A typical piping system consists of combination of pipes and various fitting components like bends, Tees, O’lets etc. The plant piping systems are subjected to various types of loading due to weight, pressure, temperature, wind, water hammer etc. causing possible failure modes, based on type of loading, as plastic, rupture, fatigue, creep etc. In addition, pipe exhibits different geometric characteristics at fittings which have notable effect on the flexibility of the piping system. This in turn has influence on stress concentration at fittings and the loads produced due to it. This article attempts to explain basic concepts of flexibility, stress intensification factors and their equations provided in ASME B31 codes.

Two pipes can be connected as pipe to pipe joint or by means of various fittings viz. bends, Tee‟s, O‟lets etc. Simple beam theories which can be applied to straight pipe may not be able to reflect true behavior of the piping fittings due to varying cross sections, thickness, curvatures etc. Hence it is essential to consider additional stresses at the fittings by introducing Stress Intensification Factor (SIF). Here, stress intensity calculations followed in Process Piping Plants referring to code ASME B31.3 is explained.

## FLEXIBILITY CHARACTERISTICS, FLEXIBILITY FACTOR & STRESS INTENSIFICATION FACTOR

To elaborate the concept of Stress Intensification factor (SIF), an example of bend has been considered. Abbreviations:

h =Flexibility characteristics

T =Nominal wall thickness of header pipe or bend, in

R1 =Bend radius, in

r2 =Mean radius of matching pipe, in

Sb =Bending stress, PSI

M =Bending moment, lb-in

Z =Section modulus of pipe, in^3

i =Stress intensification factor

N =Number of load cycles

**Flexibility Characteristics, h**

It is a geometric characteristics based on the nominal wall thickness and mean radius of the fitting. ASME B31.3 defines it as a unit less number calculated based on type of fitting.

Example: for a bend

h = T R1 / r2^2

Flexibility characteristics is used to calculate Flexibility factor and SIF. It is in inverse proportion to Flexibility factor and SIFs.

**Flexibility factor, k**

The most common fitting used in Piping system is “Bend” due to its inherent flexibility characteristic which results due to its ability to ovalize under the action of bending moment. Consider a straight pipe with length ‘l’ which will produce rotation ‘Ө’ under the action of bending moment ‘M’. A bend having same diameter and thickness with same arc length ‘l’ under the action of same bending moment ‘M’ will exhibit ‘k Ө’ rotation. In nutshell, bend shows k times flexibility than the straight pipe, called as Flexibility factor.

**Stress Intensification Factor (SIF)**

The behavior of a straight pipe and a bend under the externally applied bending moment is different. Straight pipe acts like a beam retaining the cross section as circular whereas, the bend takes oval shape. Due to ovalization of the bend the outer fiber comes closer to the neutral axis reducing moment of inertial and subsequently the section modulus of the bend which in turn enhances bending stress.

The bending stress in a straight pipe is calculated as

Sb = M / Z

The bending stress in a bend is calculated as

Sb’ = M / Z’ where Z’ is reduced section modulus.

Thus the stresses in the bend are higher compared to straight pipe of same size due to the reduced cross section.

The SIF of Bend = Sb’ / Sb.

SIF can be defined as ‘the relation of rotation per unit length of the part in question produced by a moment, to the rotation per unit length of a straight pipe of the same nominal size and schedule or weight produced by the same moment or simply Actual Bending Stress to the Calculated Bending Stress.

*The content of this article is taken from web open source. The blogs are intended only to give technical knowledge to young engineers. Any engineering calculators, technical equations and write ups are only for reference and educational purpose.*

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