Curved Beam Roark's Formulas for Stress and Strain

[Struct123ure]

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

 

[Geoff13]

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.

 

[Geoff13]

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.

 

[rb1957]

why not show your Tx work (since your answer agrees with the text, but OP's doesn't) ?

 

[Geoff13]

What's to show? The formulas are in Roark's and give the numbers in the example.

If Struct123ure posts their file I'll be happy to review it.

 

[rb1957]

I guess the OP will say the same ...

 

[Struct123ure]

What's to show? The formulas are in Roark's and give the numbers in the example.

If Struct123ure posts their file I'll be happy to review it.

Thank you, it all clicked once I read chapter 8. I was stuck for multiple days with this.
I would appreciate your work, but I'll post my file instead for anyone wondering in the future. And also post the snippet from the textbook chapter 8 explaining.

I put a simply "=if(" function at the beginning and then all the numbers were in line.

I will add one thing:
I don't get maximum Mx at both ends. I get positive max Mx=38495 at 0°, negative maximum Mx=-24054 at 60° and not a max, but relatively high moment of Mx=19243 at 180°. (In case anyone anyone looks at their results and still thinks something is wrong.

 

[Geoff13]

Glad you figured this out for yourself.

I like to use cell names as it makes the formulas easier to read when things go wrong. I also prefer to convert degrees to radians only once (column C) and then use that for my sin and cos calcs. As for the "maximum" values I think it's just a difference in terminology. You are correct the Mb is not a maximum compared to Ma.

You may also like my method for the step function as I only need one copy of each formula.