Mechanics of Solids

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Mechanics of Solids [3 1 0 4] CIE 101 / 102 First Year B.E. Degree

Mechanics of Solids

PART- I Mechanics of Rigid Bodies

PART- II Mechanics of Deformable Bodies

COURSE CONTENT IN BRIEF

PART I Mechanics of Rigid Bodies 1. Resultant of concurrent and non-concurrent coplanar forces. 2. Equilibrium of concurrent and non-concurrent coplanar forces. 3. Centroid of plane areas 4. Moment of Inertia of plane areas 5. Kinetics: Newton’s second law, D’Alembert’s principle, Work- Energy, and Impulse- Momentum principle. Mechanics of Deformable bodies

PART II

6. Simple stresses and strains 7. Statically indeterminate problems and thermal stresses 8. Stresses on inclined planes 9. Stresses due to fluid pressure in thin cylinders

Books for Reference 1.Engineering Mechanics, by Meriam & Craige, John Wiley & Sons. 2.Engineering Mechanics, by Irwing Shames, Prentice Hall of India. 3.Mechanics for Engineers, by Beer and Johnston, McGraw Hills Edition 4.Engineering Mechanics, by K.L. Kumar, Tata McGraw Hills Co. 5. Machanics of Materials, by E.P.Popov 6. Machanics of Materials, by E J Hearn 7. Strength of materials, by Beer and Johnston 8. Strength of materials, by F L Singer & Andrew Pytel 9. Strength of Materials, by B.S. Basavarajaiah & P. Mahadevappa 10. Strength of Materials, by Ramamruthum 11. Strength of Materials, by S S Bhavikatti

PART - I MECHANICS OF RIGID BODIES

PART - I

Mechanics of Rigid Bodies

INTRODUCTION Definition of Mechanics : In its broadest sense the term ‘Mechanics’ may be defined as the ‘Science which describes and predicts the conditions of rest or motion of bodies under the action of forces’. This Course on Engineering Mechanics comprises of Mechanics of Rigid bodies and the sub-divisions that come under it.

Branches of Mechanics Engineering Mechanics Mechanics of Solids Deformable Bodies

Mechanics of Fluids

Rigid Bodies

Ideal Fluids

Viscous Fluids

Compres Fluids

Statics Dynamics

Theory of Theory of Plasticity Strength of Elasticity Materials

Kinematics

Kinetics

Concept of Rigid Body : It is defined as a definite amount of matter the parts of which are fixed in position relative to one another under the application of load. Actually solid bodies are never rigid; they deform under the action of applied forces. In those cases where this deformation is negligible compared to the size of the body, the body may be considered to be rigid.

Particle A body whose dimensions are negligible when compared to the distances involved in the discussion of its motion is called a ‘Particle’. For example, while studying the motion of sun and earth, they are considered as particles since their dimensions are small when compared with the distance between them.

Force It is that agent which causes or tends to cause, changes or tends to change the state of rest or of motion of a mass. A force is fully defined only when the following four characteristics are known: (i) Magnitude (ii) Direction (iii) Point of application (iv) Sense.

Force: characteristics of the force 100 kN are : (i) Magnitude = 100 kN (ii) Direction = at an inclination of 300 to the x-axis (iii) Point of application = at point A shown (iv) Sense = towards point A A 100 kN 300

Scalars and Vectors A quantity is said to be a ‘scalar’ if it is completely defined by its magnitude alone. Example : Length, Area, and Time. A quantity is said to be a ‘vector’ if it is completely defined only when its magnitude and direction are specified. Example : Force, Velocity, and Acceleration.

Principle of Transmissibility : It is stated as follows : ‘The external effect of a force on a rigid body is the same for all points of application along its line of action’. P A B P

For example, consider the above figure. The motion of the block will be the same if a force of magnitude P is applied as a push at A or as a pull at B. P O The same is true when the force is applied at a point O. P

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