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Aug1-04, 02:53 PM
Sci Advisor
PF Gold
P: 477
A little addendum:

I just realized you may have meant that the loading was solely due to the weight of the pipe. If so, consider the expression for the maximum deflection in a beam under a uniform load (you can get these too if you work out the Euler beam bending equation):

if it's cantilevered:
[tex] \delta_{max} = \frac{qL^4}{8EI} [/tex]
if it's simply supported at both ends (max deflection occurs at center of beam here):
[tex] \delta_{max} = \frac{5qL^4}{384EI} [/tex]

(If you are unfamiliar with the definitions of any of these terms, please ask.) In either case (and assuming both beams are made of the same material (E)), the maximum deflection is proportional to the term q/I.

For the solid beam:

[tex] \frac q I = \frac{\frac{\rho L \pi d^2 g}{4L} }{\frac{\pi d^4}{64}} = \frac{16\rho g}{d^2} [/tex]

For the hollow beam:

[tex] \frac q I = \frac{\frac{\rho L \pi \left(d^2-d^2_i\right) g}{4L} }{\frac{\pi \left(d^4-d^4_i\right)}{64}} = \frac{16\rho g}{d^2+d_i^2} [/tex]

Assuming I haven't messed up my math here, the bending for the hollow beam is less than the bending for the solid beam. The solid beam is still more stiff, but it also undergoes more loading (because the solid beam weighs more). I hope that helps.