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What is a Miter Bend? Design Formulas for Miter Bend Calculation

Written by Rehan Ahmad Khan in Engineering Materials,Mechanical,Pipeline,Piping Design Basics,Piping Interface

In the Piping and Pipeline Engineering field, Miter Bend plays an important role because standard Elbows are not easily available and economical for larger pipe sizes. The site Engineer or the Fabrication supervisor is responsible for the perfect delivery of the joints made for the miter bend.
This article will provide detailed calculation procedures for finding out the required dimensions, angles of cut, and weight of the pipe.

What is a Miter Bend?

A Miter Bend or Miter Elbow is prepared by mitering (angle cutting) and welding pipe ends of the cut pieces, usually at 45° and 90° to form a corner. There are two types of miter bend, one non-perpendicular bend & another is 3-D bend. Miter Elbow/Bend is made from miter-cut pieces of pipe. The Miter pieces also called gores, There are two end gores and two middle gores in a 4-piece Miter bend.

Miter Bend/Elbow
Fig. 1: Miter Bend/Elbow

Miter Bend as per ASME B31.3

ASME B31.3 defined miter bend as follows:

A miter bend is a piping or pipeline bend where two or more straight pipe sections are joined in a plane bisecting the angle of the junction that produces a directional change of more than 3 degrees. If the angular offset is 3 degrees or less, the design consideration as per miter bend is not required.

The pressure design of mitered bends is covered in clause 304.2 of ASME B31.3.

Limitations of Miter Bend Applications as per ASME B31.3

  • For normal fluid service, the miter bend can be used but the maximum allowable pressure limits provided in Equations 4a, 4b, and 4C must have to be satisfied.
  • For category D fluid service, a mitered bend can be used when the single joint makes a direction change greater than 45 degrees.
  • For severe cyclic conditions, miter bend can only be used when the direction change angle is 22.5 degrees or less.
  • For high-pressure piping systems, the use of miter bends is not permitted.

Standards Associated with Miter Bend

  • AWWS (American Water Work Association): For sizing and the number of cuts/miter.
  • ASME B16.9: For end preparation of the miters
  • ASME B31.3: For pressure design

Note: According to ASME B31.3, the number of miters is restricted to a maximum of 5.

Features of Miter Bends

  • Miter bends are not standard pipe fittings but fabricated piping components.
  • It is also called a fabricated bend or mitered elbow.
  • Highly skilled welders and fitters are required for perfect miter bend preparation.
  • Used mainly in general services (category “D” fluid).
  • If used in process lines then above 14” pipe size.
  • Used above 6” for utility lines.
  • Miter bend can be fabricated with 2, 3, 4, & 5 miters.
  • The number of cuts will be a maximum of 5.
  • The miter thickness is usually different from the parent pipe thickness.
  • The radius of miter bends can be 1D, 1.5D, 2D, 3D, 5D, 10D, or Customized per the application requirement.

Note:
1. The number of miters will be decided according to the pressure and temperature of the line.
2. Application size range can vary from company to company.

Mitered bends are considered in piping applications when standard elbows are not easily available in the required schedule and the cost becomes too high. These are usually the last choice for every project.

Limitations of Miter Bend

There are certain limitations of miter bends as listed below:

  • Poor strength as the number of weld joints is higher.
  • Higher pressure drop.
  • Higher turbulence.
  • Used mostly for low-pressure piping systems only.
  • Higher risk of corrosion because of more numbers of weld joints.
  • Less strength.
  • Not suitable for pigging.
  • High-skilled manpower is required.
  • Not economical for lower line sizes.
  • It is not suitable for pigging operations.

Advantages of Miter Bend

Miter elbows provide certain benefits like

  • Low cost.
  • No thinning required
  • It can be made at the site or in the workshop.

Inputs Required for Miter Bend Calculation

Pipe/Line SizeSchedule NumberMaterial of Construction or Material TypeBend AngleNumber of CutRadius of Bend
8″SCH 120CS (Carbon Steel)9032.5 D
Table No. 1
Note: D = Pipe/Line size

Steps for Calculation

Step-1: Write down the available data(refer to Table No. 1)

We have,

D = 8”,     OD (Outer Diameter) of pipe =  219 mm
Schedule- SCH120
Material- CS (Carbon Steel)
Bend Angle = 90°
No. of cuts = 4
R = 2.5 D = 2.5*8*25.4 = 508 mm

Step-2: As per the number of cuts, Sketch the drawing as below (refer to Fig. 2)

Sketch of Miter Bend for Calculation
Fig. 2: Sketch of Miter Bend for Calculation

Step-3: Find the Angle of the Cut (refer to Fig. 2 for all the steps)

We know,

Step-4: Find the Center Line Length (CL1) of the First Miter

We know from Pythagoras’s formula,

Important Note:

  1. The first and last miter always will be of the same length at each point.
  2. Except for the last miter, all the miter’s length will be double of the first miter at every point.

