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Flexible Metal Hoses: An essential guide

Written by Anup Kumar Dey in Engineering Materials,Mechanical,Piping Design Basics,Piping Interface,Piping Stress Analysis,Piping Stress Basics

A flexible hose is a type of piping used to connect two distant points to transport or transfer fluid. In Oil & Gas applications, hoses are used when there is a considerable relative movement. A variety of fluids and fluidized solids can easily be transferred through flexible hoses to other locations. These are most commonly known as hosepipes. Along with loading and unloading services in processing plants, these are widely used by homeowners as garden hoses. Normal Flexible hoses are made of non-metals like soft plastic material or synthetic rubber. However, flexible hoses of chemical industries that are designed to absorb pipe movements are made of metallic materials.

Non-metallic Flexible Hoses

Flexible hoses are made by extrusion or vulcanization process. To add strength to the non-metallic flexible hoses, they are reinforced using a crisscrossed grid of fibers combined together through braiding, spiraling, or knitting. These reinforced hoses can be long enough. Basically, flexible hoses have four parts; inner tube, reinforcement, End fittings, and protective outer cover.

Flexible Metal Hoses

Metallic flexible hoses consist of corrugated tubing, braid, braid collars, and end-fittings as shown below:

Typical Flexible hoses
Fig. 1: Typical Flexible hoses

Metallic flexible hoses are available in various end connections like welded pipe ends, flanged ends, threaded ends, tube ends, coupling ends, etc to meet a broad range of application requirements.

Flexible Hose End Connections
Fig. 2: Flexible Hose End Connections

Types of Metallic Flexible Hoses

Two types of metallic flexible hoses are widely used in industries.

  • Corrugated hoses and
  • Interlocked hoses

Fig. 3 below shows the basic construction of corrugated and interlocked flexible hoses.

Corrugated vs Interlocked flexible hoses
Fig. 3: Corrugated vs Interlocked flexible hoses

Corrugated Hose:

A corrugated hose is constructed with a bellow of very long length. Fundamentally, the behavior of a corrugated flexible hose is the same as the bellow expansion joint. The flexible hose has to resist the hoop pressure stress, but cannot sustain the longitudinal pressure stress. Also, it has a tendency to squirm under internal pressure. To resist the longitudinal pressure stress and prevent squirm, corrugated hoses are often constructed with braids wrapping around the outside surface as shown in Fig. 4. The braided cover also protects the corrugation from scratch and wear. The braided hose, similar to a tied expansion joint, cannot accommodate any axial movement. On the other hand, the un-braided hose can sustain very small internal pressure.

Due to the lack of a limiting mechanism, a corrugated flexible hose is prone to abuse. It should not be bent beyond its acceptable range. For braided hoses, the situation is even more critical.

As the corrugations are not visible from the outside, a braided hose does not show immediately when damaged. Therefore, for manual handling in such situations as loading/unloading and switching operations corrugated hose is not suitable. The corrugated flexible hose has a continuous metal wall thus making it pressure-tight. It is suitable for handling any type of gas and liquid as long as it is compatible with the hose material.

Unbraided and braided flexible hose
Fig. 4: Unbraided and braided flexible hose

Interlocked Hose:

An interlocked hose is constructed with links that are kept tight with packing material. There are clearances provided between the links that afford the capability of accommodating some axial movement. As the hose is being bent, the clearances gradually close. The hose becomes stiff and cannot bend any further at a certain point when the clearances are completely closed. This sudden stiffening effect serves as a warning to the handler, preventing the interlocked hose from being over-bent. This automatic warning feature makes the interlocked hose especially suitable for manual handling.

The packing mechanism at the interlocked links does not offer a perfect seal. Therefore, the interlocked hose is satisfactory for carrying low-pressure air, steam, and water, but is generally not suitable for conveying gases and “searching” liquids such as kerosene and alcohol. The outside of the interlocked hose is relatively smooth, making it easy to handle without any covering.

Stress Analysis Consideration for Flexible Hoses

The flexible hose assembly is normally not analyzed. In most situations, the end displacements from piping or equipment connections are calculated from pipe stress analysis software and those values are transferred to the vendor for their consideration. Accordingly, the hose length and installation space are determined.

Pipe Supporting for optimum flexible hose working

A piping system that utilizes a flexible metal hose to absorb pipe movement must be properly anchored and guided to assure correct functioning and maximum service life of the metal hose assembly. The following basic principles should be observed:

  • The direction of pipe motion must be perpendicular to the centerline (axis) of the hose.
  • To prevent torsional stress, the pipe shall be anchored at each change of direction where a flexible metal hose is employed. Typical examples of correct and incorrect guiding are shown below in Fig. 5.
Pipe Supporting Examples
Fig. 5: Pipe Supporting Examples

Installation considerations for Flexible Hoses

Flexible Hoses are used to accommodate piping and equipment displacements. Hoses are extremely flexible, installations are very easy. However, a few general precautions should be exercised during installation to avoid hose failures.

  • The hose should not be subjected to twisting; Also, the installation should be such that flexing takes place only in the plane of bending.
  • The length of the hose should be sufficient to accommodate the offset and movement
  • The installation space should be adequate to accommodate the length.
  • Sharp bends should be avoided while installing flexible hoses. The Technical Data Section of the vendor catalog should be followed to maintain the minimum centerline bend radius for intermittent flexing.

While installing flexible hoses, the allowable minimum bend radius is the most fundamental limitation. For interlocked hoses, the limiting radius depends largely on the clearances between links. It has less to do with stress and fatigue, so it generally has only one limiting radius for all applications. For corrugated hoses, on the other hand, the limiting radius depends on the stress at the corrugations.

