## How to perform a pipe stress analysis

**Learning objectives**

- Define and evaluate the pipe stress analysis process.
- Understand pipe stress analysis.
- Learn how to model a piping system and pressure design basics.

Pipe stress analysis is an analytical method to determine how a piping system behaves based on its material, pressure, temperature, fluid, and support. Pipe stress analysis is not an accurate depiction of the piping behavior, but it is a good approximation.

The analytical method can be by inspection, simple to complex hand calculations, or a computer model. The computer models can vary from 1-D beam elements to complex, finite element models. For instance, if it is a water system with no outside forces applied to the piping system, inspection or hand calculations are usually sufficient. If it is a high-pressure, high-temperature, hazardous-fluids system, and/or large outside forces are applied to the piping system, a computer-aided model may be required.

Understanding pipe stress analysis software does not make for a solid foundation of pipe stress analysis. It’s important to understand the various types of pipe stresses, the process, and other items related to pipe stress analysis for best practices in performing a pipe stress analysis.

There are many piping codes and standards that could be used during a pipe stress analysis depending on the application (power, process chemical, gas distribution) and location (country or local jurisdiction). However, to keep things simple, this discussion is based on American Society of Mechanical Engineers (ASME) B31.1 Power Piping. The physics of pipe stress analysis does not change with piping code.

Pipe stress analysis should be done primarily to provide safety to the public, whether you are designing a building heating system or a high-pressure gas line in a refinery. Public safety is paramount. The National Society of Professional Engineers (NSPE) Code of Ethics’ first cannon is: “Hold paramount the safety, health, and welfare of the public.”

On a good day, a pipe failure is only a broken support that the owner does not call the designer/engineer about. On a bad day, the owner requires the designer/engineer to pay for the damage and the engineer to provide a solution for free. On a horrible day, someone is killed.

Another reason a pipe stress analysis is performed is to increase the life of piping. Most engineers won’t consider a piece of pipe to be equipment, but it is no different than a pump. Both have moving parts and must be designed and maintained properly to ensure a proper life. Pipe stress analysis also is used to protect equipment, because a pipe is nothing more than a big lever arm connected to a delicate piece of equipment. If not properly supported and designed, it can have devastating effects on that equipment.

There are several common reasons that could warrant a pipe stress analysis, in addition to those above. They include:

- Elevated temperatures (>250°F).
- Pressure mandated (300 psig).
- Sensitive equipment connections.
- Large D/t ratio (>50).
- Piping subject to external pressures.
- Critical services.

The key when performing a pipe stress analysis is determining the required level of detail.

**How to model the piping system**

Pipe stress analysis computer models are a series of 3-D beam elements that create a depiction of the piping geometry. Three-dimensional beam elements are the most efficient way to model the piping system, but not necessarily the most accurate; and without complex finite element models, it is nearly impossible to account for everything. However, it is known from historical empirical testing that these methods and 3-D beam computer models demonstrate enough behavior that they are a good approximation. In addition, piping codes, such as ASME B31, have safety margins that allow for approximation. That being said, there are some pitfalls with modeling piping systems that one should avoid:

The computer models are only as good as the information entered into them. It is important when developing a pipe stress analysis, as with any finite element analysis (FEA) model, to also understand the physics and boundary conditions of the model.

Elements used to model the piping system have their limitations. One-dimensional beam elements are great for straight pieces of piping, but not so good with pipe fittings (elbows, tees, reducers, etc.). Therefore, ASME has developed stress-intensification factors (SIFs) for piping fittings through empirical testing. They allow for greater approximation without using complex FEA models with shells, plates, and brick elements.

It is important to make sure these limitations are considered when developing a pipe stress analysis. Most pipe stress analyses do not perform like a high-powered FEA software package.

**Three-dimensional beam element**

The 3-D beam element behaviors are dominated by bending moments. As mentioned above, it is efficient for most analyses and sufficient for system analysis. However, there are downsides to using a 3-D beam element:

- No localized effects will be seen on the pipe wall.
- No second-order effects.
- No large rotation.
- No accounting for a large shear load.
- Wall deflection occurs before bending failure.
- Short, fat cantilever versus long and skinny.

- No shell/wall effects can be seen.

**The main types of piping stresses**

There are five primary piping stresses that can cause failure in a piping system: hoop stress, axial stress, bending stress, torsional stress, and fatigue stress.

