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This document discusses the topic of equilibrium of rigid bodies. It covers: - Analytical and graphical conditions for equilibrium of co-planar forces. - Different types of beam supports like simple, pinned, roller, and fixed supports. - Free body diagrams and their application in analyzing equilibrium and determining reactions. - Lami's theorem which states that for three forces in equilibrium, each force is proportional to the sine of the angle between the other two forces. - Examples of problems involving cylinders, pulleys, beams, and friction on inclined planes.

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Engineering Mechanics Pdf

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

Assignment no.2

This document contains 18 problems related to the equilibrium of rigid bodies and friction. It begins with definitions of key terms like equilibrium and equilibrant. It then discusses principles of equilibrium like Lami's theorem. The remaining problems involve calculating reactions and forces in systems with objects resting on surfaces or supported by other objects. They include spheres, cylinders, rollers and blocks on inclined planes and interacting with forces of friction. The document covers assessing and establishing equilibrium as well as determining coefficients of friction.

Coplanar Non-concurrent Forces

The document discusses coplanar non-concurrent force systems where multiple forces act in the same plane but at different points. It defines moment as the product of a force and its perpendicular distance from the point of interest. A couple is formed by two equal and opposite forces that rotate a body without translating it. Varignon's principle states that the sum of the moments of individual forces equals the moment of the resultant force about any point. Conditions for equilibrium of coplanar non-concurrent forces on a body are also presented. An example problem finds the resultant and location of a non-concurrent force system.

Chapter 8 principle of virtual work

The document introduces the principle of virtual work which states that for a system of bodies in equilibrium, the net work done by external forces during an arbitrary virtual displacement is zero. It describes how the principle can be used to solve problems involving the equilibrium of machines. It also discusses potential energy and how the stability of equilibrium positions can be determined from the second derivative of potential energy with respect to position. Several sample problems demonstrate applying these concepts to determine forces, positions of equilibrium, and stability.

Strength of materials_by_r_s_khurmi-601-700

1. The document presents an example problem of calculating the moments and reactions for a continuous beam ABC that has span AB of 8m and span BC of 6m, with the beam fixed at A and simply supported at B and C.
2. The beam carries a uniformly distributed load of 1 kN/m along its entire length. Using Clapeyron's theorem of three moments, the fixing moments MA, MB, and MC are calculated.
3. The bending moment and shear force diagrams are drawn, showing the moments and reactions calculated at each support.

engineering statics :equilibrium

This document provides an introduction to the concept of equilibrium in statics. It discusses how to isolate a mechanical system and draw a free body diagram showing all external forces acting on it. For equilibrium in two dimensions, the forces must sum to zero in both the x and y directions. In three dimensions, six equations are required - the forces and moments must sum to zero in the x, y, and z directions as well as around each axis. Examples are given of two-force and three-force members in equilibrium. The document also defines statically determinate and indeterminate bodies.

Engineering Mechanice Lecture 04

1) The document discusses force-couple systems and how a single force can be replaced by an equivalent force-couple system. It explains that a force produces both translational and rotational effects, while a couple only produces rotational effects.
2) It provides an example of replacing a force F acting at point A with two equal and opposite forces F and -F acting along parallel lines at point B, which form a couple with moment Fd. This force-couple system is equivalent to the original single force.
3) The concept of a force-couple equivalent enables the transfer of a force to another location outside its line of action, which has many applications in mechanics.

Moh'r circle2

1) The document discusses Mohr's circle for analyzing stresses in plane stress, including how to construct Mohr's circle, determine principal stresses and maximum shear stresses, and stresses on inclined planes.
2) It provides the equations for transforming stresses between reference frames and deriving Mohr's circle.
3) An example is worked through applying Mohr's circle to determine stresses for a given stress element.

Engineering Mechanics Pdf

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

Assignment no.2

This document contains 18 problems related to the equilibrium of rigid bodies and friction. It begins with definitions of key terms like equilibrium and equilibrant. It then discusses principles of equilibrium like Lami's theorem. The remaining problems involve calculating reactions and forces in systems with objects resting on surfaces or supported by other objects. They include spheres, cylinders, rollers and blocks on inclined planes and interacting with forces of friction. The document covers assessing and establishing equilibrium as well as determining coefficients of friction.

Coplanar Non-concurrent Forces

The document discusses coplanar non-concurrent force systems where multiple forces act in the same plane but at different points. It defines moment as the product of a force and its perpendicular distance from the point of interest. A couple is formed by two equal and opposite forces that rotate a body without translating it. Varignon's principle states that the sum of the moments of individual forces equals the moment of the resultant force about any point. Conditions for equilibrium of coplanar non-concurrent forces on a body are also presented. An example problem finds the resultant and location of a non-concurrent force system.

Chapter 8 principle of virtual work

The document introduces the principle of virtual work which states that for a system of bodies in equilibrium, the net work done by external forces during an arbitrary virtual displacement is zero. It describes how the principle can be used to solve problems involving the equilibrium of machines. It also discusses potential energy and how the stability of equilibrium positions can be determined from the second derivative of potential energy with respect to position. Several sample problems demonstrate applying these concepts to determine forces, positions of equilibrium, and stability.

Strength of materials_by_r_s_khurmi-601-700

1. The document presents an example problem of calculating the moments and reactions for a continuous beam ABC that has span AB of 8m and span BC of 6m, with the beam fixed at A and simply supported at B and C.
2. The beam carries a uniformly distributed load of 1 kN/m along its entire length. Using Clapeyron's theorem of three moments, the fixing moments MA, MB, and MC are calculated.
3. The bending moment and shear force diagrams are drawn, showing the moments and reactions calculated at each support.

engineering statics :equilibrium

This document provides an introduction to the concept of equilibrium in statics. It discusses how to isolate a mechanical system and draw a free body diagram showing all external forces acting on it. For equilibrium in two dimensions, the forces must sum to zero in both the x and y directions. In three dimensions, six equations are required - the forces and moments must sum to zero in the x, y, and z directions as well as around each axis. Examples are given of two-force and three-force members in equilibrium. The document also defines statically determinate and indeterminate bodies.

Engineering Mechanice Lecture 04

1) The document discusses force-couple systems and how a single force can be replaced by an equivalent force-couple system. It explains that a force produces both translational and rotational effects, while a couple only produces rotational effects.
2) It provides an example of replacing a force F acting at point A with two equal and opposite forces F and -F acting along parallel lines at point B, which form a couple with moment Fd. This force-couple system is equivalent to the original single force.
3) The concept of a force-couple equivalent enables the transfer of a force to another location outside its line of action, which has many applications in mechanics.

Moh'r circle2

1) The document discusses Mohr's circle for analyzing stresses in plane stress, including how to construct Mohr's circle, determine principal stresses and maximum shear stresses, and stresses on inclined planes.
2) It provides the equations for transforming stresses between reference frames and deriving Mohr's circle.
3) An example is worked through applying Mohr's circle to determine stresses for a given stress element.

Lecture Notes on Engineering Statics.

This document provides an overview of engineering mechanics statics. It covers topics including:
- Defining mechanics as the science dealing with bodies at rest or in motion under forces.
- Dividing mechanics into statics, dynamics, and other subfields. Statics deals with bodies at rest.
- Introducing fundamental concepts of forces, units of measurement, and representing forces as vectors that add according to the parallelogram law.
- Providing examples of adding forces graphically using the parallelogram law and triangle rule to determine the resultant force.
- Discussing problems involving determining the magnitude and direction of resultant forces from multiple forces acting on structures, stakes, and brackets

Trusses, frames & machines

The document discusses various structural analysis concepts including trusses, frames, and machines. It defines trusses as structures composed of slender members joined at their endpoints that lie in a single plane. Two common methods for analyzing trusses are presented: (1) the method of joints, which involves solving equilibrium equations at each joint; and (2) the method of sections, which involves cutting a section and applying equilibrium equations to the cut forces. The document also discusses analyzing frames using a similar process of applying equilibrium to members, and defines machines as mechanisms used to change the magnitude and direction of forces.

moments couples and force couple systems by ahmad khan

To determine the resultant force acting at the top of the tower (point D), I would:
1. Resolve each cable force into its x and y components.
2. Use the parallelogram law of forces to combine the x-components of each cable force into a single x-component force. Do the same for the y-components.
3. The x and y component forces obtained from step 2 are the x and y components of the resultant force acting at D.
4. Use the Pythagorean theorem to determine the magnitude of the resultant force from its x and y components.
5. Use trigonometry to determine the direction of the resultant force relative to the x-axis

Basics and statics of particles unit i - GE6253 PPT

THANGA KASI RAJAN,S
ASSISTANT PROFESSOR,
KAMARAJ COLLEGE OF ENGINEERING AND TECHNOLOGY,
VIRUDHUNAGAR

Statics free body diagram

This document provides an introduction to statics and static equilibrium for particles. It defines key terms like particles, equilibrium, and free-body diagrams. It explains that a particle is in equilibrium if the net force acting on it is zero. Free-body diagrams show all forces acting on a particle and are used to apply the equations of equilibrium to solve problems. Examples are provided of drawing free-body diagrams and using them to determine unknown forces on mechanical components in static equilibrium.

Theory of structures I - STUDENT NOTE BOOK (Polytechnics Revision 2015)

This note is not fully verified. Scanned copy of Student note book. May be helpful for polytechnic students and teachers. Inshaa Allaah

Coplanar concurrent forces

Outline of coplanar concurrent forces with its equilibrium conditions, resultant forces and Lami's theorem.

