Strength of Materials

Course Objective:
To analyze and solve problems related to different types of stress and strain and to design basic components of structure and machines on the basis of stiffness, strength and stability.

1. Introduction(2 hours)
1. Types of Stresses and strains
2. Normal stress, shear stress, bearing stress
3. Normal strain, shear strain
4. Ultimate stress, allowable stress, factor of safety


2. Stress and strain – axial load(6 hours)
1. Stress – strain diagram
2. Hooke's law, modulus of elasticity
3. Deformation under axial load
4. Temperature effects
5. Poisson’s Ratio
6. Multi-axial loading, Generalized Hooke’s Law
7. Bulk Modulus
8. Shearing Strain
9. Relationship among modulus of elasticity, shear stress and Poisson’s ratio
10. Stress Concentration and Plastic Deformation
11. Statically Indeterminate problems


3. Pure Bending(5 hours)
1. Introduction of pure or simple bending
2. Deformation of a symmetric member in pure bending in elastic range. (Relationship between transverse loads, bending moment and bending stresses, position of neutral axis and neutral layer)
3. Beams with composite section.
4. Stress concentration, plastic deformation
5. Eccentric axial loading
6. Unsymmetrical loading.


4. Torsion(5 hours)
1. Introduction Torque, Shaft, Torsion
2. Stress and deformation in a uniform shaft in elastic range
3. Torsion moment diagram.
4. Torsion formula for circular cross-section
5. Statically Indeterminate Shaft
6. Design of Transmission of shaft (by strength and stiffness)
7. Comparison between hollow and solid shaft.
8. Shafts in series and parallel
9. Composite shafts
10. Stress concentrations in circular shafts.


5. Transverse loading(3 hours)
1. Basic assumptions and distribution of normal stress.
2. Relationship between shear stress and shear force in a beam.
3. Distribution of Shear stress in common beam sections.


6. Transformation of stress and strain(6 hours)
1. Uniaxial stress system, biaxial stress system, pure shear stress system.
2. General plane stress system, principal stresses, maximum shearing stress, principal planes
3. Graphical method: Mohr’s circle for plane stress
4. Application to three- dimensional state of stress
5. Yield criteria for ductile and brittle material.


7. Deflection of Beams by Integration Method(6 hours)
1. General deflection equation for beams.
2. Deflection equation for beams with different end conditions.
3. Method for superposition.
4. Deflection in statically indeterminate beams.
5. Direct determination of the elastic curve from the load-distribution.


8. Deflection of Beams by Moment- area Method(4 hours)
1. Moment- Area Theorems.
2. Application to symmetrical structure and symmetrical loading, unsymmetrical structure and symmetrical loading, symmetrical structure and unsymmetrical loading.
3. Maximum deflection in beams.


9. Design of Beams and shafts(5 hours)
1. Basic Consideration for the design of prismatic beams ( for ductile, brittle material and for short and long beam)
2. Principal stresses in beams
3. Design of prismatic beams


10. Columns(3 hours)                                                     
1. Introduction: Strut, column, buckling load
2. Euler’s formula for different end conditions.
3. Design of columns under central and eccentric loading.

Practical:

1. Material Properties in simple bending and compression test.
2. Torsion test: Behavior of ductile and brittle materials in torsion, shear modulus
3. Stresses and strains in thin wall cylinders
4. Column behavior and buckling: effect of end conditions on buckling load of beams.
5. Beam reactions: Relationship between deflection and  transverse load, end conditions, Young’s modulus of elasticity, moment of inertia

References:

1. F.P. Beer and E. R. Johnson, “ Mechanics  of Materials”, McGraw Hill,
2. R.K. Rajput, “ Strength of Materials”, S.chand & Co. Ltd.,
3. E. P. Popov, “ Engineering Mechanics of Solids”, Prentice Hall Inc., Englewood Cliffs, N. J.

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

Chapters	Hours	Mark distribution *
1&2	8	16
3	5	8
4	5	8
5	3	8
6	6	12
7&8	10	16
9	5	8
10	3	4
Total	45	80

*Note: There may be minor deviation in mark distribution