For pressure hoses with braided reinforcement, the corrugation stress comes mainly from the bending of the hose. Therefore, the corrugation stresses can be controlled by setting a limitation on the bending. In other words, the installation is acceptable if the hose is not bent beyond the limiting radius. Similar to the situation discussed in the bellow expansion joint, the mode of failure of the hose corrugation is due to fatigue. Therefore, the bend radius limitation depends also on the number of operating cycles expected. Most manufacturers provide two limiting radii, one for static applications involving a one-time fit-up installation, and the other for operational movement involving many cycles of intermittent flexing. The whole design and installation process actually ensures that this minimum radius is maintained during the initial layout and throughout the operation.

Factors for Metallic Flexible Hose Selection

The main factors that should be considered while selecting a flexible hose are:

  • Design and maximum working pressure.
  • Maximum service temperature of the material.
  • Fluid flow velocity
  • Axial, Angular, Offset, Radial, and unpredictable displacements if any.
  • Vibration tendency if any.
  • Required cycle/service life.

Materials for Metallic Flexible Hoses

The most common materials used for metallic flexible hoses are:

  • Carbon Steel
  • Stainless Steel
  • Bronze
  • Monel
  • Inconel
  • Copper
  • Brass
  • Aluminum
  • Aluminized Fiberglass
  • Silicone coated fiberglass

Depending on the operating service temperature range, these materials are decided.

Codes and Standards for Flexible hoses

The codes and standards used for design guidance are listed below:

  • The Society of Automotive Engineers (SAE) SAEJ513: Requirements for Hydraulic hoses.
  • ISO 10807: Corrugated flexible metallic hose assemblies for the protection of electrical cables in explosive atmospheres
  • Interlocked hoses are manufactured from a helically (spiral) wound and overlapping profiled strip in accordance with BS EN ISO 15465.
  • Pressure equipment directive (PED 97/23/EG)
  • DIN EN 14585-1: Pipework-Corrugated metal hose assemblies for pressure applications
  • EN 12434: Cryogenic vessels – cryogenic flexible hoses
  • DIN EN ISO 10380: Pipework-Corrugated metal hoses and metal hose assemblies
  • ISO 10806: Pipework – Fittings for corrugated metal hoses
  • ISO 21969: High-pressure flexible connections for use with medical gas systems
  • EN 2827: Hose assemblies of stainless steels for chemical products
  • DIN 3384: Stainless steel flexible hose assemblies for gas applications-safety requirements, testing, marking
  • EN 14800: Corrugated safety metal hose assemblies for the connection of domestic appliances using gaseous fuels

Applications of Flexible Hoses

Specific applications of flexible hoses include the following:

  • to water plants or to convey water to a sprinkler (Garden hose).
  • to water crops in agriculture (tough hose) for drip irrigation.
  • to convey water to the site of the fire for firefighting service (fire hose).
  • to carry air from a surface compressor (Air hose) or from air tanks.
  • In chemistry and medicine, flexible hoses are used to move liquid chemicals or gases around.
  • A fuel hose carries fuel.
  • to move liquids under high pressures in the oil industry.
  • For Heat Tracing
  • For Auto heater tubing, Ventilating ducting, Moderate suction lines, Automotive exhaust, Dust collecting Ducting,  Air Blower ducting, Wiring conduit, Refrigeration tubing armor, Carburetor air intake, hot ash granulate, etc

Data required for ordering a flexible hose

The following data must be supplied while ordering a flexible hose:

  • Size of hose and connected fittings
  • Design & Operating temperature
  • Design and Operating Pressure
  • Displacements
  • Service and Application
  • End-fitting attachment type
  • Developed Assembly length

All flexible hoses are subject to aging and their performance deteriorates after a number of years. So flexible hoses must be inspected following a company-approved inspection plan or as per manufacturer recommendation.

What are Slip Joints in Piping?

Written by Anup Kumar Dey in Engineering Materials,Mechanical,Piping Design Basics,Piping Interface,Piping Stress Analysis,Piping Stress Basics

What is a Slip Joint?

Slip Joints are mechanical joints that allow the contact surfaces of the pipes joined together to slip away from each other. When there is a large thermal movement of pipe and an expansion loop can not be provided due to other constraints, slip joints can be used to solve expansion stress problems. The slip joint has a rugged construction that makes it suitable for hostile environments, such as inside a ditch, underwater, or underground. However, as the sliding surfaces do not create perfect sealing, leakage may develop along the surface. This concern limits the use of slip joints in hazardous materials. To ensure the slip joint tightness, a considerable force needs to be maintained on the gasket or packing. This results in a fairly large internal friction force resisting the slipping movement. In some cases, this internal friction force is so huge that the joint simply losses its flexing capability. Slip joints are sometimes also known as slip-type expansion joints.

Types of Slip Joints

Depending on the modes of the sliding motion, slip joints are divided into two main types:

  • Axial slip joint and
  • Rotational slip joint.

Axial Slip Joint:

An axial slip joint allows the pipe to slide into it axially and at the same time allows the pipe to also rotate axially. Axial slip joints come in different styles. For low-pressure and temperature lines, the compression sleeve as shown in Fig. 1 (b) is used. When some moderate thermal expansion needs to be absorbed similar types of clamp-on couplings are commonly used. The compression sleeve, also known as Dresser Coupling, is very popular in water distribution systems where the temperature change is mainly due to climate change. For large movements at higher temperatures and pressures, an internally guided construction with a secure packing gland as shown in Fig. 1 (c) is used. All axial slip joints need main anchors to resist the pressure thrust force similar to bellow expansion joints.

Schematic of Slip Joints
Fig. 1: Schematic of Slip Joints

To ensure column stability, properly located guides are needed. However, joints with internal guides are not required.

