Design Dead Load in Buried Pipe

Existing soil above buried pipe is categorized as external dead load. Unlike truck load which is categorized as live load, soil load is given evenly along buried pipe. Soil load (Figure 1) can be calculated using the following formula:

P_d = g H γ_s OD

Where:

P_d         = soil load (N/m)

H         = depth of buried pipe in the ground (m)

γ_S         = density of soil (kg/m³)

OD      = outer diameter of buried pipe (m)

So the total amount of external load is transferred to buried pipes due to soil load (dead load) and truck load (live load) is:

P = P₁ + P_d

Where:

P          = total load on buried pipe

P_l         = load truck

P_d         = soil load

As an interpretation of the model loading pipes in the soil with the combination loads, in this case is a truck, it can be seen in Figure 2 below.

Figure 1: Design Dead Load in Buried Pipe
(source: book-Structural Mechanics of Buried Pipes by Reynold KW, Loren RA) 

Figure 2: Modeling Load on Buried Pipe
(source: book-Structural Mechanics of Buried Pipes by Reynold KW, Loren RA) 

Design Live Load in Buried Pipe

The external loads in the buried pipe stress analysis that must be considered in calculation are live load and dead load. Live load will always changes according to position or distance, while dead load is not depend on these factors but it is determined by design value of dead load itself.  The examples of design live loads in buried pipe are truck load, car load, train load and the others.

As for example: truck is located above buried pipe or truck across ground area where pipe is buried in it. Truck is modeled as live load so it will add external load to buried pipe. This truck load is vertical load for buried pipe. It is assumed that the truck load is single load (W) above ground as shown in Figure 1 below.

Figure 1: Truck as Live Load on Buried Pipe
(source: book-Structural Mechanics of Buried Pipes by Reynold KW, Loren RA) 

The amount of truck load that is received by buried pipes at point A (right above pipe) is:

P₁ = N W / H²

Where:

P_l         = truck load (N/m²),

W        = single truck load (N)

H         = height of soil above pipe (m)

R         = horizontal distance from the center of pipe to single load (m)

N         = coefficient Boussinesq = (3 (H/R)⁵) / (2π)

Coefficient value of N can be seen from Figure 2. To know the value of N can use the relationship of R (distance W of center pipe) with H (depth pipe in soil). Then the relationship between R / H with N can be obtained as shown in the chart below.

Figure 2: Relationship of R/H vs N
(source: book-Structural Mechanics of Buried Pipes by Reynold KW, Loren RA) 

Multiphase Flow

A fluid can flow along pipes which have different shape; fluid flow direction can be divided into four categories, namely: vertical flow, horizontal flow, inclined flow, and directional flow. The direction of inclined and directional flow make angle of inclination between 0 to 90 degrees to horizontal axis. Figure 1 below shows the contribution of each category of flow direction on a production system.

Figure 1: Direction of Flow in a Production System

Vertical and directional flow direction is typically used in pipelines beneath surface, the pipe connecting fluid from reservoir to surface (wellhead) of offshore platform. Once the fluid reaches surface, directions of flow is frequently involved are horizontal and inclined flow direction. The use of flow direction type is closely related in terms of determining the value of changes in pressure along pipe flow.

Multiphase flow in pipes can be defined as the concurrent movement of free gas and liquid in the pipe that can occur in various flow patterns. Gas and liquid can flow as homogeneous mixture, the liquid is at the front with the gas push behind liquid, liquid and gas may flow in parallel, or in various combinations of flow patterns that may occur.

Generally, the pattern of multiphase flow is divided into three types as follow:

1. Segregated multiphase flow

In the segregated multiphase flow, the flow of gas phase is separated from liquid phase; it means that gas phase can flow above liquid phase or between the flow of liquid phase as shown in Figure 2.

