Drawing No. EH–CS–001 // Civil & Structural Engineering
Beam & Column Calculator
Reviewed September 2026
Two checks that decide most member sizes. Work out reactions, shear, bending moment, stress and deflection for a beam under a given support and load arrangement — then, for a member in compression, the Euler critical load at which it would buckle.
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
Column buckling
A member in compression can fail by buckling long before the material yields. The Euler critical load is the upper bound for an ideal, perfectly straight, elastically loaded column.
Column and end conditions
Buckling results
Euler assumes a straight, concentrically loaded, elastic column. Real columns carry initial crookedness, eccentricity and residual stress, and stocky columns yield before they buckle — design codes cap the Euler curve accordingly. Treat Pcr as an upper bound, not a capacity.
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.
Match the real restraint, not the drawing convention. A beam sitting on two walls is close to simply supported; one cast into a concrete core at both ends approaches fixed. The difference is large — a fixed-ended beam under uniform load deflects about a fifth as much as a simply supported one of the same span.
For ordinary spans in steel and timber, the section that satisfies the stress check is often too flexible to be serviceable. Deflection limits like span/360 tend to control before bending stress reaches allowable. Check both and size on whichever is worse.
K converts a real column's end restraint into the length of an equivalent pinned-pinned column. Pinned at both ends is 1.0, fixed at both ends 0.5, fixed-pinned about 0.7, and a cantilever fixed at one end with the other free is 2.0. Because K enters the formula squared, getting it wrong is expensive.
The smaller one. A column buckles about its weak axis unless it is braced against that direction, so for an I-section in an unbraced condition it is the minor-axis value that matters, not the major-axis figure used for bending.
No — it is an upper bound for an ideal column. Real members carry initial crookedness, load eccentricity and residual stress, all of which reduce capacity, and stocky columns yield before they ever reach the Euler load. Design codes replace the Euler curve with a capped column curve for exactly that reason. Use this to understand sensitivity to length and end conditions, then size to the code.
Only if you include it in the applied load. The calculator works from the loads you enter, so add the member's own weight as a distributed load where it is significant relative to the imposed load.
Yes for the elastic calculations, provided you enter the right modulus — about 70 GPa for aluminium and 8-14 GPa for structural timber. But material-specific effects such as timber's load-duration and moisture factors, or aluminium's behaviour in heat-affected zones at welds, are not modelled here.