The internal friction force of an axial slip joint is very significant and should be taken into consideration in the design and analysis of piping and supports. Because an axial joint is normally installed to accommodate the expansion of a straight piping run, the anchor design load can be accurately estimated by the simple addition of the pressure thrust force plus the joint internal friction force plus the support external friction forces.

A computerized analysis normally requires for piping systems that are not entirely straight. The internal friction force can be simulated as the spring force of the axial flexible joint. Because the internal friction force is the product of movement and spring constant, it varies with the actual movement. The analysis may require a couple of iterations to match the spring force with the internal friction force provided by the manufacturer of the joint.

Axial Slip Joints
Fig. 2: Axial Slip Joints

The axial slip joint can also accommodate the axial rotation of the pipe. Occasionally, a joint is specially constructed to accommodate only the axial rotation of the pipe. Because no axial movement is allowed, internal lugs can be installed to resist the pressure thrust force. Therefore, for this type of axial rotation joint, no anchor is needed. By strategically locating a couple of these types of rotational joints, the resulting piping system, much like a multi-hinged system, can accommodate very large movements.

Rotational Slip Joint:

A rotational slip joint is also known as a ball joint or a ball-and-socket joint. As shown in Fig. 1(a), the common type of ball joint is constructed with three main pieces. It has an inner ball-shaped adapter enclosed by a two-piece, dome-shaped housing. At the junction of the two housing pieces, the gasket is placed. As permitted by the opening of the outer housing, the joint can rock at a specific range. It is also capable of rotating 360 degrees axially. It is considered capable of rotating in any direction in a practical sense.

The rotational slip joint or ball joint is a very rugged component that is suitable for hostile environments, such as offshore and loading dock applications. It can sustain considerable abuse by piping and equipment operators. Again, to maintain the tightness of the joint, sufficient force has to be applied and maintained at the gasket or packing. This results in a considerable friction force creating a fairly large resisting moment against the rotation of the joint. The moment required to rotate the joint is called the break-off moment, whose magnitude is available from the manufacturer of the joint. This break-off moment can have a very significant effect on the flexibility of the piping and has to be taken into consideration in the design and analysis of the piping system.

Applications of Slip Joints

Slip joints are widely used in the wastewater plumbing industry. Also, they are popular in the piping industry for non-hazardous piping systems. Other applications of slip joints are:

  • Slip joints are used in large structures for allowing independent motion of large components while enabling them to be joined. Bridges and overpasses frequently have slip joints that allow a deck to move relative to piers or abutments. The joints are constructed with elastomeric pads to permit motion or can use rollers on flat surfaces to allow the ends to move smoothly.
  • Slip joints are used to adjust the length of the propeller shaft when demanded by the rear axle movements in the Automobile industry.

Hooke’s Law: Statement, Equation, Graph, Applications, Limitations

Written by Anu Sharma in Civil,Engineering Materials,Mechanical,Pipeline,Piping Interface,Piping Stress Analysis,Piping Stress Basics

What is Hooke’s Law?

Hooke’s law is a principle of engineering mechanics and physics related to the properties of a material. There are basically two statements for Hooke’s law; discovered by the English scientist Robert Hooke. The first statement relates to the elongation of spring subject to the application of force. And the second statement is known as the law of elasticity and relates the relation of stress and strain of materials. In this article, we will explore more details about Hooke’s law.

Hooke’s Law Statement for Springs

For Springs, Hooke’s law states that the force (F) required to extend or compress a spring by some distance (x) varies proportionately with respect to that distance. This means more force will be required to elongate a spring more and vice versa.

When elastic materials like springs are stretched using a force (F), deformation of atoms and molecules occurs until stress is applied and they get back to their initial state when the stress is removed.

Hooke’s Law Equation for Spring

Mathematically, Hooke’s law for Springs is expressed as:

F= -k.x

Where, In the SI unit

  • F is the force; N
  • x is the extension or compression of the spring; mm
  • k is the constant of proportionality also known as the spring constant in N/m

The negative sign in Hooke’s law is explaining the force as a restoring force that is trying to return the spring to its equilibrium position

Let us consider a spring with the load application as shown in the figure.

Hooke's Law for Springs
Fig. 1: Hooke’s Law for Springs

The figure above (Fig. 1) shows the stable condition of the spring when no load is applied to the spring at x=0; the condition of the spring when it gets elongated to the amount x1 under the load of m1; and the condition of the spring when it gets elongated to x2 under the influence of load m2.

Depending on the material, different springs will have different spring constants.

Hooke’s Law Statement relating Stress & Strain

With respect to the stress and strain of a material, Hooke’s law states that the stress of a material is proportional to its strain within the elastic limit of the material.

The strain will remain in the body as long as the stress acts and when the stress is removed the body will regain its shape. This property of materials is known as elasticity. So basically, Hooke’s law provides the basis for elasticity and so it is known as the elasticity principle or law of elasticity.

Hooke’s law Formula

Mathematically, within the elastic region of a material, Hooke’s law formula is expressed as

σ = Eε

Where, in SI units

  • σ is the stress; Pa
  • E is the modulus of elasticity or Young’s modulus, Pa (Normally GPa)
  • ε is the strain, dimensionless

Hooke’s Law Graph

The below graph (Fig. 2) shows the stress-strain curve for a low-carbon steel material to explain Hooke’s law

Stress Strain Curve explaining Hooke's law
Fig. 2: Stress-Strain Curve explaining Hooke’s law

The material tends to have elastic behavior up to the yield strength point (Point B), after that the material loses its elasticity and exhibits plasticity.

From the origin until the proportional limit (Point A) near the yield point (Point B), the straight line implies that the material is following Hooke’s law. But, beyond the elastic limit that is between the proportional limit and yield strength, the material starts losing its elastic nature and exhibits plasticity. The area that is under the curve from the origin to the proportional limit falls under the elastic range. The area that is under the curve from a proportional limit to the rupture point falls under the plastic range. In the plastic region, Hooke’s law is not applicable.

