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Course Co-ordinated by IIT Kanpur
Dr. Priyanka Ghosh
IIT Kanpur


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This course is to serve as an introduction to mechanics of deformable solid bodies. The primary course objective is to equip the students with the tools necessary to solve mechanics problems, which involves (a) static analysis of a component to find the internal actions (forces and moments), (b) determine stresses, strains and deformation due to internal actions, and (c) compare them with known acceptable values. This requires the familiarity with the vocabulary of the subject, skill of drawing free body diagrams and the understanding of the material behavior under loads. It is expected to improve your engineering design skills.




Free body diagram with examples on modeling of typical supports and joints, Conditions for equilibrium in 3D and 2D, Friction: limiting and non-limiting cases


Force-displacement relationship and geometric compatibility (for small deformations) with illustrations through simple problems on axially loaded members and thin walled pressure vessels


Concept of stress at a point, Plane stress case: transformations of stresses at a point,
Principal stresses and Mohr TMs circle


Displacement field, Concept of strain at a point, Plane strain case: transformation of strain at a point, Principal strains and Mohr TMs circle, Strain rosette


Discussion of experimental results on 1D material behavior, Concepts of elasticity, plasticity, strain hardening, failure (fracture/yielding), Idealization of 1D stress-strain curve, Generalized Hooke TMs law (with and without thermal strains) for isotropic materials, Complete equations of elasticity


Force analysis (axial force, shear force, bending moment and twisting moment diagrams) of slender members


Torsion of circular shafts and thin-walled tubes (plastic analysis and rectangular shafts not to be discussed


Moment curvature relationship for pure bending of beams with symmetric cross-section, bending stress, shear stress (shear center and plastic analysis not to be discussed)


Cases of combined stresses, Concept of strain energy, Yield criteria


Deflection due to bending, Integration of the momentcurvature relationship for simple
boundary conditions, Method of superposition


Strain energy and complementary strain energy for simple structural elements (those under axial load, shear force, bending moment, and torsion), Castigliano‚€TMs theorems for deflection analysis and indeterminate problems


Concept of elastic instability, Introduction to column buckling, Euler‚€TMs formula (post-buckling behavior not to be discussed)


1. Crandall, S. H., Dahl, N. C. and Lardner, T. J. (2012).
2. An Introduction of the Mechanics of Solids, 3rd ed., Tata McGraw Hill. Shames, I. H. (2004). 3.
Engineering Mechanics: Statics and Dynamics, 4th ed., Prentice Hall of India. Meriam, J. L. and Kraige, L. G. (2004). 4.
Engineering Mechanics Statics, 5h ed., John Wiley and Sons. 5.
Popov, E. P. (1998). Engineering Mechanics of Solids, Pearson.



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