Cable Tension from Sag
Cable Tension from Sag
A cable under a uniform load takes a parabolic shape; its tension follows from the span, load and how much it sags.
The horizontal tension is T = w·L²/(8·d). where w is the load per unit length, L the span and d the mid-span sag.
Inputs
w := 2 kN/m=2000 kg/s^2
L := 40 m=40 m
d := 2 m=2 m
Apply the parabolic-cable tension formula.
T := w·L^2/(8·d)=200000 N
Results
Less sag means much higher tension — a nearly straight cable pulls enormously hard. Designers trade sag against tension and clearance.
Assumptions & limitations
- Uniform load per horizontal length (parabolic cable).
- Small sag-to-span ratio.
- Flexible, inextensible cable.