Analysis of Stress in Nozzle/Shell of Cylindrical Pressure Vessel under Inter...
PROJECT FINAL REPORT
1. A PROJECT
ON
WIND AND ICE LOAD ANALYSIS ON RECLOSER UNIT AND ANALYTICAL
STRESS ANALYSIS OF THE FRAME DESIGNED FOR RECLOSER UNIT
By
ADDEPALLI LAVA KUMAR 2012A4PS297G
AT
EATON TECHNOLOGIES PVT. LTD., PUNE
Practice School II Station of
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
December, 2015
2. A PROJECT
ON
WIND AND ICE LOAD ANALYSIS ON RECLOSER UNIT AND ANALYTICAL
STRESS ANALYSIS OF THE FRAME DESIGNED FOR RECLOSER UNIT
By
ADDEPALLI LAVA KUMAR 2012A4PS297G B.E. Mechanical Engineering
AT
EATON TECHNOLOGIES PVT. LTD., PUNE
Practice School II Station of
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE, PILANI
December, 2015
3. i
ABSTRACT SHEET
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE
PILANI (RAJASTHAN)
Practice School Division
Station: Eaton Technologies Private Limited Centre: Pune
Duration: 5 months
Date of Commencement: 4th
July, 2015
Date of Completion: 4th
December, 2015
Title of the Project: “Wind and Ice load Analysis for Recloser Unit and Analytical Stress
Analysis of the Frame designed for Recloser Unit.”
Student Details:
Name: Addepalli Lava Kumar ID No.: 2012A4PS297G Discipline: B.E. Mechanical Egg.
Mentor Details:
1) Name: Mr. Dinesh Sonawane Designation: Senior Engineer, Electrical Systems
2) Name: Mr. Mangesh Pingle Designation: Engineer, Electrical Systems
PS Faculty Details:
Name: Mr. Dinesh Wamanrao Wagh
Key Words: Wind Load, Ice load, Switchgear, Von-Mises Stress
Project Areas: Wind and Ice Load Analysis and Analytical Stress Analysis.
Abstract: Extreme Wind and Ice Load Analysis on a Recloser unit is necessary whether the
equipment that is mounted on a pole can withstand those loads and these loads are also been
included in the Stress Analysis of the frame on which the whole Recloser Equipment is mounted.
The Stress Analysis is done Analytically following the conventional rules and is required to
ensure whether the frame can withstand all the weight of the components that are to be mounted
and having a specified factor of safety.
Signature of Student and Date Signature of Faculty and Date
4. ii
BIRLA INSTITUTE OF TECHNOLOGY & SCIENCE
PILANI (RAJASTHAN)
PRACTICE SCHOOL DIVISION
Response Option Sheet
Station: Eaton Technologies Pvt. Ltd. Centre: Pune
Name & ID No.: Addepalli Lava Kumar ; 2012A4PS297G
Title of the Project: Wind and Ice load Analysis for Recloser Unit and Theoretical Stress
Analysis of the Frame designed for Recloser Unit
Usefulness of the project to the on-campus courses of study in various disciplines: Project should
be scrutinized keeping in view the following response options. Write Course No. and Course
Name against the option under which the project comes. Refer Bulletin for Course No. and
Course Name.
Code
No.
Response Options Course No. & Name
1.
A new course can be designed out of this project
Yes, Wind and Ice load
Analysis for Buildings
and other Structures.
2.
The project can help modification of the course content of some
of the existing Courses
Yes, How to calculate
VMS for 3D loaded
structure
3. The project can be used directly in some of the existing
Compulsory Discipline Courses (CDC)/Discipline Courses Other
than Compulsory (DCOC)/ Emerging Area (EA) etc. Courses
No
4. The project can be used in preparatory courses like Analysis and
Application Oriented Courses (AAOC)/ Engineering Science
(ES)/ Technical Art (TA) and Core Courses
Yes, AAOC
5. This project cannot come under any of the above mentioned
options as it relates to the professional work of the host
organization
--
Signature of Student Signature of Faculty
5. iii
ACKNOWLEDGEMENT
I’m so excited to share the experience and thank those who helped me in going through and
showed a way to solve the problems I have faced while doing the project.
Firstly I want to thank Mr. Jayesh Maru (Manager, Electrical Systems) and Mr. Sunil Barot
(Manager, Electrical Systems) assigning me under this project and it helped me in lot more ways
to apply the knowledge I have and build it up by learning a lot more new things that are required
to complete the assigned job. I’m so grateful to Mr. Dinesh Sonawane (Senior Engineer,
Electrical Systems) and Mr. Mangesh Pingle (Engineer, Electrical Systems) as they have helped
me to come out of my mistakes while doing the analysis and favored me towards its completion.
I would also like to thank Late Dr. Vijay Arora for his constant guidance in how to go through in
hard times of the project and how to get the problem solved with critical thinking of assumptions
made and Mr. Dinesh Wamanrao Wagh for his guidance at the end for completing the project
report.
6. iv
GLOSSARY
Circuit Breaker: A device which is automatically operated electrical switch designed to protect
an electrical circuit from damage caused by overload or short circuit.
Switchgear: In an electric power system, switchgear is the combination of electrical disconnect
switches, fuses or circuit breakers used to control, protect and isolate electrical equipment.
Wind Profile Power Law: The wind profile power law is a relationship between the wind
speeds at one height, and those at another.
The wind profile power law relationship is:
Gust effect Factor: The gust effect factor accounts for the loading effects in the along wind
direction due to wind turbulence structure interaction.