Design and analysis of slabs

This document provides an overview of analysis and design methods for concrete slabs, including:
1. Elastic analysis methods like grillage analysis and finite element analysis can be used to determine moments and shear forces in slabs.
2. Yield line theory is an alternative plastic/ultimate limit state approach for determining the ultimate load capacity of ductile concrete slabs. It involves assuming yield line patterns that divide the slab into rigid regions and equating external and internal work.
3. Examples are provided to illustrate yield line analysis for one-way spanning slabs and rectangular two-way slabs. Conventions, assumptions, and calculation procedures are explained.

SFD & BMD Shear Force & Bending Moment Diagram

The document discusses shear force and bending moment in beams. It defines key terms like beam, transverse load, shear force, bending moment, and types of loads, supports and beams. It explains how to calculate and draw shear force and bending moment diagrams for different types of loads on beams including point loads, uniformly distributed loads, uniformly varying loads, and loads producing couples or overhangs. Sign conventions and the effect of reactions, loads and geometry on the shear force and bending moment diagrams are also covered.

Principle of Virtual Work in structural analysis

The document provides an overview of the principle of virtual work (PVW) for structural analysis. Some key points:
1) PVW is based on the concept of work and energy methods. It states that for a structure in equilibrium under applied forces, the total virtual work done by these forces due to a small arbitrary displacement is zero.
2) PVW can be used to determine unknown internal forces or displacements in statically indeterminate structures by applying virtual displacements or forces.
3) Examples demonstrate using PVW to calculate the bending moment at a point in a beam and the force in a member of an indeterminate truss by equating the external virtual work to internal virtual work.

Elasticity problem formulation Att 6582

This document summarizes the formulation of elasticity problems. It discusses the field equations, boundary conditions, and general solution strategies for elasticity problems. The fundamental problem can be formulated using either a displacement formulation or stress formulation. General solution strategies include direct, inverse, and semi-inverse methods. Mathematical methods for solving problems include analytical, approximate, and numerical techniques.

Parallelogram Law Force | Civil Engineering

The mathematics of vectors is quite different from the mathematics of scalar quantities. For Example, in the multiplication of scalar quantities we use the “dot product”, whereas in the multiplication of vector quantities we use the “cross product” or the vector product method to account for direction. Copy the link given below and paste it in new browser window to get more information on Parallelogram Law Force:-
http://www.transtutors.com/homework-help/civil-engineering/fundamental-concepts/parallelogram-law-force.aspx

Shear force and bending moment diagram

The document discusses shear force and bending moment diagrams. It defines shear force and bending moment, explaining that shear force acts perpendicular to the beam's axis while bending moment acts to bend the beam. It outlines the procedure to determine shear force and bending moment diagrams: (1) calculate support reactions, (2) divide the beam into segments based on loading, (3) draw free body diagrams and calculate expressions for each segment. As an example, it analyzes a simply supported beam with two loads to derive the shear force and bending moment expressions and diagrams.

Mechanics Lec 1

This document provides an overview of engineering mechanics, which is divided into statics and dynamics. Statics deals with forces acting on bodies at rest, while dynamics looks at forces on moving bodies and is further divided into kinetics (motion due to forces) and kinematics (motion without considering forces). Key concepts discussed include types of forces and systems of forces. Laws of forces such as the parallelogram, triangle, and polygon laws are introduced to determine resultant forces. Other topics covered are Lami's theorem on forces in equilibrium, the definition of moment of force, and the concept of a couple formed by two equal and opposite forces.

Equilibrium & equation of equilibrium in 3D

This document provides information about equilibrium and related concepts in physics. It defines equilibrium as a state where opposing forces neutralize each other such that there is no net force acting on an object. Key points discussed include:
- The definition of equilibrium is derived from Latin words meaning "equal balance".
- Equilibrium can be static, with zero net force and no movement, or dynamic, with zero net force but constant motion.
- Newton's first law relates to equilibrium, stating that an object at rest stays at rest unless a net force acts on it.
- For an object to be in equilibrium, the net force and net torque on it must equal zero.
- Free body diagrams are used to visualize all

Stiffness matrix method of indeterminate Beam5

This document discusses the finite element analysis of continuous beams. It provides the steps to solve continuous or indeterminate beams using finite element methods. These steps include: 1) dividing the beam into elements, 2) identifying degrees of freedom, 3) determining element stiffness matrices, 4) assembling the global stiffness matrix, 5) imposing boundary conditions and determining the reduced stiffness matrix, 6) determining element nodal loads, 7) determining equivalent loads, 8) solving for unknown displacements using equilibrium equations, and 9) determining reactions and moments.

COPLANNER & NON-CONCURRENT FORCES

The document discusses non-concurrent forces and how to find their resultant. It defines non-concurrent forces as those whose lines of action do not meet at a single point. It provides examples of such forces, like those on a ladder leaning against a wall. The document discusses using graphical and algebraic methods to resolve non-parallel, non-concurrent forces into components. It also addresses calculating the total moment of such force systems to find the resultant force and its location.

Lateral earth pressure

This document summarizes Rankine and Coulomb's theories of lateral earth pressure. It discusses how lateral earth pressure is important for designing retaining walls, basements, tunnels, and other geotechnical structures. It defines key terms like coefficient of earth pressure, active pressure, and passive pressure. It explains the assumptions and equations used in Rankine's theory, which assumes a straight failure plane and no friction. It also covers Coulomb's theory, which uses limit equilibrium and accounts for wall friction and non-vertical backfills.

Contact mechanics unit3

- When two surfaces are brought into contact, contact only occurs at discrete contact spots or junctions due to surface roughness. The sum of the areas of these contact spots is the real area of contact, which is typically much smaller than the apparent area of contact.
- The real area of contact depends on surface texture, material properties, and loading conditions. It determines the degree of interaction between surfaces and thereby influences friction and wear.
- During loading, contact initially occurs at a few high asperities. With increasing load, more asperities contact each other and existing contacts grow. Deformation can be elastic, plastic, or viscoelastic depending on stresses.

Lecture 3 and 4 - Earth Retaining Structure (Lateral Earth Pressure)

Lecture 3 and 4 - Earth Retaining Structure (Lateral Earth Pressure)NED University of Engineering and Technology

Lectures of Earth Retaining Structures as a Compulsory Course for M. Engg Program at NEDUET, Karachi.
Author:
Engr. Shoaib Yaqub
Asssitant Professor
Department of Urban & Infrastructure Engineering
NEDUET, Karachi.
Note: Lectures have no copyrights and shared here as the gestures to share knowledge among the students and Engineering fraternity. 2 d equilibrium-split

The document discusses equilibrium of rigid bodies and provides examples of analyzing static equilibrium for two-dimensional structures. It defines key terms like rigid body, free body diagram, and reactions at supports. It also provides examples of determining tensions in cables and reactions at supports by drawing free body diagrams and using the equations of equilibrium. Sample problems are presented on finding tensions and reactions for systems with three applied forces acting on a rigid body.

Rigid body equilibrium

This document provides an overview of the key concepts related to equilibrium of rigid bodies, including:
- Developing free-body diagrams to represent the forces acting on a rigid body and identify unknown support reactions.
- Using the equations of equilibrium (sum of forces equals zero in x and y directions, sum of moments equals zero) to solve for unknown forces and support reactions.
- Analyzing two-force and three-force members, as well as statically determinate and indeterminate structures.

Lecture Notes on Engineering Statics.

This document provides an overview of engineering mechanics statics. It covers topics including:
- Defining mechanics as the science dealing with bodies at rest or in motion under forces.
- Dividing mechanics into statics, dynamics, and other subfields. Statics deals with bodies at rest.
- Introducing fundamental concepts of forces, units of measurement, and representing forces as vectors that add according to the parallelogram law.
- Providing examples of adding forces graphically using the parallelogram law and triangle rule to determine the resultant force.
- Discussing problems involving determining the magnitude and direction of resultant forces from multiple forces acting on structures, stakes, and brackets

Trusses, frames & machines

The document discusses various structural analysis concepts including trusses, frames, and machines. It defines trusses as structures composed of slender members joined at their endpoints that lie in a single plane. Two common methods for analyzing trusses are presented: (1) the method of joints, which involves solving equilibrium equations at each joint; and (2) the method of sections, which involves cutting a section and applying equilibrium equations to the cut forces. The document also discusses analyzing frames using a similar process of applying equilibrium to members, and defines machines as mechanisms used to change the magnitude and direction of forces.

moments couples and force couple systems by ahmad khan

To determine the resultant force acting at the top of the tower (point D), I would:
1. Resolve each cable force into its x and y components.
2. Use the parallelogram law of forces to combine the x-components of each cable force into a single x-component force. Do the same for the y-components.
3. The x and y component forces obtained from step 2 are the x and y components of the resultant force acting at D.
4. Use the Pythagorean theorem to determine the magnitude of the resultant force from its x and y components.
5. Use trigonometry to determine the direction of the resultant force relative to the x-axis

Basics and statics of particles unit i - GE6253 PPT

THANGA KASI RAJAN,S
ASSISTANT PROFESSOR,
KAMARAJ COLLEGE OF ENGINEERING AND TECHNOLOGY,
VIRUDHUNAGAR

Statics free body diagram

This document provides an introduction to statics and static equilibrium for particles. It defines key terms like particles, equilibrium, and free-body diagrams. It explains that a particle is in equilibrium if the net force acting on it is zero. Free-body diagrams show all forces acting on a particle and are used to apply the equations of equilibrium to solve problems. Examples are provided of drawing free-body diagrams and using them to determine unknown forces on mechanical components in static equilibrium.

