Piping Elbow or Bend SIF (Stress Intensification Factor)

The term SIF is too confusing for many of the piping engineers. Thats why the following article is taken to explain the bend SIFs in simple language.
Every piping Engineer who possess a little basic of Piping Stress Analysis theory must be aware of the term SIF or Stress Intensification Factor. The term indicates a multiplier of Bending and Torsional stresses. This Intensifier acts local to a piping Component ( tees, elbows, bends, Olets ,etc) and Its value depends on component geometry. The minimum value of SIF is 1.0. It is widely used by piping stress engineers in places where the actual stress calculation is quite difficult due to its difficult geometry (Varying thickness, cross section, curvature etc) as unlike straight Pipes the simple Beam theory is not applicable. So in this situation it is required to assume additional stresses by suitably incorporating a SIF. The following article will provide an example of SIF calculation of piping elbow or piping bends following process piping code ASME B31.3.
Stress Intensification Factor for a Piping Bend/Elbow:
  • In layman’s language the SIF of a bend or elbow can be defined as the ratio of bending stress of an elbow to that of straight pipe of same diameter and thickness when subjected to same bending moment. Whenever the same bending moment is applied to a bend because of ovalization the bending stress of the elbow will be much higher than that of strainght pipe. That is why the SIF value will always be greater than or equal to 1.0 (for straight pipe).
  • The process piping code ASME B 31.3 provides a simple formula to calculate the SIF of a bend or elbow. As per that code
SIF in-plane = 0.9 / h^(2/3)
SIF out-plane = 0.75 / h^(2/3)
Here h=T R1 / r2^2
h =Flexibility characteristics, dimensionless
T =Nominal wall thickness of bend, in
R1 =Bend radius, in
r2 =Mean radius of matching pipe, in
The inplane and outplane concept for a bend can be obtained from the attached figure from code or in layman’s language the same can be explained as follows:
The in-plane bending moment is the bending moment which causes elbow to close or open in the plane formed by two limbs of elbow.
In a similar way the out plane bending moment can be defined as the bending moment which causes one limb of elbow to move out of the plane keeping other limb steady.
From the above mentioned equations the following can be interpreted:
For the same pipe size and same pipe thickness
  1. A short radius elbow is having more SIF as compared to a long radius elbow.
  2. With increase in bend radius the SIF decreases and finally reaches to 1.0 for straight pipe.
  3. The SIF for a 45 degree elbow and a 90 degree elbow is same as bend radius is same.
  4. With increase in nominal pipe thickness or schedule the SIF of a bend (90 degree) keeps on decreasing till its value is equal to 1.0.

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