MECHANICS OF SOLIDS Credit Hours: 6

Transcription

1 MECHANICS OF SOLIDS Credit Hours: 6 Teaching Scheme Theory Tutorials Practical Total Credit Hours/week Marks A. Objective of the Course: Objectives of introducing this subject at second year level in civil branches are: B. Outline of the course: No. Title of the unit Number of hours. Introduction 0 Fundamentals of Statics 08. Applications of Fundamentals of Statics Friction Centroid and Moment of Inertia Simple Stresses & Strains 0 7. Stresses in Beams Torsion Principle Stresses 04 Total hours (Theory): 56 Total hours (Lab):8 Total hours (Tutorial):00 Total hours: 84

2 C. Detailed Syllabus: Theory Course Content No Topic Name Hours Introduction. Terminologies: space, time, particle, rigid body, deformable body. Force: Definition, categorization of forces, Characteristics of a force, System of forces and resolution of forces.. Principles of mechanics: Principles of Transmissibility, superposition, Gravitational Law and Parallelogram Law of Forces. Fundamentals of Statics 8. Force and Force system: System of Forces its definition and application in Engineering.. Coplanar concurrent force system: Derivation of resultant force and equilibrant force using analytical and graphical methods. Triangle law of forces and Polygon law of forces.. Equilibrium of rigid bodies: Conditions of equilibrium, Lami s theorem and its derivation. Concept of Free body diagram in engineering. Application of Lami s theorem in various problems..4 Coplanar non-concurrent forces: Definition of moment, couple and its effect on rigid bodies. Properties of couple, equivalent force couple system with examples, Varignon s theorem and its derivation..5 Resultant of Coplanar non-concurrent Force system: Calculation of resultant force in coplanar non-concurrent force system by analytical and graphical methods. Analysis of Determinate Beams 8. Classification of loads, supports and beams. Support Reactions: Calculation of support reactions for determinate beams subjected different loads viz. (i) Concentrated loads and moment, (ii) Uniformly distributed load, and (iii) Uniformly Varying loads.. Internal forces in beams: Definition of shear force and bending moment. Correlation between loading, shear force & bending moment in beams..4 Shear Force and Bending Moment Diagrams: Bending 4 moment and shear force diagrams for beams subjected to; i) Concentrated loads and moment, (ii) Uniformly distributed load, and (iii) Uniformly Varying loads. Point of Contra flexure and maximum bending moment in a beam. 4 Concepts and Application of Static Friction 6 4. Introduction: Theory, Classification and laws of Static and Dynamic friction. 4. Glossary of Terms: Angle of friction, Coefficient of friction, Angle of repose and Cone of friction. 4. Application of Static Friction - (a) Block friction: Solutions of problems involving block friction in horizontal and inclined planes. (b) Ladder Friction: Solution of various problems. (c) Wedge, Belt and Rope Friction: Solution of various problems. 5 Centroid and moment of inertia 9

3 5. Centroid: Definition, concept, and evaluation of centroid for one-dimensional standard geometry viz. horizontal, vertical, inclined and circular curved lines. 5. Centroid of Standard Geometrical shapes: Determination of centroid for standard two-dimensional and three-dimensional shapes viz. rectangular, triangular, circular, semi-circular, quarter circular, circular segments, cylindrical, conical, spherical and cubical shapes. 5. Calculation of Centroid: Calculation of centroid for composite lines, areas and volumes. 5.4 Pappus-Guldinas Theorem: Pappus Guldinus theorem and its application in calculating surface area and volume. 5.5 Introduction to Moment of Inertia: Definition and concept of Moment of Inertia. Perpendicular axis, Parallel axis theorem, Polar Moment of inertia, and radius of gyration. 5.6 Moment of Inertia for Planar cross-sections: Determination of Moment of Inertia for planar sections using parallel axis theorem for standard lamina. 5.7 Moment of Inertia for composite planar elements: Determination of moment of Inertia for composite lamina. 6 Simple stresses & strains 0 6. Introduction: Definition and types of simple stresses (direct and indirect) and strains (linear and lateral) in an element and its importance in engineering. 6. Relation between stress and strain: Hooke s law, Poisson s ratio, Modulus of Elasticity, Rigidity, and Bulk modulus. 6. Stresses and strains Members: Evaluation of stresses and 4 strains in members subjected to axial and shear loading for homogenous, composite, prismatic and tapered sections. 6.4 Thermal Stresses: Evaluation of stresses in elements subjected to temperature effects in homogeneous and composite members 6.5 Inter-relationship between various Moduli: Relationship between modulus of elasticity, rigidity, bulk modulus and Poisson s ratio with problems. 6.6 Multidirectional Stresses: Volumetric strains, effect of multidirectional stresses on homogeneous members. 7 Stresses in Beams 6 7. Theory of Pure Bending Assumption, theory and derivation of equation for pure bending. Determination of bending stresses at various sections. 7. Flexural stresses Section modulus and determination of flexural stress distribution in beams of various cross sections. 7. Equation of Shearing stress Derivation of equation for shear stress across the cross section in a beam. 7.4 Shear stresses Qualitative and Quantitative determination of shear stress distribution in beams having various cross sections. 8 Torsion 0 8. Equation of Pure Torsion: Definition of Torsion, Assumption and derivation of equation for pure torsion in circular shafts, Torsional rigidity and its application. 8. Stresses due to Torsion: Torque generated due to Power transmitted in shaft. Stresses generated in members subjected to circulatory motion in circular and hollow circular shafts. 9 Principle stresses Introduction: Two-dimensional stress system. Evaluation of stresses in an inclined plane for members subjected to orthogonal

