A 50 story building is being planned. It is to be 200 m high with a base 41 m by

Question

A 50 story building is being planned. It is to be 200 m high with a base 41 m by 70 m. Its total mass will be about 1.8 107 kg and its weight therefore about 1.8 108 N. Suppose a 200 km/h wind exerts a force of 840 N/m2 over the 70 m wide face (Fig. 9-73). Calculate the torque about the potential pivot point, the rear edge of the building (where FE acts in Fig. 9-73), and determine whether the building will topple. Assume the total force of the wind acts at the midpoint of the building's face, and that the building is not anchored in bedrock.  [FE represents the force that the Earth exerts on the building in the case where the building is just beginning to tip.]

N*m

Explanation / Answer

area of the face = 70 x 200 m

therefore force F of the wind = pressure x area

= 840 x 70 x 200 = 1.176 x 10^7 N

anti-clockwise torque about edge = F x (200/2) = 1.176 x 10^9

clockwise torque due to weight W of building

= (1.8 x 10^8) x (41/2) Nm = 3.69 x 10^9

resultant torque = clockwise = - [(3.69 x 10^9) – (1.176 x 10^9)] Nm

= - 2.514 x 10^9 Nm

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