When the loading is distributed along the cable the cable is analyzed as.

When the loading is distributed along the cable the cable is analyzed as.

• A. Parabolic cable
• B. Catenary
• C. Projectile
• D. Rotation

Answer: (B)

A hanging flexible cable under its own weight distributes load along its length, so the horizontal component of tension stays the same along the span while the vertical component must rise to support the infinitesimal weight of each element. Balancing forces for a small element leads to a differential equation whose solution is a hyperbolic cosine curve. This shape, called a catenary, is described by y = a cosh(x/a) with a = H/w, where H is the horizontal tension at the lowest point and w is the weight per unit length. That’s why the cable is analyzed as a catenary when the loading is distributed along the length. A parabola would arise only as a simpler approximation if the loading were uniform per horizontal length rather than along the cable’s length.

A hanging flexible cable under its own weight distributes load along its length, so the horizontal component of tension stays the same along the span while the vertical component must rise to support the infinitesimal weight of each element. Balancing forces for a small element leads to a differential equation whose solution is a hyperbolic cosine curve. This shape, called a catenary, is described by y = a cosh(x/a) with a = H/w, where H is the horizontal tension at the lowest point and w is the weight per unit length. That’s why the cable is analyzed as a catenary when the loading is distributed along the length. A parabola would arise only as a simpler approximation if the loading were uniform per horizontal length rather than along the cable’s length.