# Flexibility Stresses: Code Equations

Flexibility stresses

The piping system experiences different type of stresses when it is installed, tested and in operation. There are different codes according to which the system is designed, each code has different formula for calculating the stress induced in the piping system. Below mentioned are the code equations:

## 1. ANSI B 31.1 – Power Piping

The Power Piping Code ANSI B 31.1 specifies that the developed stresses due to sustained, occasional and expansion stresses be calculated in the following manner.

• 1.1 Sustained Where, Ss = Sustained stress

i     = Stress Intensification factor

MA= Resultant moment due to Primary loads Sh = Basic allowable stress at the operating temperature

Z   = Stress Intensification factor

• 1.2 Occasional Where, So  = Occasional stress

i     = Stress Intensification factor

MB = Resultant moment due to occasional loads K   = Stress Intensification factor

= 1.2 for loads occurring less than 1% of the time

= 1.15 for loads occurring less than 10% of the time

• 1.3 Expansion Where, SE  = Expansion stress range

MC = Resultant moment due to expansion (Secondary) loads SA  = Allowable e+xpansion stress range

## 2. ANSI B 31.3 – Process Piping

• 2.1 Sustained iiio = In-plane & out-plane stress intensification factor

Sh= Basic allowable stress at the operating temperature

• 2.2 Occasional

The code states that calculate the stresses due to sustained and occasional loads independently as per the above equation and then add them absolutely. The sum should not exceed 1.33 Sh.

• 2.3 Expansion Where, Mi  =Range of inplane bending moment due to expansion (secondary) load

Mo  = Range of outplane bending moment due to expansion (secondary)load

MT  = Range of torsional bending moment due to expansion load

SE = Expansion stress range

SA   = Allowable stress range

## 3. ANSI B 31.4 – Fuel gas piping

The code requires that the sustained, operating, expansion & occasional stresses be calculated and checked as below.

• 3.1 Sustained Where, Slp = Longitudinal pressure stress Sb  = Bending stress due to sustained loads

• 3.2 Expansion Where, Sb  = Range of bending stress due to varying loads St = Range of torsional stress due to varying loads Sy = Specified Minimum Yield stress

• 3.3 Operating Where, F = % of axial restraint

= 1 for buried pipe lines

= 0 for above ground pipelines

E = Modulus of Elasticity

a = Thermal expansion coefficient of pipe material

dT= Temperature change from ambient

V = Poisson’s Ratio

SH = Hoop stress = • 3.4 Occasional Where, Slp = Longitudinal pressure stress

Sb  = Resultant moment due to occasional loads

## 4. ANSI B 31.4 – Fuel gas piping

Like B 31.4 code B 31.8 also requires calculations and check of sustained, expansion, operating and occasional stress.

• 4.1 Sustained Where, Slp = Longitudinal pressure stress Sb  = Bending stress due to sustained loads

Sy = Specified Minimum Yield of pipe material

F  = Factor for construction type specified in table 841.114A

T  = Temperature derating factor specified in 841.116A

• 4.2 Expansion Where, Sb  = Bending stress due to varying loads

St  = Range of torsional stress due to varying loads

• 4.3 Operating • 4.4 Occasional Where, K  = Occasional load factor