Therefore,

            CL2 = CL1 * 2 = 272 mm
            CL3  = CL1 * 2 = 272 mm
            CL4 = CL1 = 136 mm

Step-5: Calculate the Inside and Outside Radius (IR & OR) of the bend.

We know from Fig. 2,

Step-6: Calculate the Inside Length (IL1) of the First Miter.

We know from Pythagoras formula,

Therefore,

            IL2 = IL1 * 2 = 214 mm
            IL3  = IL1 * 2 = 214 mm
            IL4 = IL1 = 107 mm

Step-7: Find out the Outside Length (OL1) of the First Miter

We know from Pythagoras’s formula,

Therefore,

            OL2 = OL1 * 2 = 330 mm
            OL3  = OL1 * 2 = 330 mm
            OL4 = OL1 = 165 mm

Step-8: Find the “Length of Pipe required” for the Miter Bend.

Length of pipe required = CL1 + Cutting allowance + CL2 + Cutting allowance + CL3 + Cutting allowance + CL4
Note- Cutting allowance depends upon the cutting method used, we are assuming 5 mm, refer to Fig. 3.

Thus,
         L = 136+5+272+5+272+5+136
        L = 831 mm

Calculated Dimensions for Miter Bend
Fig. 3: Calculated Dimensions for Miter Bend

Step-9: Calculate the Weight of the Pipe.

Check the Plain End Mass in the code book under the code “ASME B36.10 for 8” SCH 120 Pipe (refer to Fig. 4).

Part of Table 1 of ASME B 36.10M-2015
Fig. 4: Part of Table 1 of ASME B 36.10M-2015

Plain End mass is given 90.44 kg/m as per ASME B 36.10 M
Now,
find the weight using the following formula-

Weight of the Pipe = Plain End Mass * Length of Pipe ( in meters)

Weight (W) = 90.44 * 0.831 = 75 kg.

Step-10: Get the Cut-back (optional).

Cut-back = CL1 – IL1

Cut-back = 136 – 107 = 29 mm

Maximum Allowable Internal Pressure for Miter Bends

Clause 304.2.3 of ASME B31.3 provides equations for calculating the maximum allowed internal pressure for miter bends. The equations are provided for two types of meter bends:

  • Single Miter Bend, and
  • Multiple Miter Bends

The nomenclature used for the calculations is given in Fig. 5 below:

Nomenclature for Miter Bend
Fig. 5: Nomenclature for Miter Bend

Formulas for Single Miter Bends

For a single miter bend, the code provides two equations based on the angle of cut (θ):

When θ<=22.5 degrees, the maximum allowable internal pressure for a single miter is calculated using the following equation:

On the other hand, when θ>22.5 degrees, the equation for determining the maximum allowable internal pressure is as follows:

Formulas for Multiple Miter Bends

For multiple miter bends, the maximum allowable internal pressure is the lesser value calculated as per equations 4a and 4b below. These equations are valid for θ<=22.5 degrees.

In the above equations:

  • Pm = Maximum allowable internal pressure
  • S = Allowable stress for pipe material
  • E = Quality factor for longitudinal weld joints in pipes
  • W = Weld joint quality reduction factor
  • T = Ordering thickness of the pipe as per the Piping Material Specification
  • c = Sum of mechanical, corrosion, and erosion allowances
  • θ = Angle of the miter cut
  • r2 = Mean radius of the pipe = (D-T)/2
  • D = Outer diameter of the pipe
  • R1 = Radius of the miter bend

Few more useful resources for you.

Piping Elbows vs Bends: A useful literature for piping engineers
Piping Elbow or Bend SIF (Stress Intensification Factor)
Tee Connection: A short literature for piping engineers
Technical requirements for Pipes & Fittings for preparation of Purchase Requisition
“Pipe Coupling”-A short Introduction for the piping professionals
Comparison of Pipe and Tube (Pipe Vs Tube)
Details about Spectacle Blind and Spacers

Engineering Deliverables for Chemical, Oil & Gas Projects

Written by Rehan Ahmad Khan in Civil,Instrumentation,Mechanical,Piping Design Basics,Piping Stress Basics,Process

For the completion of any Engineering Project, It is very important to exchange information among the different Engineering Disciplines for starting the work simultaneously. The documents or objects used for exchanging information to help progress the project is called deliverables. This article will provide a list of common deliverables from various disciplines of an oil and gas project.

