Coping With Stress in Piping Systems

When piping fails, is it because the pipe designer doesn’t know how to deal with stress? Pipe designer David Willoughby, POE, discusses the essentials of piping system stress analysis.

Variable spring stress relief pipe hangers in a jet fuel system. Courtesy of Burns & McDonnell Engineering Co., Inc.

If you have been involved in the design or construction of piping systems for very long, you probably have seen some system failures. Most of us have seen the pipe section that failed, the weld that broke or the joint that separated.

Often, the first reaction is to blame the material. While faulty material is sometimes the cause, the culprit is often an improper design that results in over-stressing the piping material. The piping system designer who fails to consider pipe stress can often be faced with significant problems once the system is operational. In coping with piping stress, the proverbial ounce of prevention certainly saves a pound of cure.

Piping system stress analysis is an integral part of the design process. Optimizing the design can reduce installation and operating costs while maintaining reliability and safety. Many piping systems are designed and installed using rules of thumb and experience with similar systems. While these methods may result in a working system, they are not likely to minimize installation or operating costs.

With the help of computer programs available today, the piping designer can make quick and accurate decisions concerning pipe material selection, hydraulics and stress analysis. By considering these factors during the design, the designer can optimize the piping, and the installation and operating costs may be reduced.

During the design process, our main job is to develop a piping system that will deliver the product from Point A to Point B in a safe, reliable and economical way. Normally, the first thing we do is select the piping material based on the product to be handled, the design temperature and the design pressure. The pipe is then sized to meet the hydraulic requirements. Finally, the pipe supports, guides, anchors and expansion compensation are selected based on the system geometry and pipe stress analysis.

Photo 1: The Alyeska Pipeline in Alaska originates from the North Slope oilfields and travels through an earthquake zone. The “accordian pleat” configuration of the 42-inch diameter pipeline, one of the largest examples of stress relief engineered into a pipeline, allows for excessive movement of the pipeline in all directions.

What is stress analysis?
The stress analysis of a piping system consists of the calculations to determine the static and dynamic loads imposed on the pipe by:

  • Gravity
  • Temperature
  • Internal and external pressures
  • Fluid flow rates
  • Seismic and wind activity

The analysis of piping stress is a system design function that closely considers piping layout, pipe supports and hydraulic profile. Each of these items can affect the other, so they must be considered as a whole. When designing a piping system, the layout should be examined until balances between the stresses and layout efficiency are obtained. After the layout has been determined, the piping supports are designed and checked for stress.

For petroleum piping systems, the main categories of stress are primary and secondary. Primary stresses are the loads imposed by external forces (weight) and internal forces (pressure).

If a primary stress exceeds the yield strength of the pipe material, then the pipe will fail. Primary loads are also divided into two categories, sustained and occasional, based on the duration of the load. Sustained loads, such as pressure and weight, are present throughout normal piping system operations. Occasional loads, such as earthquakes, wind and fluid transients (e.g., waterhammer), are experienced at infrequent intervals (see Photo 1).

Secondary stresses are developed by the restraint of the piping system. Displacements in the piping system are caused by thermal expansion or contraction. As the displacement is restrained by anchors or other piping system equipment, expansion stresses are developed. Yielding and minor distortions in the piping system tend to relieve these forces. However, for sections of piping restrained by equipment, such as pumps or tanks, these stresses can be damaging if the system is not properly designed.

Figure 2: Longitudinal Stress of Different Pipe Materials
		Temperature (ºF)

Sustained load from pressure
Internal pressure in the piping normally causes stresses in the pipe wall rather than loads on the pipe supports (see Photo 2).

This is because pressure forces are balanced by tension in the pipe wall that results in zero pipe support loading. The longitudinal stress developed in the pipe due to internal pressure is calculated as follows (see also Figure 1 and 2):

SLP = Longitudinal stress (psi)
P = Internal design pressure (psig)
D = Outside pipe diameter (inches)
t = Pipe wall thickness (inches)

When expansion joints are used in piping systems, the pressure forces cannot be balanced by the tension in the pipe wall. In this case, the pressure forces are resisted by the pipe supports and anchors.

Photo 2: Laboratory testing can be performed with a pressure tank to determine the internal pressure within a pipe. Piping with a flexible wall eases stress seen by system joints and fittings and absorbs shocks. Courtesy of Total Containment, Inc.

Photo 3: This is a crush test done in a laboratory setting. It determines the hoop strength of the pipe necessary when calculating primary stress due to sustained loads from weight. Courtesy of Total Containment, Inc.

Sustained load from weight
The total design weightload of pipe should include the weight of the pipe, fittings, insulation, product in the pipe, all piping components (e.g., valves and flanges) and pipe supports (see Photo 3).

Pipe supports should be designed and spaced to support the load that will be placed on the pipe (see Photo 4).