Hoop stress is the result of pressure being applied to the pipe either internally or externally. Because pressure is uniformly applied to the piping system, hoop stress also is considered to be uniform over a given length of pipe. Note that hoop stress will change with diameter and wall thickness throughout the piping system. Hoop stress is most commonly represented by the following formula:

**Axial stress** results from the restrained axial growth of the pipe. Axial growth is caused by thermal expansion, pressure expansion, and applied forces. If a pipe run can grow freely in one direction, there is no axial present—at least in theory. When comparing axial growth caused by pressure, steel-pipe growth is minimal at over 100 ft and can be ignored. Composite piping such as fiber re-enforced pipe (FRP) or plastic pipe will exhibit noticeable growth, as much as 2 to 3 in. over 100 ft under the right conditions (200 to 300 psi). The primary reason for the difference in growth rates under pressure is related to the modulus of elasticity. Steel has a modulus of elasticity of approximately 30 x 106 psi, whereas composites will be 2 to 3 orders of magnitude or less. Axial stress is represented by the axial force over the pipes cross-sectional area:

**Bending stress** is the stress caused by body forces being applied to the piping. Body forces are the pipe and medium weight, concentrated masses (valves, flanges), occasional forces (seismic, wind, thrust loads), and forced displacements caused by growth from adjacent piping and equipment connections. Body forces create a resultant moment about the pipe, for which the stress can be represented by the moment divided by the section modulus:

**Torsional stress** is the resultant stress caused by the rotational moment around the pipe axis and is caused by body forces. However, because a piping system most likely will fail in bending before torsion, most piping codes ignore the effects of torsion.

**Fatigue stress** is created by continuous cycling of the stresses that are present in the piping. For example, turning a water faucet on and off all day will create a fatigue stress, albeit low, because of the pressure being released and then built up. In power-cycle applications, the cycling of a steam turbine from low to high pressure/temperature creates a fatigue stress. Fatigue stress results in a reduction of allowable strength in the piping system and is commonly caused by cycling of:

- Pressure.
- Temperature.
- Vibration, flow induced or cause by rotating equipment.
- Occasional loads (a gentle breeze caused the Tacoma Narrows Bridge in Washington State to collapse from fatigue).

**Allowable code stresses**

Piping codes, such as those published by ASME, provide an allowable code stress, which is the maximum stress a piping system can withstand before code failure. A code failure is not necessarily a piping failure. This is because of safety factors built into piping codes. ASME codes consider three distinct types of stress: sustained stress, displacement (thermal or expansion) stress, and occasional stress.

**Sustained or longitudinal stress** is developed by imposing loads necessary to satisfy the laws of equilibrium between external and internal forces. Sustained stresses are not self-limiting. If the sustained stress exceeds the yield strength of the piping material through the entire thickness, the prevention of failure is entirely dependent on the strain-hardening properties of the material.

**Displacement stress** is developed by the self-constraint of the piping structure. It must satisfy an imposed strain pattern rather than being in equilibrium with an external load. Displacement stresses are most often associated with the effects of temperature; however, external displacements, such as building settlements, are considered a displacement stress.

**Occasional stress** is “The sum of longitudinal stresses produced by internal pressure, live and dead loads, and those produced by occasional loads,” according to ASME B31.1, paragraph 102.3.3(A). Occasional stresses can exceed the allowable code stress by a given percentage depending on frequency and duration of the load; for ASME piping codes, this is typically 15% or 20%. For example, wind loads can only exceed the allowable code stress by 15% due to their frequency, but seismic loads can exceed by 20% due to the relative infrequency of the loads.

**Pressure design basics**

As a pipe stress analyst, it is critical to understand how wall thickness is determined. If the pipe wall is too thin, it will not matter how the pipe is supported; it will fail. Typically, the engineer designing the system also will determine the wall thickness; however, the wall thickness is also verified during the pipe stress analysis. Most engineers are more concerned with mass flow and pressure drop, therefore the effects of pipe size and wall thickness may be lost on them. Going to a thicker pipe wall or a larger pipe size may be worth the material costs, versus facing design issues and added pipe-support costs in labor and materials.

Hoop stress (simplified) is PDo4tn. ASME codes apply a safety factor of two when determining wall thickness based on hoop stress, yielding:

.

The safety factor is to account for the additional stresses caused by bending and axial stresses to be applied later. Through basic algebraic manipulation, the code equation for wall thickness is:

*A* is the additional thickness added to the pipe corrosion, erosion, and wear during normal operation. The value of A is left up to the designer by ASME. However, most people consider 0.0625 in. to be an acceptable value.

The minimum will thickness (actual) shown above is based on the internal diameter (ID) of the piping. The main difference in the two wall thickness equations is the simplified version is more conservative, quicker, and easier to calculate for scheduled pipe. The actual version is closer to the measured hoop stress. Most stress analysis programs default to calculating hoop stress based ID.

Lastly, ASME codes require that minimum thickness account for the 12.5% mill tolerance:

Please note that when factoring in the 12.5% mill tolerance, multiplying by 1.125 is not the same as dividing by 0.875.

**Sustained stresses**

For someone who is new to pipe stress analysis—there is no reason sustained stresses in the pipe should be greater than 55% of the standard allowable stress. There are a couple of reasons why. First, recommended pipe support spans are governed by deflection, and not by allowable stress, to ensure proper flow and drainage. The second is from the discussion above, the wall thickness is based on a safety factor of two, which is removed from the sustained-stress equation.

