This document provides an overview of stresses and deformations in thick-walled cylinders. It begins with introducing the topic and presenting the basic relations used to analyze thick cylinders under internal and external pressures. It then derives the stress components for closed-end and open cylinders. Expressions are also developed for the stress components and radial displacement of a closed cylinder under constant temperature. Finally, an example problem is worked out to determine the stresses, maximum shear stress, and change in diameter for a hollow aluminum cylinder under internal pressure.
Springs - DESIGN OF MACHINE ELEMENTS-IIDr. L K Bhagi
Introduction to springs, Types and terminology of springs, Stress and deflection equations, Series and parallel connection, Design of helical springs, Design against fluctuating load, Concentric springs, Helical torsion springs, Spiral springs, Multi-leaf springs, Optimum design of helical spring
Springs - DESIGN OF MACHINE ELEMENTS-IIDr. L K Bhagi
Introduction to springs, Types and terminology of springs, Stress and deflection equations, Series and parallel connection, Design of helical springs, Design against fluctuating load, Concentric springs, Helical torsion springs, Spiral springs, Multi-leaf springs, Optimum design of helical spring
Bending Stresses are important in the design of beams from strength point of view. The present source gives an idea on theory and problems in bending stresses.
Every material has certain strength, expressed in terms of stress or strain, beyond which it
fractures or fails to carry the load. Failure Criterion: A criterion used to hypothesize the failure.
Failure Theory: A Theory behind a failure criterion.
Need of Failure Theories:
(a) To design structural components and calculate margin of safety.
(b) To guide in materials development.
(c) To determine weak and strong directions.
Bending Stresses are important in the design of beams from strength point of view. The present source gives an idea on theory and problems in bending stresses.
Every material has certain strength, expressed in terms of stress or strain, beyond which it
fractures or fails to carry the load. Failure Criterion: A criterion used to hypothesize the failure.
Failure Theory: A Theory behind a failure criterion.
Need of Failure Theories:
(a) To design structural components and calculate margin of safety.
(b) To guide in materials development.
(c) To determine weak and strong directions.
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
descarga el contenido completo de aqui http://paralafakyoumecanismos.blogspot.com.ar/2014/08/libro-para-mecanismos-y-elementos-de.html
Diseno en ingenieria mecanica de Shigley - 8th ---HDes
descarga el contenido completo de aqui http://paralafakyoumecanismos.blogspot.com.ar/2014/08/libro-para-mecanismos-y-elementos-de.html
What is the Difference Between a Pressure Vessel Tank and a Storage Tank? The primary difference between these two is that pressure vessels contain liquids/gases at a pressure above the atmospheric pressure. On the other hand, storage tanks store either liquids or gases at normal atmospheric pressure.
In developing electric motors in general and induction motors in particular
temperature limit is a key factor affecting the efficiency of the overall design. Since
conventional loading of induction motors is often expensive, the estimation of temperature
rise by tools of mathematical modeling becomes increasingly important. Excepting for
providing a more accurate representation of the problem, the proposed model can also
reduce computing costs. The paper develops a three-dimensional transient thermal model in
polar co-ordinates using finite element formulation and arch shaped elements. A
temperature-time method is employed to evaluate the distribution of loss in various parts of
the machine. Using these loss distributions as an input for finite element analysis, more
accurate temperature distributions can be obtained. The model is applied to predict the
temperature rise in the stator of a squirrel cage 7.5 kW totally enclosed fan-cooled induction
motor. The temperature distribution has been determined considering convection from the
back of core surface, outer air gap surface and annular end surface of a totally enclosed
structure.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
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Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
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The Thick-Walled cylinder
1. Namas Chandra
Advanced Mechanics of Materials Chapter 11-1
EGM 5653
The Thick Walled CylinderThe Thick Walled Cylinder
CE 527
Duaa FADIL
Submitted by:
Submitted to:
Asst.Prof.Dr. Nildem TAYŞİ
Advanced Mechanics of Materials
2. Namas Chandra
Advanced Mechanics of Materials Chapter 11-2
EGM 5653CE 527
Presentation OverviewPresentation Overview
Introduction
Basic Relations
Closed End Cylinders
Open Cylinder
Stress Components and Radial Displacement for
Constant Temperature
Stresses and Deformations in Hollow cylinder
Advanced Mechanics of Materials
3. Namas Chandra
Advanced Mechanics of Materials Chapter 11-3
EGM 5653
Introduction
This chapter deals with the basic
relations for axisymmetric
deformation of a thick walled cylinder
In most applications cylinder wall
thickness is constant, and is subjected
to uniform internal pressure p1,
uniform external pressure p2, and a
temperature change ΔT
CE 527
Advanced Mechanics of Materials
4. Namas Chandra
Advanced Mechanics of Materials Chapter 11-4
EGM 5653
Introduction contd.