What is a Deliverable?

An engineering deliverable is a document that is prepared by one department and used by another department for the execution of a project. Some deliverables are dependent on other deliverables, so for preparation of dependent deliverables first needs to complete the interconnected deliverables.

Co-ordination between departments
Co-ordination between departments

Deliverables Prepared by Different Departments

Process Engineering Deliverables

Major process engineering deliverables for any EPC project are:

Static Equipment Department

Major mechanical engineering deliverables for oil and gas projects are

  • Mechanical Data Sheet (MDS)
  • Equipment Installation Plan
  • Equipment fabrication Drawing
  • Vendor Drawing for Review

Rotating and Package Equipment Department

  • Mechanical Data Sheet (MDS)
  • Equipment Specification List
  • Vendor Drawing with Detail

Deliverables from Instrumentation Department

Some of the important instrumentation engineering deliverables are

  • Instrument Data Sheet
  • Instrument Hook-up
  • System Block Diagrams
  • Control Room and Control Building Layouts
  • Instrument Location Drawings
  • Instrument Cable Routing
  • Instrument Power and Utility Requirements
  • Instrument Index
  • Relief and Safety Device Index
  • Alarm and Trip Schedule
  • Data Transfer Cable Tray Layouts
  • Air Distribution Diagram
  • Instrument Junction Boxes and Panels Block Diagrams

Electrical Department

Important electrical engineering deliverables for a project are

  • Grounding layouts
  • Cable Tray Route Layouts
  • Plant and Buildings Lighting Layouts
  • Substation Sizing and Layout
  • Wiring Drawings and Terminal Connections
  • Electrical Equipment and Component Data Sheet
  • Heat Tracing Panel Schedules
  • Load List
  • Tray Sizing
  • Emergency Power Load Specification

HVAC Department

The HVAC team produces the following engineering deliverables for the project:

  • Air Handling Unit (AHU) Layout
  • Duct Layout
  • Cooling/Chilled Water Piping Layout

Civil and Structural Department

Common civil engineering deliverables for oil and gas projects are

  • Foundation and Structural Layouts
  • Reinforced Concrete Specification
  • Steel-work Specification
  • Foundation Settlement Data
  • Procedures for Earthworks like Excavation and Leveling
  • Floor or Wall cut-out section Layout
  • Drawing of Platform, Ladders, Stairs, and Hand-railing
  • Road Layouts

Fire Fighting and Safety Department

The fire fighting and safety department produces the following engineering deliverables

  • Hazards Study Report
  • Layout Approval Report
  • P&ID for Fire Water Piping
  • Fire Fighting Equipment Layout
  • Water Storage Tank Data Sheet
  • Operating Manuals for Fire Fighting Equipment
  • Extinguishing System Design

Deliverables of Piping Department

Major deliverables that piping engineers produce are

Piping Engineering Deliverables by Piping Layout or Piping Design Team

Piping Engineering Deliverables by Piping Material Engineers

Piping Engineering Deliverables by Piping Stress Team

Major piping deliverables that piping stress engineers produce are

Deliverables or Information Provided by Client

  • Product Concept
  • Operating Guidelines
  • Codes and Standards as per Location
  • Statutory Requirement Details
  • Metro-logical Data

Users and Uses of Piping Deliverables

Overall Plot Plan

  • Used by all the departments including clients.
  • For the Finalization of pipe racks, trenches, and underground facilities (Pipes/Cables).

Zero-Level MTO

  • Used by the procurement department.
  • For estimation of cost and bidding.

Intermediate MTO

  • Used by the procurement department.
  • For ordering purposes.

Final MTO

  • Used by the procurement department.
  • For review purposes.

Unit Plot Plan

  • Used by all departments.
  • For finalizing the work breakdown structure (WBS).
  • For match line and scope finalization.

Equipment Layout

  • Piping Department: for preparation of GA key plan and piping layout.
  • Civil Department: for equipment foundation location & building layout for designing of foundation/building.
  • Electrical Department: for electrical cable/junction box layouts.
  • Instrument Department: for data transfer cable layouts.
  • Equipment Department: for preparation of installation plan.

GA Key Plan

  • Used by the piping department.
  • For the finalization of exact piping layouts, north/east coordinates of match lines which are required for continuation.

