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Short, practical guides on the beam theory behind the calculators. Every formula here is worked through with numbers you can check by hand.

Beam Sign Conventions: Stop Losing Marks

Sagging-positive, upward-positive, or the other way round? What the conventions mean, where they differ, and how to stay consistent.

Overhanging beams flip shear and moment signs past the support, lift loads off supports, and create counter-intuitive deflection shapes.

How cantilevers work, the fixed-end moment, why the support carries everything, and the formulas for the standard load cases.

Maximum deflection and slope formulas for the standard beam and load cases, with the assumptions behind each one.

Step-by-step: find support reactions for simply supported beams with point loads, uniform loads and moments — with worked examples.

Second moment of area formulas for rectangles, circles, hollows and I-sections — with the parallel axis theorem for built-up shapes.

Read shear and bending-moment diagrams without integrating: the load–shear–moment relationships, rules of thumb, and shapes to expect.

The conversion factors worth memorising, the traps that catch engineers, and a checking habit that catches the rest.

Clapeyron's theorem explained and applied to a two-span continuous beam, step by step, with the equilibrium check.

How to handle triangular and trapezoidal loads: resultants, shear and moment shapes, and the standard formulas.