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Chapter 14

Q. 14.8

As shown schematically in Figure 14.31, square columns 4 in. × 4 in. and 10 ft tall are to be used in the construction of a porch in south Florida. If the columns are exposed to hurricane force winds of 100 mph(= 147 ft/s), what force must each column withstand?

14.31

Step-by-Step

Verified Solution

The Reynolds number of the flow is found to be

Re=\frac{UD}{\nu}=\frac{(147\ \mathrm{ft}/s)(4\ in.)(\mathrm{ft}/12  in.)}{1.64×10^{−4}\ \mathrm{ft}^2/s }=3\times 10^5

which is above the value Re > 104 for which the data for a square section in Table 14.3 are valid. Thus it is appropriate to use the drag coefficient in this table for our analysis. In Table 14.3 we see that for a square section, the maximum CD = 2.4 is at 45° angle to the wind, thus the maximum force will occur for a wind that comes from this direction. This is the force the column must potentially withstand in the worst case. To calculate it, we will assume 70°F air and use A = (4/12 ft)(10 ft) = 3.33 ft2 and U = 147 ft/s. The drag force is then found to be

FD = \frac{1}{2} ρU2ACD = \frac{1}{2} (2.329 × 10−3 slug/ft3)[147 ft/s]2(3.33 ft2)(2.4) = 200 lbf

TABLE 14.3 Drag Coefficients for selected 2D sections.

Geometry Drag Coefficient, CD, and Remarks
θ(Deg) 0 5 10 15 20 25 30 35 40 45
C_D 2.2 2.1 1.8 1.3 1.9 2.1 2.2 2.3 2.4 2.4

Re ≥ 10^4