bending property solid metal pipe vs hollow metal pipe

insatcool

i wanted the techinical information.
bending property of solid pipe and hollow pipe with same diameter.
which will bend more and why ???????????????????
i wanted the technical answer plz help me out

FredGarvin

If you look at a beam that is cantilevered and a force applied to the free end, the deflection of the beam at the end is calculated as:

[tex]\delta = \frac{PL^3}{3EI}[/tex] where

[tex]\delta[/tex] is the deflection
[tex]P[/tex] is the applied load
[tex]L[/tex] is the length from the fixed end
[tex]I[/tex] is the area moment of inertia
[tex]E[/tex] is the modulus of elasticity

So for two beams (one hollow and one not) of equal length, identical material and the same applied load, the only variable is the area moment of inertia. Since the deflection is inversely proportional to the area moment of inertia, the beam with the larger moment will have the lower deflection.

The tube will a lower area moment of inertia so it will deflect more.

What loading conditions and constraints were you thinking of?

insatcool

which rod (hollow or solid) will break at a apllied load (pressure) at a repeated frequency 1 min holding time and 10 mins withdrawal time ??????????

FredGarvin

This is not a static deflection problem any more. It is now a fatigue issue. It depends completely on the load applied and if there is a static offset load (preload). Many situations have an infinite number of cycles that can be applied and not fail. I can't answer this question without a lot more information.

Astronuc

Adding what Fred mentioned, the hollow tube (presumably of the same material and similar microstructure (which infers similar thermomechancial processing)) has less cross-sectional area, which means for a given load will have higher local stress, which implies more strain.

For fatique, for a given delection, the internal stresses will be greater in the hollow tube - which will generally reduce fatigue life for a given load/deflection.

And as Fred indicated, more information is needed to give a more definitive statement.