Figure 2: Segregated Multiphase Flow

2. Intermittent multiphase flow

Flow pattern that can be included in the form of intermittent multiphase flow is the flow of liquid phase which hit the gas phase (Figure 3 bottom side) or the flow of liquid phase inhibit the flow of gas phase (Figure 3 top side).

Figure 3: Intermittent Multiphase Flow

3. Distributed multiphase flow

The pattern of distributed multiphase flow, gas and liquid phase are dispersed uniformly inside pipe flow, as shown in Figure 4.

Figure 4: Distributed Multiphase Flow

Flow in Pipe Concept

Flow in pipe can consist of single phase flow (gas, oil, or water only) or more which can be called multiphase (gas and liquid). In general, fluid in pipe can flow from an inlet point to outlet point if the pressure at outlet point is smaller than the pressure at inlet point, Pout < Pin (ΔP>0). If the pressure at inlet point is equal to the pressure at outlet point, Pout = Pin (ΔP=0), then fluid flow along pipe will not happen.

Figure 1: Flow in Pipe Concept

Figure 1 is a figure that show pipeline with inlet point consist of three pipe segments, segment 1 with pressure P1 and flow rate Q1 , segment 2 with pressure P2 and flow rate Q2, and segment 3 with pressure P3 and flow rate  Q3. The fluid of three pipe segments will be streamed to a gathering pipe with outlet pressure as Pout and fluid flow rate as Qout. Flow rate Qout shall be the sum of Q1, Q2, and Q3, because the pipeline in Figure 1 is assumed there is not inhibitor there.

If Qout is not summation of three flow rate (Q1, Q2, and Q3), it indicate that there is leak in pipe flow. As was explained earlier that the fluid flows from high pressure to low pressure, so fluid from the third inlet segments will flow into outlet segment if the value of P1, P2, and P3 respectively is greater than Pout.

A case that could possibly occur on the fluid in pipe is the pressure in the inlet segment is smaller than Pout, so the fluid will experience back-flow. Backflow can occur in variety of possibilities, namely the fluid from inlet segment which has higher pressure will flow into inlet segment which has lower pressure. When this condition occurs, then the flow rate that reaches outlet point will not optimal. Similarly, for fluid flow in the production pipeline, if backflow occur, the fluid flow rate through separator will not optimal.

Pipeline System in Offshore Platform

A pipeline consists of several segments of pipe that has very complex and diverse forms. Figure 1 shows a scheme of pipeline surface that connects the fluid of some wellheads which are located at each platform to separator. The pipeline consists of several platforms, each of which has several wellheads.

Figure 1: Scheme of Pipeline Production System between Offshore Platform

Fluid flow that occurs comes from well which then when it reaches the surface of fluid will go to the wellhead. Fluid from each wellhead will be streamed into a pipe flow, starting point of the meeting is called gathering point fluid, fluid then flows into the header platform. Fluid derived from multiple platforms header will be channeled back into separator. This section serves as separator between phases of fluid.

More details of the pipeline production scheme that lies beneath surface to the surface is shown in Figure 2. In the Figure 2 shows that the fluid source is derived from 3 pieces of reservoirs. Fluid jetting processes that occur on the surface similar to those seen in Figure 1, it is from wellhead to separator. In an oil field, production processes often experience a variety of obstacles, one of them is bottleneck. This bottleneck can lead to the production of wells are not optimal.

Figure 2: Scheme of Pipeline Production in 1 Offshore Platform

Frequently Used Pipe Material

There are two types of pipe material which is frequently used either in oil and gas industry, power plant and other industries:

1. Carbon Steel

Carbon Steel is one of pipe material and it is the most widespread of use in the oil and gas Industry, power plant and other industries. Almost all of these pipe materials have specifications issued by ASTM (American Society for Testing and Materials) and ASME (American Society of Mechanical Engineering.

There are three types of Carbon Steel are the most widely used, namely:

-          ASTM A106, This type has three grades, namely Grade A, B, and C. This grade refers to the amount of Tensile Strength materials. The amount of Tensile Strength of ASTM A106 are:

·         Grade A: 48 ksi

·         Grade B: 60 ksi

·         Grade C: 70 ksi

Among the third grade, pipe material which is usually used is ASTM A106 Grade B.

