Question

a 2-m-diameter smokestack stands 60 m high. it is designed to resist a 40-m/s wind. at this speed, what total force would be expected, and what moment would the base be required to resist? assume atmospheric-820c air.

Answer 1

The total force expected on the smokestack is approximately 9043.71 N. The moment the base needs to resist is approximately 542,622.6 Nm.

Step-by-step explanation:

To calculate the total force expected on the 2-m-diameter smokestack, we can use the formula:

Force = (0.5) * (density of air) * (wind speed)^2 * (cross-sectional area)

Plugging in the given values, we get:

Force = (0.5) * (1.14 kg/m³) * (40 m/s)^2 * (π * (1 m)^2)

Calculating this, we find that the total force expected on the smokestack is approximately 9043.71 N.

To calculate the moment the base of the smokestack needs to resist, we can use the formula:

Moment = Force * (height of smokestack)

Plugging in the given values, we get:

Moment = 9043.71 N * 60 m

Calculating this, we find that the moment the base of the smokestack needs to resist is approximately 542,622.6 Nm.