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Formulas to Calculate deflection/bending of FreeStanding Pipe 
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#1
Jul2514, 03:41 AM

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Hello Everyone,
I have several questions regarding the deflection of a freestanding pipe wherein Force is applied on top. Appreciate any feedback that I can get. Supposing I have the following Pipe Specifications: OD: 7in ID: 6in Yield Strength: 80,000psi Modulus of Elasticity: 30000000psi Poisson’s Ratio: 0.3 Here are my questions: 1. How do we calculate the maximum height that the above mentioned size of pipe will freely stand (without any support or braces)? 2. Assuming that the above mentioned pipe has a length of 15feet and for the sake of argument can be placed vertically without any support (freestanding) but fixed at the bottom end. If we apply 10,000lbs of Force at the top end, how do we calculate the: A. Amount of maximum deflection relative to the center line of the pipe B. Location of the maximum deflection – Is this going to be halfway through the length of the pipe (@7.5feet)? 3. Supposing the above mentioned pipe 7in OD, 6in ID is placed concentrically inside another pipe. Let’s assume that the ID of the outer pipe is 8in (and assuming that the outer pipe is fully rigid). And supposing that on the 7in OD inner pipe, 20,000lbs of Force is applied on top of it. For the sake of argument let’ say that the deflection caused by the 20,000lbs of Force applied will exceed the annular clearance between the OD of the Inner Pipe and Outer Pipe. How do we then calculate the amount of Force effectively transferred by the inner pipe onto the fully rigid outer pipe? Thanks, Soji 


#2
Jul2514, 09:26 AM

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PF Gold
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http://en.wikipedia.org/wiki/Buckling To be sure, the lateral deflection of any vertical column is a sign that failure and collapse may be imminent. Run away. 


#3
Jul2514, 10:45 AM

P: 851

that's just standard stress/strain calculations, though the lateral elongation of a tube due to axial compression can sometimes be tricky when trying to reason out the equations. 


#4
Jul2614, 08:29 AM

P: 3

Formulas to Calculate deflection/bending of FreeStanding Pipe
Steam King – Thanks for the inputs.
Let me modify my first question. 1. Supposing that the 7in OD, 6in ID pipe has a material density of 490lbm/ft3, if it were to be fixed at the bottom end, how tall/high can this pipe rise without swaying/bending due to its own weight? What formula can I apply? Thank you, Soji 


#5
Jul2614, 08:54 AM

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#6
Jul2714, 12:27 AM

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Steam King – Thanks for reiterating where to find the formula for selfbuckling. Appreciate it.
There’s a statement that followed the formula for SelfBuckling on the link you posted – “and B is the first zero of the Bessel function of the first kind of order 1/3, which is equal to 1.86635086...” Just want to clarify on the formula: h_critical=((9B^2)/4 EI/(ρgπr^2 ))^(1/3) Can I simply apply the 1.86635086 value mentioned above as the for B on the above equation? Or it’s on a casetocase basis. I’m not familiar with the Bessel function. Thanks, Shodji 


#7
Jul2714, 03:27 AM

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The classic reference for this the "Buckling Strength of Metal Structures" (1952) by F. Bleich, but it's long been out of print and copies are hard to come by. http://structurae.net/persons/data/index.cfm?id=d009664 


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