tube analysis 1

[xpert999]

can someone tell me how to calculate the best value (ie lowest weight for a given stress) value for t/r for a straight tube loaded: in pure tension, and pure bending?<br>
<br>
My background is medical and I need this info for an assignment in Biomechanics.

 

[Motorhead]

Not sure what t/r is (tube thickness to tube radius ration?), but here's what I would do:<br>
<br>
In tension: Stress(s) = Axial Load(P)/Area(A), so if you know your stress level, solve for A. This is the area of the tube and would be equal to 0.25*PI(Do^2-Di^2). You will need to pick the inside or outside diameter and then solve for the other value.<br>
<br>
For Bending, the thot process is similiar with just a different equation for stress. In Bending:<br>
Stress = Applied Moment(M)*C/Moment of Area(I)<br>
<br>
Moment is the force being applied to the tube at some distance. You will want to pick the worst case since it is a function of distance or they may have already specified the bending moment.<br>
<br>
C is the distance the neutral axis to extreme fiber. In your case, it is a fancy way of saying the outside radius of the tube (Do/2).<br>
<br>
I is the moment of area and for a tube cross section would be equal to PI*(Do^4-Di^4)/64.<br>
<br>
Again, with a known stress, do some algebra and solve for one of the diameters. <br>
<br>
If you need to solve the combined loading case, you can assume the stress are additive and get something like:<br>
<br>
Total Allowed Stress = Axial Stress + Bending Stress <br>
<br>
or another way:<br>
S = P/A + M*c/I<br>
Solving for a dia. will get alittle messy, but will work.<br>
<br>
If you need some references, goto the library and look for Machinery Handbook or any undergrad engineering text on strength of materials<br>
<br>
Post back if more questions.