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Curved Beam Roark's Formulas for Stress and Strain

Struct123ure

Structural
May 16, 2023
39
I have a curved steel beam very similar to the example attached from page 300 of 7th ed Textbook by Roark's ...
My question is that the solution values don't make sense.
1. If you plug x=37.59 and x=130.9 into the Tx formula you don't get 13,100 in-lb & 8790in-lb respectively. (I get from calculating in excel 18,137 & -8788 (close enough)). I would attribute this to a typo, but nothing works out.
T is not 8330lb-in at the load position (60 degrees) because (60-60)^0 is error....
"M shows a max value a the ends" that's not what happens when you input from 0-180 degrees into Mx equation...

Anyone who is either better at math or has delt with curved beams before can help me understand where I went wrong? I read the chapter, but feel like something is missing from this example
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I have not played with the equations, however I wonder if you've interpreted <x-60°>0 correctly?

It is a step function as explained on page 131, and has a value of either 0, 1 or undefined.
 
This looked like fun so I did it quickly in Excel. Used the tabulated coefficients from Table 9.4 Case 1f for end values and the formulas from Case 1 for Mx and Tx.

For x = 37.59° I get Tx = 13,101 in lb. For x = 130.90° I get Tx = -8,790 in lb. For x = 60° I get Tx = 8,336 in lb. I also get Mx to be maximal at the two ends.

I assume the remainder of the example will work out with these values matching.
 

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