Manufacturers Standardization Society (MSS) SP-58: Pipe Hangers and Supports—Materials, Design, Manufacture, Selection, Application, and Installation recommends support spans to be based on deflection criteria of approximately 0.125 in. or less between supports. The deflection criteria assume a simply supported beam. However, a supported piping system is a continuously supported beam that reduces reaction and moments at each support, further reducing the deflection between supports. This negates the bending moments between supports and reduces the bending moment term of sustained stress.

Below is the sustained equation from ASME B31.1:

The simplified hoop-stress term is in the equation above, is based on minimum wall thickness, and is approximately at 50% of allowable stress, based on the wall thickness safety factor. However, in the equation above, hoop stress is based on nominal wall thickness, which is at least 1/0.875 times greater than minimum wall thickness. Conversely, if hoop stress as a function of minimum wall thickness is 50% of allowable code stress, then hoop stress as a function of nominal wall thickness is 50% x 0.875 = 43.75%.

As mentioned above, the sustained-stress equation is based on nominal wall thickness, with extra wall thickness for milling and corrosion. Because there is extra wall thickness, the pipe has extra strength available to resist deflection. Furthermore, to achieve pipe failure from deflection, the supported pipe spans would be at least three to four times greater in length than the recommended MSS SP-58 spans. The moment due to dead weight contributes approximately 10% code stress to the equation above when using MSS SP-58 recommended pipe-support spans.

Looking back at the sustained-stress equation above, if you assume 10% code stress from the deadweight moments and 44% code stress from hoop stress, the sustained stress should be approximately 54% or less. If this is not the case, there are usually excessive deflections at a bend and/or concentrated mass in the piping, creating a higher-than-expected bending moment from an unbalanced system (see Table 2).

**Standard span guidelines**

Below are some general thoughts on standard pipe spans to consider:

- Fluid has a greater impact as the pipe size becomes larger. Water weight is more than pipe weight for 12 in. nominal pipe size (NPS) for standard wall thickness (STD), or greater.
- When concentrated loads, such as flanges, valves, and piping specialties, are present between pipe supports, the recommended span should be reduced to account for them.
- A pipe support should be placed within one-third the recommended span of a rotating equipment connection to minimize vertical load and moments at connection. In most cases, this support should be a variable spring to help with adjustment and reduce translation vibration.
- When piping changes horizontal direction, the recommended span between pipe supports shall be reduced by 25%.

**Displacement stresses**

In most cases, if displacement or expansion stresses are perceived to be a concern (e.g., elevated temperatures), then a computerized pipe stress analysis is required. If a computerized analysis is performed, displacement stresses should be kept at 80% to 90% of what the code allows.

Typically, this recommendation is met by ensuring the equipment connection loads are within published allowable code stresses through adding flexibility to the piping system. Flexible piping systems typically have low displacement stresses because the piping can grow freely.

**Occasional stresses**

Occasional stresses in the piping system are caused by short-term events, such as seismic, wind, and relief-thrust loads. These three loads comprise most of the possible occasional load combinations. Because occasional stresses are short-term, most piping codes allow for increased pipe stresses for a brief period. ASME codes typically allow an increase of:

- Fifteen percent if the event lasts less than 8 hours and no more than 800 hours per year
- Twenty percent if the event lasts less than 1 hour and no more than 80 hours per year.

Typically, wind loads fall under the 15% increase category, where seismic and relief thrust would be a 20% increase.

If occasional stresses are perceived to be a concern or are complex in nature, a computerized pipe stress analysis is warranted. However, in most cases. adding lateral restraints for every three or four nominal pipe-support spans will cover most seismic or wind loadings, unless they are in a high seismic zone, such as California, or are subjected to coastal wind loading with sustained hurricane winds.

**Keep pipe analysis records**

Most people believe that a computer printout is a sufficient record of a pipe stress analysis. This a big mistake that can be avoided with little effort. Creating a record of your work is about more than keeping a hard copy or PDF of the computer-aided pipe stress analysis. It means documenting a trail of all inputs, not just the drawings used to create the piping geometry. Items that could be included are the piping and instrument diagrams, system parameters, load cases, and any corresponding external forces applied to the piping system, pipe-support locations, and type of pipe support used. Most pipe stress analysis records will fill a three-ring binder.

As most consulting engineers have internal quality assurance/quality control procedures, develop a standard list of the inputs commonly used and corresponding reference for the information. This would provide the checker of a calculation a place to sign off, indicating they concur with the input and acknowledge the source of the input. In the end, your documentation should tell a complete story.

**Monte Engelkemier** is the group engineering lead for piping, mechanical, and equipment in the starches, sweeteners, and texturizers division of Cargill. Prior to that, he was a member of Stanley Consultants for 12 years, where he authored this article before taking his current position.