MECHANICS OF DEFORMABLE BODIES�NA20201

Ritwik Ghoshal

Autumn 2025

Syllabus

Introduction to deformable bodies, stress-strain relation, compatibility. Bending of beams load, shear and moment in beams, properties of cross-sectional area, stresses in beams, equation of elastic curve, deflection. Energy Methods-minimum potential and complementary energy, Betti-Maxwell Reciprocal theorem. Torsion of cylindrical bars, torsional stress, modulus of rigidity and deformation. Shear in beam (vertical, longitudinal shear, shear center in thin-walled beam).

Column-long and short, buckling of slender columns, Euler buckling load for different end conditions. Transformation of stress and strain, principal stresses, principal strains, Mohr’s circle for stress and strain, plain stress and plain strain problem, combined loading: axial and torsional; axial and bending; axial, torsional and bending. Pressure vessel, Hoop stress, Theories of failure- practical considerations for design, stress concentration, shear lag.

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Resources

• Books
• Mechanics of Materials by Beer, Johnston et al. �(preferably the latest edition, but any edition will do)
• Advance reading
• Elements of strength of material by Timoshenko, Young
• Engineering mechanics of solids by Popov
• Structural analysis by Hibbler
• Advanced mechanics of solids by Srinath
• Class notes
• https://sites.google.com/site/ritwikghoshal/teaching

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Intended Learning Outcomes

• After completing this course, it is intended that students will:

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• Be able to describe and determine various kinds of deformations and stresses in engineering structures in a systematic, modern, mathematical way that can be utilized for computer-based design and analysis

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• Obtain the prerequisite knowledge for advanced courses in elasticity, advanced mechanics of solids, finite elements methods, composites, tribology that are necessary in both core jobs as well as in higher studies

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• Be able to read and understand research papers that will be directly helpful for B.Tech and Dual Degree Projects

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Time Table

Structure of Learning

• Academic Calendar:
• Classes will commence for all UG 22.07.2024
• MID-AUTUMN SEMESTER EXAMINATION for all theory subjects (17.09.2024 to 25.09.2024)
• Autumn break for students (05.10.2024 to 13.10.2024)
• There will be, tentatively, 14 weeks in the semester
• 8 Weeks Before Mid-Sem
• 6 Weeks After Mid-Sem
• The total number of contact hours prescribed for a 3-credit course like MoDB of Solids is 3 hours per week. As per requirement, the instructors may add an hour in certain weeks (to the extent possible such measures will be avoided).

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Week 1

• Review of the concepts of stress and strain

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• Concept of stress
• Concept of strain
• Stress-strain relations (Generalized Hooke’s law)

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Week 2-3

• Bending of beams

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• Shear and bending moment diagrams
• Relationship between load, shear, and bending moment
• Bending deformation
• Flexure formula

Week-4

• Shear in beams and thin-walled members

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• Shear in straight beams
• Shear formula
• Shear flow in built-up members
• Shear centre in open thin-walled members (may be dropped/May be covered in the end)

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Week 5

• Torsion 

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• Torsion of shafts with circular cross-section
• Angle of twist
• Statically indeterminate shafts
• Basics of transmission shaft design

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Week 6-7

• Transformation of stress and strain

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• Plane stress transformation
• Principal stresses and maximum in-plane shear stress
• Mohr’s circle for plane stress
• Absolute maximum shear stress
• Plane strain transformation
• Mohr’s circle for plane strain (may be dropped)
• Absolute maximum shear strain
• Recap of material property relations
• Strain rosettes

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Week 8-9

• Miscellaneous applications

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• Thin-walled pressure vessels
• Principal stresses in a beam
• Stresses under combined loads
• Theories of failure practical considerations for design

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Week 10

• Deflection of beams

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• Deformation under transverse loading
• Statically indeterminate beams
• Macaulay's Method
• Method of superposition

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Week 14

• Energy methods

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• External work and strain energy
• Elastic strain energy for various types of loading
• Impact loading
• Principle of virtual work
• Castigliano’s theorem: deflections; statically indeterminate structures
• Minimum potential and complementary energy
• Betti-Maxwell Reciprocal theorem

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Week 13

• Buckling of columns

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• Column-long and short
• buckling of slender columns
• Euler bucking load for different end conditions
• Stability of columns
• Ideal column with pin supports
• Columns having various types of supports

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Marks distribution

• Class test I (2 nos)+Assignments + Attendance : 20
• CT: 5x2 or Best of Two (10); Assignments: (5); Attendance: (5)
• Mid-sem – 30
• End-sem – 50

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• Total - 100

Guidelines for writing assignments

• The written-scanned assignment submissions must be made in a neat and clean fashion.

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• The solution steps must be clearly explained. Just writing some formulae and presenting an answer after a messy derivation/working out will be very severely penalised.

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• It is not the responsibility of the grader to extract meaning out of the student’s work. It is the responsibility of the student to present everything clearly. 

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• Clear communication of one’s ideas is an essential part of training to be an engineer.

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Grading

• The cut-off for P grade will be set between 30 and 35.

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• The cut-off for EX grade is usually 90. However, depending on the difficulty level of the tests, this cut-off may be slightly relaxed. As mandated by the institute, “even the best student of any class needs to be good enough to be awarded the ‘EX’ grade.”

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• Cut-offs for grades A to D will be decided based on the overall performance of the class. There will be no limits to the number of students who may obtain a particular grade.

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Important Disclaimer: If there are fresh directives from the institute regarding grading policies, the following guidelines and policies will be superseded by those new directives.

Request for re-checking and re-grading

• If a student truly thinks that a particular question has been unfairly marked, then s/he may request for rechecking. If a genuine mistake in the marking is found then again appropriate modifications in the mark will be made.

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• Requests to “discuss” grades will be summarily ignored. Please do NOT send such emails. Please do NOT approach the faculty for such discussions.

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• If a student receives F grade, then the student must understand that s/he is missing the cut-off for P grade by a non-negligible margin. Therefore, no request for changing F grade to P grade will be entertained. 
• The student with the F grade must wait till the Supplementary Examination.

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