Calculating the Stiffness of a Structure 2

[aswierski]

I have been given the task of calculating the stiffness of a pipe support. In this particular area a vibration analysis was done on the piping system, which dictates that my support needs to have a stiffness of at least 2,000,000 LBS/IN in the pipe's longitudal direction (The pipe is 12" sch. 40). I have never done anything like this before, and in fact have only worked with stiffness calculations for springs (in college). See the attached PDF for a detail of the support itself (W8x31's). With that said, how do I proceed? I don't even know where to start. I can figure out how much load this support can take, but as far as stiffness goes I'm lost. From what I gather, stiffness is defined as the amount of load required to produce a unit amount of deflection (in my case, 1"). So should I simply calculate how much load will be required to deflect my support by 1"?? Any insight you guys could share would be greatly appreciated. Thanks.

 

[SlideRuleEra]

Start with simplifying assumptions:

1. Since your drawing does not show how the structure is anchored to the foundation, assume that the anchorage is rigid.

2. Assume that a force is applied at the pipe centerline to created 2,000,000 in-lb moment. Since you know the height (about 9.5') you can calculate the force.

3. This makes the structure a pair of cantilevered beams (W8x31) with a force at the end. Assume that the calculated force is equally shared between the beams (since the pipe appears to be halfway between the two beams).

4. Compute maximum deflection. This is your "First Order Approximation" of an answer. If it is MORE than 1", the structure is inadequate, no matter what else is assumed. If deflection is LESS than 1", you may need to investigate other details of the design to get a more accurate answer.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[cntw1953]

I may try a simpler approach - apply an unit load on the bent, obtain deflection, then k = 1/deflection.

I would assume the base is fixed for a single bent; fixed or pinned for a system of bents.

 

[desertfox]

hi aswierski

To expand on what SlideRuleEra stated I have uploaded a file to help.
All I have done is calculated approx what force is req on the end of one beam to deflect it 1".
However its only to give you a starter and it sadly falls short of the stiffness your looking for.
You need to speak to someone were your working and get some help from a more senior engineer.
Another consideration is how that structure is held down its okay having the structure stiff but no good if it rips the anchors out.

desertfox

 

[Stillerz]

something seems out of sorts here....if your pipe support is truly cantilevered (in/out of the paper), you're going to require some massive columns and foundations to for your 2,000 kip, 1" deflection requirement.
That requirement seems unreasonable.
Just scratching out some rough numbers, you'll need a section with Ix = 15,000 in^4.

That's a big shape.
Is the foundation for this already designed?

Maybe I am missing something here.

 

[jike]

I agree with Stillerz that you will probably need a structure alot stiffer than sketched out. Perhaps a concrete pier or a steel column with a diagonal brace. The engineer that has assigned this to you probably just wants you to come to that realization on your own.

 

[desertfox]

Hi

I think looking at it again that the requirement does seem rather unreasonable.
Wonder whether the OP made a typo in the post

desertfox

 

[SlideRuleEra]

Stillez, jike, desertfox - I see what you mean. I misread the OP as 2,000,000 in-lb (moment)... but that is certainly NOT what it says.

http://www.SlideRuleEra.net

http://www.VacuumTubeEra.net

 

[steve1]

Most likely the pipe stress engineer is basing his request on the fact that he assumed a "rigid" support in his calculations for what appears to be a line stop. My suggestion would be to calculate your actual stiffness (as delineated by others here) and ask the pipe stress engineer to include it as the support stiffness rather than assume rigid. Chances are your support will work for the decreased demand once the anchor flexibility is included in the pipe stress run.

 

[Stillerz]

What Steve is saying makes sense.
I used to do a lot of power plant work and piping like this was often not rigidly attached to the support but were more or less "sliders".