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.
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:
1.Elevated temperatures (>250°F).
2.Pressure mandated (300 psig).
3.Sensitive equipment connections.
4.Large D/t ratio (>50).
5.Piping subject to external pressures.
6.Critical services.
The key when performing a pipe stress analysis is determining the required level of detail.
They include:
1.Elevated temperatures (>250°F).
2.Pressure mandated (300 psig).
3.Sensitive equipment connections.
4.Large D/t ratio (>50).
5.Piping subject to external pressures.
6.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.
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:
1.No localized effects will be seen on the pipe wall.
2.No second-order effects.
3.No large rotation.
4.No accounting for a large shear load.
4.1. Wall deflection occurs before bending failure.
4.2.Short, fat cantilever versus long and skinny.
5.No shell/wall effects can be seen.
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:
1.No localized effects will be seen on the pipe wall.
2.No second-order effects.
3.No large rotation.
4.No accounting for a large shear load.
4.1. Wall deflection occurs before bending failure.
4.2.Short, fat cantilever versus long and skinny.
5.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:
Zigma (hoop) = PD/4t
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:
Zigma (hoop) = PD/4t
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:
Zigma (axial) = F/A
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:
Zigma (axial) = F/A
Bending stress⬇️⬇️
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:
Zigma (b) = M/Z
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:
Zigma (b) = M/Z
⬇️⬇️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:
1. Pressure.
2. Temperature.
3. Vibration, flow induced or cause by rotating equipment.
4. Occasional loads (a gentle breeze caused the Tacoma Narrows Bridge in Washington State to collapse from fatigue).
1. Pressure.
2. Temperature.
3. Vibration, flow induced or cause by rotating equipment.
4. 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.
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.
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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.
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.
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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.
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.
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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.
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.
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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.
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.
Basic of Caesar 2 API610 analysis ⬇️