De Alembert’s Principle and Generalized Force, a technical discourse on Class...Manmohan Dash
A technical discourse on formal classical mechanics. This is a 12 slide introduction to the basics of how Newton's Laws are generalized into a Lagrangian Dynamics apt at the level of an advance student of Physics.
De Alembert’s Principle and Generalized Force, a technical discourse on Class...Manmohan Dash
A technical discourse on formal classical mechanics. This is a 12 slide introduction to the basics of how Newton's Laws are generalized into a Lagrangian Dynamics apt at the level of an advance student of Physics.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Dimensional analysis is one of the important topic of the fluid mechanics. It is useful for transferring data from one system to other system and also useful in reducing complexity of the equation.
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
MAHARASHTRA STATE BOARD
CLASS XI AND XII
CHAPTER 4
THERMODYNAMICS
CONTENT
Introduction
Thermal equilibrium
Zeroth law of
Thermodynamics
Heat, internal energy and
work
First law of
thermodynamics
Specific heat capacity
Thermodynamic state
variables and equation of
state
Thermodynamic processes
Heat engines
Refrigerators and heat
pumps
Second law of
thermodynamics
Reversible and irreversible
processes
Carnot engine
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Dimensional analysis is one of the important topic of the fluid mechanics. It is useful for transferring data from one system to other system and also useful in reducing complexity of the equation.
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
MAHARASHTRA STATE BOARD
CLASS XI AND XII
CHAPTER 4
THERMODYNAMICS
CONTENT
Introduction
Thermal equilibrium
Zeroth law of
Thermodynamics
Heat, internal energy and
work
First law of
thermodynamics
Specific heat capacity
Thermodynamic state
variables and equation of
state
Thermodynamic processes
Heat engines
Refrigerators and heat
pumps
Second law of
thermodynamics
Reversible and irreversible
processes
Carnot engine
This session covers the basics that are required to analyse indeterminate trusses to maximum of two degree indeterminacy which includes,
strain energy stored due to axial loads and bending stresses,
maxwell's reciprocal deflection theorem,
Betti's law,
castigliano's theorems,
problems based on castigliano's theorems on beams and frames,
unit load method,
problems on trusses with unit load method,
lack of fit in trusses,
temperature effect on truss members.
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visit us: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
coplanar forces res comp of forces - for mergeEkeeda
Learn Online Courses of Subject Engineering Mechanics of First Year Engineering. Clear the Concepts of Engineering Mechanics Through Video Lectures and PDF Notes. Visi tus: https://ekeeda.com/streamdetails/subject/Engineering-Mechanics
Coplanar forces res & comp of forces - for mergeEkeeda
Ekeeda Provides Online Video Lectures for Civil Engineering Degree Subject Courses for All Engineering Universities. Visit us: https://ekeeda.com/streamdetails/stream/civil-engineering
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
The basis for kinetics is Newton's second law, which states that when an unbalanced force acts on a particle, the particle will accelerate in the direction of the force with a magnitude that is proportional to the force.
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.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
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.
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.
1. PURBANCHAL UNIVERSITY
KHWOPA ENGINEERING COLLEGE
SOLID MECHANICS
PRINCIPLE OF VIRTUAL WORK
REENA SUWAL (ME07814)
SACHIN POKHAREL (ME07815)
SAMI DANGOL (ME07816)
SUNDAR BARTAULA (ME07817)
Assoc. Prof. Dr. Manjip Shakya
Department of Earthquake Engineering
8th March 2023
2. Introduction
Virtual displacement and virtual Work
• Virtual work is the work done by a real force acting through a virtual displacement or a
virtual force acting through a real displacement.
• A virtual displacement is any displacement consistent with the constraints of the
structure, i.e., that satisfy the boundary conditions at the supports.
• A virtual force is any system of forces in equilibrium.
Principle of virtual Work
The principle of virtual work states that in equilibrium the virtual work of the forces
applied to a system is zero. Newton's laws state that at equilibrium the applied forces are
equal and opposite to the reaction, or constraint forces. This means the virtual work of the
constraint forces must be zero as well.
3. F1 = 1
F1
F3
F2 M1
M2
M3
F2 = 2
F3 = 3
Virtual linear displacement
Virtual Work
8. Mathematical expression
• Consider an elastic system subjected to a number of forces (including
moments) F1, F2, . . . , etc. Let 𝛿1, 𝛿2, . . ., etc. be the corresponding
displacements.
• These are the work absorbing components (linear and angular
displacements) in the corresponding directions of the force as shown
in figure.
9. • Let one of the displacements 𝛿1 be increased by a small quantity
∆𝛿1. During this additional displacement, all other displacements
where forces are acting are held fixed, which means that additional
forces may be necessary to maintain such a condition.
• Further, the small displacement ∆𝛿 1 that is imposed must be
consistent with the constraints acting. For example, if point ‘I’is
constrained in such a manner that it can move only in a particular
direction, then ∆𝛿1 must be consistent with such a constraint.
• A hypothetical displacement of such a kind is called a virtual
displacement. In applying this virtual displacement, the forces F1, F2,
. . ., etc. (except F1) do no work at all because their points of
application do not move (at least in the work-absorbing direction).
• The only force doing work is F1 by an amount F1 ∆𝛿1. plus a fraction
of∆F1 ∆𝛿1. , caused by the change in F1. This additional work is
stored in strain energy ∆𝑈.
11. The work done by the forces must be equal to the strain energy
which is stored up in the system. This fact can be expressed in
another form known as the principle of virtual work, i.e.
12. • In the equations above,
V denotes the material domain,
S the surface completely enclosing V,
and the variational symbol signifies a virtual quantity
upon applying the divergence theorem
13. We know, WE = WI
Substituting the value of WE and WI
………(i)
………(ii) a
………(ii) b
Eqn (i) is a field eqn
Eqn (ii) specify boundary conditions.
14. Conclusion
This principle is applicable to any elastic body
• linear elastic materials
• Non-linear elastic materials