Solutions are derived for open cylinders or for cylinders with
negligible “end cap” effects.
The solutions are axisymmetrical- function of only radial
coordinate r
Thick walled cylinders are used in industry as pressure vessels,
pipes, gun tubes etc..
CE 527
Advanced Mechanics of Materials
5. Namas Chandra
Advanced Mechanics of Materials Chapter 11-5
EGM 5653
Basic Relations
Equations of equilibrium derived neglecting the body force
( )rr
rr rr
d d
r or r
dr dr
θθ θθ
σ
σ σ σ σ= − =
Strain- Displacement Relations and Compatibility Condition
, ,rr zz
u u w
r r z
θθε ε ε
∂ ∂
= = =
∂ ∂
Three relations for extensional strain are
where u= u(r,z) and w= w(r,z) are
displacement components in the r and z
directions
CE 527
Advanced Mechanics of Materials
6. Namas Chandra
Advanced Mechanics of Materials Chapter 11-6
EGM 5653
Basic Relations Contd.
At sections far from the end shear
stress components = 0 and we
assume
εzz= constant. Therefore, by
eliminating u = u(r)
( )
rr rr
d d r
r or
dr dr
θθ θθ
θθ
ε ε
ε ε ε= − =
CE 527
Advanced Mechanics of Materials
7. Namas Chandra
Advanced Mechanics of Materials Chapter 11-7
EGM 5653
Basic Relations Contd.
Stress Strain Temperature Relations
The Cylinder material is assumed to be Isotropic and linearly elastic
The Stress- Strain temperature relations are:
[ ]
[ ]
[ ]
1
( )
1
( )
1
( ) constant
rr rr ZZ
rr ZZ
zz zz rr
T
E
T
E
T
E
θθ
θθ θθ
θθ
ε σ ν σ σ α
ε σ ν σ σ α
ε σ ν σ σ α
= − + + ∆
= − + + ∆
= − + + ∆ =
Where, E is Modulus of Elasticity
ν is Poisson’s ratio
α is the Coefficient of linear thermal expansion
ΔT is the change in the temp. from the uniform reference temp.
CE 527
Advanced Mechanics of Materials
8. Namas Chandra
Advanced Mechanics of Materials Chapter 11-8
EGM 5653
Closed End Cylinders
Stress Components at sections far from the ends
.
The expressions for the stress components σrr,σθθ, σzz for a cylinder
with closed ends and subjected to internal pressure p1, external
pressure p2, axial load P and temperature change ΔT.
From the equation of equilibrium, the strain compatibility equation and
the stress- strain temperature relations we get the differential
expression, 0
1
rr
d E T
dr
θθ
α
σ σ
ν
∆
+ + = ÷
−
CE 527
Advanced Mechanics of Materials
9. Namas Chandra
Advanced Mechanics of Materials Chapter 11-9
EGM 5653
Closed End Cylinders
Stress Components at sections far from the ends contd.
