Lecture

Mod-2 Lec-4 Truss Analysis Part-2

This module introduces the concept of friction and its applications in engineering mechanics. Students will explore:

  • Coulomb dry friction laws and their implications in contact problems.
  • Friction angles and the various types of friction problems, including wedges.
  • The mechanics of disk friction in thrust bearings and belt friction in flat and V configurations.
  • Analysis of square-threaded screws, including self-locking mechanisms and the operation of screw jacks.

Through practical examples, students will understand how friction influences mechanical systems and engineering design.


Course Lectures
  • Mod-1 Lec-1 Fundamentals Of Engineering Mechanics
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on the fundamental principles of engineering mechanics that form the basis for understanding statics. Key topics include:

    • Vector algebra and Newton’s laws of motion.
    • Gravitation and the distinction between external and internal forces.
    • The concept of couples and moments, including their calculations about points and axes.
    • Varignon’s theorem and the resultant of concurrent and non-concurrent coplanar forces.
    • Understanding static equilibrium and the use of free body diagrams.
    • Reactions and constraints in static systems.

    Students will learn problem formulation concepts and delve into 2-D and 3-D statics, gaining insight into members under two and three forces, stability, and constraints.

  • Mod-1 Lec-2 Equations of Equilibrium
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module delves into the analysis of structures, emphasizing trusses, frames, and machines. It covers:

    • Assumptions in truss analysis, differentiating between rigid and non-rigid trusses.
    • Techniques for analyzing simple trusses using the method of joints and method of sections.
    • Compound trusses, ensuring students understand statically determinate conditions and rigidity.
    • Analysis techniques for frames and machines, bringing practical applications to theoretical concepts.

    Through various examples and problem-solving exercises, students will gain a solid foundation in structural analysis principles.

  • Mod-2 Lec-3 Truss Analysis Part-I
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on the analysis of internal forces in beams and cables. Key topics include:

    • The different types of loading and support configurations for beams.
    • How to construct shear force, bending moment, and axial force diagrams.
    • Interrelations between external loads and internal forces using equations.
    • Analysis of coplanar cables, emphasizing assumptions and the behavior of parabolic and catenary cables.

    Students will engage with various examples to strengthen their understanding of shear and moment diagrams in real-world structures.

  • Mod-2 Lec-4 Truss Analysis Part-2
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module introduces the concept of friction and its applications in engineering mechanics. Students will explore:

    • Coulomb dry friction laws and their implications in contact problems.
    • Friction angles and the various types of friction problems, including wedges.
    • The mechanics of disk friction in thrust bearings and belt friction in flat and V configurations.
    • Analysis of square-threaded screws, including self-locking mechanisms and the operation of screw jacks.

    Through practical examples, students will understand how friction influences mechanical systems and engineering design.

  • Mod-2 Lec-5 Analysis of Frames&Machines
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module expands on the principles of friction, focusing on specific applications in engineering contexts. Topics include:

    • Analysis of journal bearings and their implications for axle friction.
    • Understanding wheel friction and rolling resistance in mechanical systems.

    Students will engage in real-world problem-solving to apply the principles of friction to various mechanical designs, enhancing their engineering skills.

  • Mod-3 Lec-6 Internal Forces
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module covers the concepts of center of mass and area moments of inertia, fundamental for understanding body mechanics. It includes:

    • Definition and calculation of the center of mass for various bodies.
    • Understanding centroids of lines, areas, volumes, and composite shapes.
    • Calculation of area moments and products of inertia, including the radius of gyration.
    • Techniques for the transfer of axes and the application of Mohr’s circle for principal area moments of inertia.

    Students will apply these concepts in practical scenarios to enhance their understanding of mechanical behavior.

  • Mod-3 Lec-7 Internal Forces in Beams
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module delves into the internal forces experienced by beams under various loading conditions. Students will learn to analyze shear forces and bending moments, which are crucial in determining the structural integrity of beams. Through a series of practical examples, the course covers:

    • Types of supports and loading on beams.
    • Shear force diagrams and bending moment diagrams.
    • Equations that relate shear forces and bending moments to external loads.
    • Applications in real-world engineering scenarios.

