Question

A 17.0-m-high and 11.0-m-long wall and its bracing under construction are shown in the figure. Calculate the force, in newtons, exerted by each of the 10 braces if a strong wind exerts a horizontal force of 655 N on each square meter of the wall. Assume that the net force from the wind acts at a height halfway up the wall and that all braces exert equal forces parallel to their lengths. Neglect the thickness of the wall.

Answer 1

The force, in newtons, exerted by each of the 10 braces is 2.135 x 10⁴ N.

What is force?

The force is defined as the shear stress or pressure applied per unit area.

F = P/A

Given is a 17.0-m-high and 11.0-m-long wall and its bracing under construction are shown in the figure(attached). The force is exerted by each of the 10 braces, if a strong wind exerts a horizontal force of 655 N on each square meter of the wall. Assume that the net force from the wind acts at a height halfway up the wall and that all braces exert equal forces parallel to their lengths.

Considering the pivot at the base of wall.

From the equilibrium of forces, we have

r₁ x Fwind = r₁ x Fbsinθ

Put the values, we get

Fb = Fwind /10sin35°.............(1)

The wind force is also given by

Fwind = Horizontal force or pressure x Area

Fwind = F/A x hw

           =655 x 17 x 11

F wind = 122,485 N

From equation (1), we have

Fb = Fwind /10sin35°

Fb =  122,485 /10sin35°

Fb = 21,354.6080 N

0r Fb = 2.135 x 10⁴ N

Thus, the force exerted on each of the 10 brace is 2.135 x 10⁴ N.

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