Theory of structures I - STUDENT NOTE BOOK (Polytechnics Revision 2015)

This note is not fully verified. Scanned copy of Student note book. May be helpful for polytechnic students and teachers. Inshaa Allaah

Coplanar concurrent forces

Outline of coplanar concurrent forces with its equilibrium conditions, resultant forces and Lami's theorem.

Design and analysis of slabs

This document provides an overview of analysis and design methods for concrete slabs, including:
1. Elastic analysis methods like grillage analysis and finite element analysis can be used to determine moments and shear forces in slabs.
2. Yield line theory is an alternative plastic/ultimate limit state approach for determining the ultimate load capacity of ductile concrete slabs. It involves assuming yield line patterns that divide the slab into rigid regions and equating external and internal work.
3. Examples are provided to illustrate yield line analysis for one-way spanning slabs and rectangular two-way slabs. Conventions, assumptions, and calculation procedures are explained.

SFD & BMD Shear Force & Bending Moment Diagram

The document discusses shear force and bending moment in beams. It defines key terms like beam, transverse load, shear force, bending moment, and types of loads, supports and beams. It explains how to calculate and draw shear force and bending moment diagrams for different types of loads on beams including point loads, uniformly distributed loads, uniformly varying loads, and loads producing couples or overhangs. Sign conventions and the effect of reactions, loads and geometry on the shear force and bending moment diagrams are also covered.

Principle of Virtual Work in structural analysis

The document provides an overview of the principle of virtual work (PVW) for structural analysis. Some key points:
1) PVW is based on the concept of work and energy methods. It states that for a structure in equilibrium under applied forces, the total virtual work done by these forces due to a small arbitrary displacement is zero.
2) PVW can be used to determine unknown internal forces or displacements in statically indeterminate structures by applying virtual displacements or forces.
3) Examples demonstrate using PVW to calculate the bending moment at a point in a beam and the force in a member of an indeterminate truss by equating the external virtual work to internal virtual work.

Elasticity problem formulation Att 6582

This document summarizes the formulation of elasticity problems. It discusses the field equations, boundary conditions, and general solution strategies for elasticity problems. The fundamental problem can be formulated using either a displacement formulation or stress formulation. General solution strategies include direct, inverse, and semi-inverse methods. Mathematical methods for solving problems include analytical, approximate, and numerical techniques.

Parallelogram Law Force | Civil Engineering

The mathematics of vectors is quite different from the mathematics of scalar quantities. For Example, in the multiplication of scalar quantities we use the “dot product”, whereas in the multiplication of vector quantities we use the “cross product” or the vector product method to account for direction. Copy the link given below and paste it in new browser window to get more information on Parallelogram Law Force:-
http://www.transtutors.com/homework-help/civil-engineering/fundamental-concepts/parallelogram-law-force.aspx

Shear force and bending moment diagram

The document discusses shear force and bending moment diagrams. It defines shear force and bending moment, explaining that shear force acts perpendicular to the beam's axis while bending moment acts to bend the beam. It outlines the procedure to determine shear force and bending moment diagrams: (1) calculate support reactions, (2) divide the beam into segments based on loading, (3) draw free body diagrams and calculate expressions for each segment. As an example, it analyzes a simply supported beam with two loads to derive the shear force and bending moment expressions and diagrams.

Mechanics Lec 1

This document provides an overview of engineering mechanics, which is divided into statics and dynamics. Statics deals with forces acting on bodies at rest, while dynamics looks at forces on moving bodies and is further divided into kinetics (motion due to forces) and kinematics (motion without considering forces). Key concepts discussed include types of forces and systems of forces. Laws of forces such as the parallelogram, triangle, and polygon laws are introduced to determine resultant forces. Other topics covered are Lami's theorem on forces in equilibrium, the definition of moment of force, and the concept of a couple formed by two equal and opposite forces.

Equilibrium & equation of equilibrium in 3D

This document provides information about equilibrium and related concepts in physics. It defines equilibrium as a state where opposing forces neutralize each other such that there is no net force acting on an object. Key points discussed include:
- The definition of equilibrium is derived from Latin words meaning "equal balance".
- Equilibrium can be static, with zero net force and no movement, or dynamic, with zero net force but constant motion.
- Newton's first law relates to equilibrium, stating that an object at rest stays at rest unless a net force acts on it.
- For an object to be in equilibrium, the net force and net torque on it must equal zero.
- Free body diagrams are used to visualize all

Stiffness matrix method of indeterminate Beam5

This document discusses the finite element analysis of continuous beams. It provides the steps to solve continuous or indeterminate beams using finite element methods. These steps include: 1) dividing the beam into elements, 2) identifying degrees of freedom, 3) determining element stiffness matrices, 4) assembling the global stiffness matrix, 5) imposing boundary conditions and determining the reduced stiffness matrix, 6) determining element nodal loads, 7) determining equivalent loads, 8) solving for unknown displacements using equilibrium equations, and 9) determining reactions and moments.

COPLANNER & NON-CONCURRENT FORCES

The document discusses non-concurrent forces and how to find their resultant. It defines non-concurrent forces as those whose lines of action do not meet at a single point. It provides examples of such forces, like those on a ladder leaning against a wall. The document discusses using graphical and algebraic methods to resolve non-parallel, non-concurrent forces into components. It also addresses calculating the total moment of such force systems to find the resultant force and its location.

Lateral earth pressure

This document summarizes Rankine and Coulomb's theories of lateral earth pressure. It discusses how lateral earth pressure is important for designing retaining walls, basements, tunnels, and other geotechnical structures. It defines key terms like coefficient of earth pressure, active pressure, and passive pressure. It explains the assumptions and equations used in Rankine's theory, which assumes a straight failure plane and no friction. It also covers Coulomb's theory, which uses limit equilibrium and accounts for wall friction and non-vertical backfills.

Contact mechanics unit3

- When two surfaces are brought into contact, contact only occurs at discrete contact spots or junctions due to surface roughness. The sum of the areas of these contact spots is the real area of contact, which is typically much smaller than the apparent area of contact.
- The real area of contact depends on surface texture, material properties, and loading conditions. It determines the degree of interaction between surfaces and thereby influences friction and wear.
- During loading, contact initially occurs at a few high asperities. With increasing load, more asperities contact each other and existing contacts grow. Deformation can be elastic, plastic, or viscoelastic depending on stresses.

Lecture 3 and 4 - Earth Retaining Structure (Lateral Earth Pressure)

Lecture 3 and 4 - Earth Retaining Structure (Lateral Earth Pressure)NED University of Engineering and Technology

Lectures of Earth Retaining Structures as a Compulsory Course for M. Engg Program at NEDUET, Karachi.
Author:
Engr. Shoaib Yaqub
Asssitant Professor
Department of Urban & Infrastructure Engineering
NEDUET, Karachi.
Note: Lectures have no copyrights and shared here as the gestures to share knowledge among the students and Engineering fraternity. Lecture Notes on Engineering Statics.

Lecture Notes on Engineering Statics.

Trusses, frames & machines

Trusses, frames & machines

moments couples and force couple systems by ahmad khan

moments couples and force couple systems by ahmad khan

Basics and statics of particles unit i - GE6253 PPT

Basics and statics of particles unit i - GE6253 PPT

Statics free body diagram

Statics free body diagram

Theory of structures I - STUDENT NOTE BOOK (Polytechnics Revision 2015)

Theory of structures I - STUDENT NOTE BOOK (Polytechnics Revision 2015)

Coplanar concurrent forces

Coplanar concurrent forces

Design and analysis of slabs

Design and analysis of slabs

SFD & BMD Shear Force & Bending Moment Diagram

SFD & BMD Shear Force & Bending Moment Diagram

Principle of Virtual Work in structural analysis

Principle of Virtual Work in structural analysis

Elasticity problem formulation Att 6582

Elasticity problem formulation Att 6582

Parallelogram Law Force | Civil Engineering

Parallelogram Law Force | Civil Engineering

Shear force and bending moment diagram

Shear force and bending moment diagram

Mechanics Lec 1

Mechanics Lec 1

Equilibrium & equation of equilibrium in 3D

Equilibrium & equation of equilibrium in 3D

Stiffness matrix method of indeterminate Beam5

Stiffness matrix method of indeterminate Beam5

COPLANNER & NON-CONCURRENT FORCES

COPLANNER & NON-CONCURRENT FORCES

Lateral earth pressure

Lateral earth pressure

Contact mechanics unit3

Contact mechanics unit3

Lecture 3 and 4 - Earth Retaining Structure (Lateral Earth Pressure)

Lecture 3 and 4 - Earth Retaining Structure (Lateral Earth Pressure)

2 d equilibrium-split

The document discusses equilibrium of rigid bodies and provides examples of analyzing static equilibrium for two-dimensional structures. It defines key terms like rigid body, free body diagram, and reactions at supports. It also provides examples of determining tensions in cables and reactions at supports by drawing free body diagrams and using the equations of equilibrium. Sample problems are presented on finding tensions and reactions for systems with three applied forces acting on a rigid body.

Rigid body equilibrium

This document provides an overview of the key concepts related to equilibrium of rigid bodies, including:
- Developing free-body diagrams to represent the forces acting on a rigid body and identify unknown support reactions.
- Using the equations of equilibrium (sum of forces equals zero in x and y directions, sum of moments equals zero) to solve for unknown forces and support reactions.
- Analyzing two-force and three-force members, as well as statically determinate and indeterminate structures.