    Understanding these concepts is vital for engineers who design structures capable of withstanding various forces.

  • Mod-3 Lec-8 Cables
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on the analysis of cables, particularly in coplanar systems. Students will explore fundamental assumptions and characteristics of cable systems, including:

    • Understanding the parabolic and catenary shapes of cables under load.
    • Applications in real-world structures such as bridges and suspension systems.
    • Methods to calculate tensions and reactions in cables.

    By the end of this module, students will grasp the essential principles governing cable mechanics, enabling them to apply this knowledge in engineering designs.

  • Mod-4 Lec-9 Friction
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    In this module, students will explore the principles of friction and its application in various mechanical contexts. The content includes:

    • The laws of Coulomb dry friction and their implications.
    • Analysis of surface contact problems and friction angles.
    • Practical examples of wedge problems and the behavior of disks and belts under friction.
    • Applications in real-world engineering challenges, including machinery design.

    Through hands-on examples and theoretical discussions, students will develop a strong understanding of how friction affects mechanical systems.

  • Mod-4 Lec-10 Application of Friction Part-1
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module covers advanced applications of friction in various mechanical systems. Focus areas include:

    • Analysis of journal bearings and axle friction.
    • Understanding wheel friction and rolling resistance.
    • Practical scenarios where these principles apply, enhancing machinery performance.

    Students will learn through examples and case studies how friction plays a critical role in the design and operation of mechanical systems.

  • Mod-4 Lec-11 Application of Friction Part-2
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module introduces students to the concepts of center of mass and area moments of inertia, which are fundamental in mechanical engineering. Key topics include:

    • Calculating the first moment of mass and determining the center of mass for various shapes.
    • Understanding the concepts of centroids for lines, areas, and volumes.
    • Exploring moments and products of inertia and their significance in structural analysis.
    • Application of Mohr’s circle in determining principal area moments of inertia.

    This foundational knowledge is crucial for analyzing the stability and performance of structural components.

  • Mod-5 Lec-12 Application of Friction Part-3
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    In this module, students will learn about mass moment of inertia, a critical concept in understanding the dynamics of rigid bodies. The topics covered include:

    • Calculating the second moment of mass for various shapes and composite bodies.
    • Understanding the transfer of axes and its applications in dynamics.
    • Exploring the relationship between area moments and mass moments of inertia.
    • Application of principal mass moments of inertia in dynamic analysis.

    This module equips students with the knowledge necessary for analyzing the behavior of rigid bodies under various loading conditions.

  • Mod-6 Lec-13 Centroids&Center of Mass
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module delves into the concepts of centroids and centers of mass, essential for understanding the distribution of mass in various shapes. Key topics include:

    • Definition and significance of centroids and center of mass
    • Methods to calculate centroids for various geometric shapes
    • Applications in engineering and physics
    • Examples demonstrating practical calculations in different scenarios

    Understanding these concepts is crucial for further analysis in mechanics, especially when dealing with systems of particles and rigid bodies.

  • Mod-6 Lec-14 Centroids&Area of Moments
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on the area moments of inertia, crucial for studying the resistance of an object to bending and rotation. Key topics include:

    • Definition of moments of inertia and their significance
    • Calculation methods for area moments and products of inertia
    • Applications in structural engineering and material science
    • Composite bodies and their moments of inertia calculations

    Through practical examples and exercises, students will gain a comprehensive understanding of how these principles apply to real-world engineering problems.

  • This module covers the product of inertia, rotation of axes, and principal moments of inertia, fundamental concepts in dynamics and structural analysis. Topics include:

    • Understanding product of inertia and its calculation
    • Rotation of axes and its effects on moment of inertia
    • Principal moments of inertia and their determination
    • Applications in mechanical design and analysis

    Students will explore the implications of these principles in various engineering applications, particularly in analyzing the stability of structures.

