When Joseph Strauss designed the piers that serve as the foundations for the tow

Question

When Joseph Strauss designed the piers that serve as the foundations for the towers of the Golden Gate Bridge, he determined the forces that the piers would have to support. To perform a simplified version of his analysis we start by drawing the free-body diagram of the north tower as shown. Assume that the tension acting on the main cable as it passes over the tower is T1 253.7 MN and T2-265.4 MN, the tower weight is 196 MN -68.8", and -63.0. Using this nformation find the loads (reactions) acting on the north tower at its base at B. 27 m T2 tower 227 m Step-by-step solution

Explanation / Answer

from the FBD
T1 = 253.7 *10^6 N
T2 = 265.4*10^6 N
weight of tower W = 196*10^6 N
alpha = 68.8 deg
beta = 63 deg

now using force balance along the three directions
Rx = 0 N
Ry = 2(T1sin(alpha) - T2sin(beta)) = 2(253.7sin(68.8) - 265.4sin(63))*10^6 = 114833.6975 N = 0.1148336975 MN
Rz = W + 2(T1cos(alpha) + T2sin(alpha)) = 196*10^6 + 2(253.7cos(68.8) + 265.4cos(63))*10^6 = 196*10^6 + 424466464.121 N = 620.466464121 MN

From symmetry Mz = 0
Mx = 2(T1sin(alpha) - T2sin(beta))*227 = 0.1148336975*227*10^6 = 26.0672 *10^6 Nm
My = 0

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