second moment of area

[ijtatner]

I have a horizontal section of pipe with another section of pipe joined at 90 degrees (mid span) and am trying to work out the stiffness of the section. Calculating the stiffness of the horizontal section is easy but can anybody help calculating the stiffness increase due to the vertical pipe?

 

[ijtatner]

simply what I'm after is the stiffness of a branched pipe section

 

[HVACctrl]

Indeterminate statics maybe?
Perhaps the Constant Deformation Method or the Method of Superposition.

These are just guesses at what I would look at as possible starting points. I really don't work with this type of thing normally.

Ed

http://www.engineerboards.com

 

[rb1957]

i'm not quite sure what you're asking about ...

the 2nd mooment of inertia of a pipe is easy enough (look in any structures book, something like pi*r^3*t).

but i think you're more interested in the deflection of the end of the vertical pipe. Consider this pipe to be cantilevered off the horizontal pipe, which is subject to deflection to support the load applied to the vertical pipe (it sees a moment applied, this will cause the base to rotate, the axis of the undeformed vertical pipe will be normal to the deflected horizontal pipe) and the vertical pipe deflects under bending from the applied load.

 

[ijtatner]

what I'm after is the second moment of area (and hence the stiffness) of the vertical pipe. Imagine trying to bend a ring?

 

[rb1957]

thats pi*r^3*t (2nd moment of inertia for a ring)
or pi/4*(ro^4-ri^4) (... subs ro = ri + t)

 

[JStephen]

You have a horizontal pipe with a tee in the middle, and you're wondering what effect that tee has on the stiffness of the horizontal pipe? That's how I read your question. The answer is: Indeterminate. For lack of better information, I'd say assume the tee doesn't affect stiffness. If it's critical, then FEA to the rescue.

 

[prex]

In piping codes such as B31.1 the flexibility factor of a tee is taken as unity (the flexibility factor is the ratio of stiffness in the bare pipe to that of actual component).
This is valid of course only for tees properly reinforced for pressure usage.
It should be noted that the flexibility factor is used in piping analysis for the calculation of expansion stresses, so that the use of a factor not higher than one is a safe assumption. Personally would expect some reduction in stiffness (fl.factor>1), but, as also noted above, there are no data in the literature that I know of.

prex

http://www.xcalcs.com

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