-          ASTM A 53: This material is also often used by elements of pipe that are coated by zinc (galvanized), or often used as an alternative for the A106 type. Grade A53 has three grades, namely Grade A, B, and C. In addition, A53 also has three types, namely:

·         Type E: Electric Resistance Weld

·         Type F: Furnace Butt Weld

·         Type S: Seamless

A53 Grade A and B have same Tensile Strength with ASTM A106 Grade A and B.

-          ASTM A 333: This material is often used on the fluid having low temperature, ranging from -50^oF.

2. Stainless Steel

Pipes are often categorized in Stainless Steel pipe is actually having the full name of austenitic stainless steel. But this pipe material is more often known by the name of Stainless Steel.

Stainless Steel has Grade 18, but type 304L is often used. In essence, Type 304 is the type that has low carbon content with the aim of strengthening the ability to withstand corrosion. With the addition of L letters behind his name, the 304L, it shows that this type has lower carbon content, much lower than just 304.

Thus, in application, there are two types of stainless steel that is commonly known and used in oil and gas industry and other industries as follow:

-          ASTM A312: This standard is used for pipe sizes under 8 inches.

-          ASTM A358: This standard is used for pipe sizes above 8 inches.

There are many other types of pipe material is quite often used beside two pipe materials above (carbon steel and stainless steel) such as:

-          Chrome-Moly Pipe: namely Chromium-Molybdenum Alloy Pipe, which consist of 10 grades, and refer to ASTM A335.

-          Nickel and Nickel Alloy Pipe: example that is widely used is Inconel, Incoloy and Monel.

-          Piping Cast iron, Cooper Piping

-          Plastic Pipe, concrete pipe.

Pipe Ends in Piping System

The pipe which has produced and used commonly in piping system has three types of pipe ends as follow:

1. Plain Ends (PE)

Plain end is the end of the pipe which is cut square, often used for connections such as sockets weld, slip-on flanges and mechanical couplings.

2. Beveled Ends (BE)

Beveled end is the end of the pipe which is cut to form bevel so it is suitable and often used for butt-weld connections.

3. Threaded Ends (TE)

Threaded end is pipe which is created to have a threaded on the ends and it is used for the connection type Screw Joints. There are two options, whether threaded on both sides (TBE = Threaded Both Ends) or only on one side (TOE = threaded one end).

Pipe Wall Thickness

Pipes are produced in various thicknesses that have been standardized. Each pipe wall thickness is given a name pipe in the form of schedule number, not in the form of actual pipe wall thickness.

Initially, the pipe wall thickness is classified into three groups as following below:

-          Double Extra Strong (XXS)

-          Extra Strong (XS)

-          Standard

Currently the naming of pipe wall thickness has been replaced with schedule which providing certain number, starts from 5 and 5S, then followed with 10 and 10S, so in multiples of 10 to Schedule 40 (20, 30, 40), and then have multiple of 20 such as pipe wall thickness schedule 60, 80 , 100, 120, 140, 160.

The pipe wall thickness which has schedule 40 is generally same with schedule STD pipe sizes 1/8 inch up to 10 inch. Likewise, schedule 80 is the same as the schedule XS for pipe sizes 1/8 inch up to 10 inch.

One thing should be considered is the use of pipe that has Schedule 5 and 10 are more widely used on stainless steel pipe. While the pipes which are classified as Small Bore, usually have minimum pipe wall thickness of Schedule 80, although it may have thickness more than that, it's just going to make a pipe becomes excessive strength than is needed.

Pipes are usually produced with having different length depending on the material, size and schedule. But in general the pipes are produced with having average length of 20 feet or 6 feet for pipe Carbon Steel. This length is also called as random length. Sometimes pipe which having length twice than random length are also widely available and include preferred especially for use in the pipe rack. This size is also called as Double Random Length, or equal to 12 meters.