Use the following general formula for calculating the maximum unsupported span length based on stress:

L = Maximum unsupported span length based on stress (feet)
S = Pipe pressure parameter (psi)

Note: To find “S” (the pipe pressure parameter) for use in Formula 2 for pipe containing water (or other liquid) during test or operation of the pipeline, use the following formula.

S = Pipe pressure parameter (psi)
Y = SMYS-Specified Minimum Yield Strength of pipe (psi)
H = Test or operating pressure (psig)
D = Outside diameter of pipe (inches)
t = Wall thickness of pipe (inches)
Z = Section modulus of pipe (cubic inches)
W = Weight of pipe, wrap and contents per linear foot, (pounds/foot )

Photo 4: Example of spaced pipe supports for supporting weight of pipe and fluid (jet fuel), Kingsford-Smith International Airport, Sydney, Australia. Courtesy of Burns & McDonnell Engineering Co., Inc.

Thermal expansion loads
For weight analysis, the more pipe supports that are installed, the lower the stress developed in the pipe. The opposite is true for piping thermal loads. When thermal expansion or contraction of the piping is restrained at supports, anchors, penetrations and other equipment, large thermal stresses and loads may develop.

If the piping system is free to move, the linear expansion due to thermal conditions can be calculated by the following formula:

E = Elongation (same unit as L)
C = Coefficient of linear expansion (inches per inch per degrees F)
steel 6.80E-06
cast iron 6.60E-06
copper 9.00E-06
plastic 9.0E-05
L = Length (inches, feet, or metric)
T = Temperature (degrees F)

If the piping system is restrained, the longitudinal stress that will be seen at the supports, due to the temperature change, is:

S = Stress (psi)
E = Modulus of elasticity (psi)
C = Coefficient of linear expansion (inches per inch per degrees F)
T = Temperature (degrees F)

A good piping system design will make effective use of elbows, bends and pipe expan-sion loops (see Photo 5) to provide adequate flexibility for thermal loads.

Photo 5: An expansion loop in jet fuel storage tank piping. Courtesy of Burns & McDonnell Engineering Co., Inc.

In Figure 1, there is no specific dimension for W; however W is usually the same as L, but can be as little as 1/2 L when necessary for installation space requirements. To calculate the length required to absorb movement without damage, the following formula is used:

L = Pipe leg length (feet)
D = Nominal outside diameter of pipe (inches)
E = Change of dimension of pipe run (length in inches). This number is calculated from the expansion coefficient of the pipe material (Formula 4).

Figure 3: Expansion loop diagram. In Formula 6, there is no specific dimension for W; however, W is usually the same length as L.

If it is not possible to provide adequate flexibility in the piping system, an expansion joint is normally used to absorb the expansion and contraction of the pipe. In general, expansion joints are used where:

  • thermal movements cause excessive stress in the piping system;
  • space is inadequate to design flexibility into the piping system;
  • reactions transmitted by the pipe supports or anchors create large loads on supporting structures; and
  • reactions to equipment are in excess of the allowable material stresses.

Many types of expansion joints are available, ranging from a piece of rubber hose to metal bellows. Restraints are usually installed on both sides of an expansion joint to prevent the pressure force from pulling the joint apart. The pressure force devel-oped in the expansion joint is equal to the internal pressure multiplied by the cross-sectional area over which the pressure is applied.

Occasional loads
Occasional loads are loads caused by wind, earthquake and fluid transients. These loads are considered primary loads during a stress analysis. Depending on your geographic location and the location of the piping system aboveground or underground, the wind and seismic loads may be a factor. Transient, or dynamic loads, can also be a factor depending on the hydraulic profile of the system.

Photo 6: Relaxed primary pipe

Transient loads are often caused by waterhammer and relief valve discharge (see Photo 6). (Water hammer is discussed my article, “Tips on Getting a Good Large Petroleum Piping System,” PE&T, April 1999, page 11).

If your piping system has frequent hydraulic cycles, such as pump shut-on and shut-off valves that open and close and pressure relief valve discharge, transient stresses can develop. The fluid transient loads can cause forces on the pipe wall, pipe components, pipe supports, and anchors that exceed the material strength. Dynamic loading must be evaluated during the piping system design to ensure the stresses developed do not exceed the specified material capabilities.

Photo 7: Stressed primary pipe

Photo 8: Photos 6 and 7 combined

Analyzing for stress
Piping systems, large and small, are subject to many types of stress that can have potentially damaging effects to the system. The piping system designer is required by code, and the practice of good design, to ensure that the piping design is not over-stressing any of the materials or components within the piping system. Stress analysis of the piping system can be performed by following the steps and calculations specified in the applicable codes and standards.