Piping Layouts

  • Piping Department: for preparation of intermediate MTO, construction isometrics, nozzle orientation, and pipe support layout.
  • Civil Department: for knowing piping cut-offs.
  • Electrical Department: for the development of cable layouts of instruments that are mounted on pipes.
  • Instrument Department: for the development of cable layouts of instruments that are mounted on pipes.

Nozzle Orientation

  • Mechanical Department: for updating MDS (Mechanical Data Sheet) as input to the vendor.
  • Vendor: for equipment fabrication to weld nozzles to equipment.

As-built Drawing

  • Used by the client.
  • For record purposes, future review, and modification.

Few more useful Resources for you..

Significance of HOLD in process piping engineering deliverable.
A SHORT OVERVIEW OF PROCESS ENGINEERING DELIVERABLES for EPC of Oil and Gas industries
Basics of Piping Design and Layout
Piping Stress Analysis Basics
Mechanical Design Basics
Process Engineering Design Basics
Instrumentation Basics
Pipeline Basics
Civil Engineering Basics
Piping Materials Basics

Dish and Nozzle Center line Distance Calculation from Nozzle Orientation of Pressure Vessel

Written by Rehan Ahmad Khan in Mechanical,Piping Design Basics,Piping Interface,Piping Stress Basics

Many a time during our day-to-day engineering services we need to calculate several important dimensions from the Nozzle Orientation drawing (Part of the Equipment GA drawing) of the pressure vessel. This article will provide a sample case study for distance calculation between the center lines of the Dish and Nozzle from the Pressure Vessel Nozzle Orientation Drawing. Before starting the calculation, we need to know the different types of Dishes used for the pressure vessel and the terms related to it.

Types of Pressure Vessel Dishes

There are mainly three types of Dishes used for pressure vessels–

  1. Tori-spherical
  2. Ellipsoidal
  3. Hemispherical

1. Tori-spherical Dish –

It is also called Tori-spherical Head or Ends. This dish is used for both horizontal and vertical both types of vessel, which is used to store liquids and gasses, with a pressure range of 0.2 N/mm2 to 1.5 N/mm2.

Crown Radius (CR) for Tori-Spherical Dish is equal to the Inside Diameter (ID) of the shell/dish. The Knuckle Radius is between 6% to 10% of the Inside Diameter (ID) of the shell/dish and the Straight Face (SF) is between 10mm to 30mm depending upon the thickness of the shell/dish.

Tori-spherical Dish
Fig. 1: Tori-spherical Dish

Crown Radius, Knuckle Radius, and Straight Face

Refer to Fig. 2 below.

  • Crown Radius (CR)- The radius of the sphere is called the crown radius (radius with reference to the shell).
  • Knuckle Radius (KR)- The radius of the torus is called the knuckle radius (radius with reference to the dish).
Knuckle and Crown Radius
Fig. 2: Knuckle and Crown Radius
  • Straight Face (SF)- The straight face is normally considered 3.5 times the thickness of the shell/dish.

2. Ellipsoidal Dish-

It is also called Ellipsoidal Head or Ends. It is comparatively deeper than a Tori-spherical dish and therefore able to resist higher pressures. This is costlier to form than a Tori-spherical dish and the pressure range is above 1.5 N/mm2.

Crown Radius (CR) for Ellipsoidal Dish is 0.9 times the Inside Diameter (ID) of the shell/dish and Knuckle Radius (KR) is 0.177 times the Inside Diameter (ID) of the shell/dish.

Ellipsoidal Dish
Fig. 3: Ellipsoidal Dish

3. Hemispherical Dish-

It is also called Hemispherical Head or Ends. It is clear from the name that this type of dish is a Hemisphere with throughout constant radius. This type of dish is used for a high-pressure application, which is of higher thickness, therefore not preferred where space is less. It does not consist of Crown Radius (CR) and Knuckle Radius (KR) but, is replaced with the Radius (R) I; e 0.5 times the Inside Diameter (ID) of the shell/dish.

Hemispherical Dish
Fig. 4: Hemispherical Dish

Formulas required for calculation

Dish typeCrown Radius(CR)Knuckle Radius(KR)Dish Height
Tori-spherical= ID0.06*ID
0.1*ID (mostly used)
0.16*ID		0.194*ID
Ellipsoidal0.9*ID0.177*ID0.25*ID
Hemispherical0.5*ID0.5*ID0.5*ID
Table No. 1
Notes:
1. For Hemispherical, crown and knuckle radius will be replaced with Constant Radius(R).
2. ID means the Inside Diameter of the dish/shell.