Pipe Material

Piping systems we often encounter in our lives, whether in the office, buildings, power plants, offshore plants, and so forth. Pipes can also easily be found on the construction of a fertilizer factory, or in refineries processing crude oil, both for the processing of oil on land and at sea.

Most often we find and see is the pipelines system to deliver water to the houses made almost entirely of metal and sewerage pipes from plastics material or also commonly called Polyvinyl chloride (PVC).  Pipe has certain size, ranging from the smallest with diameter of ½ inch to an enormous size so that people can enter into it, that is a pipe with a diameter of 72 inches or approximately 1.8 meters.

In general, pipe materials that are widely used for piping and its components are divided into two main categories namely:

-          Metallic pipe material

-          Non-metallic pipe material

Especially for metallic pipe material, this pipe material can be subdivided into two main groups namely Ferrous and Non-Ferrous pipe material, including nickel, alloys, copper and aluminum. Finally, from the manifold types of ferrous materials, the pipe material can again be divided into two general categories:

-          Wrought iron, cast iron

-          Steel

Almost all pipe materials are widely used in oil and gas industry is made of steel, with the following main characteristics:

-          Chemical: major elements (iron for Ferrous Metal), alloying elements (nickel, chromium, etc.), impurities, and others.

-          Physical properties; density, modulus of elasticity, coefficient of thermal expansion, and others.

-          Micro Structure: atomic structure, phase metallurgy, type and grain size.

-          Mechanical Properties: strength (yield strength, ultimate strength, elongation) and toughness.

Code ASME B31.1 for Piping Stress Analysis

Piping stress analysis can use code ASME B31.1 as reference calculation and design. Code ASME B31.1 for power piping analysis is belonging to the American society of mechanical engineers. In code ASME B31.1 there are empirical formulas that apply to the sustain load, expansion load, and the combination of sustain and expansion load (during operations), and also occasional load are described as the following below:

1. Sustain load

The stresses (S) that occur due to sustain the load such as pressure, weight and other mechanical loads can be expressed by the equation as follows:

(P D_o / 4 t_n) + 1000(0.75 i M_a / Z) ≤ 1.0 S_h

2. Range Thermal Expansion Load

The stresses that occur due to thermal expansion can be expressed as the equation below:

S_E = 1000(i Mc / Z) ≤ S_A + f(S_h – S_L)

3. Combination Load of Sustain load and Thermal Expansion Load

The stresses due to combination of sustained load and thermal expansion load (S_ls + S_E), can be calculated with the equation:

S_ls + S_E = (P D_o / 4 t_n) + 1000(0.75 i M_a / Z) + 1000(i Mc / Z) ≤ (S_h + S_a)

4. Occasional Load

The stresses that occur due to pressure, weight, and other sustain load can be expressed as the equation below:

(P D_o / 4 t_n) + 1000(0.75 i M_a / Z) + 1000(i Mc / Z) ≤ K S_h

Where:

P          = internal design pressure (psi)

Do       = outside diameter (in)

Ma       = Moment due to sustain load (in-lbs)

Mb       = Moment due to occasional load (in-lbs)

Mc       = Range of the moment due to thermal expansion (in-lbs)

Z          = section modulus of the pipe (in³)

tn         = nominal wall thickness of pipe (in)

i           = stress intensification factor

K equal to 1.15 for the occasional load which work less than 1% of the operating period and is equal to 1.20 for the occasional load which work less than 10% of the operating period.

Name Size of Pipe

There are two methods commonly used to name the size of a pipe, namely:

1. NPS: Nominal Pipe Size, widely used in North America, with inch units.
2. DN: Nominal Diameter used by countries in mainland Europe, with millimeters units.

DN and NPS show the size of diameter. Therefore need to know how to find the naming of pipe thickness sizes which is commonly referred to as Schedule. Schedule is the naming of pipe sizes that show the size of pipe wall thickness.

