Mechanics of Solids

Course Objectives:
The main objective of this course is to provide fundamental knowledge and skills to solid mechanics. After completion of this course the students will be able to know in depth knowledge of general stress and strain.

Course outline:

1. Load on Structure and Response of Material(1 hour)
1. General Load on Structure and its Effects
2. Elastic and Non-elastic Response of  Solids
3. Isotropy, Anisotropy, Continuity and Homogeneity
4. Effect of temperature on Elastic and Plastic range of Solids


2. Stress Tensor(6 hours)
1. Definition
2. Stress at a point
3. Stresses on Structure due to General Load
4. Stress Notation and Sign Convention
5. Stresses Acting on Arbitrary Planes
6. Transformation of Stress and Principal Stress
7. Stress on Deformable Body
1. Differential Equation in Rectangular Co-ordinate System
2. Differential Equation in Polar Co-ordinate System
3. Application of Differential Equation and Its Solution  
8. Relevant Problems


3. Deformable Body and Strain Tensor(4 hours)
1. Definition
2. Strain at a point
3. Strain on Structure due to General Load
4. Strain Notation and Sign Convention
5. Strain Acting on Arbitrary Planes
6. Transformation of Strain and Principal Strain
7. Small Displacement Theory
8. Volumetric Strain
9. Relevant Problems


4. General Hooke’s Law (2 hours)
1. Definition
2. Internal Energy Density
1. Strain Energy
2. Complementary Strain Energy
3. Anisotropic and Isotropic Elasticity
4. Equations of Thermo-elasticity for Isotropic Materials


5. Deflections and Slope of Statically Determinate and Indeterminate Structures(6 hours)
1. Definition
2. Application in Engineering Field
3. Energy Method
4. Unit Force Method
5. Castigliano’s Theorem
6. Relevant Problems


6. Curved Beams(4 hours)
1. Definition
2. Circumferential Stress in Curved Beams
3. Radial Stresses
4. Deflections
5. Statically Indeterminate Closed Ring
6. Relevant Problems


7. Non Symmetrical Bending of Straight Beams(4 hours)
1. Definition
2. Bending Stresses due to Non symmetrical Bending
3. Deflections due to Unsymmetrical Bending
4. Relevant Problems


8. Thick- Wall Cylinders(4 hours)
1. Basic Relations
2. Stresses for a cylinder with Open and Closed Ends
3. Linear and Volumetric Strain
4. Criteria of Failure
5. Composite Thick Cylinder
6. Stress Solution for Temperature Change Only
7. Relevant Problems


9. Torsion(6 hours)
1. Definition
2. Torsion of Non Circular Solid Section
1. Saint- Venant’s Semi- Inverse Method
2. The Prandtl Elastic Membrane Analogy
3. Torsion of a Narrow Rectangular Cross Section
3. Torsion of Hollow Thin Wall Section
4. Relevant Problems


10. Shear Centers for Thin- Wall Beam Cross Sections(4 hours)
1. Shear Flow in thin- Wall Beam Cross Sections
2. Shear Centre for a Channel Section
3. Composite Beams
4. Box Beams
5. Relevant Problems


11. Contact Stresses (2 hours)
1. Introduction; the Problem of Determining Contact Stresses
2. Point and Line Contact
3. Assumptions Involved in the Solution
4. Expressions for Principal Stresses


12. Introduction to Plastic Range Stress and Strain(2 hours)
1. Curve Beam
2. Structure Having Non Symmetrical Bending
3. Thick Wall Cylinder
4. Torsion member

References

1. A.p. Boresi and O. M. Sidebottom, ‘Advanced Mechanics of Materials’, Wiley, Fourth Edition
2. Ugural and Fenster, ‘ Advanced Strength and Applied Elasticity’, Elsevier, Second Edition, S. I. Version
3. Popov, E.P., ‘Engineering Mechanics of Solids
4. Hibbler R.C., Mechanics of Solids

Practical:

1. Nonlinear Behaviour of Materials in Tension   
1. Tensile Test on a Rubber Specimen
2. Creep Test and relaxation Test on a Plastic Specimen
2. Deflections and Stresses in Indeterminate Shafts of Beams:
1. Control of stresses and deflections using a central support
2. Application of Maxwell’s reciprocity law
3. Torsion of Non Circular tubes:
1. Torsion test of circular, square and rectangular closed thin walled tubes
2. Torsion of closed and open circular thin- walled tubes
4. Curved Beams and Thick- Walled Cylinders
1. Deflections and Stresses in curved beams
2. Stress and strain in thick walled cylinders
5. Shear stresses in beams and the shear centre:
1. Shear stresses in beams and stiffness effects for layered beams
2. Finding the shear centre for a beam with a channel cross section
6. Effects of Suddenly Applied Dynamic Loads:
1. A tension member subjected to dynamic loads
2. Sudden transverse loading of a beam

Evaluation scheme:
The questions will cover all the chapters of the syllabus. The evaluation scheme will be as indicated in the table below.