  • Mod-7 Lec-16 Second Moment of Mass
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module introduces the second moment of mass, building on previous concepts related to mass distribution in bodies. Key aspects include:

    • Definition and significance of the second moment of mass
    • Calculating the second moment for various shapes
    • Applications in determining resistance to bending and torsion
    • Illustrative examples and practical applications in engineering

    Mastering these principles is essential for engineers who need to analyze the behavior of materials and structures under various loading conditions.

  • Mod-7 Lec-17 Principle Mass Moments of Inertia
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module addresses the principal mass moments of inertia, which are vital for assessing the rotational characteristics of rigid bodies. It encompasses:

    • Concepts of mass moments of inertia and their importance in dynamics
    • Methods for calculating principal mass moments
    • Applications in analyzing stability and motion of structures
    • Real-world examples illustrating the principles in action

    Understanding these concepts equips students with the skills necessary to design and analyze systems that involve rotational motions.

  • Mod-8 Lec-18 Virtual Work of Ideal System
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module examines the virtual work principle as applied to ideal systems, a critical concept in mechanics for analyzing systems in equilibrium. Topics include:

    • Understanding virtual displacements and their implications
    • Application of virtual work principles to rigid body systems
    • Degrees of freedom and their significance in system analysis
    • Examples illustrating concepts through problem-solving

    By the end of this module, students will be able to apply the principles of virtual work to various mechanical systems, enhancing their analytical skills.

  • Mod-8 Lec-19 Principle of Virtual Work
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module covers the fundamentals of statics, introducing essential concepts such as:

    • Vector algebra and Newton’s laws
    • Gravitation and forces, including external and internal forces
    • The concepts of couples, moments, and Varignon’s theorem
    • Resultants of concurrent and non-concurrent coplanar forces
    • Static equilibrium and the free body diagram
    • Reactions and problem formulation in 2-D and 3-D statics

    Students will understand the principles behind static determinacy and constraints, equipping them to analyze static systems effectively.

  • Mod-8 Lec-20 Systems with Friction
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on the analysis of structures, specifically trusses, frames, and machines. Key topics include:

    • Understanding assumptions related to rigid and non-rigid trusses
    • Analysis techniques such as the method of joints and sections
    • Exploration of simple and compound trusses
    • Introduction to the analysis of frames and machines

    Students will gain the skills necessary to analyze and design robust structural systems using these foundational concepts.

  • Mod-9 Lec-21 Potential Energy
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module provides in-depth knowledge about beams, cables, and internal forces. The key areas of study include:

    • Types of loading and supports for beams
    • Shear force, bending moment, and axial force diagrams
    • Shear force and bending moment equations connected to external loads
    • Analysis of cables, focusing on parabolic and catenary cables

    Through this module, students will learn to visualize and calculate internal forces within static structures effectively.

  • Mod- 9 Lec-22 Stability of Equilibrium
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module delves into the principles of friction. Key topics include:

    • Coulomb’s dry friction laws and surface contact problems
    • The concept of friction angles and types of problems
    • Wedge friction and applications in various engineering scenarios
    • Disk friction (thrust bearings) and belt friction (flat, V)
    • Insights into square-threaded screws and self-locking mechanisms

    Students will explore practical applications of friction and develop solutions to complex engineering problems involving friction.

  • Mod-10 Lec-23 Kinematics of a Particles
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module continues the exploration of friction, focusing on:

    • Journal bearings and axle friction
    • Wheel friction and rolling resistance
    • Applications of these concepts in mechanical systems

    Students will understand the behavior of different frictional systems and how they affect the performance of machines and structures.

  • Mod-10 Lec-24 Kinematics of a Particle Moving on a Curve
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on the concepts of center of mass and area moments of inertia. Key topics include:

    • First moment of mass and centroids of lines, areas, and volumes
    • Area moments and products of inertia, radius of gyration, and transfer of axes
    • Composite areas and rotation of axes
    • Principal area moments of inertia using Mohr's circle

    Through this module, students will gain essential skills for analyzing and designing structures regarding mass distribution and stability.