For countries which always use millimeter as their units will commonly confuse if use NPS (Nominal Pipe Size) to naming size of pipe.  The size of pipe in NPS is not always measure and show outside diameter (OD) actually. The difference between NPS and OD is starting from pipe sizes NPS ¼ "up to pipe size NPS 12". But for pipe size NPS above 12 inches show size of outside diameter actually or in other word, size NPS above 12 inch is same with size in millimeter.

In some literatures explained that the difference is more due at the beginning of pipe manufacturing in 1930s are based on inside diameter pipe with 1/16" wall thickness, so the size becomes larger outer diameter 1/8".  Over time, technology of pipe manufacturing is advancing so pipe manufacturer can produce pipe with smaller wall thickness but can maintain outside diameter pipe size.

Octahedral Shear Theory

Octahedral shear theory is referred to as Von Mises theory too. Based on octahedral shear theory, failure takes place if the octahedral shear stress within a system is higher when compared with the octahedral shear stress at yield in a specimen put through to uniaxial tension experiment. This is equivalent in text to the assertion of the previous 2 theories besides that octahedral shear stress is applied as consideration with regard to comparability as towards maximum theory stress used in the Rankine principle or maximum shear stress used in Tresca principle.

This octahedral shear stress is explained with regard to the 3 stresses theory as following below:

τ_oct = 1/3 [(S₁-S₂)² + (S₂-S₃)² + (S₃-S₁)²]^0.5

Where:

τ_oct        = Octahedral shear stress

Becuase of the stresses theory explained pertaining to a specimen under uniaxial load previously, that octahedral shear stress on yield in the specimen could be established to become as equation below:

τ_oct = √2 . Sy / 3

Furthermore, the Von Mises theory expresses that failure takes place in a piping system when octahedral shear stress while in the piping system surpasses (√2 . Sy / 3) or more.

Regarding stress analysis associated computations, almost all of the current time piping rules use a modified version of Tresca principle

Maximum Shear Principle

Maximum shear principle is also known as Tresca principle. Based on this principle, failure happens if the maximum shear stress within a system τ_max is higher when compared with the maximum shear stress at yield in a specimen put through to uniaxial tension experiment. Be aware that it is equivalent in text, to the record of the previous principle besides that maximum shear stress is utilized as considerations for comparability as towards maximum stress principle used within the Rankine principle.

Within uniaxial test, maximum shear stress at yield situation of maximum shear experiment provided previous can be

τ_max = 0.5 [(S_L - S_C )² + 4 τ²]^0.5

       = S_L/2 = Sy/2

The Tresca principle therefore only states that failure happens if the maximum shear stress within a system is much more as compared to half the yield stress in the material (Sy). The maximum shear stress within the system must be determined as previous.

It must also be exciting to verify the implication of this principle upon the situation while a pipe is put through to internal pressure. When the circumferential stress caused by internal pressure (S_C) is two times the axial stress (S_L) and the shear stress is not caused specifically (τ = 0) the uppermost level of shear stress in the pipe according to the previous provided method could be following below:

τ_max = 0.5 [(S_L - S_H)² + 4 τ²]^0.5

       = 0.25 S_H

This condition must be fewer as compared with 0. 5Sy based on Tresca principle to get secure design. This results in a various criteria that circumferential tension in a pipe must be fewer than two times the yield stress. The Tresca principle and the design consideration applied in the membrane principle for pipe will be incompatible.

Maximum Stress Principle

The maximum stress principle is usually known as Rankine principle. In accordance with this principle, failure happens if the highest basic principle stress within a system (S₁) is actually higher when compared with the highest tensile stress principle at yield within a specimen put through to uniaxial tension experiment.

