##
__Detailed Syllabus of Strength of Materials__

## COURSE OBJECTIVE:

1. This subject is useful for a detailed study of forces and their effects.

2. To study the rigid and deformable solids.

3. To give an ability to calculate stresses and deformations of objects under external forces.

4. To give an ability to apply the knowledge of strength of materials on engineering applications and design problems

Strength of Materials |

## EXPECTED OUTCOMES:

1. Describe the concepts and principles, understand the theory of elasticity including strain/displacement and Hooke’s law relationships; and perform calculations, relative to the strength and stability of structures and mechanical components;

2. Define the characteristics and calculate the magnitude of combined stresses in individual members and complete structures; analyze solid mechanics problems using classical methods and energy methods;

3. Analyze various situations involving structural members subjected to combined stresses by application of Mohr’s circle of stress; locate the shear centre of thin wall beams;

4. Calculate the deflection at any point on a beam subjected to a combination of loads; solve for stresses and deflections of beams under unsymmetrical loading; apply various failure criteria for general stress states at points; solve torsion problems in bars and thin-walled members;

##
__Detailed Topics in Units:__

## UNIT 1:

## Simple Stresses and Strains-

Concept of stress and strain, St. Venant’s principle, stress and strain diagram, Elasticity and plasticity – Types of stresses and strains, Hooke’s law– stress-strain diagram for mild steel – Working stress – Factor of safety – Lateral strain, Poisson’s ratio and volumetric strain – Elastic modules and the relationship between them –Bars of varying section – composite bars – Temperature stresses. Strain Energy – Resilience– Gradual, sudden, impact and shock loadings – simple applications

## Compound Stresses and Strains-

Two-dimensional system, stress at a point on a plane, principal stresses and principal planes, Mohr circle of stress, the ellipse of stress and their applications. Two-dimensional stress-strain system, principal strains and principal axis of strain, circle of strain and ellipse of strain, relationships between elastic constants.

## UNIT 2:

## Bending moment and Shear Force Diagrams-

Bending moment (BM) and shear force (SF) diagrams.BM and SF diagrams for cantilevers simply supported and fixed beams with or without overhangs. Calculation of maximum BM and SF and the point of contra-flexure under concentrated loads, uniformly distributed loads over the whole span or part of the span, the combination of concentrated loads (two or three) and uniformly distributed loads, uniformly varying loads, application of moments.

## UNIT 3:

## Flexural Stresses-

Theory of simple bending – Assumptions – Derivation of the bending equation: M/I = f/y = E/R - Neutral axis – Determination of bending stresses – Section modulus of rectangular and circular sections (Solid and Hollow), I,T, Angle and Channel sections – Design of simple beam sections.

## Shear Stresses-

Derivation of formula – Shear stress distribution across various beam sections like rectangular, circular, triangular, I, T angle sections

## UNIT 4:

## Slope and deflection-

Relationship between moment, slope and deflection, Moment area method, Macaulay’s method, Use of these methods to calculate slope and deflection for determinant beams.

## UNIT 5:

## Torsion-

Derivation of torsion equation and its assumptions. Applications of the equation of the hollow and solid circular shafts, torsional rigidity, Combined torsion and bending of circular shafts, principal stress and maximum shear stresses under combined loading of bending and torsion. Analysis of close coiled helical springs.

## Thin Cylinders and Spheres-

Derivation of formulae and calculations of hoop stress, longitudinal stress in a cylinder, and sphere subjected to internal pressures.

1. Tension test

2. Bending tests on simply supported beam and cantilever beam.

3. Compression test on concrete

4. Impact test

5. Shear test

6. Investigation of Hook’s law that is the proportional relation between force and stretching inelastic deformation,

7. Determination of torsion and deflection,

8. Measurement of forces on supports in statically determinate beam,

9. Determination of shear forces in beams,

10. Determination of bending moments in beams,

11. Measurement of deflections in statically determinate beam,

12. Measurement of strain in a bar

13. Bend test steel bar;

## List of Experiments:

1. Tension test

2. Bending tests on simply supported beam and cantilever beam.

3. Compression test on concrete

4. Impact test

5. Shear test

6. Investigation of Hook’s law that is the proportional relation between force and stretching inelastic deformation,

7. Determination of torsion and deflection,

8. Measurement of forces on supports in statically determinate beam,

9. Determination of shear forces in beams,

10. Determination of bending moments in beams,

11. Measurement of deflections in statically determinate beam,

12. Measurement of strain in a bar

13. Bend test steel bar;

## TEXT/REFERENCE BOOKS:

*1. S S Rattan, ―Strength of Materials‖, McGraw Hill Education.*

2. M L Gambhir, ―Fundamentals of Solid Mechanics‖, Prentice Hall India Learning Private Limited.

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3. James M. Gere, Barry J. Goodno, ―Mechanics of Materials‖, 8th edition, Cengage Learning.

4. Timoshenko, S. and Young, D. H., ―Elements of Strength of Materials‖, DVNC, New York,USA.

5. Kazmi, S. M. A., ―Solid Mechanics‖ TMH, Delhi, India.

6. Hibbeler, R. C. Mechanics of Materials. 6th ed. East Rutherford, NJ: PearsonPrentice Hall, 2004

7. Crandall, S. H., N. C. Dahl, and T. J. Lardner. An Introduction to the Mechanics of solids. 2nd ed. New York, NY: McGraw Hill, 1979

8. Mechanics of Materials - Ferdinand P. Beer, E. Russel Jhonston Jr., John T. DeWolf– TMH 2002.

9. Strength of Materials by R. Subramanian, Oxford University Press, New Delhi.2. M L Gambhir, ―Fundamentals of Solid Mechanics‖, Prentice Hall India Learning Private Limited.

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3. James M. Gere, Barry J. Goodno, ―Mechanics of Materials‖, 8th edition, Cengage Learning.

4. Timoshenko, S. and Young, D. H., ―Elements of Strength of Materials‖, DVNC, New York,USA.

5. Kazmi, S. M. A., ―Solid Mechanics‖ TMH, Delhi, India.

6. Hibbeler, R. C. Mechanics of Materials. 6th ed. East Rutherford, NJ: PearsonPrentice Hall, 2004

7. Crandall, S. H., N. C. Dahl, and T. J. Lardner. An Introduction to the Mechanics of solids. 2nd ed. New York, NY: McGraw Hill, 1979

8. Mechanics of Materials - Ferdinand P. Beer, E. Russel Jhonston Jr., John T. DeWolf– TMH 2002.

9. Strength of Materials by R. Subramanian, Oxford University Press, New Delhi.

**Books and e-Books I recommend for Strength of Materials:**

**S.S. Rattan- https://amzn.to/3cX8Mez**

**R.K. Bansal- https://amzn.to/2SRJUhi**

**S.S. Bhavikatti- https://amzn.to/35H7sZ0**

**Timoshenko- https://amzn.to/3cZg9lO**

**R.K. Rajput- https://amzn.to/3cYsPZR**

**R.S. Khurmi- https://amzn.to/2Ut6VaX**

**U.C. Jindal- https://amzn.to/3zKMXIQ**

***Taken from the official website of Uttarakhand Technical University.**

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