Plane Stress Condition: Plane stress typically occurs in thin flat plates that are acted upon only
by load forces that are parallel to them. In certain situations, a gently curved thin plate may also
be assumed to have plane stress for the purpose of stress analysis.
Von-Mises Stress: The Von Mises yield criterion suggests that the yielding of materials begins
when the second deviatoric stress invariant reaches a critical value. A material is said to start
yielding when its von Mises stress reaches a critical value known as the yield strength, .
7. v
LIST OF TABLES, FIGURES AND GRAPHS
List of Tables :
S.No. Table No. Table Description Page No.
1 2.1 Description of Exposure Categories 10
2 2.2 Gradient Height and Wind Velocity Exponent values 11
3 2.3 Importance Factor Co-efficient for different categories 13
4 2.4 Wind Speed Conversions to Pressure 17
List of Figures:
S.No. Figure No. Figure Description Page No.
1 1.1 Power Transmission and Distribution Layout 3
2 1.2 Showing some of the components of MV Switchgear unit 4
3 1.3
Showing some of the components of MV Pole Mount
Switchgear unit
4
4 1.4 Basic Operation of Current Transformer 6
5 1.5 Surge Arrester 7
6 1.6
Typical Figures showing Electric Isolators in Distribution
Network
7
7 2.1 Various Exposure Categories 10
8 3.1 Figure showing 3D state of stress 18
9 3.2
Schematic View of CAD Model of frame for GeNex Recloser
Assembly
20
10 3.3
FBD of the Frame in Front View (X-Y Plane) and showing
Loads and distances of Loads from reference point
21
11 3.4 Plane stress Condition 26
12 3.5
FBD of frame in Right side View showing Loads and the
Distances of the Loads from the a reference point
27
13 3.6 3D state of stress 30
List of Graphs:
S.No. Graph No. Graph Description Page No.
1 2.1 Wind Speed variation with height from the ground 12
2 2.2 Wind Speed vs Pressure 17
8. vi
TABLE OF CONTENTS
Serial No. Topic Page No.
I Abstract Sheet i
II Response Option Sheet ii
III Acknowledgement iii
IV Glossary iv
V List of Tables, Figures and Graphs v
1
1.1
1.2
1.3
1.3.1
1.3.2
1.3.3
Introduction
A Brief about Organization
Power Transmission and Distribution Network
A brief about Switchgear Unit
What is Switchgear Unit?
Components of Switchgear Unit
Main Functions of Switchgear Unit
1
2
4
4
5
8
2
2.1
2.1.1
2.1.1.1
2.1.1.2
2.1.2
2.2
2.2.1
2.3
Wind Load and Ice Load Analysis
Wind Load
Analytical Design Method for Wind Load Calculation
Exposure Category
Factors affecting Wind Load
Design of Wind Load
Ice Load
Design of Ice Load
Extreme Ice loading with concurrent Wind Load
9
9
9
11
14
16
16
17
3
3.1
3.2
3.3
3.4
3.4.1
3.4.2
3.5
3.5.1
3.5.2
3.6
Methodology To Find Von-Mises Stress At a particular
location on frame for given loading conditions
Introduction to Stress
Nomenclature and Definitions used in calculations
Assumptions
Free Body Diagram of Frame in Front View (X-Y Plane)
Calculation of stresses and Bending Moments in front View
Calculation of Normal Stress and Shear Stress
Free Body Diagram of Frame in Right side View (Y-Z Plane)
Calculation of stresses and Bending Moments in Right side View
Calculation of Normal Stress and Shear Stress
Von-Mises Stress Calculation
18
19
21
21
22
25
27
28
30
30
4 Recommendations and Conclusions 31
5 Appendix I 32
6 Appendix II 33
7 Appendix III 34
10. 1
1. INTRODUCTION
1.1. A BRIEF ABOUT THE ORGANISATION:
Eaton is a global technology leader in power management solutions that make electrical,
hydraulic and mechanical power operate more efficiently, effectively, safely and sustainably.
The company is a global technology leader in electrical products, systems and services for power
quality, distribution and control, power transmission, lighting and wiring products; hydraulics
components, systems and services for industrial and mobile equipment; aerospace fuel, hydraulic
and pneumatic systems for commercial and military use; and truck and automotive drivetrain and
powertrain systems for performance, fuel economy and safety. Eaton acquired Cooper Industries
plc in November 2012. The 2013 revenue of the combined companies was $22 billion on a pro
forma basis. Eaton has approximately 100,000+ employees worldwide and sells products to
customers in more than 175 countries.
In 2003, Eaton set up a best-in-class engineering center in Pune – the Eaton India Engineering
Center (EIEC). Since then, EIEC has become a major product engineering, design and
development center for Eaton’s global customers.
EIEC is an innovative global design chain where technologists, engineers and designers work in
virtual teams with their counterparts from Eaton’s businesses and Innovation Centers worldwide.
The strategic value creation by EIEC is in sustaining engineering, product development,
application engineering and advanced technology through cutting edge innovation.
EIEC has engineering and design teams for multiple businesses and has developed Centers of
Excellence in Modeling and Simulation, Controls and Reliability, Embedded Control Systems
and Intellectual Property.
In June 2004, when Eaton completed its global acquisition of Powerware from Invensys, the
New Delhi based facilities of Powerware were also integrated into Eaton’s India operations.
