Roarks Circular Ring Problem
Roarks Circular Ring Problem
(OP)
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!
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!






RE: Roarks Circular Ring Problem
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.
RE: Roarks Circular Ring Problem
Mike McCann
MMC Engineering
RE: Roarks Circular Ring Problem
RE: Roarks Circular Ring Problem
RE: Roarks Circular Ring Problem
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!
RE: Roarks Circular Ring Problem
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.
RE: Roarks Circular Ring Problem
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Roarks Circular Ring Problem