Solid Deformation · free game
Bridge Load Tester
Find the thinnest cable that carries the convoy without breaking and without letting the deck reach the limit line.
- LOAD on the worst hanger
- 41.2 kN
- AREA A = πd²/4
- 314.2 mm²
- Mild steel
- E 210 GPa · σᵧ 250 MPa · L₀ 6 m
Steel, six-metre hangers, thirty millimetres of room. Nothing but strength can stop you here: σ = F/A has to stay under σᵧ.
Span 01 ready. This cable would peak at 225 of 250 MPa and 6.4 of 30 mm. Drag the lorry to feel it, then run the convoy.
How the physics works
- Simple definition
- A cable stretches in proportion to the stress in it: stress is the load divided by the cross-sectional area, and strain is that stress divided by the Young modulus.
- Example
- Doubling the diameter quadruples the area, so the same lorry produces one quarter of the stress and one quarter of the stretch.
One lorry is ever on the deck at a time, and the hanger it is standing next to carries all of its weight plus half the deck. That is the peak force in the run, and it never depends on the cable you chose.
Area is what carries load, and it grows as the square of the diameter. Since 1 N/mm² is exactly 1 MPa, newtons over square millimetres give megapascals straight off.
Young modulus turns stress into strain, and strain is a fraction of the original length. A 14 m hanger stretches more than twice as far as a 6 m one at the same stress — which is why span 02 is a stiffness problem.
Strength wants A ≥ F/σlimit; stiffness wants A ≥ FL₀/(E·clearance). The wider of the two wins, and on this span it is strength. Score is how close you got to it.
Honest limits: g = 9.81 m s⁻², textbook material data rather than a batch certificate, both hangers treated as identical, and the vertical stretch drawn to an exaggerated scale so millimetres are visible. Yield is treated as failure because a permanently stretched deck is a condemned deck. Cable self-weight, temperature and joint detail are outside the model.