900 Views 5 Replies Latest reply: Jun 21, 2013 10:31 AM by WE
2 posts since
Jun 18, 2013
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## Beam Deflection in a Tapered Pipe

I need help comparing the deflection of pipe with two different cases. Case 1 is a regular non-tapering pipe. The case 2 is a tapered pipe that should deflect less than the straight pipe. I am working in MathCad and can change the value of my variables, so I have set the two cases to be equal to one another (by saying that the variable D.w is equal to D) for the sake of comparison. The answers should be equal to one another so I know that there is a problem but I am not sure where. I think that it is within setting up the double integral since I checked the case 1 pipe deflection against a different pipe deflection calculator. Any help would certainly be appreciated.

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• 4,914 posts since
Nov 3, 2009
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Jun 18, 2013 5:31 PM (in response to ptc-4863626)
Re: Beam Deflection in a Tapered Pipe

Which values should be the same? y1 and y2=y3?

The way you had setup your double integral is not desireable as in the inner integral you use x as intgration variable and as upper limit. The upper limit should be changed to another name and this would be the integration variable of the outer intgeral. Doing so does not change the result, though.

y1 and y3 would only be the same if x^2*(3*L-x)=L^3.

If you look at your definition of y3 you get (by symbolical evaluation)

L^3*W/(6*E*I)

and compare this to your definition of y1

W*x^2*(3*L-x)/(6*E*I)

So for L=x you are missing a factor 2 to get the same result with y3 as with y1.

• 1,278 posts since
Jun 8, 2010
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Jun 19, 2013 3:07 PM (in response to ptc-4863626)
Re: Beam Deflection in a Tapered Pipe

When you set Dw equal to D the integrals in y2 are easy to solve analytically (by hand).  You get a result which is a factor of 2 different from y1, which is what the numerical results are telling you.  Where you have pi/64 you should probably have pi/128

Alan

• 1,774 posts since
Nov 28, 2006
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Jun 19, 2013 12:19 PM (in response to ptc-4863626)
Re: Beam Deflection in a Tapered Pipe

When in doubt, go bac to basics.

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