Input from Client

Case No.Dish TypeInside Diameter(ID) in mmThickness of DishNozzle SizeNozzle Projection in mmNozzle TypeRating
1.Tori-spherical3000206″200WN150#
2.Ellipsoidal4500258″200WN150#
3.Hemispherical8500352″150WN150#
Table No. 2

Steps for Calculation

Step-1. Draw the free-hand cross-section drawing of the shell and dish as drawn in figure no. 5

Note: We are solving case no. 1, refer to table no. 2
Typical Nozzle Orientation Drawing
Fig. 5: Nozzle Orientation Drawing

Step-2. Finding CR-KR, IR-KR, and Dish Height (refer figure no. 5 for each step).

We know from the formula,
CR=ID=3000 mm
KR=0.1*ID=0.1*3000=300 mm
Dish Height=0.194*ID=0.194=3000=582 mm
So,
CR-KR (Distance AB) = 3000-300=2700 mm
IR-KR (Distance EB) = 1500-300=1200 mm

Step-3. Finding Ɵ using the Pythagoras theorem

Step-4. Finding Distance FC using the Pythagoras theorem.    

Step-5. Calculation of the center-line distance

Now, we can get the Distance between the CL of Nozzle and to CL of Shell as follows:

So,
     CL to CL Distance = 1333 – (84+25) = 1224 mm
Note- This is the minimum distance required for Installing Nozzle for this particular case. Similarly, we can calculate the distance for different sizes of nozzles and for other Heads.

Step-6. Calculate the Distance between the Tangent Line(TL) of the Dish to the Face of the Flange (FOF)

It is also an important dimension for Nozzle Orientation Drawings.
TL to FOF Distance = Nozzle Projection + Thickness of Dish + Distance EG

Note- a. Check the Projection of the Nozzle in Databook or Equipment MDS.
           b. Thickness is given in Table no.- 2.
           C. Distance EG needs to calculate Using the Pythagoras theorem.

EG= AG-AE
So,

Hence, EG=2739-2418=321 mm
Therefore,                   TL to FOF Distance = 200+20+321 = 541 mm

Important Note- These are the dimensions that will be constant, But the Angle Projection can be any as per the requirements of the project.

Few more related resources for you..

A short Presentation on Basics of Pressure Vessels
Brief Explanation of Major Pressure Vessel Parts
10 points to keep in mind while using project-specific pressure vessel nozzle load tables during stress analysis.
Understanding Pressure and Temperature in the context of Pressure Vessel Design
A Presentation on Vessel Clips or Vessel Cleats
Few Articles related to Heat Exchanger Basics

Online Course on Pressure Vessels

If you wish to learn more about Pressure Vessels, their design, fabrication, installation, etc in depth, then the following online courses will surely help you:

Case Study of Tank Farm Design and Dike Wall Height Calculation

Written by Rehan Ahmad Khan in Piping Design Basics

The following article will provide a sample case study for Tank Farm Design based on OISD 118. It will also provide a sample tank dike wall calculation for the same tank farm. Let’s assume that the following inputs were received from the client for the tank farm design.

Inputs Received from Client

TANK TAG NO.CAPACITY (CUBIC METER)HEIGHT (METER)DIAMETER (METER)PETROLEUM CLASS of Storage Fluid
T14259.67.5CLASS-B
T245098CLASS-A
T34009.37.4CLASS-B
T43809.17.3CLASS-B
T54559.77.7CLASS-A
T670012.58.5CLASS-C
Total2810NANANA
Notes:
1. Foundation Height for all the Tanks is 400 mm and the Diameter is Tank diameter + 500 mm.
2. The Foundation shape is circular and without a shoulder.
3. All Tank type is Conical.

Tank Farm Design Consideration as per OISD-118

  1. The total capacity of all six tanks is not exceeding 5000 cubic meters and the diameter of the largest tank is not exceeding 9 meters, hence Firewalls are not required for this case.
  2. The largest Tank’s Capacity is not exceeding 50000 cubic meters, hence there will be two rows of tanks in the Tank Farm.
  3. The separation distance between the tanks will be as per table 5 of OISD-118 as Capacity and Diameter are not exceeding 5000 cubic meters and 9 meters respectively (0.5D for class A & B and 0.5D/6 meters (whichever is minimum) for Class A & C or B & C)
    Note- Take the diameter of the larger tank always.
  4. The minimum distance between the Tank’s Shell and the inside surface of the dike wall will be 0.5 times the height of the Tank (0.5*H).
  5. The tank roof type is a fixed roof and the total capacity of Tanks are not exceeding 60000 cubic meters. So, there will be only one Dike Encloser/Tank Farm.

