Fluid Mechanics - Drag (Bending Moment)

[MrWinesy]

A television transmitting antenna is placed on top of a mast which is 30m high and 300mm in diameter. The mast is on top of a tall building. The wind blows at 35m/s and at normal atmospheric pressure (1.225kg/m^3). If the drag coefficient for the mast is 0.2. calculate:

(i) the total drag force on the mast.
(ii) the bending moment at the base of the mast.

(i) Fd=.5*Cd*ρ*U^2*A=.5*.2*1.225*35^2*(30*0.3)=1350.6N

(ii) but how do you do this question?

(the answer is M=20.26kNm but i do not know how to get there)

thank you in advance for your help.

 

[timthereaper]

I think they're assuming the drag force is an even distributed load over the entire mast. With that as the case, you can place the 1350.6 N force at the midpoint of the mast (15m). The FBD yields 1350.6 N * 15m = 20259 Nm.

 

[MrWinesy]

that was potentially the most stupid question i have ever asked. thanks for your help sir.

 

[timthereaper]

Hahaha you're welcome. Glad I could help.

 

[rezeew]

To calculate the bending moment at the base of the mast, we need to use the equation M=Fd*h, where Fd is the drag force calculated in part (i) and h is the height of the mast. In this case, h=30m. Therefore, M=1350.6N*30m=40,518 Nm=40.52 kNm. This is the bending moment at the base of the mast caused by the drag force.