4 stresses. Definition of principal plane, principal stresses, angle of obliquity, and resultant stress. 9. Principal Stress and Strain: Evaluation of Principal plane and principal stresses using analytical method. 9. Analysis of Principal stresses and principal planes for twodimensional stress system. 9.4 Application of Mohr s circle and ellipse of stress. Total 56 Laboratory Course Content No Topic name Hours Equilibrium of coplanar concurrent forces Equilibrium of coplanar non-concurrent forces Equilibrium of coplanar parallel forces: Determination of reactions of simply supported beam 4 Verification of principle of moment: Bell crank lever 5 Determination of member force in a triangular truss 6 Determination of coefficient of static friction using inclined plane 7 Determination of parameters of machines (Any two). Wheel and differential axles. Single purchase crab. Double purchase crab 4. System of pulleys 8 Determination of hardness of metals: Brinell /Vicker/Rockwell hardness test 9 Determination of impact of metals: Izod/Charpy impact test 0 Determination of compression test on. Metals mild steel and cast iron. Timber along and parallel to the grains Determination of tensile strength of metals Determination of shear strength of metals Total 8 D. Instructional Method and Pedagogy:. For a real industrial building having roof truss arrangement, (a) take photograph & identify type of truss, (b) draw sketch of truss with all geometrical dimension, cross sections details, type of joints, type of support conditions (c) prepare a model of truss (d) identify & determine types of load acts on it (d) determine support reactions & member forces due to dead load & live load only.. Take a case of the Mery-Go-Round used in the fun park. Draw its sketch showing radius of wheel, no of seats, capacity of each seats and other related information. Determine the amount of resultant produced at the centre of wheel during rest position, when (i) it is fully loaded () it is 0% loaded with symmetric arrangement. Draw support arrangement and determine support reactions. Also determine amount of torque required to start its operation.

5 . Prepare working models for various types of beams with different shape of cross section, supporting conditions and study the effect of cross section on the deflection of beams. 4. Prepare working model of simple lifting machine using different types of pulley systems and calculate various parameters like load factor, velocity ratio, law of machine, efficiency of machine etc. E. Students learning outcomes: After studying this subject students will be able to: Apply fundamental principles of mechanics & principles of equilibrium to simple and practical problems of engineering. Determine reaction at supports for determinate beam subjected to various loading and support conditions. Determine centroid and moment of inertia of a different geometrical shape and able to understand its importance. Understand the fundamentals of friction and its application in general problems. Understand the different types of stresses and strains generated in the member subjected to axial, bending, shear torsion & thermal loads. Know behaviour & properties of engineering materials. F. Recommended Study Material: Text Books:. Applied Mechanics S. B. Junarkar & H. J. Shah-Charotar Publication. Engineering Mechanics : Bhogayata, Shah, Vora & Dhankot - Tata McGraw hills Reference Books:. Engineering Mechanics by G. S. Sawhney; PHI New Delhi. Mechanics of Materials: Beer and Johnston, TMH. Mechanics of Materials: Gere & Timoshenko; CBS Publishers & Distributors, Delhi 4. Mechanics of Materials: Hibbler R C; Pearson Education 5. Strength of materials; Ramamutthram 6. Engineering Mechanics of Solids: Popov E.P; Prentice Hall of India, New Delhi