2 mark question engineering mechanics

THANGA KASI RAJAN S
ASSISTANT PROFESSOR,
DEPARTMENT OF MECHANICAL ENGINEERING,
KAMARAJ COLLEGE OF ENGINEERING AND TECHNOLOGY,
VIRUDHUNAGAR

Dissertation report

This document presents the layout and introduction for a dissertation report on analyzing multi-storey partially braced frames subjected to seismic and gravity loads using V-braces. The layout includes sections on introduction, literature review, structural analysis methods, earthquake analysis methods, theoretical formulation, results and discussion, conclusion, and references. The introduction discusses the importance of tall structures and braced frames, noting advantages of braced frames include increased strength, stiffness, and reduced member sizes.

Projectile Motion

The document discusses projectile motion and circular motion. It defines key terms related to projectile motion such as trajectory, angle of projection, horizontal range, time of flight, and velocity of projection. It then derives equations for the trajectory, time of flight, horizontal range, maximum height, and velocity at impact of a projectile. Examples and problems are provided to demonstrate the application of these equations.

ABC Of Project Management

This document provides an overview of project management. It discusses that projects are needed to generate profits for businesses, as profits come from operations which give birth to projects. However, only 34% of projects succeed currently. The document then outlines the basic project life cycle of initiation, planning, execution, controlling, and closing phases. It provides some ABCs of project management, emphasizing always properly defining the project, ensuring stakeholder identification, being aware of constraints and knowledge areas, and cultivating good project management habits and processes within an organization to improve success rates. The overall message is that projects can only succeed by being properly managed to meet defined objectives and baselines.

Work power energy

1) This document discusses work, power, and energy. It defines work as the product of force and displacement, and defines the units of work as newton-meters (Nm) or joules (J).
2) Power is defined as the rate of doing work, or the ratio of work to time. The units of power are watts (W).
3) Energy exists in various forms including mechanical, thermal, chemical, light, sound, nuclear, and electrical. Mechanical energy includes potential energy, which depends on position or height, and kinetic energy, which depends on motion or velocity.
4) The work-energy principle states that the work done on an object equals its change in

Chapter no. 6 linear mo

This document discusses linear motion and its related concepts. It defines kinematics as the study of motion without consideration of forces, and kinetics as the study of motion with consideration of forces. It then discusses various types of linear motion including rectilinear motion, motion under gravity, and motion under variable acceleration. Key concepts defined include displacement, velocity, acceleration, uniform motion, and graphical representation of motion using displacement-time and velocity-time curves. Equations of motion are provided for rectilinear motion and motion under gravity with uniform acceleration.

2. linear kinematics i

1. Linear kinematics describes motion using position, velocity, and acceleration without regard to forces. It includes linear (straight line) and curvilinear (bent line) motion.
2. Angular kinematics describes rotational motion like elbow flexion or spinning.
3. General motion combines translation and rotation, describing most human and sports motions.
4. Key descriptors include position, distance/displacement, speed/velocity, and acceleration. Displacement is the straight-line distance between start and end points while distance is the total path length. Velocity describes speed with direction and acceleration is the rate of change of velocity.

Chapter 2 beam

This chapter discusses beams and support reactions. It defines statically determinate beams and describes the following topics: types of beam supports including simple, pin/hinged, roller, and fixed supports; types of beams such as simply supported, cantilever, overhang, and continuous beams; types of loading including concentrated/point loads and distributed loads such as uniform, uniformly varying, and non-uniform loads; and the procedure to find support reactions of statically determinate beams using equilibrium conditions. It also discusses compound beams and the concept of virtual work.

Centre of Gravity

1) The document discusses concepts related to centroid and moment of inertia including: the centroid is the point where the total area of a plane figure is assumed to be concentrated; formulas are provided for finding the centroid of basic shapes; the difference between centroid and center of gravity is explained; properties and methods for finding the centroid are described such as using moments.
2) Formulas are given for moment of inertia including how it is calculated about different axes and the parallel axis theorem.
3) Example problems are provided to demonstrate calculating the centroid and moment of inertia for various shapes.

Water Management

This document provides information about water management topics including sources of water, dams, canals, and irrigation methods. It discusses surface and underground water sources like ponds, lakes, rivers, wells, and tube wells. It describes different types of dams such as earth dams, rock-fill dams, gravity dams, and arch dams. Canals are described as the trenches that distribute water from reservoirs for irrigation. Various irrigation methods are outlined including flow irrigation, flood irrigation, storage irrigation, drip irrigation, and spray irrigation. Rainwater harvesting is introduced as a way to conserve water by collecting and filtering rainwater runoff and roof runoff to recharge underground water sources.

Assignment no 3

This document contains 18 problems related to calculating beam support reactions using concepts like types of beam supports, virtual work, simply supported beams, overhanging beams, cantilever beams, beam bents, and compound beams. The problems include calculating support reactions for various beams under different loading conditions like point loads, uniformly distributed loads, and concentrated moments. Solutions are provided for some of the problems.

Lahaja za kiswahili kwa ujumla

Lahaja za Kiswahili zimekuwa zikichanganya watumiaji wengi na watu wengi wanaojifunza lugha ya Kiswahili, hivyo matini hii imekusudia kuondoa mkanganyiko huo.

D alemberts principle

D'Alembert's Principle states that the resultant of all external forces and inertia forces acting on a body is zero for the body to be in dynamic equilibrium. Inertia forces are represented as minus mass times acceleration. The principle allows equations of static equilibrium to be applied to bodies undergoing translational motion by considering an imaginary inertia force equal and opposite to actual inertia. Several example problems are provided applying the principle to analyze motion of connected bodies over pulleys, motion on inclined planes, and motion within elevators.

Assignment no. 4

This document contains an assignment on analyzing forces in truss structures using the method of joints and method of sections. It provides 10 problems analyzing different truss configurations, requesting the forces in specific members given load and support conditions. The problems include trusses with various spans, loads, and support types, including cantilever trusses.

02 - Structure and Properties of Organic Molecules - Wade 7th

The document summarizes key concepts from Chapter 2 of an organic chemistry textbook, including:
1) Molecular orbital theory and how atomic orbitals combine to form sigma and pi bonds via hybridization. Common hybridizations include sp, sp2, and sp3.
2) Molecular shapes are determined by hybridization and VSEPR theory. Common geometries are linear, trigonal planar, and tetrahedral.
3) Intermolecular forces like hydrogen bonding, dipole-dipole interactions, and London dispersion forces influence physical properties like boiling points and solubility.
4) Isomerism can occur via constitutional isomers with different bonding connectivities or geometric isomers with different spatial arrangements.

01 - Introduction and Review - Wade 7th

This document provides an introduction to organic chemistry, covering topics such as:
- The definition of organic chemistry as the study of carbon compounds.
- Electronic structure of atoms and how they bond through ionic and covalent bonding.
- Resonance structures and how they are used to represent molecules.
- Factors that influence acidity such as electronegativity, size, and resonance.
- The definitions of nucleophiles and electrophiles and their roles in bond formation.

Oganic II - Klein - chapter 22

This document introduces reactions that take place at the alpha carbon of carbonyl compounds. It discusses enols and enolates, which are reactive intermediates that allow substitutions and additions to occur at the alpha carbon. Specifically, it covers alpha halogenation, aldol reactions, and aldol condensations. These reactions are important methods to form carbon-carbon bonds and install functional groups at the alpha position of carbonyls.

2 d equilibrium-split

2 d equilibrium-split

Rigid body equilibrium

Rigid body equilibrium

2 mark question engineering mechanics

2 mark question engineering mechanics

Dissertation report

Dissertation report

Projectile Motion

Projectile Motion

ABC Of Project Management

ABC Of Project Management

Work power energy

Work power energy

Chapter no. 6 linear mo

Chapter no. 6 linear mo

2. linear kinematics i

2. linear kinematics i

Chapter 2 beam

Chapter 2 beam

Centre of Gravity

Centre of Gravity

Water Management

Water Management

Assignment no 3

Assignment no 3

Lahaja za kiswahili kwa ujumla

Lahaja za kiswahili kwa ujumla

Mofolojia ya kiswahili

Mofolojia ya kiswahili

D alemberts principle

D alemberts principle

Assignment no. 4

Assignment no. 4

02 - Structure and Properties of Organic Molecules - Wade 7th

02 - Structure and Properties of Organic Molecules - Wade 7th

01 - Introduction and Review - Wade 7th

01 - Introduction and Review - Wade 7th

Oganic II - Klein - chapter 22

Oganic II - Klein - chapter 22

Stresses and strains (Part 1)

Free-body diagrams, stresses, strains, elastic constants, mechanics, mechanics of solids, strength of materials.

Gr

This document provides an overview of coplanar non-concurrent force systems and methods for analyzing them. It defines key terms like resultant, equilibrium, and equilibrant. Examples are provided to demonstrate determining resultants and support reactions for coplanar force systems, beams under different loading conditions, and plane trusses. Methods like Lami's theorem, free body diagrams, and the principles of equilibrium are used to solve for unknown forces. Truss analysis is also briefly discussed, noting trusses are articulated structures carrying loads at joints, with members in axial tension or compression.