In many real-life situations such as wind blowing on a tall building, and a musician plucking a string of a guitar, the deformation is proportional to the stress/Force and Hooke’s law holds good.

Applications of Hooke’s Law

The applications of Hooke’s Law are as follows:

  1. Hooke’s Law is used in all branches of science and engineering; For understanding the behavior of elastic materials there is no substitute for Hooke’s law.
  2. It is used as the fundamental principle behind the manometer, the balance wheel of the clock, and a spring scale.
  3. Foundation for seismology, molecular mechanics, and acoustics.

Limitations of Hooke’s Law

Even though Hooke’s law is used extensively in Engineering, it’s not a universal principle. The law is not applicable as soon as the elastic limit of a material is exceeded. Normally for solid particles, Hooke’s law provides accurate results when the deformations are small. Many materials deviate from Hooke’s law even well before reaching the elastic limit.

Hooke’s Law calculations

  • In Engineering studies, Hooke’s law equation is widely used to calculate the Force required for getting the desired deformation. For example, in spring hanger supports used in piping engineering Hooke’s law is used to know how much pipe weight the spring will carry while allowing desired thermal movement.
  • Spring Constant or Young’s modulus is decided following Hooke’s law calculations. For Example, If 2,000 N force is applied to displace a spring by 0.5 m, it’s Spring Constant as per Hooke’s law calculation will be k=F/x=2000/0.5=4000 N/m

Is Pipe Stress-Range Calculated Correctly?

Written by Andrew Weighell in Caesar II,Piping Stress Analysis,Piping Stress Basics,Start-Prof

Objective

To explain why pipe stress-range calculations might not be correct if pipe support friction is not properly considered. The magnitude of the potential error in stress-range calculation is dependent on the geometry of the pipe layout, the type of supports used, and the coefficient of friction. Margins of potential error in the stress range could be large enough to invalidate the pipe stress analysis.

Most pipe stress software does not give any warning of the potential error discussed below.

Fundamental assumptions for pipe stress analysis

The calculation of stress range is fundamental to every pipe stress analysis.  Calculated values of stress range are necessary to assess cyclic loads that could cause fatigue failure of a component in the piping system.

Cyclic loading is the repeated application and removal of temperature, displacement, pressure, or any other mechanical loads. A load cycle consists of two halves. 

  • i)            “Loading”.  e.g.  From “cold” to “hot” (or “unloaded” to “loaded”)
  • ii)            “Unloading”.  From “hot” to “cold” (or “loaded” to “unloaded”).

A fundamental and implicit definition of a load cycle is that each load cycle must begin and end at the same point and stress state.  A particular sequence of loading and unloading is not a cycle if it does not begin and end at the same point and stress state. 

The stress difference between “cold” to “hot” is not equal and the opposite to that from “hot” to “cold” is not a stress range.  If a stress difference is not a stress range, then it is not valid for use in fatigue and design code calculations.

Design code requirements for stress-range

ASME B31.3 2018 section 319.2.3 Displacement Stress Range sub-section (b) states  

              “While stresses resulting from displacement strains diminish with time due to yielding or creep, the algebraic difference between strains in the extreme displacement condition and the original (as-installed) condition (or any anticipated condition with a greater differential effect) remains substantially constant during any one cycle of operation.  This difference in strains produces a corresponding stress differential, the displacement stress range, that is used as the criterion in the design of piping for flexibility“.

The key phrase from 319.2.3 that is sometimes not considered in pipe stress calculations is “(or any anticipated condition with a greater differential effect)“.

Calculated stress-range

Most pipe stress analysis software calculates the stress difference from the “as installed position” to the first “hot position” (or “loaded position”).

Typical load cases starting from “as-installed‑position” would be

Load CaseDescriptionComments
L1W + P1 + T1 (Weight + Pressure + Temperature)Stress and sustained loading in the operating condition.  i.e.  First “hot‑position” (or “loaded-position”).
L2W + P1 (Weight + Pressure)Stress and sustained loading in the “as-installed-position” . 
L3L1 – L2 = (W + P1 + T1) – (W + P1) = T1The stress difference caused by temperature change T1 between the “as-installed-position” and “hot-position”.

The stress-differential L3 can only be used as a stress range for fatigue calculation for a particular load sequence if two conditions are met.

Condition 1 The stress difference between the “as-installed-position” and “hot-position”. Must be equal and opposite to The stress difference between the “hot-position” and “cold-state position”.
AND
Condition 2 All subsequent cycles based on the same loading must begin and end at the same points as the first cycle.  [See Fig. 1].  

Therefore, the “cold-state position” must be the same as the “as-installed position”.  The pipe system must return to its “as-installed position” after the load has been removed.

              The first half of a loading and unloading sequence is not a stress range if the stress difference is not equal to that of all subsequent cycles for the same sequential load.
[See Fig. 2]. 

              “Cold-state position” is defined for this discussion as the point to which the pipe returns after the removal of thermal or mechanical loads associated with the load sequence being considered.

              “Hot position” means the same as  “loaded position”.

              “Cold-state position” means the same as “unloaded position”.             

Stress-range when the system returns to its "as-installed position"
Fig. 1: Stress-range when the system returns to its “as-installed position”
Stress-range when the system does not return to its "as-installed position".
Fig. 2: Stress-range when the system does not return to its “as-installed position”. (Pipe support friction creates a small stress reversal in this example)

Accounting for the adverse effects of friction in Stress-range calculations

 As discussed above, pipe stress analysis based on stress-range calculations is only correct if the pipe returns to its “as-installed position” at the end of every loading and unloading sequence.