Eliminating the stress component σθθ and integrating, we get
2
2
12 2 2
1
(1 )
r
rr
a
CE a
Trdr C
r r r
α
σ
ν
= − ∆ + − + ÷
−
∫
Using this in the previous expression and evaluating σθθ, we get
2
2
12 2 2
1
(1 ) 1
r
a
CE E T a
Trdr C
r r r
θθ
α α
σ
ν ν
∆
= − ∆ − + + − ÷
− −
∫
CE 527
Advanced Mechanics of Materials
10. Namas Chandra
Advanced Mechanics of Materials Chapter 11-10
EGM 5653
Closed End Cylinders
Stress Components at sections far from the ends contd.
The effects of temperature are self- equilibrating. The expression for εzz
at section far away from the closed ends of the cylinder can be written
in the form
( )
2 2
1 2closed end 2 2 2 2 2 2
1 2 2
( )
( ) ( ) ( )
b
zz
a
P
p a p b Trdr
E b a b a E b a
ν α
ε
π
−
= − + + ∆
− − − ∫
( )
2 2
1 2
closed end 2 2 2 2 2 2
2
( ) 1 (1 )( )
b
zz
a
p a p b P E T E
Trdr
b a b a b a
α α
σ
π ν ν
− ∆
= + − + ∆
− − − − − ∫
The expression for σzz at section far away from the ends of the cylinder can
be written in the form
CE 527
Advanced Mechanics of Materials
11. Namas Chandra
Advanced Mechanics of Materials Chapter 11-11
EGM 5653
Open Cylinder
No axial loads applied on its ends.
The equilibrium equation of an axial portion of the
cylinder is:
2 0
b
zz
a
r dzπ σ =∫
2 2
2 1
(open end) 2 2 2 2
2 ( ) 2
( ) ( )
b
zz
a
p b p a
Trdr
b a E b a
ν α
ε
−
= + ∆
− − ∫
The expression for εzz and σzz may be written
in the form
CE 527
Advanced Mechanics of Materials
12. Namas Chandra
Advanced Mechanics of Materials Chapter 11-12
EGM 5653
Stress Components and Radial Displacement
for Constant Temperature
.
For a closed cylinder (with end caps) in the absence of temperature
change ΔT = 0 the stress components are obtained as
2 2 2 2
1 2
1 22 2 2 2 2
( )
( )
rr
p a p b a b
p p
b a r b a
σ
−
= − −
− −
2 2 2 2
1 2
1 22 2 2 2 2
( )
( )
p a p b a b
p p
b a r b a
θθσ
−
= + −
− −
2 2
1 2
2 2 2 2
constant
( )
zz
p a p b P
b a b a
σ
π
−
= + =
− −
CE 527
Advanced Mechanics of Materials
13. Namas Chandra
Advanced Mechanics of Materials Chapter 11-13
EGM 5653
Radial Displacement for an Closed Cylinder
The radial displacement u for a point in a thick wall closed cylinder may
be written as
2 2
2 2
(closed end) 1 2 1 22 2 2
(1 )
(1 2 )( ) ( )
( )
r a b P
u p a p b p p
E b a r
ν
ν ν
π
+
= − − + − −
−
Radial Displacement for an Open Cylinder
2 2
2 2
(open end) 1 2 1 22 2 2
(1 )
(1 )( ) ( )
( )
r a b
u p a p b p p
E b a r
ν
ν
+
= − − + −
−
CE 527
Advanced Mechanics of Materials
14. Namas Chandra
Advanced Mechanics of Materials Chapter 11-14
EGM 5653
Example 1
Stresses and Deformations in Hollow cylinder
A thick walled closed-end cylinder is made of an aluminum alloy,
E = 72 GPa, ν = 0.33,Inner Dia. = 200mm, Outer Dia. = 800 mm,
Internal Pressure = 150 MPa.
