- #1

Bramle

- 7

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I have a moment problem that I am struggling with.

I have an oil-well, that is modeled as a series of joined-up circular arcs. The arcs are not all in one plane, as the well twists and turns. Using vector theory and theory of planes, I have modeled the trajectory of the well from top to bottom. It is a technique known as the "minimum curvature method".

I am pushing a pipe down the well. I assume no fluids in there, and that the pipe is massless and that there is no gravitational field.

I assume a perfect sliding fit between the pipe I am pushing down the well, and the containment diameter of the inside of the well.

I assumed no friction.

The containment diameter compels the pipe to curve in the same arc, and in compelling it to curve, there is a line load along the line of contact. The line of contact for the first arc is along the outer bend of the pipe.

From what bending theory I know...

E*I*d2y/dx2 = -m

...tells me that in order to bend the pipe into a circlular arc, that the line load is not uniform. Effectively I worked back from a circular solution for the curvature, and differentiated it twice to get the moment function... and when expressed as a function of x, it's awful!

I used to think that a uniform line load... lamda, lbf/ft... would give me a circular arc, but I really cannot prove it. I am no longer convinced that I am right in that assumption.

At the top of the topmost arc, the moment there is zero?... because it is a cut surface... but if I apply a uniform line load for the first arc.

Also, is it true to say that if I work out what the disturbing moment is (from a line load along an arc) for the first arc, that I can simply hand that to the top of the second arc as a moment vector, and use that to "kickstart" the moment balance for the second arc?

I can handle 3D force vectors reasonably, but 3D moment vectors are new to me... I really cannot picture them easily. Does a moment vector have to have a position vector associated with it? I know it has to have a direction vector describing the axis about which it is turning?... or is the moment hand-over a "directional" quantity, comprising a modulus and a direction vector about which it turns?

Thanks.

Bramle.