Chapters

This is a static copy of the chapter for search engines. The interactive version has animated figures, check questions, and buttons that load the example into the calculator.

Open the interactive version →

1. 01 From a straight beam to a bent one

   A bent beam — a lomený nosník in Czech, a knekket bjelke in Norwegian — is a bar whose axis is not one straight line but a chain of straight pieces jo…

2. 02 Geometry, developed length & sign conventions

   Before anything can be computed, the shape has to be described unambiguously.…

3. 03 Supports, reactions & determinacy

   A bent bar in space has six degrees of freedom per point: three translations (u x , u y , u z ) and three rotations (θ x , θ y , θ z ).…

4. 04 What happens at a corner

   This is the heart of the subject. Take a rigid corner with no load applied exactly on it, cut the bar immediately before and immediately after, and wr…

5. 05 Reading the diagrams

   FrameLab gives you two views of the same numbers, and both are worth using. 1 — Diagrams drawn on the structure Each value is plotted perpendicular to…

6. 06 Frames: thrust and frame action

   Close a bent bar down onto two supports and you get a frame . What makes a frame more than the sum of its members is that the corners are rigid: the b…

7. 07 Out of plane: bending becomes torsion

   Everything so far kept the loads inside the plane of the frame. Now push the bar sideways, out of that plane.…

8. 08 Stresses & design checks

   Once the internal actions are known, the stress at any cross-section follows from the ordinary formulae — you just have more of them to add up than in…

9. 09 Deflections of bent bars by hand

   You will not integrate w″ = M/EI twice for a bent bar — the axis changes direction, so there is no single w(x) to integrate.…

10. 10 How the calculator works

    FrameLab is a small displacement-method (stiffness-method) finite-element solver written from scratch in plain JavaScript.…