Uniaxial tension experiment can be essentially the most popular experiment performed regarding to every material of construction. The tensile stress within a consistent cross-section specimen will be described as yield stress (Sy) at yield with regard to every material as well as usually available. In uniaxial experiment, the utilized load provides increase solely to axial stress (S_L) and also circumferential stress (S_C), radial stress (S_R) and also shear stresses tend to be omitted.

Furthermore, the following equation below can be taken from uniaxial experiment:

S₁ = S_Y                        S₂ = 0              S₃ = 0

S_L = S_Y            S_H = 0              S_R = 0

The highest tensile stress principle at yield is so equivalent to the typically described yield stress. The Rankine principle hence only states that failure happens if the maximum stress principle in a system (S₁) is much more when compared with the yield stress on the material (Sy). The maximum stress principle in the system must be determined as before. This will be exciting to examine the implication of that principle upon the event if a pipe is put through to internal pressure.

According to the membrane principle pertaining to design pressure of pipe, provided that the circumferential stress is a smaller amount compared to the yield stress from the material construction, the design will be secure. That can be recognized that circumferential stress (S_C) caused by external pressure is two times the axial stress (S_L).

The stresses in the pipe depending on the previously assigned formulation could be as following below:

S₁ = (S_L + S_C)/2 + [{(S_L - S_C)/2}² + τ²]^0.5

     = S_L

S₁ = (S_L + S_C)/2 - [{(S_L - S_C)/2}² + τ²]^0.5

     = S_H

The maximum stress principle within the following scenario is S₂ (=S_C). The Rankine principle and the design considerations used in the membrane principle will be consequently appropriate. This principle is commonly applied for calculation of strain thickness for piping layout and pressure vessels employs Rankine principle as considerations to get failure.

Maximum Shear Stress Theory

Maximum shear stress theory states that failure will occur if maximum shear stress equal to or greater than maximum shear stress when perform failure test to uniaxial tension. The formula can be shown as follows:

| σ₁ -  σ₂ |  ≥  | σ_f |

| σ₂ -  σ₃ |  ≥  | σ_f |

| σ₃ -  σ₁ |  ≥  | σ_f |

Where:

σ_f                     = uniaxial tensile strength

σ₁, σ₂, σ₃          = main stresses

Graphical representation of maximum shear stress theory is shown is Figure 1 below:

Figure 1: Graphic of Maximum Shear Stress Theory

Maximum Normal Stress Theory

Maximum normal stress theory states that failure will occur if maximum main stress equal to or greater than maximum normal stress on failure in testing of uniaxial tension. The equation mathematically can be shown as follows:

σ₁ ≥ σ_f             σ₁ ≥ σ_c

σ₂ ≥ σ_f             σ₂ ≥ σ_c

σ₃ ≥ σ_f             σ₃ ≥ σ_c

Where:

σ₁, σ₂, σ₃          = main stresses

σ_f                     = uniaxial tensile strength

σ_c                     = uniaxial compressive strength

According to maximum normal stress equation above, failure will occur when uniaxial tensile or compressive strength is greater than main stress. Graphical representation of maximum normal stress theory is shown is Figure 1 below:

Figure 1: Graphic of Maximum Normal Stress

Stress Equation

At the stress component, the equations of normal stress (σ) and shear stress (τ) as following below:

Equation 1       → σ = (σ_x + σ_y)/2  +  ((σ_x - σ_y) cos 2θ)/2 + (τ_xy sin 2θ)

Equation 2       → τ = - ((σ_x - σ_y) sin 2θ)/2 + (τ_xy cos 2θ)

The equation 1 is derived to θ and make the result equal to zero will be obtained the following stress equation:

Equation 3       → σ₁, σ₂ = (σ_x + σ_y)/2  ±  √(((σ_x - σ_y)/2)² + τ_xy²)

Equation 4       → τ₁, τ₂ = ±  √(((σ_x - σ_y)/2)² + τ_xy²)

σ₁ shows maximum normal stress and σ₂ shows minimum normal stress. Meanwhile τ₁ shows maximum shear stress and τ₂ shows minimum shear stress. From stress equation 3 and stress equation 4, Mohr Circle can be made as shown in Figure 1 below. 