Stress ranges based on the “as-installed position” will only be correct in a real system if:

  • a)           The pipe system is supported on hanger rods.  i.e.  The pipe will naturally “swing back” to its “as‑installed position.
  • b)           The pipe system has no intermediate supports between fixed (anchor) points.

Any sliding support involving friction will prevent the pipe from returning to its “as‑installed position” by some amount. 

The only way to ensure that stress-range calculations based on “as-installed positions” are reasonably valid for design is to ensure that the pipe is fully controlled. 

Pipe supports must be designed to ensure that the pipe system always returns to “near enough” and its “as-installed position” to ensure errors are within acceptable limits.  For example, by fitting guides or line-stops, using hangers, using low friction sliding supports, etc.   

Pipe stress software

Default load cases for most pipe stress analysis applications calculate the stress range from the “as‑installed position” to the “first hot position”.  Results could be in error if the user is not aware of the effect of friction on stress range. 

Some pipe stress applications can calculate the stress difference for both the loading and unloading half-cycles.  For example, PASS/START-PROF 

The additional functionality enables the user to determine if the unloading half‑cycle is a B31.3 319.2.3 “anticipated condition with a greater differential effect”.

Example

Description:

 The purpose of the simplified example pipe system below is to demonstrate the effect of friction on the calculated stress differences discussed above.  Two scenarios are considered using identical geometry.

  • i)            High friction – coefficient of pipe support friction = 0.3
  • ii)            Low friction – coefficient of pipe support friction = 0.1

Each scenario considers the effect of friction preventing the pipe from returning to its “as‑installed position” after the first “cool-down” (unloading). Each scenario includes load cases to compare stress differences for:

  • a)           “heat-up” (loading) from the “as-installed position” to the first “hot position”.
  • b)           “cool-down” (unloading) from the first “hot position” to the “cold-state position”.

This example assumes that the pipe system continues to cycle between the first “hot position” and the “Cold‑state position” at the end of the first load cycle. [See Fig. 2 and Fig. 4].

The effect of “Stiction” has not been considered.  However, it is noted that “stiction” will exaggerate the effect of friction discussed here.

Example system geometry
Fig. 3: Example system geometry

Pipe 90 mm OD, 6 mm wall, E = 202713 MPa, n = 0.292,  Density = 7833.413 kg/m3, g = 9.807 m/s2, 

Full of water (1000 kg/m3) (Arbitrary numerical values for purpose of this example only).

NodeDescription
10Anchor
15Rest support, with friction
25Rest support, with friction
30RY rotational restraint to represent the mutual rotational restraint of legs 10 – 30 and 30 – 40 Displacement DZ 100 mm “hot”, 0 mm displacement “cold”.
30 – 40Represents a straight section of pipe.  The expansion of 30 – 40 would cause 30 to expand 100 mm in Z direction. (The axial expansion of 10 to 30 is ignored for simplicity of calculation)
Example system subject to deflection and friction
Fig. 4: Example system subject to deflection and friction

Table 1 Results (Manual calculation) Friction Coefficient = 0.1 [See Figure 4]

Load case/loadsUnit10Node 15Node 25Node 30
LC1 W + D1 + F1 “hot position” Deflection DZmm034.791.6100
LC2 W (Sustained) Support loads FYN418849756–
LC3 W + D2 + F2 “cold-state postion” Deflection DZmm0310
F1 Friction forces resisting “heat up”  m = 0.1 x self weight Z direction, added as a force to simulate friction.N–-85-76–
F2 Friction forces resisting “cool-down” m = 0.1 x self weight Z direction, added as a force to simulate friction.N–8576–
LC4 = L1 – L2 (“Hot Position” minus “As-installed” position)MPa33.110.526.645.1
LC5 = L1 – L3 (“Hot Position” minus “cold-state” position)MPa27.814.626.751.8
LC3 – LC2 (“Residual stress” in “cold-state” position)MPa5.3-4.1-0.1-6.7
LC5 – LC4 Error in “stress-range” calculation based on “as‑installed” positionMPa5.3 (-16%)3.9 (44%)0.1 (0%)6.7 (15%)
D1 = DZ deflection at node 30 = 100 mm, D2 = DZ deflection at node 30 = 0 mm

Table 2 Results (Manual calculation) Friction Coefficient = 0.3 [See Figure 4]

Load case/loadsUnitNode 10Node 15Node 25Node 30
LC1 W + D1 + F1 “hot position” Deflection DZmm028.889.7100
LC2 W (Sustained) Support loads FYN418849756–
LC3 W + D2 + F2 “cold-state postion” Deflection DZmm08.92.90
F1 Friction forces resisting “heat up”  m = 0.3 x self weight Z direction, added as a force to simulate friction.N–-255-227–
F2 Friction forces resisting “cool-down” m = 0.3 x self weight Z direction, added as a force to simulate friction.N–255227–
LC4 = L1 – L2 (“Hot Position” minus “As-installed” position)MPa22.518.726.058.5
LC5 = L1 – L3 (“Hot Position” minus “cold-state” position)MPa6.63126.478.5
LC3 – LC2 (“Residual stress” in “cold-state” position)MPa15.9-12.3-0.4-20.0
LC5 – LC4 Error in “stress-range” calculation based on “as‑installed” positionMPa15.9
(-71%)		12.3 (66%)0.4 (1%)20 (34%)
D1 = DZ deflection at node 30 = 100 mm, D2 = DZ deflection at node 30 = 0 mm

Table 3 Results (PASS/START-PROF) Friction Coefficient = 0.1 [See Figure 4]