Determine the Principal stresses, Maximum shear stress at the inner
radius (r= a = 100 mm), and the increase in the inside diameter caused
by the internal pressure
Solution:
2p 0and r a= =
2 2
1 12 2
150rr
a b
p p MPa
b a
σ
−
= = − = −
−
2 2 2 2
1 2 2 2 2
100 400
150 170
400 100
a b
p MPa
b a
θθσ
+ +
= = =
− −
2 2
1 2 2 2 2
100
150 10
400 100
zz
a
p MPa
b a
σ = = =
− −
The Principal stresses for the conditions that
CE 527
Advanced Mechanics of Materials
15. Namas Chandra
Advanced Mechanics of Materials Chapter 11-15
EGM 5653
Example 1
Stresses and Deformations in Hollow cylinder
contd.
max min
max
170 ( 150)
160
2 2
MPa
σ σ
τ
− − −
= = =
2 0and r ap P= = =
The maximum shear stress is given by the equation
The increase in the inner diameter caused by the internal pressure
is equal to twice the radial displacement for the conditions
( )
2 21
( ) 2 2
2 2
2 2
(1 2 ) (1 )
( )
150(100)
1 0.66 100 (1 0.33)400
72,000(400 100 )
0.3003
r a
p a
u a b
E b a
mm
ν ν=
= − + + −
= − + + −
=
The increase in the internal pressure caused by the internal pressure
is 0.6006 mm
CE 527
Advanced Mechanics of Materials
17. Namas Chandra
Advanced Mechanics of Materials Chapter 11-17
EGM 5653
Advanced Mechanics of Materials
CE 527
Thank you for listeningThank you for listening
Editor's Notes
The practical application of mathematics and science to create, design, test, improve, and develop knowledge, research, money, business, economics, and technology.
This is why engineering is such a challenging and demanding field of study: It involves areas of expertise that continue to evolve independently yet are required to perform together as part of the engineering process. Thus, an engineer must be expert in many areas, must know how to communicate knowledge between those areas, and must apply that knowledge to create, design, study, research, and invent all kinds of things. It is not uncommon for engineers to begin their careers as mathematicians, applied scientists, or even economists
The practical application of mathematics and science to create, design, test, improve, and develop knowledge, research, money, business, economics, and technology.
This is why engineering is such a challenging and demanding field of study: It involves areas of expertise that continue to evolve independently yet are required to perform together as part of the engineering process. Thus, an engineer must be expert in many areas, must know how to communicate knowledge between those areas, and must apply that knowledge to create, design, study, research, and invent all kinds of things. It is not uncommon for engineers to begin their careers as mathematicians, applied scientists, or even economists
The practical application of mathematics and science to create, design, test, improve, and develop knowledge, research, money, business, economics, and technology.
This is why engineering is such a challenging and demanding field of study: It involves areas of expertise that continue to evolve independently yet are required to perform together as part of the engineering process. Thus, an engineer must be expert in many areas, must know how to communicate knowledge between those areas, and must apply that knowledge to create, design, study, research, and invent all kinds of things. It is not uncommon for engineers to begin their careers as mathematicians, applied scientists, or even economists
The practical application of mathematics and science to create, design, test, improve, and develop knowledge, research, money, business, economics, and technology.
This is why engineering is such a challenging and demanding field of study: It involves areas of expertise that continue to evolve independently yet are required to perform together as part of the engineering process. Thus, an engineer must be expert in many areas, must know how to communicate knowledge between those areas, and must apply that knowledge to create, design, study, research, and invent all kinds of things. It is not uncommon for engineers to begin their careers as mathematicians, applied scientists, or even economists
The practical application of mathematics and science to create, design, test, improve, and develop knowledge, research, money, business, economics, and technology.
This is why engineering is such a challenging and demanding field of study: It involves areas of expertise that continue to evolve independently yet are required to perform together as part of the engineering process. Thus, an engineer must be expert in many areas, must know how to communicate knowledge between those areas, and must apply that knowledge to create, design, study, research, and invent all kinds of things. It is not uncommon for engineers to begin their careers as mathematicians, applied scientists, or even economists