5. Stress Categories

As explained on the other lesson: Piping Loading, a piping system will experience two types of loads: Sustained Load and Thermal Load, which will in turn resulting into two types of Stress into piping system, namely:

A. PRIMARY STRESS

Primary Stress is a type of stress caused by Sustained Load. This stress has a basic characteristic as not self-limiting. This is very hazardous stress, because if this stress occurs in the pipe and it exceeds the yield strength of material through the entire cross section of the piping, it will cause a failure of the pipe material, which in the end can cause an accident.

In the piping system, if this happens when stress analysis calculations are carried out, then the solution is usually very easy, which is by properly supporting the piping system, then the problem is solved. Primary stresses are the direct, shear, or bending stresses generated by the imposed loading which are necessary to satisfy the simple law of equilibrium internal and external forces and moments.

Primary Stress consists of the following components:

1. HOOP STRESS

This Stress is also called as Circumferential Stress, where the ratio of the pipe diameter to its wall thickness, D/t, is greater than 20, then the pipe may be considered to be Thin Wall, in accordance with Cooper, BS 8010. In this case, the Hoop Stress is nearly constant through the wall thickness and equal to:

Where:

• P = design pressure, psi
• D = Outside pipe diameter, in.
• t = pipe wall thickness, in.  

Hoop Stress is compared to Basic Allowable Stress at Operating Temperature.

2. LONGITUDINAL (AXIAL) STRESS (SL)

The Longitudinal Stress due to internal pressure is also constant through the wall and equal to half of the hoop stress. The total Longitudinal Stress is not only due to Internal Pressure, but also due to axial force and bending stress, as formula below:

SL = SL due to Axial Force + due to Internal Pressure + due to Bending Stress

SL = SL1 + SL2 + SL3

SL1 = Longitudinal Stress due to Axial Force
SL12 = Longitudinal Stress due to Internal Pressure
SL12 = Longitudinal Stress due to Internal Pressure

Legend:

• Fa = Axial Force, Lb.
• Am = Metal area of pipe, in2
• P = Internal Design Pressure, Psig
• D = Outside Diameter of Pipe, inches
• t = Wall thickness of pipe, inches
• Mb = Bending Moment, Pound – in
• Z = Section Modulus, in³

Total Longitudinal Stress will be checked against Code Allowable Stress or also known as Basic Allowable Stress at operating temperature (S_h).

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Radial Stress different with other stress since it varies through the wall, from P at the inner surface of the pipe to zero on the outer of surface.

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B. SECONDARY STRESS

Secondary stress is a stress caused by thermal loads. That is due to the temperature of the fluid which causes the pipe to expand or to contract ( expansion or contraction). It must satisfy an imposed strained pattern rather than being in equilibrium with an external load. The Basic characteristic of this secondary stress is that it is self-limiting.

In the piping system, if this happens when stress analysis calculations are carried out, then the solution is usually very easy, which is by properly supporting the piping system, then the problem is solved. Primary stresses are the direct, shear, or bending stresses generated by the imposed loading which are necessary to satisfy the simple law of equilibrium internal and external forces and moments.

Secondary Stresses are usually of bending nature which  acts on the cross section of the pipe wall thickness which varies from negative to positive and arising generally because of differential radial deflection of the pipe wall. Secondary Stress is not a direct cause of ductile material failure due to a single load application. If the stress that passes and above the Yield Strength, then the effect local deformation which results in a redistribution of the loading and a reduction of the stress in the operating condition. Only if this happens repeatedly, cyclic, will there be a so-called “local strain range” which has the potential to cause fatigue  failure.

Secondary Stress is also known as Expansion Stress or Displacement Stress Range, SE. The components of the Expansion Stress are Bending Stress (Sb) and Torsional Stress (St), in accordance with the latest SME B31.3 – 2020 paragraph 319.4.4. equation 17:

This equation is based on maximum shear theory, while the Expansion Stress will be checked against the SA, Allowable Displacement Stress Range.

The formula for each component is:
Sa = Axial Stress range due to displacement
Sb = Bending Stress range due to displacement
St = Torsional Stress range due to displacement

Where:

• Ap = Cross Sectional Area of pipe, in2
• Fa = Axial Force, lbf.
• ia = Axial stress intensification factor. If no data, then for Elbow, pipe bends, miter bends, use 1.0. or other components, i_a = io
• i_t = Torsional stress intensification factor. Use value from ASME B31J.
• i_i = In-plane stress intensification factor. Use value from ASME B31J.
• i_o = Out-plan stress intensification factor. Use value from ASME B31J.
• M_i = In-plane Bending Moment range between any two Conditions being evaluated.
• M_o = Out-plan Bending Moment range between any two Conditions being evaluated
• S_E = Equivalent Stress to be compared with Allowable Thermal Expansion Stress, psi
• Z = Section Modulus of pipe, in³
• A_m = pipe metal area, in²

Furthermore, there is one more stress category as described on Piping Handbook by Mohinder L. Nayyar, which is Peak Stress. Peak Stresses are the highest stresses in the region under consideration and are responsible for causing fatigue failure. Common types of peak stresses are stress concentrations at a discontinuity and thermal gradients through a pipe wall.