Determine the cable stiffness tb2 in torsion and compare

Question

The following data on the Golden Gate Bridge was obtained from reports provided by the district engineer for the bridge:

l=4200 ft,

h=470 ft,

b=90 ft,

ω_t=28,720 lb/ft (total weight per lineal per lineal foot ,including cables)

Determine the cable stiffness Tb2 in torsion and compare with the old and new cable stiffnesses of the Tacoma Narrows Bridge found in Problem.

Problem

The new Tacoma Narrows Bridge, reopened on October 14, 1950, has the following data:

l= 2800 ft(between towers)

b=60 ft(width between cables)

k=280 ft(maximum sag of cables)

ω_t=8570 lb/lineal ft

J₀=(w_t/g)*P²(rotational mass moment of inertia)

Calculate the new cable tension, the cable torsional stiffness, the new vertical and torsion al vibration frequencies, and compare with previous values. (Assume a reasonable value for the radius of gyration p in determining the torsional mass moment of inertia.)