Today, Eaton’s Electrical business in India is geared up to provide power distribution, power
quality and back-up, control and automation, power monitoring and management solutions and
services to commercial, residential, utility, alternative energy, IT and data centers, public sector
institutional and OEMs. Eaton is a world leader and premier innovator in providing cutting-edge
systems, solutions and technologies to the global aerospace industry. Eaton designs, develops,
manufactures and integrates the industry’s most advanced offerings in the areas of cockpit
interface, electrical power management, engine solutions, fuel and inerting, hydraulic systems
and motion control.
11. 2
1.2. POWER TRANSMISSION AND DISTRIBUTION NETWORK:
Electrical power is generated at different generating stations. These generating stations are not
necessarily situated at the load center. During construction of generating station number of
factors to be considered from economical point of view. These all factors may not be easily
available at load center, hence generating stations are not normally situated very nearer to load
center. Load center is the place where maximum power is consumed. Hence there must be some
means by which the generated power must be transmitted to the load center. Electrical
transmission and distribution system is the means of transmitting and distributing power from
generating station to different load centers.
There are two types of Power distribution:
• Primary Power Distribution (usually medium/high voltage) :
• In this high voltage from Transmission lines that act as feeder to the transformer in
Primary Substation is stepped down to a voltage that is mainly used by Heavy industries
• Secondary Power Distribution (low voltage) :
• The distributor lines from Primary power distribution acts as feeder to the transformers in
Secondary Substation and is further stepped down to a value that is used by Households,
Light industries etc.,
Voltage Classification:
Low Voltage : Up to 1kV
Medium Voltage : 1kV to 35kV
High Voltage : 35kV to 230kV
Extra High Voltage : above 230kV
12. 3
Fig 1.1 : Power Transmission and Distribution Layout
During the transmission and distribution of electric power there is high possibility of occurrence
of line faults, short circuits etc., Surging of current happens because of these faults and can cause
great damage to then equipment. So in order to protect the equipment from these fault currents
there have been implemented different Power system protection devices like Circuit breakers,
Electric fuses, Switchgear units.
13. 4
1.3. A BRIEF ABOUT SWITCHGEAR UNIT
1.3.1.What is Switchgear Unit?
A switchgear or electrical switchgear is a generic term which includes all the switching devices
associated with mainly power system protection. It also includes all devices associated with
control, metering and regulating of electrical power system. All such devices are assemble in a
logical manner to form a switchgear.
There are two kinds of Switchgear units:
1) Pole mount switchgear for overhead protection.
2) Pad mount switchgear unit.
Fig 1.2 : Showing some of the components of the MV Switchgear unit
Fig 1.3 : Showing some of the Components of the MV Pole Mount Switchgear Unit
14. 5
1.3.2. Components of Switchgear:
Switchgear performs the tasks like making, breaking and carrying of load currents and it has
provision for regulating and metering of various parameters of electric power system.
a) Circuit Breaker
Electrical circuit breaker is basically a switching device that can be operated manually as well
as automatically for controlling and protection of electrical power system. Now-a-days, Power
system has to deal with huge currents, so high attention should be given for designing the circuit
breaker and proper interruption of arc should be done which is produced during fault. So during
the operation the fixed and moving contacts are separated by the arc formed and is to be
quenched to increase the dielectric strength of the medium between them so that no arc is
produced after every crossing of current aero in alternating current.
Types of Circuit Breakers:
Based on quenching process
1) Oil circuit breaker 2) Gas(SF6) Circuit breaker
3) Air Circuit breaker 4) Vacuum Circuit Breaker.
Based on Operating Mechanism
1) Spring Actuated Circuit breaker 2) Pneumatic Circuit Breaker
3) Hydraulic Circuit Breaker
Based on Voltage applied
1) Low Voltage Circuit Breaker 2) Medium Voltage Circuit Breaker
3) High Voltage Circuit Breaker
b) Voltage Transformer
Voltage transformers (VT), also called potential transformers (PT), are a parallel connected type
of instrument transformer, used for metering and protection in high-voltage circuits.
There are three primary types of voltage transformers (VT):
1) Electromagnetic,
2) Capacitor, and
15. 6
3) Optical.
The electromagnetic voltage transformer is a wire-wound transformer.
The capacitor voltage transformer uses a capacitance potential divider and is used at higher
voltages due to a lower cost than an electromagnetic VT.
An optical voltage transformer exploits the electrical properties of optical materials
Measurement of high voltages is possible by the potential transformers.
c) Current Transformer
A current transformer (CT) is an electric device that produces an alternating current (AC) in
its secondary which is proportional to the AC in its primary. Current transformers, together with
voltage transformers (VTs) or potential transformers (PTs), which are designed for measurement,
are known as instrument transformers.
Fig 1.4 : Basic Operation of Current transformer.
d) Surge Arresters:
A surge arrester is a device to protect electrical equipment from over-voltage transients caused
by external (lightning) or internal (switching) events.
These are used in both transmission and distribution network systems.
16. 7
Fig 1.5 : Surge arrester
e) Protective Relay :
A relay is automatic device which senses an abnormal condition of electrical circuit and closes
its contacts. These contacts in turns close and complete the circuit breaker trip coil circuit hence
make the circuit breaker tripped for disconnecting the faulty portion of the electrical circuit from
rest of the healthy circuit
f) Electric Isolator:
Circuit breaker always trip the circuit but open contacts of breaker cannot be visible physically
from outside of the breaker and that is why it is recommended not to touch any electrical circuit
just by switching off the circuit breaker.
So for better safety there must be some arrangement so that one can see open condition of the
section of the circuit before touching it. Isolator is a mechanical switch which isolates a part of
circuit from system as when required.