Figure 1: Mohr Circle

Stress Components

In three dimensions, the elements of primary stress can be described in Figure 1 where the three normal stresses are shown in σ_x, σ_y, and σ_z and six shear stresses are shown in τ_xy, τ_yx, τ_yz, τ_zy, τ_zx, and τ_xz in positive direction. The condition of biaxial stress or plane stress is shown in Figure 2 which all of them are shown in positive direction. The stress is depicted in xy plane.

Figure 1: Primary Stress Elements

Figure 2: (a) Biaxial Stress (b) Stress on Inclined Cut

If figure 2 (a) is cut by inclined plane with angle θ to x axis as shown in Figure 2 (b), so by adding all of forces which caused by all of stresses is equal with zero and the equation can be written as follow:

σ = (σ_x + σ_y)/2  +  ((σ_x - σ_y) cos 2θ)/2 + (τ_xy sin 2θ)

τ = - ((σ_x - σ_y) sin 2θ)/2 + (τ_xy cos 2θ)

Shear Stress due to Torque Moment

Shear stress on a straight beam due to torque moment can be shown in the figure 1. This stress will has maximum value on the surface which is located at longest distance from twist axis.

Figure 1: Shear Stress due to Torque Moment

Shear stress due to torque moment (σ) can be calculated using the following equation:

σ = T c / I_p

Where:

T          = torque moment

c          = distance element from center point  

I_p         = section polar of moment inertia

σ          = shear stress due to torque moment 

Normal Stress due to Bending Moment

Normal stress on a straight beam that gets bending moment is shown in the figure below. In contrast to shear stress due to shear force, the magnitude of normal stress due to bending moment will has maximum value in the longest distance from neutral axis.

Figure 1: Normal Stress due to Bending Moment

Normal stress due to bending moment can be calculated using the following equation:

σ = M / I

Where:

I           = section of moment inertia

M         = normal force

σ          = normal stress due to bending moment 

Shear Stress due to Shear Force

In contrast to normal stress due to axial force, the magnitude of shear stress due to shear force is not same for every part of beam. The amount depends on distance from neutral axis. Highest shear stress occurs in area close to neutral axis, on contrary the lowest stress occurred in area located on surface of beam. The figure below shows the shear force on straight beam.

Figure 1: Shear Stress due to Shear Force

Shear stress due to shear forces can be calculated using the following equation:

Where:

I           = section of moment inertia

t           = width of cross section

y          = distance element to neutral axis

τ          = shear stress

Normal Stress due to Axial Force

Normal stress which acting on straight beam due to axial force will has maximum value on the plane perpendicular to axis because the plane has smaller area than other planes. The following below is the equation of normal stress due to axial force:

σ = P / A

Where:

A         = plane area

P          = normal force

σ          = normal stress

The following below is figure that show normal stress due axial force.

Figure 1: Normal Stress due to Axial Force

Stress and Strain Analysis

Stress is the result of forces acting in specified element parallel or perpendicular to the sliced plane of element. The force perpendicular to the plane is called normal force and generates normal stress. Meanwhile, the force parallel to the plane is called shear force and produce shear stress. Both of them are shown in the following equation:

σ = P / A   and   τ = V / A

Where:

σ          = normal stress

τ           = shear stress

P          = normal force

V         = shear force

A         = plane area

The external force which is given on the element will cause internal reaction force that called as deformation. Deformation can be a change in geometry and dimension. Deformation that occurs on a unit length is called strain and can be shown in the following equation:

ε = (l – l_o) / l_o

Where:

ε          = strain

l_o          = length before deformation

l           = length after deformation

Tensile test on specimen material can be carried out to determine the strength of material against forces. This specimen is slowly pulled until failure (fracture). Tensile force and length specimen is always measured continuously during tensile test.