Manual calculations for stress analysis can be performed on the piping system. However, on all but the simplest piping systems, this process can be time consuming and will require many repetitive calculations. While each of the steps can be performed using manual calculations and accepted guidelines, computer modeling can integrate these steps and allow the designer to vary the system’s parameters. The designer can then quickly optimize the overall system. With this approach, the designer can deal with questions such as:

  • Should I use six-inch API 5L steel pipe with a .250 pipe wall thickness supported every 15 feet? Or should I use a six-inch API 5L steel pipe with a .375 wall thickness supported every 30 feet? Would the increased material (thicker wall) and increased support spacing reduce the overall operating and installation costs?
  • If I use thinner wall pipe will it take the pressure and temperature?
  • What is the best pipe material for the pressures and temperatures that the piping system will be subjected to? n How much expansion compensation will be needed for the system?
  • At what intervals will I need to place the pipe supports?

Photo 9: Flexible piping eliminates the need for expansion joints to absorb shocks, simplifying system installation. Courtesy of Total Containment, Inc

Restrained and unrestrained systems
All piping systems are subjected to loads. Provision must be made for the piping system to have the strength and flexibility to prevent excessive stresses from damaging the piping system. The stresses that may develop in the piping system are functions of both the loads on the piping system and the degree of restraint against the motion. Stresses may be reduced to acceptable levels by a combination of anchors; extra depth for buried piping; the use of bends (see Photo 9), loops and offsets in the piping; heavier wall piping; and other means (see photo on Top).

Piping systems can be classified as restrained or unrestrained. Restrained systems are restrained from movement by anchors, supports, other equipment or by being buried. Unrestrained systems are free to move. A challenge in piping system design is finding the balance between too much restraint and too much movement. Too much restraint can cause excessive forces on the piping system. Too much movement can cause problems at equipment connections, laterals and piping components such as elbows and tees.

Buried piping is usually considered restrained against expansion or contraction due to the overburden of soil and soil pipe friction. However, thermal expansion of buried piping may cause movement at a transition from buried to aboveground piping. There may also be movement where buried piping changes direction if there is insufficient soil restraint. The piping system must be designed with adequate flexibility in these areas, or anchors should be provided.

For buried piping, the interaction of the pipe material and the soil will have an opposing friction effect with the maximum stress due to soil friction occurring at the middle of the pipe section. The friction stress is calculated by the following formula:

SLP = Stress longitudinal friction (psi)
L = Length of pipe section
H = Depth of soil cover above the pipe
ð = Unit weight of the soil cover
p = Coefficient of friction between the piping and the soil
t = Piping wall thickness

Photo 10: Four-inch bottom loading arms with API bottom loading couplers. Stress analysis for this type of system is usually based on ASME B31.4. Photo courtesy of OPW Engineered Systems.

Codes and standards
Various codes and standards govern the stress analysis in different kinds of piping systems. These codes and standards contain the reference data, formulas and equations required for piping system design and stress analysis.

Codes usually establish the minimum requirements for the design, materials, fabrication, construction, testing and inspection of piping systems. Compliance with codes is generally required by regulations imposed by the regulatory agencies. Standards contain design and construction requirements for piping components such as elbows, tees, flanges, valves and other in-line items. Compliance with standards is normally required by the applicable codes or the project specifications.

Each code has limits on its jurisdiction, which is defined in the code. Similarly, the scope of application for each standard is defined in the standard. The piping system designer must be familiar with the codes that apply to the particular piping system. Codes and standards that do not apply to the piping system being designed should not be used, as they may impose unnecessary requirements and increase cost.

The codes and standards which relate to piping systems and piping components are published by various organizations. In addition to any local codes, the primary national codes and standards organizations are the:

  • American Society of Mechanical Engineers (ASME)
  • American National Standards Institute (ANSI)
  • American Society For Testing and Materials (ASTM)
  • American Petroleum Institute (API)

The ASME Codes are primarily used for stress analysis in the design of petroleum piping systems. Depending on what type of petroleum piping system is being designed, the following ASME Codes will apply:

ASME B31.3, Chemical Plant and Petroleum Refinery Piping

ASME B31.4, Liquid Transportation Systems for Hydrocarbons, Liquid Petroleum Gas, Anhydrous Ammonia, and Alcohols

It is beyond the scope of this article to cover the codes and standards in depth. Each code imposes its own set of calculations that must be performed for stress analysis. Regardless of the calculations used, each code checks and limits the following stresses:

  • Stresses due to sustained loads
  • Stresses due to occasional loads
  • Stresses due to expansion loads

Use the computer
A piping system is subjected to many static and dynamic loads and stresses. Using effective and proven design procedures, the piping system designer can determine and control the loads and stresses and their effects on the piping system. On simple piping systems, general rules of thumb and a few hand calculations will quickly identify potential stress problems.

For complex piping systems and systems that will see excessive loads, computer stress analysis is highly recommended. Deciding which approach to take is often a difficult task within itself. If in doubt, err on the safe side. A little extra effort spent on the stress analysis during the design process can save substantial dollars that otherwise would be spent if the piping system fails once it is operational. As I said at the start, an ounce of prevention is worth a pound of cure.

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