Arrangement of the Tanks

  1. As per OISD-118, we should design the Tank farm separately for Class A & B Fluid and Separate for Class C Fluid. But, here only one tank is of Class-C so we are arranging in single Tank Farm but we will have to follow the safety consideration as per Class A & B.
  2. Make 2 rows, each of 3 Tanks.
  3. Position the largest Tank (as per diameter) at any corner of the Tank farm.
  4. Choose the smallest Tank (as per diameter) and position next to the larger one in any of the free spaces (either in a row or column).
  5. Position the second smallest Tank next to the largest Tank (at the free space either row or column).
  6. Now, Place the second-largest Tank next to the smallest or second smallest Tank.
  7. We have to arrange in the same manner as the above for the rest of the Tanks one smaller and one larger alternatively, by keeping in mind both directions X & Y.
  8. By following the above steps for the allocation of Tanks, we can find the shortest Length & Width of the Tank farm.

Refer to the attached Image (Fig. 1) below which shows the arrangement of Tanks, Minimum Separation Distances, and the Gap between the Tank’s steel and Dike wall as per OISD-118.

Tank Arrangements
Fig. 1: Tank Arrangements

After the allocation of Tanks the following steps should be followed:

  1. Calculate the length of each row and the width of each column with the given distance.
  2.  For this case L1=42.8 m, L2=40.1 m, W1=30.8 m, W2=28.5 m, W3=28.7 m.
  3. Choose the longest Length and width among all. Here L (Greater) =42.8=43 m and W(Greater) =30.8=31 m.
  4. Now the difference in length between L & L1 and L & L2 needs to accommodate in L1 and L2 for final adjustment.
  5. Now the difference in width between W & W1, W & W2, and W & W3 needs to accommodate in W1, W2, and W3 for final adjustment.
  6. After final allocation and accommodation of distances between the tanks and wall & Tank’s shell, Calculate the Origin point of the Tanks with reference to the Origin point of the Tank farm.
  7. The origin point of Tank Farm is shown in the above Image i.e, (0,0) with the coordinate Plane x (East) and y (North).
  8. The final Length and Width of the dike enclosure are L=43 and W=31 respectively.

Notes:

  • A. Do not keep a value less than the minimum value. Although, we can increase the value for adjustment of the extra length.
  • B. Try to keep all the Gaps between the Tanks and Dike Inside the wall near to equal or equal so there will be ease in operating & maintenance work.
  • C. It does not require matching the center line of all the tanks either row-wise or column-wise.

Refer to Fig. 2 below for the final allocation of Tanks within the Dike encloser with the Origin point-

Final allocation of Tanks within the Dike enclosure
Fig. 2: Final allocation of Tanks within the Dike enclosure

Dike Wall Height Calculation

A Tank Dike Wall is a barrier wall surrounding one or more tanks that have the ability to contain the full volume liquid of the largest tank in case of leakage or tank failure.

Important conditions for Dike Wall Height Calculation

  • The volume of the Dike encloser should be >= the Volume of the largest tank of the Tank Farm.
  • To get the actual volume of the dike enclosure, we have to deduct the Dead volume (Volume of the other tanks except for the largest one, tank foundation of all the tanks till the dike wall height, Firewalls, and Concrete Stairs inside the encloser) from total dike encloser volume.
  • Initially, we need to assume the dike wall height for the actual calculation.
  • Start calculating with the minimum height assumption. (Height should be between 1-2 m.
  • After deduction, the volume will be compared with the volume of the largest tank.
  • If the dike encloser Volume is >= Larger tank volume, then consider the height which is assumed otherwise go the next height till the condition is matched.
  • After finalization of the required height, add a 200 mm free board as per OISD-118 to this height, and the outcome of this sum will be the actual height of the dike wall.

The calculation for the above case-

Given Data,

Length of the Dike- L = 43 M
Width of the Dike- W = 31 M
Height of Dike Assumed: H = 1 M
Height of Foundation-h = 0.4 M
Diameter of Foundation- D = Diameter of Tank + 0.5 M
Number of Tanks- 6
Largest Tank Working Capacity- WCT6= 700 cubic meter
Stair Height- Hs = 1 M, Length (Ls) = 1.3 M, Width (Ws) = 1.2 M and Slope is 37.5 degrees (as per the related Standard) mostly we take 30 to 40 degrees.