Electrical isolators separate a part of the system from rest for safe maintenance works
Fig 1.6 : Typical Figures Showing Electric Isolators in Distribution Networks
17. 8
1.3.3. Main Functions of switchgear unit:
We all familiar with low voltage switches and fuses in our home. The switch is used to manually
open and close the electrical circuit in our home and electrical fuse is used to protect our
household electrical circuit from over current and short circuit faults. In same way every
electrical circuit including high voltage electrical power system needs switching and protective
devices. But in high voltage and extra high voltage system, these switching and protective
scheme becomes complicated one for high fault current interruption in safe and secure way. In
addition to that from commercial point of view every electrical power system needs measuring,
control and regulating arrangement. Collectively the whole system is called switchgear and
protection of power system.
Electric switchgear is necessary at every switching point in the electrical power system. There
are various voltage levels and hence various fault levels between the generating stations and load
centers. Therefore various types of switchgear assembly are required depending upon different
voltage levels of the system.
18. 9
2.WIND LOAD AND ICE LOAD ANALYSIS
2.1. WIND LOAD :
The speed of the wind or wind velocity acts as pressure when it meets with a structure. The
intensity of that pressure is the wind load. Calculating wind loads is necessary for the design and
construction of safer, more wind-resistant buildings. There are many factors that need to be
considered when calculating wind loads.
The Wind load is merely unpredictable near to the earth’s surface as there will be change in
speed of wind with height above ground level and many other structures will be interacting
making the sped of wind to get decreased. So, predicting the exact value of the wind pressure
may not be possible but approximately it can be estimated using the standards.
2.1.1 Analytical Design Method for Wind Load Calculation :
Wind Load is the force arising on the structure due to the impact of wind on it.
It can be best possibly figured out using Bernoulli’s Equation,
P1 + ½ ρV1
2
= P2 + ½ ρV2
2
Assuming ideal case in which wind goes to zero velocity at the vicinity of the structure, V2 = 0
Wind Pressure, ΔP = P2 – P1 = ½ ρV1
2
The actual Wind load is calculated as per the standards ASCE.7.2002 and NESC C2 2007
There are many factors the Wind load depends on:
1) Wind Speed 2) Velocity Exposure Co-efficient (Kzt)
3) Topographic Factor (Kzt) 4) Directionality Factor (Kd)
5) Gust Effect Factor (Grf) 6) Force Co-efficient(Shape Factor) (Cf)
7) Importance factor (I) 8) Projected Area (A)
2.1.1.1. Exposure Category:
Exposure category of the site accounts for terrain roughness on wind speed. The height and
density of topographic features and buildings in the upwind direction are considered to account
for the exposure category.
19. 10
Fig 2.1 : Various Exposure Categories [2]
Table 2.1 : Description of Exposure Categories [2]
As per NESC C2 2007 the overhead switchgear units are considered to be in Exposure category
C. So, the Exposure category C is considered in calculations as per ASCE 7 2002 and NESC C2
2007 standards.
20. 11
2.1.1.2.Factors affecting Wind load :
a) Wind Speed :
3 second gust speed at 33ft above the ground in Exposure Category “C” (see below) and depends
on geographic location. As per IEEE C37.60 2012 wind speed to be considered for experimental
evaluation is 34m/s (122 km/hr.) (76 mi/hr.)
b) Velocity Exposure Co-efficient, Kz :
The velocity pressure exposure coefficient, Kz, reflects the change in wind speed with height and
exposure category. The velocity pressure exposure coefficient is defined by ASCE Equations as:
Kz = 2.01*(z / zg)(2/α)
for 15ft ≤ z ≤ zg.
Kz = 2.01*(15 / zg)(2/α)
for z < 15ft.
where z= height above the ground level, zg= gradient height
The ground obstructions retard the wind flow close to the ground and wind speed increases with
height above ground level until the gradient height is reached and then the speed becomes
constant.
Table 1, provides values for power law exponents and gradient heights for various exposure
categories.
Table 2.2 : Gradient Height and Wind Velocity Exponent values [1]
Here in our case we are assuming the Switchgear unit is mounted at height of z = 55ft
Kz = 2.01 * (55/900)(2/9.5)
= 1.1
Exposure A B C D
zg 1500 1200 900 700
α 5 7 9.5 11.5
21. 12
Graph 2.1 : Wind speed variation with height from the ground [2]
c) Topographic factor, Kzt :
Because of the hills and escarpments make the winds to get speed up. So, taking this into the
factor we have to employ this factor into the calculation of the wind load as the equipment can be
there in a hilly areas.
The topographic factor is dependent on the gross terrain. As wind speed increases with elevation
of a building, so does wind speed increases with height up a hill. The topographic factor depends
upon exposure category, the horizontal and vertical distance from the hill and height of the hill.
Topographic factor can be calculated using the formulas in sec. 6.5.7.2 ( ASCE 7 2002) standard.
The maximum value that can be obtained for a particular condition is 2.958 for Exposure
Category C and this is considered in calculations for maximum load condition.
d) Directionality Factor, Kd :
Wind Directionality Factor accounts for two effects :
1) Reduced probability of maximum winds coming in any given direction.
2) Reduced probability of maximum pressure co-efficient occurring at any given position.
Values of Directionality factor of different structures are been tabulated in “Appendix I”
22. 13
The GeNex Switchgear unit comes into an open signs and lattice framework and so the
Directionality Factor, Kd = 0.85
e) Gust Effect Factor, Grf :
The gust effect factor accounts for the loading effects in the along wind direction due to wind
turbulence structure interaction. It also accounts for along wind loading effects due to dynamic
amplification for flexible building and structures. It does not include allowances for across-wind
loading effects, vortex shedding, instability due to galloping or flutter, or dynamic torsional
effects.