Engineering Mechanics First Year

This document discusses concepts related to static equilibrium of rigid bodies, including:
- Conditions for static equilibrium are that the net force and net torque on the body are both zero
- Free body diagrams show all forces acting on a body in isolation from its surroundings
- Types of supports include hinges, rollers, fixed supports, and smooth surfaces
- Equilibrium of two-force and three-force bodies follow specific rules
- Lami's theorem relates the magnitudes of three concurrent forces in equilibrium
- An equilibrant force can balance an unbalanced system and bring it into equilibrium

Coplanar forces equilibrium

This document discusses concepts related to static equilibrium of rigid bodies, including:
- Conditions for static equilibrium are that the net force and net moment are both zero
- Free body diagrams show all forces acting on a body in isolation
- Types of supports (fixed, hinge, roller) and the reactions they provide are described
- Concepts like two-force and three-force members, Lami's theorem, and finding equilibrant forces to balance unbalanced systems are explained
- Several example problems are provided to illustrate applying concepts to determine reactions and tensions in static systems

3. coplanar forces equilibrium

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

Beam

This document defines beams and support reactions. It discusses statically determinate beams and explains that support reactions can be determined using equilibrium conditions alone for these beams. The document outlines different types of beam supports including simple, pinned, roller, and fixed supports. It also defines types of beams such as simply supported, cantilever, overhang, and continuous beams. Finally, it discusses determining support reactions for statically determinate beams using equilibrium conditions and introduces the concept of virtual work.

Em notes

This document contains lecture notes for an Engineering Mechanics course. It lists the course code, instructor details, and a lesson plan with 30 lectures covering topics like forces, equilibrium, friction, moments of inertia, kinematics, dynamics, and motion. The lectures will discuss concepts, theories, and include example problems for each topic. Diagrams and free body diagrams are emphasized. The course appears to provide a comprehensive overview of engineering mechanics principles and their applications.

Fundamental of Statics (Part 2)

This document discusses concepts related to statics including:
1. It covers four main topics - the condition of equilibrium of coplanar concurrent forces, the concept of a free body diagram, the sine rule for triangles, and Lami's theorem.
2. Lami's theorem states that if three coplanar forces acting at a point are in equilibrium, then each force is proportional to the sine of the angle between the other two forces.
3. Several examples are provided to demonstrate how to apply the sine rule and Lami's theorem to calculate tensions in strings and magnitudes of forces.

BALANCING OF ROTATING MASSES.ppt

1. The document discusses balancing of rotating masses by counteracting centrifugal forces with balancing masses. It covers balancing a single mass with a single mass in the same plane, and with two masses in different planes.
2. Balancing a single mass with two masses in different planes requires satisfying conditions of zero net force and zero net couple on the shaft for dynamic balancing.
3. Balancing multiple masses rotating in the same plane involves constructing force and couple polygons to determine balancing masses and their positions to achieve complete balance.

Ch12 ssm

This document contains conceptual problems and questions about static equilibrium and elasticity. It includes the following:
1) True/false questions about the conditions for static equilibrium.
2) A question about the tension in different parts of a wire made of aluminum and steel.
3) Derivations of the expression for Young's modulus based on an atomic model and an estimate of the atomic force constant.
4) Questions involving calculating tensions, normal forces, and torque in situations involving objects in equilibrium, such as masts on sailboats and cylinders on steps.
5) Questions involving static equilibrium conditions to solve for quantities like the location of a person's center of gravity and the height a ladder can

STRENGTH OF MATERIALS for beginners

This book is intended to cover the basic Strength of Materials of the first
two years of an engineering degree or diploma course ; it does not attempt
to deal with the more specialized topics which usually comprise the final
year of such courses.
The work has been confined to the mathematical aspect of the subject
and no descriptive matter relating to design or materials testing has been
included.

Assignment no 1

1. The document discusses problems related to resultant of coplanar forces including the law of parallelogram of forces, component law of forces, Varignon's theorem, and finding the resultant and its properties for various force systems.
2. It provides 17 figures showing different force systems and problems require calculating the resultant, its magnitude and direction, and in some cases locating its position.
3. The document also includes theory questions related to definitions of force, laws of mechanics, characteristics of couples, and calculating resultants of concurrent and non-concurrent forces.

Equilibrium

1. The document discusses static equilibrium of coplanar force systems. It covers drawing free-body diagrams, identifying reaction forces, and applying the three equations of equilibrium.
2. Key steps for solving problems include drawing the free-body diagram, identifying known and reaction forces, and setting the sum of forces and moments equal to zero.
3. Examples show calculating unknown forces and reactions for beams, rods, and pulley systems in static equilibrium. Forces and moments are analyzed to determine the magnitude and direction of reaction forces.

Resultant of forces

This document provides an overview of the content covered in the Basic Civil Engineering course. It discusses the following topics:
1. Mechanics of Rigid Bodies and Mechanics of Deformable Bodies, which make up Parts I and II of the course.
2. Concepts in mechanics of solids including resultant and equilibrium of coplanar forces, centroids, moments of inertia, kinetics principles, stresses and strains.
3. Five textbooks recommended as references for the course.
4. Definitions of terms like particle, force, scalar, vector, and rigid body.
5. Methods for resolving forces into components, obtaining the resultant of coplanar forces, and solving mechanics problems

Tension for Concurrent and Coplanar Force System | Mechanical Engineering

This document provides an overview of concurrent and coplanar force systems. It defines concurrent forces as multiple forces acting at a single point and coplanar forces as multiple forces acting in a single plane. Lami's theorem is introduced which states that for three coplanar forces in equilibrium, each force is proportional to the sine of the angle between the other two forces. Examples are given to demonstrate determining tensions in strings for systems with concurrent and coplanar forces, including strings supporting a lamp, a sphere tied to a wall, and a string passing over pulleys with attached weights.

Engineering mechanics-question-and-answers-for-gate-ias

This document provides an overview of the topics and lectures covered in S K Mondal's Engineering Mechanics course for GATE and IAS exams. The course is divided into 8 modules covering topics such as laws of motion, vector algebra, equilibrium of bodies, trusses, friction, properties of surfaces, method of virtual work, motion in a plane, rotational dynamics, harmonic oscillators, and projectile motion. The document lists the specific lectures in each module, along with example problems and their solutions related to the engineering mechanics topics.

Freebodydigram

Here are the free body diagrams for the given systems:
1. Axle of bicycle wheel:
F_app
R_1
R_2
2. Propped cantilever:
W_1
W_2
R
3. Neoprene pad bearing functions like a roller support.
4. Circled part of building:
W
R_1
R_2
R_3
5. Dam:
W_water
R

Uni and bi axial column and design

Columns are structural elements that transmit loads in compression from beams and slabs above to other elements below. Columns can experience both axial compression and bending loads. Biaxial bending occurs when a column experiences simultaneous bending about both principal axes, such as in corner columns of buildings. The biaxial bending method permits analysis of rectangular columns under these conditions. The document provides details on analyzing a sample reinforced concrete column for adequacy using the reciprocal load method to check that factored loads do not exceed design capacity. Diagrams are presented showing interaction surfaces and stress distributions for concentrically and eccentrically loaded columns.

module 3 (Mechanics)

The document provides information about mechanics of solids-I, including:
1) It describes different types of supports like simple supports, roller supports, pin-joint supports, and fixed supports. It also describes different types of loads like concentrated loads, uniformly distributed loads, and uniformly varying loads.
2) It discusses shear force as the unbalanced vertical force on one side of a beam section, and bending moment as the sum of moments about a section.
3) It explains the relationship between loading (w), shear force (F), and bending moment (M) for an element of a beam. The rate of change of shear force is equal to the loading intensity, and the rate of change of bending

Stresses and strains (Part 1)

Stresses and strains (Part 1)

Gr

Gr

Engineering Mechanics First Year

Engineering Mechanics First Year

Coplanar forces equilibrium

Coplanar forces equilibrium

3. coplanar forces equilibrium

3. coplanar forces equilibrium

Forces 7

Forces 7

Beam

Beam

Em notes

Em notes

Fundamental of Statics (Part 2)

Fundamental of Statics (Part 2)

BALANCING OF ROTATING MASSES.ppt

BALANCING OF ROTATING MASSES.ppt

Ch12 ssm

Ch12 ssm

STRENGTH OF MATERIALS for beginners

STRENGTH OF MATERIALS for beginners

Assignment no 1

Assignment no 1

Equilibrium

Equilibrium

Resultant of forces

Resultant of forces

Tension for Concurrent and Coplanar Force System | Mechanical Engineering

Tension for Concurrent and Coplanar Force System | Mechanical Engineering

Engineering mechanics-question-and-answers-for-gate-ias

Engineering mechanics-question-and-answers-for-gate-ias

Freebodydigram

Freebodydigram

Uni and bi axial column and design

Uni and bi axial column and design

module 3 (Mechanics)

module 3 (Mechanics)

Transportation engineering

This document provides an overview of transportation engineering and related topics through a presentation. It begins with an introduction to various modes of transportation including roads, bridges, railways, airports, docks and harbors. It then provides a question bank with sample questions on these topics from previous years. The document concludes by providing detailed answers to some of the sample questions, covering areas like classifications of roads and transportation, structures of roads, and short notes on specific road types.

Chapter wise question papers_bce

This document contains a question bank for the Basic Civil Engineering subject divided into 9 units. Each unit contains 6 questions related to topics within that unit. The questions range from 3-10 marks and cover topics such as sub-branches of civil engineering, surveying, remote sensing, dams, roads, building construction principles, materials, and steel structures. This question bank can be used to prepare for exams on basic civil engineering concepts and their applications.

