Roarks Circular Ring Problem 1

[SteveyB]

I wonder if anyone can please help clear up my problem up!

Basically I am trying to solve a problem using example 9.2 in the 7th Edition of 'Roarks formulas for Stress and Strain'. Involving a solution using example 13 taken from table 9.2 a circular ring sujected to a linear varying radial unit load.(See attached image).

My problem is with the formula to calculate w, the magnitude of varying radial load at C. The formula is:

Load=2wR(1+c)/(pi-Theta)

I seem to be having issues when entering the values into mathcad and it complains about the units. I am therefore confused as too what my result should be.

I re-arraged the formula in terms of w too give:

w=(Load*(Pi-Theta))/2R(1+c)

My values are as follows:

Load = 100kN
Theta = 90deg
R = 57.5mm
c = 13.75mm

If I enter the values into the transposed equation above mathcad complains about the number 1 in the lower half of the equation being unitless and should have units length.

So I guess that my question is what does anyone else get as the answer for w in N/mm^2.

Thanks In advance!

 

[Ron]

I don't have Roark's in front of me, so I'll take what you have as correct...I will also assume that you are not a student and this is not a homework problem. Student posting is not allowed in the forums.

If R has units mm, and c has units mm, then in order to satisfy the unit load equivalence (N/mm^2), "1" must also be in mm.

2R(1+c)=2R + 2Rc....if 1 is unitless, you have (2R mm + 2Rc mm^2)...not good.

I get 92.6 N/mm^2 (assuming that theta is in radians, not degrees)...have no frame of reference to determine if this is in your ballpark or not.

 

[msquared48]

Radians instead of degrees was my first thought too in that it is being subtracted from Pi.

Mike McCann
MMC Engineering

 

[ishvaaag]

Try to get the Mathcad Roark's Handbook (i.e., there is a Roark's rendition in Mathcad) where your case is already solved... no time now to check the intricacies, sorry, but there you will find how they did.

 

[JStephen]

Check the definition of c. If that's the set of load cases I'm thinking of, c is the cosine of theta, not a dimension. It would show that in the introduction to the whole section on circular rings.

 

[SteveyB]

Thanks all for your help! Just to clarify, I'm not a student this is just to verify the result for some FEA which have done. Due to the significant lack of experience I have using Roarks.

You are right JStephen I did have my terms mixed up and c is equal to cos(theta)in radians. I also was looking for a result in N/mm for w as I had confused myself playing with units in mathcad.

The result I now get is 1.381kN/mm could anyone please verify this and make sure I still havent made any mistakes now given that:

Load=100kN
Theta=90deg
R=57.5mm
c=cos(theta)

Thanks again!

 

[Ron]

I get 683 N/mm assuming your formula and parameters are correct. I assume theta is in radians in both places. Would be a bit unusual to have it in radians in one place and degrees in another in the same formula.

JS...you get the prize! Didn't think of it before, but constants don't usually carry units!

SteveyB...everybody has problems using Roark's at one time or another. Great resource, but sometimes confusing on some relationships.

 

[IDS]

I get 1.366 kN/mm, which is double Ron's answer.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Ron]

IDS...you're right. I used the angle in radians for the cosine function on my calculator....rookie mistake!!