Alarge building shaped like a box is 40 m high with a face that is 6565 m wide. a strong wind blows directly at the face of the building, exerting a pressure of 170 n/m2 at the ground and increasing with height according to p(y)=170+2y, where y is the height above the ground. calculate the total force on the building, which is a measure of the resistance that must be included in the design of the building.

Explanation:

Given:

Pressure on the building = 170 N/m²

Pressure function P(y) = 170 + 2y

Consider a small height of the building as dy

the small force (dF) exerted on the height dy will be given as

dF = P(y)×(Area of the building face)

or

dF = (170 + 2y)(6565)dy

or

dF = 170×6565×dy + 2y×6565×dy

dF = 1116050dy + 13130ydy

integerating the function for the whole height of 40 m

; Total force exerted on the face of the building

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