E = 200 GPa, I = 5 x 10^-5 m^4: delta = (10 x 4^3) / (48 x 200e9 x 5e-5) = 0.00133 m = 1.33 mm.
Verification
Formulas verified against AISC Steel Construction Manual and Roark's Formulas (8th ed.). Last verified: August 2026.
Accuracy and Uncertainty
Results accurate to plus/minus 2% for standard beam configurations. Accuracy depends on correct material property inputs.
Frequently Asked Questions
How does the beam configuration affect deflection?
The beam configuration defines boundary conditions. Simply supported beams are free to rotate at the ends. Cantilever beams are fixed at one end and free at the other, resulting in higher deflections.
What is the flexure formula for bending stress?
The maximum normal bending stress is calculated using sigma = M_max x c / I, where M_max = maximum bending moment, c = distance to neutral axis, I = moment of inertia.
What is Euler-Bernoulli beam theory?
Euler-Bernoulli beam theory assumes plane sections remain plane after bending and neglects shear deformation. It is accurate for slender beams where length-to-depth ratio exceeds 10.
When should I use Roark's formulas?
Roark's formulas provide closed-form solutions for stresses and deflections in beams with complex loading and support conditions. Use them for non-standard beam configurations not covered by basic theory.
What is the maximum deflection limit for beams?
Common deflection limits: L/360 for live loads, L/240 for total loads, L/180 for deflection-sensitive finishes. Check local building codes for specific requirements.