# Selection of Aluminum (or steel) tubing dimension based on uniform load on supported beam

I am installing shades on a section of deck. The shade will be made of sections of fabric (which will let some wind through), but I assume a solid section. Dimensions are 3.5ft*4ft = 14ft^2 = 1.3m^2

I will put the shades on and off, but I want to make sure it won't break if there is a sudden gust of wind. Suppose a 60 mph wind gust = 26.8 m/s and 1.2kg/m^3 air density. This leads to 561.4N of force. (I know the 4X4 red cedar post will hold. I know the fabric will hold. The seam may break, but that's an easy fix.)

The shades will be supported by 2 tubes (beams), one on top, one at bottom. So, I assume an even load. I also assume the load is even on the whole length on the tube. So, 1 tube of 1.066 meter should support roughly 281 N.

I was able to find how to compute the maximum moment of 37.43 Nm.

This is where I can't finish my calculations. Will a (generic) 1in aluminum tube (1/16in thickness) I find at the store enough? I found the tensile strength of aluminum is between 33000 to 76000. So I assume the generic tube I find at the store will be the lowest one at 33000.

$$\sigma_x= \frac{M}{S}$$
$$S_{alum\ tube}= \frac{\pi*(D^4-d^4)}{32D}= \frac{\pi*(1-0.7724)}{32} =0.02233\ in^3 =365mm^3$$
$$\sigma = \frac{37430}{365}= 102.5$$ please check my numbers.