Step 1- Calculate the Volume of the dike enclosure

The volume of the dike without deduction dead volume (V1) = L*W*H = 43*31*1 = 1333 Cubic meters.

Step 2- Calculate Dead Volume

Dead volume = All tanks foundation volume + Liquid volume of tanks (other than the largest tank) up to the Height of the enclosure + Dead volume of Firewall and the Stairs)

Foundation Volume-

Volume of T1 Tank Foundation (VF1) = 3.14*r^2*h (as Foundation is circular in shape) = 3.14*4^2*.4 = 20.09 m^3
similarly, VF2=22.68, VF3=19.59, VF4=19.10, VF5=21.11 and VF6=25.43 m^3

All foundations volume (VF) = 128 m^3

Liquid Volume of all Tanks except the largest one till the height of the enclosure

Volume of liquid in T1 Tank (VL1) = 3.14*r^2*H = 3.14*3.75^2*1 = 44.15 m^3
similarly, VL2=50.24, VL3=42.98, VL4=41.83 and VL5=46.54 m^3
All Tanks Liquid volume except T6 till height of the Dike wall (VL) = 225.74 m^3

Firewall Volume

The firewall volume for this case will be zero as per OISD-118.

The volume of the Stairs at two side

According to the length and height of the Stair, we can find the number of Steps, Riser height, and Trade width.

No. of Steps (n) = height/ riser height = 1/.2 = 5
Riser height decided as per standard, here we are taking (H) = 200 mm
Trade width decided as per the standard, here we are taking (Tw) = 260 mm
Stair Length (L) = 1300 mm

Similarly, Width (W) = 1200 mm

Volume Calculation
Fig. 3: Volume Calculation

Volume of the First Step1 = L*W*H = 1300*1200*200 = 0.312 M^3
for step2 length will be Stair length – trade width = 1300-260 = 1040

Similarly, for step2=0.2496, step3=0.1872, step4=0.1248, step5=0.0624 m^3

Total volume for one stair = 0.936 m^3

Volume for the two diagonally stairs = 1.872 m ^3
So, Total Dead Volume (DV) = 355.612 m^3

Step 3- Cross check the below Condition with the calculated data.

Dike enclosure volume ≥ Working capacity of Largest tank + Dead volumes
V1 ≥ WCT6 + DV
1333 ≥ 700 + 355.612
1333 > 1055.612

So, here we can see this calculation matching the above condition. Hence, the Assumption of the height of the dike wall met the requirement.
if it would not have matched the condition then we had to take another height and recalculate the all steps again until the condition matched.
As per OISD, 200 MM free-board is to be added to the Dike height

Therefore, Final Dike wall Height = 1 m + .2 m = 1.2 m.

Few more useful resources for you.

Equipment and Piping Layout for Storage Tanks
Considerations for Storage Tanks Nozzles Orientation
A Brief Presentation on Storage Tanks
Various Types of Atmospheric Storage Tanks
Tank Settlement for Piping Stress Analysis
An article on Tank Bulging effect or bulging effect of tank shells

Difference between Primary loads and Secondary loads in a Piping System

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

Piping Stress Analysis is the scientific or engineering study of all the stresses generated in a piping system. Now from where this stress comes? From the mathematical definition of stress, we all know that Stress is the Reaction Force per unit area. So, this clarifies that piping stresses are generated because of some kind of loads or forces in the piping system. The forces the piping system faces are categorized into two distinct groups.

  1. Primary loads and
  2. Secondary loads.

In this article, we will study the differences between these two types of load categories.

What is a Primary Load in a Piping System?

Normally Force driven loads are called Primary loads. These loads are generated due to gravitational forces, internal or external fluid pressure, spring forces, relief valve discharge, pressure waves during water hammer or surge effects, etc. Hence, Primary loads originated due to some kind of force acting on the piping system. A large value of Primary loads creates plastic deformation leading to catastrophic failure. In a catastrophic failure, each individual crystal is subjected to stresses that the body can not withstand and causes rupture.

What is a Secondary Load in a Piping System?

Secondary loads are usually displacement-driven loads. These loads are generated due to some kind of displacements imposed in the piping system, for example, thermal expansion, settlement, anchor movement, vibration, etc. Most of the time (not always, for example, tank settlement) these are cyclic in nature.  Such kind of loads normally results in fatigue failure. In fatigue failure, the grains collectively fail because of incremental damage done by each cycle.

Primary Load vs Secondary Load

Primary Loads vs Secondary Loads
Primary Loads vs Secondary Loads

The following table lists the major differences between primary and secondary loads.