Gust effect factor for rigid structures is 0.85 as per ASCE 7 2002 and the rigid structure is
defined in ASCE 7 2002 Sec 6.2 and Sec C 6.2 as whose fundamental frequency is greater than
1Hz.
Gust effect factor can also be calculated by the formulation given in NESC C2 2007. Grf id
determined using height, h of the structure from the ground level. This can be calculated as
formulated in “ Appendix II ”.
The GeNex Switchgear unit is a rigid structure and Grf can be considered to be 0.85[].
By following through the formulae given in Appendix”” and assuming the unit to be mounted at
height of 55ft, the value obtained for Grf is 0.88.
f) Importance Factor, I:
Importance Factor is the measure of protection required for the building. It accounts for degree
of hazard to human life and damage to property.
So the location of the structure is basically categorized into four as per ASCE 7 2002 and the
structure which falls into a particular category can be determined from the table in Appendix III
and the values of Importance factor for the corresponding categories is tabulated below.
Table 2.3 : Importance factor co-efficient for different Categories[2]
Category Non Hurricane prone
regions, with V=85-100
mph
Hurricane prone
regions with V>100
mph
I 0.87 0.77
II 1 1
III 1.15 1.15
IV 1.15 1.15
23. 14
g) Force Coefficient (Shape Factor), Cf :
It is also known as drag coefficient and it depends on
a) Shape of Object
b) Surface Roughness
c) Reynolds Number
The value of Cf for different structures like, Cylindrical structures and components, Flat
surfaced(not latticed) structures and components and Latticed structures and is provided in
NESC C2 2007 Rule 252B, and the values can be obtained from “Appendix IV”.
The value of Cf for the GeNex Switchgear unit is “3.2” and comes under lattice structure
containing the flat members
As per ASCE 7 2002, the value of Cf can be found out from Sec 6.5.13 of ASCE 7 for
Monoslope Roofs , Chimneys, Tanks, Rooftop Equipment, & similar Structures, Solid
Freestanding Walls & Solid Signs, Open Sign and Lattice structures and Trussed Structures. The
value for respective structure can be obtained from the tables in the “Appendix V”.
The value for Cf for the GeNex Switchgear unit is “2” and comes under Open Signs and lattice
structure category.
h) Projected area:
The maximum projected area Is to be considered in the calculation so that structure is to be
subjected to maximum load condition and the analysis is done accordingly.
The maximum projected area of GeNex switchgear unit is obtained in front view and it came out
to be 15.186sq.ft.
2.1.2.Design Wind Load:
Design wind load can be calculated from
• Load (lbs) = 0.00256 * Kz * Grf * Cf * I * (V^2) * A (NESC C2-2007)
• Load (lbs)= 0.00256 * Kz * Kzt * Kd * I * (V^2) * Grf * Cf * A (ASCE 7-2002 )
and the values of variables in the equation are:
Speed of wind, V = 76 miles/hr.
Velocity Pressure Coefficient, Kz = 1.1
24. 15
Topographic Factor, Kzt= 2.958
Directionality Factor, Kd = 0.85
Gust Effect Factor, Grf = 0.88[1] or 0.85[2]
Importance factor, I = 1
Force Co-efficient, Cf = 3.2 [1], 2[2]
Projected area of the Recloser unit in Front view, A = 15.186 sq.ft
Design wind load as per both the standards is
According to terms and conditions followed as given in NESC C2-2007 and the values of the co-
efficient are taken as given by the standard and the load value is found to be
Load (lbs) = 0.00256*1.1*0.88*3.2*1*76^(2)*15.186
= 695.5 lbs
According to terms and conditions followed as given in ASCE 7-2002 and the values of the co-
efficient are taken as given by the standard and the load value is found to be
Load(lbs) = 0.00256 *1.1*2.958*0.95*1*76^(2)*0.85*2*15.186
= 1179.5 lbs
25. 16
2.2. ICE LOAD:
Ice loading is due to the accumulation of ice on the top surface of any structure.
Three general degrees of ice loading due to weather conditions are recognized and are designated
as heavy, medium and light loading.
Ice loading test and design test are performed to obtain ice breaking ability of the outdoor
switching equipment. As there will be loading due to ice accumulation the weight of ice is
considered while doing the stress analysis of the whole frame assembly.
According to IEEE C37.60-2012 10mm to 20mm thickness of ice is considered to be
representative of severe conditions. So, for design considerations 1in = 25.4 mm thickness of ice
is considered.
According to NESC C2 2007 Rule 250B, Density of Ice, ρice = 913 kg/m3
(57 lb./ft3
)
For calculating the ice load we have to find the total projected area of the whole assembly in top
view in sq.ft and thereby introducing that value into the following simple formula gives us the
Design value of ice load according to NESC C2-2007 standard.
2.2.1Design Ice load:
Density of Ice, ρ = 57lb/ft3
,
Thickness of ice, t = 1in = 25.4mm = 0.083ft
Ice load (lbs) = ρ*t*A = 57*0.083*A
Projected area in top view is obtained to be 14.94 sq.ft
Ice load (lbs) = 57*0.083*14.94 = 70.68 lbs.
