beam-statics-calc

Closed-form solutions for statically determinate beams — the simply supported and cantilever cases you find in the back of any strength-of-materials textbook (Gere & Goodno, Roark). No solver, no linear algebra, no dependencies; just the algebraic formulas evaluated for you.

Use consistent units. SI in → SI out. Downward loads are positive.

What's covered

Simply supported

• support reactions for a point load anywhere on the span
• max moment & deflection, central point load (PL/4, PL³/48EI)
• max moment & deflection, uniform load (wL²/8, 5wL⁴/384EI)

Cantilever

• tip deflection & fixed-end moment, end point load (PL³/3EI, PL)
• tip deflection, uniform load (wL⁴/8EI)

Section properties & stress

• rectangleI(b, h) → bh³/12
• circleI(d) → πd⁴/64
• bendingStress(M, I, c) → Mc/I

Example

import {
  simpleCenterMaxDeflection,
  bendingStress,
  rectangleI,
} from 'beam-statics-calc';

// 1 kN at the centre of a 2 m steel beam, I = 8e-6 m^4
const delta = simpleCenterMaxDeflection(1000, 2, 200e9, 8e-6);
// -> ~1.04e-5 m

const I = rectangleI(0.1, 0.2);        // 100 x 200 mm section
const sigma = bendingStress(1200, I, 0.1);

Scope

Determinate beams only. Continuous beams, frames and anything requiring compatibility equations are out of scope on purpose — reach for a proper FE package for those.

License

BSD-3-Clause. See LICENSE.