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 joined at rigid corners. Bend a beam once and you get an L-bracket. Bend it twice and you get a portal frame or a cranked shaft. Bend it four times and you have the frame of a hall, a machine guard, or a robot arm.
Everything you know about straight beams still applies inside each segment: the same Euler–Bernoulli assumptions, the same σ = M·c/I, the same EI·w″ = M. What changes is what happens at the corner, and that one change propagates through the whole solution.
Three things that a kink changes
- Axial force appears. In a straight beam loaded transversely, N = 0. In a bent beam the transverse force on one member is an axial force on the next. Columns of frames are compression members that also bend.
- Moments no longer come back to zero at a free-ish end. A moment generated on one leg is handed over to the next leg completely — the corner transmits it. That is why the base of an L-bracket carries the tip force times the whole lever arm.
- Loads perpendicular to the plane produce torsion. Bend a bar and push it sideways out of its plane: the bending of one leg becomes the twisting of the next. A straight beam cannot do this. Chapter 7 is entirely about it.
What this tool solves
FrameLab treats the bar as a plane frame — the axis lies in the x–y plane — but allows loads in any direction, including out of the plane. Because the geometry is planar, the problem splits neatly into two independent halves:
| In-plane problem | Out-of-plane problem | |
|---|---|---|
| Loads | Fx, Fy, moments about z | Fz, moments about x and y |
| Unknowns per node | u, v, θz | w, θx, θy |
| Internal actions | N, V, M | Vz, M⊥, T (torsion) |
| Section property used | A and I in the plane | I out of plane and Jt |
You can use only the left column and never think about torsion, or you can switch on an out-of-plane force and watch the right column come alive.
The classic L-bracket: a column 1.5 m tall, an arm 1.0 m long, a 5 kN load pushing down on the tip. Look at the axial force in the column and at the constant moment along it.