26. 17
2.3. EXTREME ICE LOADING WITH CONCURRENT WIND LOAD:
This kind of loading can be evaluated according to Rule 250D of NESC C2-2007. Considering
the thickness of ice to be 1in which is stated earlier for severe conditions and the wind load is
obtained from the table given below for particular speed of wind.
Table 2.4 : Wind speed Conversions to Pressure
As per IEEE C37.60-2012 the design wind speed to be considered is 76 mph. So, the values are
been extrapolated and the value of the pressure for corresponding speed.
Graph 2.2 : Wind Speed (vs) Pressure
Therefore, the corresponding value of wind pressure for 76 mph of wind speed is 14.64lb/sq.ft
Total load(lbs) = Wind load + Ice load
= 14.64*Area in front view + 70.68
= 14.64*15.186 +70.68
= 293 lbs.
y = 0.0027x2 - 0.0165x + 0.305
0
2
4
6
8
10
0 20 40 60 80
Pressure
(lb/sq.ft)
pressure
(lb/sq.ft)
Poly. (pressure
(lb/sq.ft))
Wind Speed
(mph)
Wind Sped
(mph)
Horizontal Wind
Pressure (lb./ft^2)
30 2.3
40 4
50 6.4
60 9.2
27. 18
3.METHODOLOGY TO FIND VON-MISES STRESS AT A PARTICULAR LOCATION
ON FRAME FOR GIVEN LOADING CONDITIONS
3.1.INTRODUCTION TO STRESS:
There will be stresses in any object those are subjected to some force.
Stress is basically classified as
1) Normal Stress
2) Shear Stress
Below we can see the 3D state of stress (Stress components acting on six sides of
parallelepiped)
Fig 3.1 : Figure showing 3D state of stress
Von Mises Yield Criterion:
This states that the yielding occurs if the following equation satisfies
{0.5*[(σx – σy )2
+ (σy – σz)2
+ (σz – σx)2
] + 3* τxy
2
+ 3* τyz
2
+3* τzx
2
}1/2
= Y
Where, Y is the stress at which yielding begins in Tensile test.
28. 19
3.2. NOMENCLATURE AND DEFINITIONS USED IN CALCULATIONS:
RA = Reaction at support “A”
RB = Reaction at support “B”
MPT1 = Moment due to PT1
MPT2 = Moment due to PT2
w = Weight per unit length of Recloser
L = Length of the continuous load of Recloser in XY Plane
L2 = Total length of frame in XY plane
WRX = Weight of Recloser of phase X
WSAX = Weight of surge arresters of Phase X
WRY = Weight of Recloser of phase Y
WSAY = Weight of surge arresters of Phase Y
WRZ = Weight of Recloser of phase Z
WSAZ = Weight of surge arresters of Phase Z
WPT1 = Weight of Potential Transformer 1 (PT1)
WPT2 = Weight of Potential transformer 2 (PT2)
W6SA = Weight of 6 Surge Arresters
W3R = Weight of 3 Reclosers
WFR = Weight of frame
Mwind,Rec = Moment due to wind load (from Left side) on Recloser
Mwind,3Rec = Moment due to wind load(from Front) on 3 Reclosers
Mwind,PT1 = Moment due to wind load(from Front) on PT1
Mwind,PT2 = Moment due to wind load (from Front) on PT2
Wice = Weight of ice on the structure.
wice = Weight per unit length of ice.
29. 20
RC = Reaction at support “C”
RD = Reaction at support “D”
K = Length of the continuous load of the Recloser in the YZ plane.
K2 = Total length of frame in YZ frame
IXX = Moment of Inertia in X-X axis
IZZ = Moment of Inertia in Z-Z axis
Frame for GeNex (Mark 4) Recloser system:
Fig 3.2 : Schematic View of CAD Model of frame for the GeNex Recloser Assembly
Front View : X-Y Plane
Right Side View : Y-Z Plane
30. 21
3.3. ASSUMPTIONS:
1. Weight of recloser is acting as a continuous load of length “L” in X-Y plane and “K” in Y-Z
plane.
2. A,B,C,D are considered to be rigid supports.
3. Surge Arrester’s and Potential Transformer’s load is considered to be as Point loads.
4. Considering frame as Rectangular Sheet of Length(a),Breadth (b),Thickness (h).
5.Total frame weight is acting at the center of mass of the frame
6. Ice load is uniform continuous load on the whole equipment
7.Wind load is acting at the centroid of the projected area of each component in the direction of
wind.
3.4. FREE BODY DIAGRAM OF FRAME IN FRONT VIEW:
First we will look at the front view of the frame and the loadings on it in X-Y Plane. The loads
on the Frame are as shown below in Fig.1
Here, we take cross-sections at different lengths along the frame and apply Equilibrium
Conditions at those points, hence we can find the Shear Force and Bending Moments at those
points.
Fig 3.3 : FBD of the Frame in Front View (X-Y Plane) and showing Loads and distances of
Loads from reference point.
31. 22
Equilibrium Conditions:
Sum of the forces in a given direction is zero, ΣF = 0
Sum of the Moments at a point is zero, ΣM = 0
3.4.1.Calculation for stresses and Bending Moment in the Front View:
Equilibrium conditions applying for the front view condition:
Sum of the forces in Y- direction is zero,
Σ Fy = Ra + Rb – WPT1 – WPT2 – WRX – WRY – WRZ-WSAX-WSAY-WSAZ – WFR – Wice = 0
Sum of the moments at point A is zero,
ΣMA = MPT1 + xRa*WPT1 + (xRa-xR1)*WR1 + xab*Rb – (xR2-xRa)*WR2 –(xR3-xRa)*WR3 – (xPT2 –
xRa)*WPT2+(xRa-xSAX)*WSAX-(xSAY-xRa)*WSAY –(xSAZ-xRa)*WSAZ–MPT2 –Mwind,Rec + wice*(xRa
2
/2)
– wice*(L2 – xRa)2
/2 = 0
Solving above two equations we can get Ra and Rb .
