Q: How is horizontal tension H calculated?

For the catenary, a is found by solving a(cosh(L/2a)−1) = d iteratively; then H = w·a. For the parabolic approximation, H = wL²/(8d) is a direct closed-form result. Both require span L (m), sag d (m), and weight per unit length w (N/m).

Q: Where does maximum tension occur in a cable?

Maximum tension occurs at the support points. For catenary: T_max = H + w·d. For the parabolic approximation: T_max = H·√(1+(wL/2H)²). The longer the span and the shallower the sag, the larger the horizontal thrust H and the closer T_max approaches H.

Q: What engineering applications is this tool useful for?

Suspension bridge main cables and hangers, overhead transmission line sag calculations, curtain-wall support cables, edge cables in membrane roof structures, and ropeway load analysis. Input cross-section area A and Young's modulus E to also obtain stress σ=T_max/A and elastic elongation ΔL=(T_max·S)/(A·E).

Question 1

What is the difference between catenary and parabolic cable approximation?

Accepted Answer

A catenary (y = a·cosh(x/a)) is the exact shape of a cable loaded only by its own weight. The parabolic approximation (y = 4d(x/L)(1−x/L)) assumes small sag and is accurate within ~0.1% for sag ratios d/L < 0.05. For large sag ratios or high-accuracy applications such as suspension bridge main cables, use catenary.

Question 2

How is horizontal tension H calculated?

Accepted Answer

For the catenary, a is found by solving a(cosh(L/2a)−1) = d iteratively; then H = w·a. For the parabolic approximation, H = wL²/(8d) is a direct closed-form result. Both require span L (m), sag d (m), and weight per unit length w (N/m).

Question 3

Where does maximum tension occur in a cable?

Accepted Answer

Maximum tension occurs at the support points. For catenary: T_max = H + w·d. For the parabolic approximation: T_max = H·√(1+(wL/2H)²). The longer the span and the shallower the sag, the larger the horizontal thrust H and the closer T_max approaches H.

Question 4

What engineering applications is this tool useful for?

Accepted Answer

Suspension bridge main cables and hangers, overhead transmission line sag calculations, curtain-wall support cables, edge cables in membrane roof structures, and ropeway load analysis. Input cross-section area A and Young's modulus E to also obtain stress σ=T_max/A and elastic elongation ΔL=(T_max·S)/(A·E).

Catenary Cable Tension Calculator

Theory