Design of staircase_practical_example

The document provides design details for staircases on three floors of a building, including dimensions, load calculations, and reinforcement details. Load calculations are performed to determine bending moments and shear forces. Reinforcement area, bar diameter, and spacing are calculated for the waist slabs of each staircase to resist the determined bending moment and satisfy code requirements for minimum steel and shear capacity.

Presentation "Use of coupler Splices for Reinforcement"

This document presents a summary of a presentation on the use of coupler splices for reinforcement. The presentation includes an introduction to coupler splices, a literature review on the topic, details on the experimental procedure used to test coupler splices, a cost analysis comparing coupler splices to lap splices, and conclusions. The experimental results show that coupler splices performed better than lap splices and welded splices in tensile loading tests. A cost analysis also determined that coupler splices provide significant cost savings over lap splices by reducing the amount of reinforcement required. The conclusion is that coupler splices are an effective and economic replacement for lap splices in reinforcement.

Guidelines_for_building_design

This document provides guidelines for the design of reinforced concrete structures in buildings according to the limit state method. It outlines the general process for building design which includes studying architectural drawings and field data, preparing reinforced concrete layouts, analyzing structural frames, and designing columns, beams, slabs, and footings. Computer programs like STAAD and in-house software are used to aid in analysis and design. Designers are advised to be familiar with relevant Indian code provisions and follow the guidelines to independently complete reinforced concrete designs for buildings.

Strength of materials_I

This document provides an introduction to strength of materials, including concepts of stress, strain, Hooke's law, stress-strain relationships, elastic constants, and factors of safety. It defines key terms like stress, strain, elastic limit, modulus of elasticity, and ductile and brittle material behavior. Examples of stress and strain calculations are provided for basic structural elements like rods, bars, and composite structures. The document also covers compound bars, principle of superposition, and effects of temperature changes.

Presentation_on_Cellwise_Braced_frames

This presentation discusses the seismic response of cellwise concentrically braced frames. It introduces cellwise braced frames as a structural system that provides lateral stability through bracing elements arranged in cells within each bay. The document describes a study that analyzed 5 bay, 12 story reinforced concrete frames with different bracing configurations, including single-cell, two-cell, and three-cell arrangements. The study found that single-cell A-braced frames provided the highest material cost savings of up to 9.59% compared to bare frames. Two-cell and three-cell configurations further improved cost savings but required additional bracing. Overall, the study shows that optimally arranged cellwise braced frames produce a stiff, strong and econom

Study of MORT_&_H

The document provides an overview of the Ministry of Road Transport and Highways (MoRTH) in India. It discusses the ministry's role in formulating policies and regulations related to road transport. It outlines the ministry's history and organizational structure. It also summarizes some of the key specifications issued by MoRTH related to road and bridge construction, including specifications for earthworks, pavement layers, drainage, and other aspects of road projects. The document thus provides a high-level introduction to MoRTH and the specifications it issues for road development and transport in India.

List of various_IRCs_&_sps

The Indian Road Congress (IRC) was established in 1934 on the recommendations of the Jayakar Committee to oversee road development in India. It is the apex body for highway engineers and professionals. IRC has over 16,700 members from both public and private sector organizations involved in roads. It aims to promote standard specifications and best practices for road and bridge construction through various technical committees. It has published over 100 codes of practice and guidelines and oversees research activities through its Highway Research Board.

Analysis of multi storey building frames subjected to gravity and seismic loa...

This document summarizes a study on the seismic response of reinforced concrete frames with varying numbers of bays and storeys. Three frame configurations - 3 bay, 5 bay, and 7 bay with 9 stories each - were modeled and analyzed under gravity and seismic loads. Both prismatic frames and frames with non-prismatic elements like stepped beams and haunches at beam-column joints were considered. The effects of variables like haunch size, beam inertia, and live load patterns on internal forces and storey drift were examined. Key results showed that non-prismatic elements can reduce bending moments and axial forces compared to conventional prismatic frames.

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

This document discusses the seismic response of reinforced concrete concentrically braced frames. It analyzes numerically various bracing patterns for a 5-bay 12-story building, including bare frames, fully braced frames, and partially braced frames with bracing applied at the bay-level or level-wise. Optimum bracing patterns are identified that reduce internal forces in columns and provide economic savings compared to bare frames or fully braced frames. Graphs show variations in axial, shear and bending forces for different bracing patterns, identifying patterns that fall within acceptable ranges. Savings of up to 7.87% are achieved with the optimum bracing patterns.

Use of mechanical_splices_for_reinforcing_steel

The document discusses the use of mechanical splices (couplers) as an alternative to traditional lap splicing for reinforcing steel. It provides details on different types of couplers, including threaded couplers. Experimental testing showed that couplers achieved similar or higher yield and ultimate stresses as compared to normal and welded reinforcing bars. While ductility was slightly reduced, factors like epoxy injection and staggered splicing can improve ductility. A cost analysis found that couplers provide significant cost savings over lap splices due to reduced steel requirements. Therefore, the study concludes that mechanical splices are an effective and economic replacement for lap splices.

Guide lines bridge_design

This document provides guidelines for bridge design in the Public Works Department. It introduces the contents and chapters, which cover aspects of bridge design, components, innovative structures, preparation of bridge projects, and other topics. The guidelines are intended to help engineers understand the department's practices for bridge design. The second edition was revised with new chapters and information to aid both new and experienced engineers.

Seismic response of cellwise braced reinforced concrete frames

The document analyzes the seismic response of reinforced concrete frames with different patterns of reinforced concrete bracing. Numerical models of 5-bay, 12-story reinforced concrete frames were analyzed with different bracing configurations including bare frames, fully braced, partially braced, outrigger braced, and cellwise braced. The responses, including internal forces, displacements, and member sizes, were compared for each configuration. Optimal baywise and levelwise locations for bracing were identified based on producing smaller internal forces within acceptable ranges. Cellwise bracing was explored as a configuration that combines advantages of other patterns while allowing for clear openings.

Chaper wise qpapers_bce

1. The document contains a question bank for the Basic Civil Engineering section covering topics like introduction to civil engineering, surveying, linear measurements, bearing, and leveling.
2. It includes 36 questions on surveying topics like chain surveying, compass surveying, and leveling with multiple parts and variations. Calculations and sketches are required to solve some questions.
3. The leveling questions provide staff readings and require entering data in a standard leveling table, calculating reduced levels using different methods, and applying arithmetic checks.

Basic Loads Cases

The document defines various types of loads that should be considered in structural analysis, including dead loads, live loads, wind loads, and earthquake loads. It provides details on how to apply these loads in both positive and negative directions of the X and Z axes. It also lists load combinations that should be analyzed according to Indian standards, including combinations for limit states of collapse and serviceability. The load combinations include factors for dead, live, wind, and earthquake loads.

Earthquake analysis by Response Spectrum Method

This document provides steps for performing an earthquake analysis using the response spectrum method in STAAD v8i. Key steps include:
1. Generating primary load cases for the X and Z directions using the specified code spectrum
2. Modeling dead and live loads
3. Obtaining support reactions for a load combination of dead + 0.25 live loads
4. Exporting the support reaction values to Excel tables
5. Importing the Excel tables back into STAAD as joint loads to apply the earthquake loads
6. Analyzing the structure with fixed supports instead of pin supports
The overall process applies earthquake loads to the structure using the response spectrum method and obtains the response of the structure under seismic loading

Earthquake analysis by psudeo static method

This document provides instructions for performing an earthquake analysis on a structure using the pseudo-static method in STAAD v8i. The steps include:
1. Defining the seismic parameters by adding a seismic definition and inputting values for the zone, response factor, importance factor, etc. based on IS 1893:2002.
2. Creating earthquake load cases in the X and Z directions and combining them with dead and live loads.
3. Assigning pin supports and obtaining support reactions for analysis.
4. Importing the support reaction values into Excel to create weight tables that are then input back into STAAD.
5. Removing the pin supports and assigning fixed supports at the foundation before running the full analysis

Basic Civil Engineering MCQ

The document contains a 58 question multiple choice test on basic civil engineering. The test covers topics such as surveying, building construction materials and techniques, structures, and other basic civil engineering concepts. The questions assess knowledge of concepts like types of surveying, building components, properties of materials like concrete and masonry, earthquake resistance techniques, and more.

PROBLEMS ON BEARINGS

1. The document provides examples of problems involving bearings observed in closed traverse surveys. It discusses calculating included angles, checking for angular errors, and correcting bearings based on lines assumed to be free from local attraction effects.
2. The first example shows calculations for a traverse with station positions, observed fore and back bearings, differences between bearings, included angles, and corrected bearings and stations free from attraction.
3. Several multi-part problems are presented involving calculating included angles from observed bearings, checking for errors, correcting bearings, and identifying stations free from local attraction for closed traverses. Step-by-step working is demonstrated for one example.

Transportation engineering

Transportation engineering

Chapter wise question papers_bce

Chapter wise question papers_bce

Design of staircase_practical_example

Design of staircase_practical_example

Presentation "Use of coupler Splices for Reinforcement"

Presentation "Use of coupler Splices for Reinforcement"

Guidelines_for_building_design

Guidelines_for_building_design

Strength of materials_I

Strength of materials_I

Presentation_on_Cellwise_Braced_frames

Presentation_on_Cellwise_Braced_frames

Study of MORT_&_H

Study of MORT_&_H

List of various_IRCs_&_sps

List of various_IRCs_&_sps

Analysis of multi storey building frames subjected to gravity and seismic loa...

Analysis of multi storey building frames subjected to gravity and seismic loa...