Sr NoParameterPrimary LoadsSecondary Loads
1DefinitionPrimary loads are Force DrivenSecondary loads are Displacement Driven
2Self-Limiting NaturePrimary loads are not self-limiting. Once plastic deformation begins it continues until force equilibrium is achieved through changes in boundary conditions or by material strain hardening or until the element fails catastrophically.Secondary loads tend to dissipate as the system deforms through yielding and hence such loads are self-limiting.
3Cyclic NaturePrimary loads are Non-Cyclic in natureSecondary loads are Cyclic (except Settlement)
4Failure ModesCatastrophic, Quick, and Sudden. Failure by primary loads is based on one or more failure theories like Von Mises, Tresca, or Rankine Theory.Fatigue and non-catastrophic in nature. Failure is not sudden and time taking.
5Failure due to a single application of loadA single application of excessive primary load (example pressure) may cause design failure by gross plastic deformation and ruptureFailure never happens because of a single application of load. Normally it takes a high number of load applications for failure to occur.
6Allowable Stress Values as per Process Piping CodeAllowable stress values for stresses generated by primary loads (Primary Stresses) are normally less and limited by Sy (Yield Stress) at maximum temperature.Allowable stress values for stresses generated by secondary loads (Secondary Stresses) are normally more than Sy.
7Load DurationFew primary loads like Weight are always present in the piping system throughout the plant life.Secondary loads are normally present only when the plant is operating.
Table listing differences between Primary and Secondary Loads

Few more useful resources for you..

Differences between ASME B 31.4 and ASME B 31.8
13 major differences between Seamless and Welded Pipe
10 Differences between Pressure and Stress
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Difference between Piping and Pipeline
Difference between Pipe and Tube

Stress or Strain: Which Comes First?

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

The knowledge of both stress and strain is very important in design as their relationship to each other defines the mechanical properties of a material. But which comes first between Stress and Strain is really a very confusing question to many. Whenever a force is applied to a body, Stress, and Strain both are believed to occur. But which one comes first? Let’s try to understand the same from the basics.

What is Stress?

Whenever a force is applied to a body from outside (external forces), its first tendency is to resist that force. So, the body will generate an internal resistance force that will resist the external force to create any damage (deformation). This internal resistance force per unit area (cross-sectional area on which Force acts) is called stress and is denoted by

Stress (Ϭ)= -F/A

What is Strain?

Refer to the image below (Fig. 1). When the pipe is pulled using a Force F, the pipe elongates i.e deformed from its original length L0

Force and Change in Length
Fig. 1: Force and Change in Length

The strain is the geometric quantity that measures the deformation of the above pipe. The ratio of this elongation (∆L, change in length) with respect to the original length (L0) is known as Strain and expressed as

Strain (δ) =∆L/L0

Which comes first: Strain or Stress?

From the above paragraphs, it is clear that for the generation of Stress or Strain, the main contributing factor is the Force, F. So force is the cause. And Once force is applied, it tries to deform the body instantaneously. So obviously, deformation or change in length will come first. This deformation can be measured using Strain gauges. Because once deformation or damage tends to appear, then only internal resistance force will be created and will try to resist that change. So, there has to be deformation first for the creation of stress. Actually, stress is a derived value, it’s only a mathematical term. You can not see or measure it. Similar to Strain gauges there is no instrument where stress can be measured. It is always calculated.

The same philosophy can be easily understood from the Stress-Strain curve, as well. For generating a curve, the standard practice is to keep the independent parameter on X-Axis and the Dependent one on Y-Axis. Now, look at the image below (Fig. 2) showing the stress-strain curve.

Stress-Strain Diagram
Fig. 2: Stress-Strain Diagram

The Strain is on the X-axis and Stress is on the Y-Axis. Hence, It is clear that Stress is dependent on Strain.

Again, the above definitions of Stress and Strain are provided based on two assumptions.

  1. The cross-sectional area (A) is considered constant throughout.
  2. The original length (L0) is considered constant.

So, Now we defined the above; Stress =Force/Area and Strain=Change in length/original length.

According to the above assumption, both Area and Original Length is constant. So the above Stress-Strain curve can be considered as a Force vs deformation curve. Which means Force is creating the deformation.

So from the above discussions, it is clear that Strain comes first, and then Stress is generated.

Few more useful resources for you..

10 Differences between Pressure and Stress
Basics of Pipe Stress Analysis
Piping Stress Analysis using Caesar II
Piping Stress Analysis using Start-Prof
Piping Design and Layout Basics
Piping Materials Basics