  • Mod-10 Lec-25 Relative Motion
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on the fundamentals of relative motion, detailing essential concepts that govern the movement of particles and rigid bodies.

    Key topics include:

    • Understanding reference frames and their impact on motion analysis.
    • Relative velocity concepts and their applications in various mechanical systems.
    • Integration of kinematic equations to analyze complex motion scenarios.

    By the end of this module, students will be equipped with the tools to effectively analyze motion in different frames of reference.

  • Mod-10 Lec-26 Plane Kinematics of Rigid Bodies
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module delves into the plane kinematics of rigid bodies, focusing on the motion of objects constrained to move in a two-dimensional plane.

    Key areas covered include:

    • Understanding rotation and how it affects rigid body motion.
    • Parametric motion and its applications in real-world scenarios.
    • Analyzing relative velocity and acceleration in rotating reference frames.

    Students will engage in problem-solving activities to reinforce their understanding of these essential kinematic principles.

  • Mod-11 Lec-27 Kinematics of a Particle
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module covers the kinematics of a particle, emphasizing the principles that govern particle motion in various coordinate systems.

    Topics explored include:

    • Rectilinear and curvilinear motion and their mathematical representations.
    • Velocity and acceleration analysis in different coordinate systems.
    • Application of Newton's laws to solve particle motion problems.

    Through practical examples, students will learn how to apply these principles to real-world engineering problems.

  • Mod-11 Lec-28 Work and Enjoy
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module engages students in the concept of work and energy within the context of mechanical systems.

    Topics include:

    • The relationship between work and kinetic energy and how they influence motion.
    • Understanding potential energy and its role in mechanical systems.
    • Applications of work-energy principles to solve practical problems.

    Students will also explore the concept of mechanical efficiency in energy systems and how to optimize work output.

  • Mod-11 Lec-29 Impulse and Momentum
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module investigates impulse and momentum, integral concepts in the dynamics of particles and rigid bodies.

    Key topics include:

    • Understanding the impulse-momentum theorem and its applications in solving problems.
    • Analysis of collisions, including direct and oblique impacts.
    • Real-world applications to illustrate the principles of impulse and momentum in engineering contexts.

    Students will gain hands-on experience in applying these concepts to various dynamic scenarios.

  • Mod-11 Lec-30 Direct and Oblique Impulse
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This final module introduces the fundamentals of vibrations in mechanical systems, focusing on both free and forced vibrations.

    Topics covered include:

    • Characteristics of damped and undamped vibrations.
    • Analysis of mechanical displacement meters and accelerometers.
    • Energy methods for solving undamped vibration problems.

    Students will learn how to model and analyze vibration in rigid bodies, preparing them for more complex vibration analysis in engineering applications.

  • Mod-11 Lec-31 Plane Kinetics of Rigid Bodies
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on the fundamentals of plane kinetics of rigid bodies. You will explore the principles governing the motion of rigid bodies subjected to various forces.

    Key topics include:

    • Kinetics of systems of particles
    • Derivation of moment equations
    • Analysis of translation and fixed axis rotation
    • General planar motion and its applications

    Students will gain insights into the underlying physics and methods for analyzing the motion of rigid bodies, crucial for engineering applications.

  • Mod-12 Lec-32 Kinetics of a Body
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module delves into the kinetics of a body, detailing the forces acting upon it and how they influence motion. Students will learn to apply Newton's laws of motion to various scenarios.

    Topics include:

    • Understanding force systems
    • Applications of kinetic principles in real-world problems
    • Problem-solving strategies in kinetics

    By the end of this module, learners will be equipped to analyze the motion of bodies under the influence of forces, fundamental for mechanics and engineering.