Load case / loadsUnitNode 10Node 15Node 25Node 30
LC1 W + D1 + F1 “hot position” Deflection DZmm034.791.6100
LC2 W (Sustained) Support loads FYN420847754–
LC3 W + D2 + F2 “cold-state postion” Deflection DZmm0310
Friction forces F1 resisting “heat up”  m = 0.1 x self weight Z direction, added as a force to simulate friction.N–-84-76–
Friction forces F2 resisting “cool-down” m = 0.1 x self weight Z direction, added as a force to simulate friction.N–8476–
LC4 = L1 – L2 (“Hot Position” minus “As-installed” position)MPa32.910.425.644.9
LC5 = L1 – L3 (“Hot Position” minus “cold-state” position)MPa27.614.525.751.5
LC5 – LC4 Error in “stress-range” based on “as‑installed” positionMPa5.3 (-16%)14.5 (39%)0.1 (0.031%6.7 (15%)

Table 4 Results (PASS/START-PROF) Friction Coefficient = 0.3 [See Figure 4]

Load case / loadsUnitNode  10Node 15Node 25Node 30
LC1 W + D1 +F1 “hot position” Deflection DZmm028.889.7100
LC2 W (Sustained) Support loads FYN420847754–
LC3 W + D2 + F2 “cold-state” postion Deflection DZmm08.92.90
Friction forces F1 resisting “heat up”  m = 0.3 Z direction, added as a force to simulate friction.N–-252-225–
Friction forces F2 resisting “cool-down” m = 0.3 Z direction, added as a force to simulate friction.N  –253227–
LC4 = L1 – L2 (“Hot Position” minus “As-installed” position)MPa22.418.525.958
LC5 = L1 – L3 (“Hot Position” minus “cold-state” position)MPa6.630.726.378
LC5 – LC4 Error in “stress-range” based on “as‑installed” positionMPa15.8 (-70%)12.2 (66%)0.4 (1%)20 (34%)

Discussion of results

Table 1 – Support friction m = 0.1

              Table 1 lists deflections and stress differences for load cycling with pipe support friction m = 0.1.

  • i)            “As-installed to “hot‑position”.  (Load case LC4).  i.e.  Warm-up (loading).
  • ii)            “Hot position to “cold-state”.  (Load case LC5).  i.e. Cool-down (unloading).

Results are calculated based on the classical beam formula using Mathcad.  (An identical Autodesk Nastran beam element model produced nearly identical results).

The stress difference for warm-up load case LC4 is less than the stress difference for cool‑down load case LC5. (Except for node 10).  Therefore, LC4 cannot be used as the basis for the maximum system “stress range” as discussed above. [See Fig. 2]. 

If the system continues to cycle between “hot-position” and “cold‑state position”, then load case LC5 would be defined as the stress range.  [See Fig. 2].  i.e.  A maximum stress range of 51.8 MPa.  (15% higher than 45.1 MPa calculated for load cycles between the “as-installed position” and “hot‑position”).

              It is noted that the LC5 stress difference at node 10 is reduced by friction.  The higher stress difference at node 10 for LC4 is not a stress range for the reasons discussed.  However, in general, LC4 would still need to be checked as a single application.

Table 2 – Support friction m = 0.3

Table 2 results are the same as Table 1 discussed above but for m = 0.3. 

Similarly, if it can be assumed that the pipe returns to the “hot position” after cooling to the “cold‑state position”, then load case LC5 would be the stress range.  [See Figure 2].  i.e.  A maximum stress range of 78.5 MPa.  (34% higher than 58.5 MPa calculated for load cycles between the “as-installed position” and “hot‑position”).

PASS/START-PROF pipe stress analysis software (For comparison)

Table 3 and Table 4 show PASS/START-PROF results equivalent to Table 1 and Table 2 respectively. PASS/START-PROF results show a close correlation with the manual calculations and general-purpose FE beam analysis (Autodesk Nastran 2021). 

Summary

  • Stress ranges used for fatigue analysis require that the stress difference for warm‑up (loading) is the same as that for cool-down / unloading.  In other words, the stress difference for warm-up/loading from the “as-installed position” is not a stress range if it is different than the stress difference for subsequent load cycles.
  • The stress difference during warm-up (loading) from its “as-installed position” is only valid as a stress range if the pipe system can be guaranteed to return precisely to the same position during cool‑down (unloading) for all subsequent load cycles.
  •  This discussion used a simple example to demonstrate that pipe stress-range calculation based on the  “as‑installed position” can be significantly in error if friction prevents the pipe from returning to the “as-installed position” after cool-down / unloading.
  •  The magnitude of the error depends on the coefficient of friction, the pipe layout, and the type of pipe supports used.  The use of guides, line-stops, and other methods of controlling pipe movement has a significant effect on the magnitude of any potential error.
  •  Care must be taken when guides or other pipe supports controlling movement are removed to reduce the calculated displacement stresses and loads from the “as-installed position”.  For example, removing guides from sliding supports to reduce calculated over-stress caused by seismic anchor movements.
  •  Pipe stress theory and piping design codes both require that the most onerous stress range is used for purpose of assessing the fatigue life of a piping system for safe operation over its design lifetime.

B31.3 2018 section 319.2.3 states “While stresses resulting from displacement strains diminish with time due to yielding or creep, the algebraic difference between strains in the extreme displacement condition and the original (as-installed) condition (or any anticipated condition with a greater differential effect) remains substantially constant during any one cycle of operation.  This difference in strains produces a corresponding stress differential, the displacement stress range, that is used as the criterion in the design of piping for flexibility“.

In the author’s experience, B31.3 319.2.3 is sometimes interpreted to mean only “the extreme displacement condition and the original (as-installed) condition”.

However, B31.3 actually states “the algebraic difference between strains in the extreme displacement condition and the original (as-installed) condition (or any anticipated condition with a greater differential effect) remains substantially constant during any one cycle of operation”.

 The simple example above demonstrates that a failure to consider the phrase  “(or any anticipated condition with a greater differential effect)” in B31.3 319.2.3 can lead to very different and potentially inaccurate calculation results.