Rb = [(xRY-xRa)*WRY+(xRZ-xRa)*WRZ+(xPT2-xRa)*WPT2+MPT2-MPT1+Mwind,Rec – wice*(xRa
2
/2)
+wice*(L2 –xRa)2
/2 - xRa*WPT1 – (xRa – xRx)* WRX +(xSAY-xRa)*WSAY +(xSAZ-xRa)*WSAZ-(xSAX-
xRa)*WSAX ]/(xRa-xRb)
Ra = WPT1 + WPT2+WRX+WRY+WRZ+WSAX+WSAY+WSAZ + Wice-Rb
X-Y PLANE :
Methodology for finding the Shear force and Bending Moment at different sections along the
frame
Apply Equilibrium conditions at every point at distance “x” from origin.
ΣFx = ΣFY =ΣFZ = 0
ΣM = 0
Formulation :
1) 0 < x < =xSAX
V(x) = WPT1 + wice*x
Mb(x) + MPT1 +wice*x2
/2+ x*WPT1 = 0
∴ Mb(x) = -wice*x2
/2 –x*WPT1 – MPT1
34. 25
Mb(x) +wice*(L2 –x)2
/2 + (xRZ – x) *WRZ +(xSAZ – x)*WSAZ + (xPT2 – x)*WPT2 +MPT2 = 0
∴ Mb(x) =-wice*x2
/2+ (wice*L2+ WRZ +WSAZ + WPT2)*x – xRZ*WRZ –xSAZ *WSAZ – xPT2*WPT2 –
MPT2 –wice*L2
2
/2
12) xRZ – L/2 < x < xRZ + L/2
V(x) = -w*(xRZ + L/2 –x) – WSAZ –WPT2 – wice*(L2 – x)
Mb(x) + MPT2 +(xPT2 –x)*WPT2 +(xSAZ – x)*WSAZ +w*(xRZ + L/2 – x)2
/2 +wice*(L2-x)2
/2= 0
∴ Mb(x) = -(w + wice)*x2
/2 + [(xRZ + L/2)*w +wice*L2 + WPT2 +WSAZ]*x – xPT2 *WPT2 – xSAZ
*WSAZ – MPT2 – w*(xRZ +L/2)2
/2 – wice*L2
2
/2
13) xRZ + L/2 < x < xSAZ
V(x) = -WSAZ – WPT2 –wice*(L2-x)
Mb(x) +wice*(L2 – x)2
/2+ (xSAZ – x)*WSAZ + (xPT2 – x)*WPT2 +MPT2 = 0
∴Mb(x) = -wice*x2
/2 +(wice*L2+ WSAZ + WPT2)*x – xSAZ*WSAZ – xPT2*WPT2 – MPT2 – wice*L2
2
/2
14) xSAZ < x < xPT2
V(x) = - WPT2 –wice*(L2-x)
Mb(x) + wice*(L2-x)2
/2 +(xPT2 –x)*WPT2 + MPT2 = 0
∴Mb(x) = -wice * x2
/2 +(wice*L2+ WPT2 )*x – xPT2*WPT2 – MPT2 –wice*L2
2
/2
3.4.2. Calculation Of Normal Stress and Shear stress
After finding the shear forces and Bending Moments at particular location on the frame we can
find Normal stress (σx) and Shear stress (τxy) in X-Y Plane.
Finding Normal Stress using Flexure Formula:
σx = (Mb*y)/Izz
Mb = bending moment at particular location
y = Distance of that location from Neutral axis
Izz = Moment of inertia of the cross-section along Z-Z axis
As the cross section in Y-Z plane is Rectangular with width = b, thickness = h
IZZ = 1/12(b*h3
)
35. 26
Maximum Bending Moment occurs at the farthest point from the neutral axis, y=h/2
∴ Normal Stress (σx) = (Mb*h/2)/(bh3
/12)
∴ σx = 6Mb/bh2
For evaluating Shear stress we shall consider Plane stress condition.
Considering Plane stress condition on the frame,
Fig 3.4 : Plane Stress Condition
ΣFx = 0
∴ (δσx
/δx) + (δτyx
/δy) = 0
- ( δτyx
/δy) = δ/δx(Mb*y/IZZ) = (V/Izz)*y
Integrating from y to h/2
τxy = (V/Izz)*[(h/2)2
– y2
]
Maximum Shear stress will occur at neutral axis, y=0
∴ τxy = (V/Izz)*(h/2)2
= (V/(bh3
/12))*h2
/4 = 3V/bh
∴ τxy = 3V/bh
3.5. FREE BODY DIAGRAM OF FRAME IN RIGHT SIDE VIEW (Y-Z PLANE):
In Y-Z Plane we get the right side view of the Frame and the loads in that view are as shown in
the Fig3.
36. 27
Here, we take cross-sections at different lengths along the frame and apply Equilibrium
Conditions at those points, hence we can find the Shear Force and Bending Moments at those
points.