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

Seismic response of _reinforced_concrete_concentrically_a_braced_frames

Use of mechanical_splices_for_reinforcing_steel

Use of mechanical_splices_for_reinforcing_steel

Guide lines bridge_design

Guide lines bridge_design

Seismic response of cellwise braced reinforced concrete frames

Seismic response of cellwise braced reinforced concrete frames

Chaper wise qpapers_bce

Chaper wise qpapers_bce

Basic Loads Cases

Basic Loads Cases

Earthquake analysis by Response Spectrum Method

Earthquake analysis by Response Spectrum Method

Earthquake analysis by psudeo static method

Earthquake analysis by psudeo static method

Basic Civil Engineering MCQ

Basic Civil Engineering MCQ

PROBLEMS ON BEARINGS

PROBLEMS ON BEARINGS

An improved modulation technique suitable for a three level flying capacitor ...

This research paper introduces an innovative modulation technique for controlling a 3-level flying capacitor multilevel inverter (FCMLI), aiming to streamline the modulation process in contrast to conventional methods. The proposed
simplified modulation technique paves the way for more straightforward and
efficient control of multilevel inverters, enabling their widespread adoption and
integration into modern power electronic systems. Through the amalgamation of
sinusoidal pulse width modulation (SPWM) with a high-frequency square wave
pulse, this controlling technique attains energy equilibrium across the coupling
capacitor. The modulation scheme incorporates a simplified switching pattern
and a decreased count of voltage references, thereby simplifying the control
algorithm.

学校原版美国波士顿大学毕业证学历学位证书原版一模一样

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6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才

integral complex analysis chapter 06 .pdf

Complex analysis

artificial intelligence and data science contents.pptx

What is artificial intelligence? Artificial intelligence is the ability of a computer or computer-controlled robot to perform tasks that are commonly associated with the intellectual processes characteristic of humans, such as the ability to reason.
› ...
Artificial intelligence (AI) | Definitio

Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024

Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.

AI assisted telemedicine KIOSK for Rural India.pptx

It gives the overall description of SIH problem statement " AI assisted telemedicine KIOSK for Rural India".

Comparative analysis between traditional aquaponics and reconstructed aquapon...

The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.

原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样

原件一模一样【微信：bwp0011】《(Humboldt毕业证书)柏林大学毕业证学位证》【微信：bwp0011】学位证，留信认证（真实可查，永久存档）原件一模一样纸张工艺/offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原。
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问微bwp0011
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四.办理各国各大学文凭(一对一专业服务,可全程监控跟踪进度)
如果您处于以下几种情况：
◇在校期间，因各种原因未能顺利毕业……拿不到官方毕业证【微bwp0011】
◇面对父母的压力，希望尽快拿到；
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留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才

Generative AI leverages algorithms to create various forms of content

What is Generative AI?

Computational Engineering IITH Presentation

This Presentation will give you a brief idea about what Computational Engineering at IIT Hyderabad has to offer.

Mechanical Engineering on AAI Summer Training Report-003.pdf

Mechanical Engineering PROJECT REPORT ON SUMMER VOCATIONAL TRAINING
AT MBB AIRPORT

Welding Metallurgy Ferrous Materials.pdf

Welding Metallurgy Explained

哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样

原版一模一样【微信：741003700 】【(csu毕业证书)查尔斯特大学毕业证硕士学历】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
本公司拥有海外各大学样板无数，能完美还原海外各大学 Bachelor Diploma degree, Master Degree Diploma
1:1完美还原海外各大学毕业材料上的工艺：水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠。文字图案浮雕、激光镭射、紫外荧光、温感、复印防伪等防伪工艺。材料咨询办理、认证咨询办理请加学历顾问Q/微741003700
留信网认证的作用:
1:该专业认证可证明留学生真实身份
2:同时对留学生所学专业登记给予评定
3:国家专业人才认证中心颁发入库证书
4:这个认证书并且可以归档倒地方
5:凡事获得留信网入网的信息将会逐步更新到个人身份内，将在公安局网内查询个人身份证信息后，同步读取人才网入库信息
6:个人职称评审加20分
7:个人信誉贷款加10分
8:在国家人才网主办的国家网络招聘大会中纳入资料，供国家高端企业选择人才

22CYT12-Unit-V-E Waste and its Management.ppt

Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.

2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf

2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building

Advanced control scheme of doubly fed induction generator for wind turbine us...

This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.

Null Bangalore | Pentesters Approach to AWS IAM

#Abstract:
- Learn more about the real-world methods for auditing AWS IAM (Identity and Access Management) as a pentester. So let us proceed with a brief discussion of IAM as well as some typical misconfigurations and their potential exploits in order to reinforce the understanding of IAM security best practices.
- Gain actionable insights into AWS IAM policies and roles, using hands on approach.
#Prerequisites:
- Basic understanding of AWS services and architecture
- Familiarity with cloud security concepts
- Experience using the AWS Management Console or AWS CLI.
- For hands on lab create account on [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)
# Scenario Covered:
- Basics of IAM in AWS
- Implementing IAM Policies with Least Privilege to Manage S3 Bucket
- Objective: Create an S3 bucket with least privilege IAM policy and validate access.
- Steps:
- Create S3 bucket.
- Attach least privilege policy to IAM user.
- Validate access.
- Exploiting IAM PassRole Misconfiguration
-Allows a user to pass a specific IAM role to an AWS service (ec2), typically used for service access delegation. Then exploit PassRole Misconfiguration granting unauthorized access to sensitive resources.
- Objective: Demonstrate how a PassRole misconfiguration can grant unauthorized access.
- Steps:
- Allow user to pass IAM role to EC2.
- Exploit misconfiguration for unauthorized access.
- Access sensitive resources.
- Exploiting IAM AssumeRole Misconfiguration with Overly Permissive Role
- An overly permissive IAM role configuration can lead to privilege escalation by creating a role with administrative privileges and allow a user to assume this role.
- Objective: Show how overly permissive IAM roles can lead to privilege escalation.
- Steps:
- Create role with administrative privileges.
- Allow user to assume the role.
- Perform administrative actions.
- Differentiation between PassRole vs AssumeRole
Try at [killercoda.com](https://killercoda.com/cloudsecurity-scenario/)

cnn.pptx Convolutional neural network used for image classication

Convolutional Neural Network used for image classification

Design and optimization of ion propulsion drone

Electric propulsion technology is widely used in many kinds of vehicles in recent years, and aircrafts are no exception. Technically, UAVs are electrically propelled but tend to produce a significant amount of noise and vibrations. Ion propulsion technology for drones is a potential solution to this problem. Ion propulsion technology is proven to be feasible in the earth’s atmosphere. The study presented in this article shows the design of EHD thrusters and power supply for ion propulsion drones along with performance optimization of high-voltage power supply for endurance in earth’s atmosphere.

An improved modulation technique suitable for a three level flying capacitor ...

An improved modulation technique suitable for a three level flying capacitor ...

Seminar on Distillation study-mafia.pptx

Seminar on Distillation study-mafia.pptx

学校原版美国波士顿大学毕业证学历学位证书原版一模一样

学校原版美国波士顿大学毕业证学历学位证书原版一模一样

integral complex analysis chapter 06 .pdf

integral complex analysis chapter 06 .pdf

artificial intelligence and data science contents.pptx

artificial intelligence and data science contents.pptx

Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024

Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024

AI assisted telemedicine KIOSK for Rural India.pptx

AI assisted telemedicine KIOSK for Rural India.pptx

Comparative analysis between traditional aquaponics and reconstructed aquapon...

Comparative analysis between traditional aquaponics and reconstructed aquapon...

原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样

原版制作(Humboldt毕业证书)柏林大学毕业证学位证一模一样

Generative AI leverages algorithms to create various forms of content

Generative AI leverages algorithms to create various forms of content

Computational Engineering IITH Presentation

Computational Engineering IITH Presentation

Mechanical Engineering on AAI Summer Training Report-003.pdf

Mechanical Engineering on AAI Summer Training Report-003.pdf

Welding Metallurgy Ferrous Materials.pdf

Welding Metallurgy Ferrous Materials.pdf

哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样

哪里办理(csu毕业证书)查尔斯特大学毕业证硕士学历原版一模一样

22CYT12-Unit-V-E Waste and its Management.ppt

22CYT12-Unit-V-E Waste and its Management.ppt

2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf

2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf

Advanced control scheme of doubly fed induction generator for wind turbine us...

Advanced control scheme of doubly fed induction generator for wind turbine us...

