Drawing No. EH–CS–002 // Civil & Structural Engineering
Beam Deflection & Stress Calculator
Reviewed August 2026
Calculate elastic reactions, shear force, bending moment, bending stress and deflection for common beam/load combinations.
Calculation workflow
Inputs are converted internally to SI, the engineering model is solved, and results are converted back to the selected unit system.
Beam and load
Cross-section
Results
Shear-force diagram
Bending-moment diagram
Elastic deflection curve
Worked example
A 4 m simply supported steel beam with a 10 kN center load and 100 × 200 mm rectangular section.
I = bh³/12 = 6.667×10⁻⁵ m⁴.
Mmax = PL/4 = 10 kN·m, giving about 15 MPa bending stress.
δmax = PL³/(48EI) ≈ 1.0 mm for E = 200 GPa.
Background
Elastic beam behavior is controlled by loading, support conditions, material stiffness and section geometry.
EI d²y/dx² = M(x)
The calculator constructs the bending-moment function along the beam and numerically integrates curvature. Simply supported boundary conditions enforce y(0)=y(L)=0; cantilever conditions enforce y(0)=0 and slope(0)=0.
σmax = Mmax c / I
This is the elastic normal stress at the extreme fiber. Local stress concentrations and lateral-torsional buckling are outside the scope of this calculator.
Frequently asked questions
Practical questions about assumptions, limits and interpretation.
The calculator uses small-deflection Euler–Bernoulli beam theory with linear-elastic material behavior and constant cross-section properties.
The built-in section library covers rectangular, solid circular, hollow circular and symmetric I-sections. It does not currently model unsymmetric bending, tapered members or composite sections.
The reported normal stress is the maximum elastic bending stress, M c / I. The tool also reports peak shear force, but it does not calculate detailed cross-sectional shear stress distributions.
Connections, local flexibility, shear deformation, residual stress, nonlinear behavior, holes, welds, temperature and imperfect supports can all change real behavior.