As per layman’s language **Piping Stress analysis** is the analysis of stresses in the piping system. Now the question arises what are these stresses? **Piping Stress is generated whenever a load acts on a piping system and tries to deform it. Due to the inertia effect, the piping system will resist that force by an internal resistance force creating the stress.** So, first, we need to know the loads that create these stresses. **There are various kinds of loads that generate stresses in a piping system as listed below:**

**Weight Loads:**Pipe Weight, Fluid Weight, Insulation Weight, Valve, Actuator, Flange Weights (Rigid Weights), Snow weight (in snowfall areas), Sand Weights (where frequent sand storms happen); Rail and Truck weights for buried piping.**Pressure:**Internal and External Design and Operating Pressures, Hydrotest Pressure.**Temperature Change:**Both maximum and minimum temperature range, Black Bulb temperature, steam out temperature condition.**Occasional Loads:**Slug force, Surge force, Vibration, Seismic Events, High-Speed Winds, Relief Valve popping, Settlement.

As we know the loads that create stresses in a piping system, let’s proceed to explore the types of stresses in a Piping System.

## Types of Piping Stresses

The following kinds of piping stresses are generated in a piping system.

**Normal Stresses**

**Normal stresses act in a direction normal to the face of the material crystal structure. Normal stresses may be tensile or compressive and can be applied in more than one direction depending on the application and type of loads.** Three types of normal stresses exist in a piping system. They are:

- Longitudinal or Axial Stress
- Hoop or circumferential Stress and
- Radial Stress.

### Axial Stress or Longitudinal Stress in a Piping System:

**Axial Stresses or Pipe Longitudinal Stresses are the normal stresses that act parallel to the longitudinal axis of the pipe centreline axis.** In a piping system, Longitudinal stress can be generated by three reasons:

- An Axial force of some kind
- Internal Design Pressure
- Bending Moment

Refer to Fig. 2 and let’s assume that force F_{ax} is acting in the pipe Axially. So this force will generate axial pipe stress or longitudinal stress in the pipe metal, S_{L}

#### Hence, The Longitudinal Stress, S_{L}=F_{ax}/A_{m}.

Here, A_{m} is the pipe metal cross sectionals are that can be calculated as follows

Now this Axial Load, F_{ax }can be created due to internal pressure, P which acts on internal pipe area A_{i}. So in that situation the longitudinal force will be given by:

As d_{m} is always greater than d_{i}, P d_{i}^{2}/4d_{m}t <Pd_{i}^{2}/4d_{i}t = Pd_{i}/4t

Conservatively, the longitudinal pressure stress is approximated as

### S_{L}=Pd_{o}/4t

Again, the axial load, Fax can be generated by bending which is given by the following equation:

Now adding all the above component stresses we get,

### S_{L}=F_{ax}/A_{m}+Pd_{o}/4_{t} + M_{b}/Z

### Hoop Stress or Circumferential Stress in a Piping System:

**The Normal Stress that acts perpendicular to the axial direction or circumferential direction is known as Hoop Stress. Hoop stress is caused by Internal pressure.**

The Hoop stress is conservatively calculated as

### S_{H}=Pd_{o}/2t

As can be seen from the simplified equations of pressure stresses, **Hoop stress is twice of longitudinal stresses and hence is of utmost importance.**

Pipe material thickness is normally decided considering this Hoop Stress Equation.

### Radial Stress in a Piping System:

Radial Stress is the normal Stress that acts parallel to the pipe radius and caused by internal pressure. It varies between the internal design pressure at the inside pipe surface and atmospheric pressure at the outside pipe surface as shown in Fig. 4 below.

Now if we compare, radial stress with respect to longitudinal pressure stress or hoop stress we can find that radial stress is many times lesser than those two stresses. This is the reason radial stress for piping systems is ignored most of the time.

### Shear Stress in a Piping System:

**Shear stresses act in a direction parallel to the face of the plane of the material crystal structure.** This stress provides a slipping tendency to one plane against the other. Shear forces can be caused by

- the shear forces acting on the pipe cross-section or
- the twisting or torsional moments.

Since the shear stresses caused by shear forces in a piping system is very small, this is neglected. However, Shear Stresses caused by torsion is of considerable amount.

Shear Stresses caused by torsion is calculated by the following equation:

### Thermal or Expansion Stresses in a Piping System:

Thermal or expansion stress in a piping system is generated when the free thermal movement of the pipe is restricted. The pipe is installed at ambient or atmospheric temperature and during operation, it carries fluids of different temperatures. So with a change in temperature, pipe length is changed. As this free thermal movement is restricted by the supports or end equipment connections expansion stress is created.

In the above figure due to change in temperature ΔT, the pipe length change ΔL= α.ΔT. L.

Thermal Strain= ΔL/L= α.ΔT

So Thermal Stress= Thermal Strain X E= E.α.ΔT

## Piping Stress Types as Per Piping Code

As per the piping code, piping stresses are categorized into three groups.

**Sustained Stress****Expansion Stress and****Occasional Stress**

**Sustained stress are stresses those present throughout the plant operating life. Weight and Pressure are called Sustained stresses.**

**Expansion stress is a displacement driven secondary stress generated due to temperature changes from installed to operating condition.**

**Occasional stresses are stresses those are present in a piping system for a very short period of time. Stresses due to Seismic event, Surge, Wind, Vibration, etc. are called occasional stresses.**

Few more related resources for you.

Basics of Pipe Stress Analysis

What does a Pipe Stress Engineer need to know?

Piping Stress Analysis Basic Theories

Piping Stress Analysis using Caesar II

Piping Stress Analysis guides using Start-Profs

## Video Tutorial on Pressure Stresses in Piping System

The following video tutorial by **EngineeringTrainer team** provides a very clear insight into the **pressure stresses in the piping system.**

Anup Sir please Explain why sustain and expansion stresses they have different allowable limits in code? Is there any derivation for that? Why sustain and expansion two different stresses exist? Why don’t we calculate stress for direct operating case(W+P+T+D) using principles stresses and theories of failure like von mises?Please Explain in brief.

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Very educative article

Well articulated.