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1. The problem statement, all variables and given/known data

I am trying to design on paper a cantelever beam made of steel rectangle tubing. One 60" vertical section will be bolted to the concrete while a 2nd section 40" long will be welded to the top hanging over horizontally. At the end of the horizontal piece there is a cable holding 2000 lbs. I need to figure out what size steel rectangle tubing to use and the wall thickness for this load. I would also assume that using the longer side of the rectangle as the height would make it stronger, correct?

2. Relevant equations

I'm using E=2.9*10^7 lbf/in^2 for elasticity of steel

I=[(b_o*h_o^3) - (b_i*h_i)]/12 where o is outside dimension and i is inside dimension for rectangle tubing

To find the deflection of the horizontal member, I would use the equation y(x)=[-w/(6*E*I)]*(3*L*x^2-x^3)

I don't know for sure where to go from here or where to even start with the vertical member.

3. The attempt at a solution

I assume you would break this problem into 2 parts, 1 for the horizontal and 1 for the vertical but without knowing the size of the tubing, you can't really find I and even if I substitute some values for I and come up with a horizontal beam deflection, what does that tell me or help me to find an adequate size tube. Is it true that an acceptable deflection is the beam's length divided by 250? So for my situation, 40"/250=0.16".

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# Cantelever Steel Tubing Beam

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