2" Pipe Deflection - in number of degrees

[npao]

Can someone please help me with the following problem:

What is the maximum deflection of 2-inch pipe in number of degrees (maximum deflection in number of degrees that the longitudinal axis of the pipe may be permanently deflected in any length along the pipe axis equal to the diameter of the pipe)?

Pipe description:
Carbon Steel, Schedule 80, wall thickness 0.218”, MAOP 2500 psig.

Thank you in advance!

[zeke]

It's not degrees, but the radius of the curve, R that limits the elastic motion.

The inverse of that radius is called the curvature, 1/R ; the moment that cause it is equal to
M=EI/R
and the stress,s is given by
s=MC/I
when s reaches the yield stress, sy, coinciding with loss of elasticity and r at the minimum radius, Rmin
Mmax=syI/c
and


Rmin=EI/Mmax
Rmin=EC/sy

M= moment
E= modulus of elasticity
c= distance from neutral axis to outer fiber of crossection
s= flexural stress
I moment of inertia of crossection
It is important to note that this radius is set at the point of yield, so that if you bend the bar with a cantilever load with increasing force the bar retains that minimum R for distance.After releasing the force that causes the bending, the only part that is set is over that radius after which the bar is straight, The angle is approximately x/Rmin in radians.where x is the distance from the start to the end of the radius, measured along the pipe.