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# Deflection and Tensile Stress in Pipe

## Deflection and Tensile Stress in Pipe

(OP)
I have a horizontal pipe with ends that are secured vertically but free to float horizontally and need to apply a load through a vertical pipe (90 degree intersection) that is radiused to provide full contact, what are the formulae for calculating deflection and max tensile stress induced into the horizintal pipe.  Both pipes have the same O.D. and wall thickness.

I'm not a structural engineer and the fact that this does not appeat to be either a concentrated nor uniformly distributed load has me baffled.

Albie2

### RE: Deflection and Tensile Stress in Pipe

What are the length of the horzontal pipe and the OD of the pipes?

### RE: Deflection and Tensile Stress in Pipe

(OP)
jmiec:

Distance between supports on horizontal pipe is 45 inches.  Center of vertical pipe is 14 inches from one support.  O.D. of both pipes is 12 inches and both have a wall thickness of 1 inch.  Pipes will be secured to each other by continuous weld.

Albie2

### RE: Deflection and Tensile Stress in Pipe

For a quick and conservative analysis, consider it a point load, in which case;

M=Pab/L, and Defl=Pa^2b^2/3EIL at the location of the load.
where, for your case/ a=14", b=31"

To consider it a partially distributed load,

R=P(2c+b)/2L  and M=R(a+(Rb/2P))
where, for your case/ a=8", b=12", c=25"

The calculated moment should shrink by 10-15% of the Point load case.

The deflection for the distributed load is not appreciably different from the concentrated load approximation.

Keep in mind that, if your vertical pipe restrains the rotation of the horizontal pipe, then these formulas don't apply.

### RE: Deflection and Tensile Stress in Pipe

what is the direction of force applied to the vertical pipe ... vertical or horizontal ?

### RE: Deflection and Tensile Stress in Pipe

yeah.. your explaination is very confusing.  You might want to draw us a free body diagram.

### RE: Deflection and Tensile Stress in Pipe

You have 12-inch pipe with a 1-inch wall thickness that is 45 inches long.  I doubt classical beam theory will work out very accurately, especially without including shear deformation.

Those are enormous pipes.  Is that a typographcial error or are you towing the moon with it?

Since you are inexperienced with this, you should have your supervisor help with this.  I doubt we can, or should, be of much help on the net since we don't know what's going on or what your end goal is with this system.

### RE: Deflection and Tensile Stress in Pipe

(OP)
All:

Thank you very much for your responses.  For those who asked, the load is applied vertically, symmetrically distributed around the centerline of the the verticle member.  With regard to the large size of the pipes, this is driven by the fact that the verticle member will be approximately 10 foot long and needs to be able to carry a varying compressive load that, including a margin of safety, will rise as high as 2.3 million pounds.

Regards,

Albie2

### RE: Deflection and Tensile Stress in Pipe

You do realize that the load you quoted, if you can evenly distribute it, comes to over 66ksi in the vertical pipe!  Using classical beam theory (which I agree isn't applicable), I get about 21ksi in bending, which isn't bad, except when you couple it with 33ksi in raw shear stress.  If you stay with these numbers, you'll won't be able to use standard pipe steels - something stronger will be in order.

Another question is how you're connecting the ends of the horizontal pipe.  For loads like that, you'll need very special end connections to transfer these forces.  You can't just rest the pipe on a hard surface...

API RP2A has guidelines on the design of the connection of large diameter pipes with large loads (and moments, btw).  As for connecting the ends, I would consult a local mechanical/structural engineer to help you.  Forces like that require immense respect...

### RE: Deflection and Tensile Stress in Pipe

is this a fluid problem ? ie, is there a fluid creating this load,
and is the fluid causing the displacement of the end of the horizontal tube (due to momentum) ?
is this a static problem, or are large displacements allowed ?

statically, i hope the support furthest from the vertical pipe is above the horizontal tube (assuming the load is acting down) 'cause these two supports need to react a couple.

i think we need to know abit more about what's happening upstream ... the vertical pipe goes somewhere, and has support somewhere ... why would the support to everything be on this little leg ?

a quick number suggests that the end support reacts 1.5* the vertical pipe load, 3.5Mlbs.  i guess your support is a roller, making point contact with the tube.  The peak moment in the tube is 0.25PR = 19.7Minlbs.  this is being reacted by some effective width of the tube, bending stress = 6M/(Wt^2) = 118M/W psi .  There is also an axial load, sensibly compression, of about 0.25P and a shear of 0.5P ... stresses would be 0.88M/W psi (axial) ... negligible compared to the bending stress.
so you can see that W needs to be greater than 45" to get reasonable stresses (118000000/W < 100000 ... W > 1180"

### RE: Deflection and Tensile Stress in Pipe

One of my first questions is will the lower pipe be cut open to permit a fluid to pass from the vertical pipe into the horizontal pipe, or are these pipes just acting a structural members?  If you notch the lower pipe, then you have an entirely different problem.  And also as mentioned above, your aspect ratio is out of whack so you may need a FE solution.  This is a tougher problem than regular beam theory.

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