Figure 1: Specimen of Tensile Test

Based on the result of test, can observed and get conclusion of properties of material which show relationship between stress and strain. This linear relationship is expressed in Hooke Law as shown in the following equation:

E = σ / ε

Analysis and diagram of stress and strain in mild steel and brittle steel can be seen in stress analysis in piping system.

Stress Analysis in Piping System

Stress in piping system must be analyzed to know the strength of overall pipe and its components. Stress analysis is required to determine material strength against all of load which occurs in piping system. Stress will be most important parameter to know the strength of material. These parameters can be known by testing material strength and show it into graphic diagram stress and strain. Generally there are two types of stress-strain diagram; stress-strain diagram for mild steel and brittle steel. Both figures can be seen below.

Figure 1: Stress-Strain Diagram

On both figures above, there is straight line profile at the beginning of loading which indicate the existence of elastic deformation phenomenon in steel material. The end point of this straight line is called the yield point. Phenomenon of plastic deformation is initiated by curvature of the curve which can be known as ludders band. The highest point on the stress-strain diagram shows the ultimate strength of material. The ultimate point is a stress value of steel material at begin experience phenomenon of necking. The end boundary point in diagram show the failure point of material and show stress value when material begins to crack.

There are differences of curve characteristic in mild steel and brittle steel.  It is influenced by properties of both materials. Mild steel tend to has relatively long strain in the elastic region and plastic region, while brittle steel tend to has relatively short strain. In the piping system, it is used as the basic consideration to select pipe material with optimum performance. 

Wind Load on Occasional Load

Wind load is one of occasional load which is caused against the pipe; the force that occurs can be calculated using equation below. Magnitude of the wind load is the result of momentum wind on pipe. Wind load is modeled as uniform force in the direction of wind along pipe. Wind force that occurs can be calculated by using Bernoulli equation as follow:

F = C_d D q / 1000

Where:

F          = win load (N/m)

C_d        = drag coefficient

D         = outside diameter of pipe include insulation (mm)

q          = dynamic pressure (N/m²)

Occasional load that occurs in piping system in certain cases will have similar properties with sustain load. Therefore stress analysis of support will be important step to get distribution of stress along pipe. However, the optimum support position to withstand occasional load is not always same for sustain load. In the design process, compromise design is required so support can hold both load type, sustain load and occasional load. For example, the rigid support can be used to hold dynamic load but will reduce flexibility of pipe, so need other type of support. The snubber support type is suitable support and generally used to hold both type of loading.

Evaluation Parameter of Pipe Material Selection

Operation of piping system will receive variety of loads from the operating condition and environment. The right and suitable selection of pipe material for operating condition and environment will be initial guarantee that failure will not occur in the operation. The following below are some of key information that can be used to evaluate the selection of pipe material in order to achieve safe condition during operation:

1.      Maximum operating pressure which working on the piping system.

2.      Calculation to determine diameter and thickness of pipe.

3.      Material strength needed to hold the weight of fluid contained therein, the weight of component piping, insulation and the weight of pipe itself.

4.      Maximum and minimum operating temperature.

5.      Production method on special order condition.

6.      Composition of fluid either gas phase or liquid phase which flow inside pipe.

7.      Erosion problem due to the flow of sand which is carried in the fluid process.

8.      Corrosive particle that potentially cause corrosion in the pipe such as H₂S, CO₂, O₂, etc.

9.      Design lifetime of piping system during operation.

In piping system can be found technical terms such as SMYS (Specific Minimum Yield Strength) and SMTS (Specific Minimum Ultimate Tensile Strength) which show yield strength and tensile strength for pipe material respectively. Naming grade in code API 5L, on some types of pipe material can be sorted by SMYS value to make easier in the analysis of pipe material selection. But on other grade, naming system does not depend on SMYS value. The following table below show pipe material in Code API 5L where the naming of its grade in accordance with SMYS value.

Table 1: Standard API  for Pipe Material Grade 5LX