deflection of piece of pipe suspended at 2 points 5

[AlaskaDE]

Hello,

I need to calculate the deflection of a 90-ft stand of drill pipe (three 30-ft joints screwed together) suspended at 2 lift points approximately 40 feet apart.

When our drilling operations commence, we will be moving hundreds of stands of pipe around our rig's storage area with a gantry crane. My concerns are:

a) The ends of the pipe sag so far as to interfere with equipment on the floor;

b) Damaging stress is induced.

Does anyone have an equation to calculate the sag of the pipe ends? And, the bonus question: does anyone have an equation to calculate the location and magnitude of the maximum bending stress?

To make matters more complex, the 2-ft long connections between individual 30-ft pieces are 4-5 times thicker than the pipe body. There are two connections per stand, and they would be inside the lift points (i.e. lift points spaced 40-ft apart, connections spaced 30-ft apart). Must these be accounted for in the calculations?

Please see the attached photo to better illustrate the issue.

Thanks for your help!

Adrienne

 

[rneill]

The calculation to get a pretty close answer should be very simple. Many engineering text books have standard equations for beam deflection and maximum stresses and you could use a beam formula that closely approximated your situation. Just substitute the properties for the drill pipe as the beam properties (i.e., moment of inertia, modulus of elasticity, etc.).

You would need to make the following assumptions:
- Uniformly distributed load (self weight of drill pipe)
- simply supported at points of crane support (free to rotate)

The connectors will provide additional rigidity at the connection points but it would be easier to ignore these and assume drill pipe all the way through. This will provide a conservative answer and make it much easier to calculate.

If you don't have any standard text books with such formulas, do a google search for something like beam equations or beam deflection, etc.

If you can't find a set of standard equations matching your situation, it really isn't that much work to derive from a basic free body diagram. As long as the support is symmetrical, it is very easy to get the reaction loads, and knowing the self weight you can derive the shear diagram which you integrate to get the moment diagram which you integrate to get the deflection diagram.

 

[AlaskaDE]

rneill,

Thanks for this. As a chemical engineer-turned-petroleum engineer who hasn't done statics since college, I wasn't sure that I could use beam equations to aproximate my situation. Now I know where to start. Your help is much appreciated!

-Adrienne

 

[IRstuff]

And you can use your photo as a sanity check on your calculations.

TTFN

FAQ731-376

 

[AlaskaDE]

IRstuff,

Definitely, and thanks for the idea. I don't know what size/wall thickness/grade of pipe is pictured in the photograph (this was taken during a test run before the crane was shipped to our location), but could probably do some digging and find out.

-Adrienne

 

[desertfox]

Hi AlaskaDE

Have a look at this beam calculator, I think it matches the case in your photograph:-

http://www.engineersedge.com/beam_bending/beam_bending5.htm

desertfox

 

[rneill]

That would be the equivalent beam ...

 

[BigInch]

The calculator isn't giving answers that match their formulas for stress in the cantilever or stress in the center span.

I have advised the webmaster.

**********************
"Being GREEN isn't easy" ..Kermit the

http://www.youtube.com/watch?v=hpiIWMWWVco

http://virtualpipeline.spaces.live.com/

 

[AlaskaDE]

Thanks, everyone! This is great. One question: How are the distances "u" and "x" defined? I'm assuming:

u: chosen distance between the outer end of the beam and the nearest support point (i.e. u=12 corresponds to a point 12 inches from the end of the beam)

x: chosen distance between the center of the beam and the nearest support point (i.e. x=12 corresponds to a point 12 inches from the center of the beam)

This makes sense, so that stress and deflection can be calculated at any point along the beam, but I wanted to make sure I had it right.

Thanks again!

 

[desertfox]

Hi AlaskaDE

I think x can be any distance you care to choose, jus be careful using the calculator "Big Inch" is saying its giving incorrect answers so I would check it against the formula.

desertfox

 

[AlaskaDE]

Hi desertfox,

After making my own spreadsheet as well as playing around with the calculator, I think that u and x are the opposite of what I wrote earlier; i.e.

u=12 corresponds to a point 12 inches from the support point toward the outer end;

x=12 corresponds to a point 12 inches from the support point toward the center of the beam.

Calculated this way, the equation for Stress between nearest support and outer end yields 0 psi for the ends of the beam (as it should be).

IMO, the diagram is a bit misleading in this respect.

Also, I believe that the small l in the denominator of the first equation should be a big L.

 

[Canadieng]

Just a word of caution - you may be encroaching on "large displacement" beam theory, where the elementary beam equations fall apart.

One rule of thumb is - if your deflection is 10x or greater than your beam depth - the elementary equations show to large of an error.

The reason is due to the assumptions in the elementary theory, specifically the elementary theory neglects the square of the first derivative in the curvature formula and provides no correction for the shortening of the moment arm as the loaded end of the beam deflects. For large finite loads, it gives deflections greater than the length of the beam! The square of the first derivative and correction factors for the shortening of the moment arm become the major contribution to the solution of large deflection problems.

 

[desertfox]

Hi AlaskaDE

I agree in the first equation l should be L.

The distances u,c,x are distances from a given support to any point on the beam.

desertfox

 

[AlaskaDE]

Canadieng,

Very interesting, thanks. Just to make sure I understand...I'm trying to predict the deflection of 4" OD pipe, so as long as the calculated deflection is less than 40", the elementary equations are suitable?

 

[Canadieng]

On further thinking, I may have mixed up my "shear deflection" and "large displacement" rules-of-thumb.

This quickly pulled up Google hit:

http://courses.washington.edu/me354a/chap3.pdf

may provide the answer. What I spoke of before is surrounding equation 3.22

(It is Friday evening and I turned off my brain at about noon. So perhaps others will correct my thumb rule)