Null Bangalore | Pentesters Approach to AWS IAM

Null Bangalore | Pentesters Approach to AWS IAM

cnn.pptx Convolutional neural network used for image classication

cnn.pptx Convolutional neural network used for image classication

Design and optimization of ion propulsion drone

Design and optimization of ion propulsion drone

- 1. EQUILIBRIUM OF RIGID BODIES Page 1 CHAPTER 2 EQUILIBRIUM OF RIGID BODIES CONTENT OF THE TOPIC: I) Equilibrium of co-planar forces Analytical and graphical conditions of equilibrium Analytical conditions of equilibrium graphical conditions of equilibrium Different types of supports and their reactions Free body diagram Concept Examples based on to draw F.B.D. Different type of supports Lami’s Theorem Concept Procedure to solve the problems Problems based on Lami’s Theorem II) Friction Concept of Friction Problems on horizontal plane and inclined plane Problems on ladder III) Types of Problems Problems on equilibrium Problems on compound beam and frame with hinged joint Problems on pulleys Friction problem on inclined plane Problems on ladder
- 2. EQUILIBRIUM OF RIGID BODIES Page 2 Equilibrium of Force: Any system of forces that keeps the body at rest is said to be in equilibrium i.e. the state of the body is not affected by the action of the force system in equilibrium. Equilibrium is applicable to those systems of forces whose resultant action is zero. Equilibrant: 1) A force that brings the system of forces in equilibrium is known as Equilibrant. 2) It is always equal, opposite and collinear with the resultant of the system. 3) When a system of forces is in equilibrium, its Equilibrant and resultant, both are zero. Free Body: Consider a body is resting against various supports and suppose all such supports are replaced by their reactions exerted on the body, such body is known as free body. Free Body Diagram: A diagram of the body in which the body under consideration is freed from all the contact surfaces and all the forces acting on it (including the reactions at contact surfaces) are drawn is called a free body diagram. Add figure Application of Free Body Diagram (F.B.D.): 1) A Free Body Diagram (F.B.D.) is helpful in analyzing the equilibrium of a constrained body. 2) A Free Body Diagram (F.B.D.) is helpful in finding reactions at the supports and internal forces in the members of frames and trusses. Moment Law of Forces:
- 3. EQUILIBRIUM OF RIGID BODIES Page 3 Algebraic sum of the moments of all the forces taken about any point in the plane of forces should be zero. ∑M = 0 Consider two forces P and Q acting on a body as shown in Fig. below. Let the angle between the two forces be θ. The diagonal AC of the parallelogram ABCD represents the resultant. Drop a perpendicular CE to AB. Now, the resultant R of P and Q is given by, R = AC R2 = AE2 + CE2 R = √𝐴𝐸2 + 𝐶𝐸2 R = √(𝐴𝐵 + 𝐵𝐸)2 + 𝐶𝐸2 But AB = P BE = BC cos θ = Q cos θ CE = BC sin θ = Q sin θ R = √(𝑃 + 𝑄 𝑐𝑜𝑠𝜃)2 + (𝑄 𝑠𝑖𝑛𝜃)2 R = √ tan α = 𝐶𝐸 𝐴𝐸 tan α = 𝑄 sin 𝜃 𝑃+𝑄 cos 𝜃 α = tan-1( 𝑄 sin 𝜃 𝑃+𝑄 cos 𝜃 ) ---------------------------------- (2) Particular cases: 1) θ = 900 R= √𝑃2 + 𝑄2 2) θ = 00 R= P + Q 3) θ = 1800 R= P - Q Lami’s Theorem: “If three forces acting at a point are in equilibrium, each force will be proportional to the sine of the angle between the other two forces.”
- 4. EQUILIBRIUM OF RIGID BODIES Page 4 Fig. 1 Suppose three forces P, Q and R are acting at a point O and they are in equilibrium as shown in Fig. 1 above. Let, α = Angle between force P and Q β = Angle between force Q and R γ = Angle between force R and P Then according to the Lami’s theorem P α sine of the angle between Q and R α sin β 𝑃 sin(𝛽) = constant Similarly, 𝑃 sin(ϒ) = constant 𝑃 sin(𝛼) = constant 𝑃 sin(𝛽) = 𝑃 sin(ϒ) = 𝑃 sin(𝛼) --------(1) Proof of Lami’s Theorem: The three forces are acting on a point, are in equilibrium and hence they can be represented by the three sides of the triangle taken in the same order. Now draw the force triangle as shown in following Figure (a).
- 5. EQUILIBRIUM OF RIGID BODIES Page 5 Figure (a). Applying the sine rule, we get 𝑃 sin(180−𝛽) = 𝑄 sin(180−ϒ) = 𝑅 sin(180−𝛼) This can also be written 𝑃 sin(𝛽) = 𝑄 sin(ϒ) = 𝑅 sin(𝛼) --------(2) This is the same equation as in equation (1) above Types of beam supports: 1) Simple support: It is a theoretical case in which the ends of the beam are simply supported or rested over the supports. The reactions are always vertical as shown in Fig.1 below Fig.1 Simple Support
- 6. EQUILIBRIUM OF RIGID BODIES Page 6 It opposes downward movement but allows rotation and horizontal displacement or movement. 2) Pin or hinged Support: In such case, the ends of the beam are hinged or pinned to the support as shown in Fig.2 below. Fig.2 (A) Hinged Support Fig.2 (B) Hinged Support The reaction may be either vertical or inclined depending upon the type of loading. If the loads are vertical the reaction is vertical as shown in Fig. 2 (A) and when the applied loads are inclined the reaction is inclined as shown in Fig. 2 (B). The main advantage of hinged support is that the beam remains stable i.e. there is only rotational motion round the hinge but no translational motion of the beam i.e. hinged support opposes displacement of beam in any direction but allows rotation. 3) Roller Support: In such cases, the end of the beam is supported on roller as shown in Fig. 3 below. Fig. 3 Roller Support The reaction is always perpendicular to the surface on which rollers rest or act as shown in Fig. 3. The main advantage of the roller support is that, the support can move easily in
- 7. EQUILIBRIUM OF RIGID BODIES Page 7 the direction of expansion or contraction of the beam due to change in temperature in different seasons. 4) Fixed Support: It is also called as Built-in-supports. It is rigid type of support. The end of the beam is rigidly fixed in the wall as shown in Fig. 4 below. Fig. 4 Fixed Support It produces reactions Ra in any direction and a moment Ma as shown in Fig. 4 above. Problems: 1) A system of connected flexible cables as shown in Fig. below. It is supporting two vertical forces 200 N and 250 N at points B and D. Determine the forces in various segments of the cable. 2) Find a. Tension in portion AB, BC and CD string b. Magnitude of P1 and P2 3) Find the reactions at the support for a bent supported and loaded as shown in Fig. below. (January 2002 12 Mks).
- 8. EQUILIBRIUM OF RIGID BODIES Page 8 Problems on Cylinder: 1) Two cylinders P and Q of 1m diameter and weighing 1000 N each are supported as shown in Fig. below. Neglect friction at contact points. Find the reactions at A, B, C and D. (January 2001 12 Mks). Problems on Pulleys: 1) Blocks A and B are connected by links and supported as shown in Fig. below. If block A weighs 300 N and block B weighs 150 N. Find the maximum and minimum values of P for which the blocks are just in equilibrium. µ = 0.25 Assignment No. 2 Equilibrium Q1. Define and explain the term ‘Equilibrium’. What do you understand by ‘Equilibrant’? Q2. State and explain ‘Principles of Equilibrium’ or ‘Equilibrium law’. Q3. What are the different conditions of equilibrium? Q4. What are the different conditions of equilibrium for: A) Non-concurrent Force System B) Concurrent Force System Q5. What do you understand by ‘Free Body’ and ‘Free Body Diagram’? What is the application of Free Body Diagram? Q6. State ‘Lami’s Theorem’. Q7. Draw the Free Body Diagram for following System:
- 9. EQUILIBRIUM OF RIGID BODIES Page 9 Q9) Two smooth cylinders, each of weight 1000N and Diameter 30 cm connected by a string of 40 cm & rest upon a smooth horizontal surface, supporting a third cylinder of weight 2000N & diameter of 30 cm which is above the two cylinder. Find out the reactions, pressure at contact surface and tension in the string.
- 10. EQUILIBRIUM OF RIGID BODIES Page 10 1. Determine the reactions at 1 and 2. Assume all the surfaces to be smooth. 2. Determine the reactions at A and B. Assume all the surfaces to be smooth. 3. Two spheres each of weight 1000 N and of radius 25 cm rest in a horizontal channel of width 90 cm as shown in following Fig. Find the reactions at point of contact. Assume all the surfaces to be smooth.
- 11. EQUILIBRIUM OF RIGID BODIES Page 11 4. Two identical rollers, each of weight 1000 N, are supported by a inclined plane and a vertical wall as shown in Fig. below. Find the reactions at point of contacts 1, 2 and 3. Assume all the surfaces to be smooth. 5. Two cylinders A and B, of weight 1000 N and 500 N respectively, are supported by a inclined plane and a vertical wall as shown in Fig. below. The radius cylinders A and B are 250 mm and 157 mm respectively. Find the reactions at point of contacts. Assume all the surfaces to be smooth.
- 12. EQUILIBRIUM OF RIGID BODIES Page 12 6. Two cylinders A and B, of weight 1000 N and 500 N respectively, are supported by a inclined plane and a vertical wall as shown in Fig. below. The radius cylinders A and B are 250 mm and 157 mm respectively. Find the reactions at point of contacts. Assume all the surfaces to be smooth. 7. Two cylinders A and B, of weight 1000 N and 500 N respectively, are supported by a inclined plane and a vertical wall as shown in Fig. below. The radius cylinders A and B are 250 mm and 157 mm respectively. Find the reactions at point of contacts. Assume all the surfaces to be smooth.
- 13. EQUILIBRIUM OF RIGID BODIES Page 13 8. Two cylinders A and B, of weight 1000 N and 500 N respectively, are supported by a inclined plane and a vertical wall as shown in Fig. below. The radius cylinders A and B are 250 mm and 157 mm respectively. Find the reactions at point of contacts. Assume all the surfaces to be smooth. 9. Two cylinders A and B, of weight 1000 N and 500 N respectively, are supported by a inclined plane and a vertical wall as shown in Fig. below. The radius cylinders A and B are 250 mm and 157 mm respectively.
- 14. EQUILIBRIUM OF RIGID BODIES Page 14