Equilibrium Conditions:
ΣF = 0
ΣM = 0
Now, applying equilibrium conditions to whole system i.e.,
Sum of forces in Y direction is zero, ΣFy = 0 and
RC + RD = WPT1 + 3*WR + WPT2 +W6SA +Wice +WFR
Sum of Moments at point D is zero, ΣMD = 0
ΣMD = zPT2*WPT2 – zCD*Rc + z3R*W3R + zPT1*WPT1 +z6SA*W6SA +Mwind,PT2 +Mwind,PT1 +Mwind,3R
+zFR*WFR + Wice*K2
2
/2 = 0
By solving above equations, RC and RD are obtained.
Here, in fig3.
zPT1, z6SA, z3R, zRc, zPT2 are the distances of the Potential transformers ,Surge arrester and
Recloser loads from support D.
Fig 3.5 : FBD of frame in Right side View showing Loads and the Distances of the Loads from
the a reference point.
3.5.1.Calculation for the stresses and the Bending moment in Right Side view:
Methodology for finding the Shear force and Bending Moment at different sections along the
frame
38. 29
Mb(z) +wice*(K2-z)2
/2+ w*[(z3R +K/2) –z]2
/2 + (zPT1-z)*WPT1 –Mwind,PT1= 0
∴ Mb(z) = -(w +wice)*z2
/2 + [wice*K2 +(z3R + K/2)*w +WPT1]*z –w*(z3R +K/2)2
/2 –zPT1*WPT1 –
wice*K2
2
/2 + Mwind,PT1
7) zPT1 < z < z3R + K/2
V(z) = wice*(K2-z) + w[(z3R + K/2)-z]
Mb(z) + wice*(K2-z)2
/2 + w * [(z3R +K/2) – z]2
/2 = 0
8) z3R + K/2 < z < zK2
V(z) = wice*(K2 –z)
Mb(z) + wice*(K2-z)2
/2 = 0
∴ Mb(z) = -wice*z2
/2 + (wice*K2)*z – wice*K2
2
/2
3.5.2.Calculation of Normal Stress and Shear Stress
After finding out the Shear forces and Bending Moments we shall follow the earlier procedure
for finding out the Normal Stresses and Shear stresses.
Finding Normal Stress using Flexure Formula:
σz = (Mb*y)/Ixx
Mb = bending moment at particular location
y = Distance of that location from Neutral axis
Ixx = Moment of inertia of the cross-section along X-X axis
As the length of frame is “a” and thickness is “h”, for this cross-section Moment of Inertia in X-
X axis is
IXX = ah3
/12
Maximum stress occurs at distance y=h/2
σZ = (Mb*h/2)/(ah3
/12)
∴ (σZ )max= 6Mb/ah2
Shear Stress :
τzy = (V/Ixx)*[(h/2)2
– y2
]
39. 30
And Maximum Shear Stress occurs at Neutral Axis, y=0
∴ (τzy )max= (V/Izz)*(h/2)2 = 3V/ah
3.6. VON - MISES STRESS CRITERION:
Fig 3.6 : 3D state of Stress
By following above procedure and calculating the respective values of the stresses we can find
the Von-Misses Stress at a particular location on frame.
Von-Misses Yield Criterion
{0.5*[(σx – σy )2
+ (σy – σz)2
+ (σz – σx)2
] + 3* τxy
2
+ 3* τyz
2
+3* τzx
2
}1/2
= Y
Where Y is the stress at which yielding begins in Tensile test.
40. 31
4. RECOMMENDATIONS AND CONCLUSIONS
After calculating the Von-Mises Stress at different locations we can draw the Shear Force
Diagram and Bending Moment Diagram and so from those diagrams we can get the maximum
Bending stress and Shear Stress so that maximum Von-Mises Stress can be found out and
thereby having the Yield strength of the material that is used in making the frame and specified
Factor of Safety value, conclusions can be made whether the design considerations are well
within the limits and if not so, measures like increasing/decreasing the thickness of the sheet
metal used in manufacturing in order to achieve the desired Factor of Safety. Therefore we can
have the Frame that can withstand loads due to all the components mounted on it and it is also so
stable that it can withstand the loads due to Winds and Ice in the extreme adverse conditions.
44. 35
8. APPENDIX IV
Following are the shape factors according to NESC C2-2007
1) Cylindrical Structure and Components:
Wind loads on straight or tapered cylindrical structures or structures composed of numerous
narrow relatively flat panels that combine to form a total cross section that is circular pr elliptical
in shape shall be computed using a shape factor of 1.0
2) Flat surfaced (not latticed) structures and components:
Wind loads on structure or components, having solid or enclosed flat sided cross sections that are
square or rectangular, with rounded corners, shall be computed using a force co-efficient (shape
factor) of 1.6
3) Lattice structures:
Wind loads on square or rectangular lattice structures or components shall be computed using a
force co-efficient (shape factor) of 3.2 on the sum of the projected areas of the members of the
front face if the structural members are flat surfaced or 2.0 if the structural surfaces are
cylindrical. The total, however, need not exceed the load that would occur on a solid structure of
same outside dimension.
Exception: The force co-efficient (shape factor) listed above may be reduced if wind tunnel tests
or a qualified engineering study justifies a reduction.
50. 41
10. REFERENCES
1. IEEE C2: National Electric Safety Code (2007)
2. ASCE 7: Minimum Design Loads for Buildings and Other Structures (2002)
3. Introduction to Mechanics of Solids by Stephen. H. Crandall and Norman. C. Dahl
4. Advanced Mechanics of Solids by Arthur P. Boresi and Richard J. Schmidt
5. http://www.electrical4u.com/electrical-switchgear-protection/
6. https://en.wikipedia.org/wiki/Electric_power_distribution
