# Moment problem

1. Nov 14, 2006

### Bramle

I am new to the forum... thanks for your help.

I have a moment problem that I am struggling with.

I have an oil-well, that is modelled 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 modelled 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.

2. Nov 14, 2006

The moment vector is a vector []. It has the same parameters as any other vector - magnitude, direction and orientation. The magnitude describes, of course the magnitude of the moment, the direction states which axis it is 'turning' about, and the orientation (the way the arrow points) states if it's positive or negative, i.e. if it rotates clockwise or counter clockwise. That's the only thing I could help about.

Last edited: Nov 14, 2006
3. Nov 14, 2006