  • This module introduces the method of momentum, a critical concept in dynamics. It emphasizes the analysis of robot manipulators, providing insight into the kinetic analysis of robotic systems.

    Core aspects include:

    • Momentum conservation principles
    • Applications to robotic systems
    • Analytical techniques for dynamics

    Students will learn to analyze and compute the dynamics of robotic manipulators, which is essential for the design and control of modern robotics.

  • Mod-13 Lec-34 Kinematics in 3D
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module focuses on kinematics in three dimensions, enhancing understanding of motion in 3D space. It covers the essential principles that govern the movement of objects.

    Key learning points include:

    • 3D motion representation
    • Coordinate systems for spatial analysis
    • Applications within engineering and physics

    Students will develop skills in interpreting and analyzing 3D motion, crucial for various engineering disciplines, particularly in mechanics and robotics.

  • Mod-14 Lec-35 Kinetics in 3D
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module covers the kinetics in three dimensions, focusing on the forces and motions that affect objects in 3D space. It provides a comprehensive approach to understanding how these dynamics work in real-world applications.

    Key topics include:

    • Force analysis in 3D environments
    • Equations of motion for rigid bodies
    • Applications in engineering fields

    Students will acquire the ability to analyze and solve problems related to 3D kinetics, essential for mechanical design and analysis.

  • Mod-15 Lec-36 Free Vibration
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module introduces free vibration, emphasizing the analysis of oscillatory motions in systems. It covers both damped and undamped vibrations, providing foundational knowledge for understanding dynamics.

    Topics include:

    • Fundamentals of vibration theory
    • Free vs. forced vibrations
    • Measurement techniques like accelerometers

    Students will learn to analyze vibrational systems, which is crucial for applications in mechanical engineering and structural analysis.

  • Mod-15 Lec-37 Forced Vibration(Damped Undamped)
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module covers forced vibration in systems, including both damped and undamped scenarios. Understanding the differences between these types of vibrations is crucial for engineers dealing with mechanical systems. Key topics include:

    • Definition and characteristics of forced vibrations.
    • Analysis of damped vs. undamped vibrations.
    • Real-world applications and implications of both types of vibrations in engineering.
    • Methods for measuring and mitigating vibrations in mechanical systems.

    Students will engage with practical examples, enhancing their comprehension of how vibrations affect system performance and stability.

  • Mod-15 Lec-38 Vibration of Rigid Bodies Part-1
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module delves into the vibration of rigid bodies, providing students with a foundational understanding of how rigid bodies respond to vibrational forces. Key aspects covered include:

    • Basic principles of vibration in rigid bodies.
    • Factors affecting vibration, such as mass distribution and external forces.
    • Real-life applications of rigid body vibration in mechanical systems.
    • Techniques for analysis and problem-solving related to vibrations.

    Through theoretical and practical exercises, students will develop skills essential for addressing vibration issues in engineering contexts.

  • Mod-15 Lec-39 Vibration of Rigid Bodies Part-2
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module continues the exploration of rigid body vibrations, focusing on advanced concepts and problem-solving techniques. It includes:

    • In-depth analysis of vibrational responses under various forces.
    • Exploration of energy methods for undamped vibration problems.
    • Case studies demonstrating vibration issues and solutions for rigid bodies.
    • Exercises aimed at reinforcing theoretical understanding through practical application.

    Students will engage in hands-on learning, enhancing their ability to predict and control vibrations in engineering applications.

  • Mod-15 Lec-40 Some Problems of Vibration
    Prof. U.S. Dixit, Dr. G. Saravana Kumar

    This module addresses various problems related to vibration, providing students with the tools to analyze and solve vibrational issues in mechanical systems. Topics include:

    • Common problems encountered in vibration analysis.
    • Methodologies for approaching and solving these problems.
    • Real-world scenarios and case studies to illustrate problem-solving techniques.
    • Interactive exercises that reinforce learned concepts and skills.

    Through collaborative learning and practical application, students will enhance their ability to effectively tackle vibration-related challenges.