** Future parts of “Pipe stress range calculated correctly?” will discuss how calculated stress range is affected by real changes of pipe support friction over the plant life.  For example, what happens to the validity of a stress calculation if one pipe support rusts more than another?

Young’s Modulus | Modulus of Elasticity | Elastic Modulus | Young’s Modulus of Steels

Written by Anup Kumar Dey in Mechanical,Piping Interface,Piping Stress Analysis,Piping Stress Basics

Young’s modulus, also known as the modulus of elasticity or elasticity modulus is named after the British physicist Thomas Young. This is a very useful parameter in material science. Young’s modulus specifies the measure of the ability of a material to withstand length changes under tensile or compressive forces. Young’s modulus is defined mathematically as the ratio of the longitudinal stress to the strain within the elastic range of the material.

Young’s Modulus Formula

As explained in the article “Introduction to Stress-Strain Curve“; the modulus of elasticity is the slope of the straight part of the curve. Young’s modulus is a fundamental mechanical property of a solid material that quantifies the relationship between tensile (or compressive) stress and axial strain. It is denoted by the letter “E” and mathematically expressed as E=Stress/Strain

E=σ/ϵ;

Here σ=Stress=Force (F)/Cross-Sectional Area (A)=F/A
ϵ=Strain=Change in Length(δl)/Original Length (l)=δl/l

So, E=(F/A)/(δl/l)=F*l/A*δl

As the strain is the ratio of two lengths, it is dimensionless.
Hence, the unit of Young’s modulus, E =the unit of stress=N/m2 in the Metric system and psi (pound per square inch) in the English System.

For a specific material, the value of Young’s modulus or the modulus of elasticity is constant at a specified temperature. But with a change in temperature the value of Young’s modulus changes. With an increase in the material temperature, the modulus of elasticity of a material decreases.

The Youngs modulus does not depend on the geometry of the material. With the change in shape, length, the moment of inertia, weight, etc. the value of the modulus of elasticity does not change.

Which is more elastic: Rubber or Steel?

Young’s modulus signifies the elasticity of a material. The more the value of elastic modulus means the more elastic the material is. For example, as compared to rubber, the value of young’s modulus is more for steel material (Refer to Table 2). So, Steel material will regain its shape more easily as compared to the rubber on the application of force. Hence, Steel is more elastic than rubber. But sometimes it creates confusion when asked all of a sudden.

Use of Young’s Modulus

Young’s modulus is used

  • To calculate the change in length (deformation or deflection) of a material under tensile or compressive loads.
  • To calculate the amount of force required for a specific extension under specified stress.
  • Young’s modulus can be used to calculate various other moduli (for example rigidity modulus, bulk modulus, etc) of a material.

Practical Applications of Young’s Modulus

There are numerous practical examples of Young’s modulus. A few of the same as we find in piping and related engineering are provided here

  • The thermal stress generated in a piping system is calculated using Young’s modulus (E). Thermal Stress= Thermal Strain X E= E.α.ΔT; Here, α=co-efficient of thermal expansion and ΔT=change in length due to temperature.
  • In flange leakage analysis using the ASME Sec VIII method, Young’s modulus is required to calculate flange stresses. Flange modulus of elasticity data is provided as input for design and ambient temperature conditions.
  • For designing the load-carrying capability of steel and concrete structures, civil engineers use Young’s modulus along with allowable deflection data.

Young’s modulus of Steel

As steel is the most widely used material in industries, we will have a look at Young’s modulus of Steel for getting a rough estimate of the values. The following table provides typical values of Young’s modulus with respect to increasing temperature for ferrous materials.

Young's Modulus for Steel
Table 1: Young’s Modulus for Steel

Approximate Young’s Modulus for Some Other Materials

Table 2 below provides approximate Young’s modulus for some other well-known materials.

Young's Modulus of Various Materials
Table 2: Young’s Modulus of Various Materials

Factors Affecting Young’s Modulus

The main parameters that affect Young’s modulus of material are:

  • Temperature (With an increase in temperature, Young’s modulus decreases)
  • Presence of Impurity in the material like secondary phase particles, non-metallic inclusions, alloying elements, etc.

Air Cooler Piping Stress Analysis using Caesar II

Written by Anu Sharma in Caesar II,Piping Stress Analysis,Piping Stress Basics

The stress analysis methodology of air cooler piping is quite different from other types of heat exchangers. This is mainly due to its different construction and supporting arrangements. The principal application of an air-cooled heat exchanger is to maintain a heat balance through the addition or removal of heat between streams of two different operating temperatures. Air fin cooler (AFC) or air cooler uses the air stream as the cooling medium. Air is circulated by multi-blade propeller-type fans as heat exchanger media. AFC unit consists of fin tube bundles with a header box attached to each end, supported horizontally by a C-shaped steel frame or structure. In the following paragraphs, we will explore the stress analysis philosophy of air cooler piping systems using Caesar II.

Documents for Air Cooler Piping Stress Analysis

The important documents required for the stress analysis of air-cooled heat exchanger piping are

  • Latest piping stress isometrics.
  • Line Designation Table or Line List
  • P&ID or PEFS
  • The latest revision of equipment GA drawing (covering all dimensions, Materials, nozzle allowable, and weight of AFC)
  • Allowable nozzle load (API 661 tables can be used in absence of vendor allowable loads if the air cooler is designed as per API 661)
  • Mechanical datasheet (Optional).

Stress Analysis with known Displacement of Air Fin Cooler From Vendor

If the vendor gives a thermal displacement value in the air cooler GA drawing then with the known value of displacements we can analyze the system. At the piping flange connecting the equipment nozzle enter the value of DX, DY, and DZ value in displacement vector -1, keeping RX, RY, and RZ values zero.

