**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, S_{s} = Sustained stress

i = Stress Intensification factor

M_{A}= Resultant moment due to Primary loads

S_{h} = Basic allowable stress at the operating temperature

Z = Stress Intensification factor

**1.2 Occasional**

Where, S_{o} = Occasional stress

i = Stress Intensification factor

M_{B }= 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, S_{E} = Expansion stress range

M_{C }= Resultant moment due to expansion (Secondary) loads

S_{A} = Allowable e+xpansion stress range

## **2. ANSI B 31.3 – Process Piping**

**2.1 Sustained**

Where, F_{ax} =Axial force due to sustained (primary) loading

M_{i} =In-plane bending moment due to sustained (primary) loading

M_{i} = Out-plane bending moment due to sustained (primary) loading

i_{i}i_{o} = In-plane & out-plane stress intensification factor

S_{h}= 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 S_{h}.

**2.3 Expansion**

Where, M_{i} =Range of inplane bending moment due to expansion (secondary) load

M_{o} = Range of outplane bending moment due to expansion (secondary)load

M_{T} = Range of torsional bending moment due to expansion load

S_{E} = Expansion stress range

S_{A} = 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, S_{lp} = Longitudinal pressure stress

S_{b } = Bending stress due to sustained loads

**3.2 Expansion**

Where, S_{b } = Range of bending stress due to varying loads

S_{t } = Range of torsional stress due to varying loads

S_{y} = 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

S_{H } = Hoop stress =

**3.4 Occasional**

Where, S_{lp} = Longitudinal pressure stress

S_{b } = Resultant moment due to occasional loads

K = Occasional load factor

**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, S_{lp} = Longitudinal pressure stress

S_{b } = Bending stress due to sustained loads

S_{y} = 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, S_{b } = Bending stress due to varying loads

S_{t } = Range of torsional stress due to varying loads

**4.3 Operating**

**4.4 Occasional**

Where, K = Occasional load factor