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6 June, 08:51

A large building shaped like a box is 60 m high with a face that is 75 m wide. A strong wind blows directly at the face of the building, exerting a pressure of 160 Upper N divided by m squared at the ground and increasing with height according to P (y) equals160plus 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.

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  1. 6 June, 11:17
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    The total force on the building, which is a measure of the resistance that must be included in the design of the building is 990 KN

    Explanation:

    Total force = total pressure * Area of that face of the building

    Taking an elemental part of the wall

    Force on that part, dF = Pressure of that part * Area on that part = (160 + 2y) (75dy)

    dF = 12000 dy + 150y dy

    dF = (12000 + 150y) dy

    Integrating both sides

    ∫dF = ∫ (12000 + 150y) dy

    Integrating the left hand side from 0 to F and the right hand side from 0 to 60 m

    F = 12000y + 75y² = 12000 (60) + 75 (60²) = 990000 N = 990 KN.
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