A symmetric building has a roof sloping upward at 38.0 above the horizontal on e

Question

A symmetric building has a roof sloping upward at 38.0 above the horizontal on each side. (A). If each side of the uniform roof weighs 1.10×104 , find the horizontal force that this roof exerts atthe top of the wall, which tends to push out the walls. (B). Which type of building would be more in danger ofcollapsing: one with tall walls or one with short walls?Explain. (C).(Not necessary but would help, lifesaver) As in part A,tall walls are in danger of collapsing from the weight of the roof.This problem plagued the ancient builders of large structures. Asolution used in the great Gothic cathedrals during the 1200s wasthe flying buttress, a stone support running between the walls andthe ground that helped to hold in the walls. A Gothic church has auniform roof weighing a total of 20000 and rising at 40 above the horizontal at each wall. The walls are 40 tall, and a flying buttress meets each wall 10 below the base of the roof. What horizontal forcemust this flying buttress apply to the wall?

Explanation / Answer

a)  If F is the horizontal force,
F x L x sin 38 = 1.1 x 104 x [ L/2] cos 38
F = 1.1 x 104 /(2 x tan 38)

   = 7039.68 N

b) It's given and intuitive that tall walls are more subject to falling due to a longer lever arm and, consequently, a greater net torque, driving the system out of equilibrium.

c) horizontal force, Fh = (20000 / 4 ) *(1/tan 40)

                                 = 5958.76 N = 5959 N

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