Bending Stress Research Paper

FLUID DRAG
Axial force is caused due to frictional drag (FF) because of fluid flow through tubing.
F_F= - ΔP/ΔL AL
Where;
ΔP/ΔL=friction pressure drop;psi/ft
Friction pressure drop is positive for flowing well.
This force generated will cause change in length but mostly the changes are small in contrast to other forces like thermal, ballooning etc. Thus in most software it is usually not considered.
BENDING STRESSES
Unlike all previous loads studied (thermal ballooning etc.) the bending loads are localized instead of being uniform. Which means that pipe bending in one part of the tubing will not impact on the stresses on other parts of the tubing. Thus the bending stresses are added into the existing axial stress profile.
Bending loads

BUCKLING
It is defined as;
“Buckling i characterized by a sudden sideways failure of a structural member subjected to high compressive stress, where the compressive stress at the point of failure is less than the ultimate compressive stress that the material is capable of withstanding”. [Wikipedia]
In tubing the presence of internal and external pressures cause complications. Assume a small section of vertical tubing, a bend is present with internal pressures acting on both sides of the tubing. Thus buckling is being promoted by compression and internal pressures (pi) whereas external pressures (po) and tension is minimizing the effect of buckling. This is categorized in the term of effective tension (Feff).
F_eff=F_total+(p_o A_o- p_i A_i)
Where;
F_Total=total axial load
If;
F_(eff )>Critical

In case of burst it will result in serious consequences. Failure of very small piece of tubing will be sufficient to cause burst failure. This differs from axial and collapse failures. Anything that affects the minimum wall thickness will impact the burst rating of the tubing. The API burst rating by Barlow’s formula is given by: p_b=Tol((2Y_p t)/D)
Where;
Y_p=Minimum yield strength;psi t=nominal tubing thickness;in
D=tubing outside diameter;in
Tol=Wall thickness tolerance
For API pipes the Tol is 0.875. This is added to allow the grinding out the tubing defects. In the API burst calculation no allowance can be made for the effect of annulus pressure except for only the reducing the differential pressure.
COLLAPSE
Collapse is the failure that requires the eventual yield of whole tubing body. It is an instability problem thus establishment of collapse rating is more difficult than the determination of burst rating. It depends upon: Tubing diameter Thickness Ovality of pipe
There are four collapse models and the slenderness ratio is the criteria of their selection. Elastic Collapse
In this collapse the deformation is elastic and the yield stress of the tubing is negligible. The collapse is given by;

Transitional Collapse
The collapse is given by;

Plastic Collapse
The collapse is given