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:
 Load on Structure and Response of Material(1 hour)
 General Load on Structure and its Effects
 Elastic and Nonelastic Response of Solids
 Isotropy, Anisotropy, Continuity and Homogeneity
 Effect of temperature on Elastic and Plastic range of Solids
 Stress Tensor(6 hours)
 Definition
 Stress at a point
 Stresses on Structure due to General Load
 Stress Notation and Sign Convention
 Stresses Acting on Arbitrary Planes
 Transformation of Stress and Principal Stress
 Stress on Deformable Body
 Differential Equation in Rectangular Coordinate System
 Differential Equation in Polar Coordinate System
 Application of Differential Equation and Its Solution
 Relevant Problems
 Deformable Body and Strain Tensor(4 hours)
 Definition
 Strain at a point
 Strain on Structure due to General Load
 Strain Notation and Sign Convention
 Strain Acting on Arbitrary Planes
 Transformation of Strain and Principal Strain
 Small Displacement Theory
 Volumetric Strain
 Relevant Problems
 General Hooke’s Law (2 hours)
 Definition
 Internal Energy Density
 Strain Energy
 Complementary Strain Energy
 Anisotropic and Isotropic Elasticity
 Equations of Thermoelasticity for Isotropic Materials
 Deflections and Slope of Statically Determinate and Indeterminate Structures(6 hours)
 Definition
 Application in Engineering Field
 Energy Method
 Unit Force Method
 Castigliano’s Theorem
 Relevant Problems
 Curved Beams(4 hours)
 Definition
 Circumferential Stress in Curved Beams
 Radial Stresses
 Deflections
 Statically Indeterminate Closed Ring
 Relevant Problems
 Non Symmetrical Bending of Straight Beams(4 hours)
 Definition
 Bending Stresses due to Non symmetrical Bending
 Deflections due to Unsymmetrical Bending
 Relevant Problems
 Thick Wall Cylinders(4 hours)
 Basic Relations
 Stresses for a cylinder with Open and Closed Ends
 Linear and Volumetric Strain
 Criteria of Failure
 Composite Thick Cylinder
 Stress Solution for Temperature Change Only
 Relevant Problems
 Torsion(6 hours)
 Definition
 Torsion of Non Circular Solid Section
 Saint Venant’s Semi Inverse Method
 The Prandtl Elastic Membrane Analogy
 Torsion of a Narrow Rectangular Cross Section
 Torsion of Hollow Thin Wall Section
 Relevant Problems
 Shear Centers for Thin Wall Beam Cross Sections(4 hours)
 Shear Flow in thin Wall Beam Cross Sections
 Shear Centre for a Channel Section
 Composite Beams
 Box Beams
 Relevant Problems
 Contact Stresses (2 hours)
 Introduction; the Problem of Determining Contact Stresses
 Point and Line Contact
 Assumptions Involved in the Solution
 Expressions for Principal Stresses
 Introduction to Plastic Range Stress and Strain(2 hours)
 Curve Beam
 Structure Having Non Symmetrical Bending
 Thick Wall Cylinder
 Torsion member
References
 A.p. Boresi and O. M. Sidebottom, ‘Advanced Mechanics of Materials’, Wiley, Fourth Edition
 Ugural and Fenster, ‘ Advanced Strength and Applied Elasticity’, Elsevier, Second Edition, S. I. Version
 Popov, E.P., ‘Engineering Mechanics of Solids
 Hibbler R.C., Mechanics of Solids
Practical:
 Nonlinear Behaviour of Materials in Tension
 Tensile Test on a Rubber Specimen
 Creep Test and relaxation Test on a Plastic Specimen
 Deflections and Stresses in Indeterminate Shafts of Beams:
 Control of stresses and deflections using a central support
 Application of Maxwell’s reciprocity law
 Torsion of Non Circular tubes:
 Torsion test of circular, square and rectangular closed thin walled tubes
 Torsion of closed and open circular thin walled tubes
 Curved Beams and Thick Walled Cylinders
 Deflections and Stresses in curved beams
 Stress and strain in thick walled cylinders
 Shear stresses in beams and the shear centre:
 Shear stresses in beams and stiffness effects for layered beams
 Finding the shear centre for a beam with a channel cross section
 Effects of Suddenly Applied Dynamic Loads:
 A tension member subjected to dynamic loads
 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.
Chapter 
Hours 
Marks distribution* 
1 
1 
2 
2 
6 
10 
3 
4 
8 
4 
2 
4 
5 
6 
10 
6 
4 
8 
7 
4 
8 
8 
4 
8 
9 
6 
10 
10 
4 
8 
11 
2 
2 
12 
2 
2 
Total 
45 
80 
*Note: There may be minor deviation in marks distribution.