This is the most simple type of analysis and In this case, there is no need to model the air cooler in CAESAR II. However, in most situations, the displacements are not available. So, the stress analysis engineer has to model the equipment by taking data from the GA drawing.

Modeling air cooler in Caesar II

Modeling up to the top or bottom of the header

  1. Model pipe up to matching flange of piping and AFC nozzle as per the given stress isometrics.
  2. From the equipment GA drawing, model as per dimensions given up to the top or bottom of the header with proper thickness and size of the nozzle.
  3. Provide a C-node anchor at the junction of the header and inlet or outlet nozzle.
Modeling of Air Cooler in Caesar II
Fig. 1: Modeling of Air Cooler in Caesar II

Modeling part after defining the c-node anchor

  1. As per Fig-1, define 520 and 620 both as ANCHOR nodes with C-node as 521 and 621 respectively for checking of nozzle load.
  2. Model equipment parts from nodes 521 to 530 and 621 to 630 as rigid elements with the same temperature of piping up to the centerline of the header without weight. 
  3. Then model header as node numbers 530 to 535, 630 to 635, and 530 to 630 with weight and temperature the same as piping (15 percent of total empty weight, total weight between 535 to 635).
  4. Break the element 530 to 630 giving node 700 half of its length.
  5. Model tube bundle with node 700 to 710 (rigid element) as per its length given in GA drawing with weight (70 percent of total empty weight) and give supports REST+ PTFE (0.1 FRICTION) at every one-meter distance along the bundle length.
  6. Model 710 to 715, 715 to 720, 710 to 725, and 725 to 730 nodes as header elements with weight and the same average temperature of inlet and outlet. (15 percent of total empty weight, distribute in these two nodes).
  7. Model 715 to 921 and 725 to 821 rigid elements without weight taking an average of inlet and outlet temperature of piping. (921 and 821 are C-nodes).

Modeling Part Of Equipment Restraint Nodes (Fixed Header)

  1. The whole AFC has been supported at four ends on PTFE (Teflon) pad.
  2. One header act as a fixed and the other as a floating end.
  3. See vendor drawing for defining support nodes as fixed or floating.
  4. As per Fig-1, the north side header (nodes 525 to 635) is fixed and hence south side header (nodes 720 to 730) is a floating end.
  5. Define fixed-end nodes 535 and 635. Give Rest (Y) support with 0.1 friction coefficient, Axial stop (X) North-south directional stop with 2 mm gap, and Guide (Z) East-West with standard 12mm gap as per API 661  at both nodes.
  6. Define floating end nodes 720 and 730. Give Rest (Y) support with 0.1 friction and Guide (Z) East-West with a standard 12mm gap as per API 661 at both nodes.

Note: The guide gap can be increased as per the lateral thermal movement of the Air fin cooler to avoid excessive nozzle load. Practically for that slot, the length can be increased after approval of the equipment department and vendor.

Modeling Part After Defining C-Node Anchor (Split Header)

Split header case modeling in CAESAR-II, is described below:

  1. As per Fig-2, define 310 to 410 both as ANCHOR nodes with C-node as 311 and 411 respectively of inlet nozzle and 510 and 610 are of outlet nozzle as C-nodes 511 and 611 for checking of the nozzle load.
  2. From C-nodes 311 and 411, model up to the centerline of the upper header in split header case as rigid elements 311 to 315 and 411 to 415 without weight but with an average of inlet and outlet temperature.
  3. Then model half depth of top header elements as 315 to 320 and 415 to 420.
  4. The top header will rest on the bottom header with a Teflon pad so define nodes 320 and 420 as +Y with 0.1 friction and C-node as 321 and 421.
  5. Model 315 to 325 and 325 to 415 as a rigid element with half of the distance between two inlet nozzles with the half weight of one header and average temperature (Distribute the weight in 315-325 and 325-415).
  6. Model 325 to 330 as a rigid tube bundle element with a length of bundle given in the drawing and provide supports along the length.
  7. Model elements 330 to 340 as rigid elements with the distance between two header center lines without weight.
  8. Model 340 to 345 and 340 to 350 as fixed header elements with the half weight of the total header weight.
  9. Model elements 340 to 355 as connecting tubes to the bottom header with an average temperature of inlet and outlet and half of the weight of the tube bundle.
  10. Model node numbers 355 to 515, 515 to 520, and 355 to 615, 615 to 620 as rigid elements indicating a lower header with the proper distance from GA and half of one header weight.
  11. Model node number 321 (C-node) to 515 and 421 (C-node) to 615 as half of the depth of the lower header without weight.
  12. Model elements 515 to 511 and 615 to 611 as rigid elements as half of the depth of the lower header.
  13. Model bottom nozzle part and give 510 and 610 as ANCHOR with C-node restrain as 511 and 611.

Modeling Part of Equipment Restraint Nodes (Split Header) is as follows:

  1. Defining of restraint for the fixed and floating end will be the same as mentioned in the fixed header case.
  2. Here in Fig 2, nodes 345 and 350 are support nodes of the fixed end whereas nodes 520 and 620 are support nodes of the floating end.
  3. There is only one extra support between two split headers at nodes 320 and 420 which are +Y with 0.1 friction coefficient and C-node as 321 and 421.
Modeling of Air Cooler Split Header in Caesar II
Fig. 2: Modeling of Air Cooler Split Header in Caesar II

Next, create the load cases in a similar way for all other equipment and check the output results for consistency with respect to codes and standards. Air cooler nozzle loads are qualified with API 661 table values in absence of vendor-given allowable loads.

Fig. 3 below shows a typical GA drawing of an air cooler.

Typical Air Cooler GA Drawing
Fig. 3: Typical Air Cooler GA Drawing

To know more about Air Cooler heat exchanger click here and to know about Air Cooler connected Piping Design Click here.