Unit 1

Introduction to the theory of elasticity: Stresses and strains at a point, equilibrium equations, boundary conditions, stress and strain transformations, principal stresses and strains, Mohr’s circle, bi-axial and tri-axial stresses, constitutive relations, plane stress and plane strain conditions, stress and displacement formulations, strain compatibility relation, governing equations, Airy’s stress function, analysis of thin and thick-walled pressure vessels.

Unit 2

Analysis of Joints: Types of riveted, bolted, and welded joints, merits and demerits of various joints, study of failure behavior and simple design of joints; Energy Methods: Strain and potential energies strain energy density, gradually applied loads and suddenly applied loads, Castigliano’s theorem I and Castigliano’s theorem II, Maxwell- Betti’s theorem, unit load method and its applications, principle of virtual work, principle of virtual displacement and principle of virtual force.

Unit 3

Buckling of columns: Euler’s formula, effective length, load versus deflection plot, load eccentricity, imperfections, South-well plot; Theories of Failure: Maximum principle stress theory, maximum principle strain theory, maximum strain energy theory, maximum shear stress (Tresca) theory, and maximum distortion (vonMises) theory.

Objectives

• To make students to understand and appreciate the importance of theories of failure, buckling, joints and energy methods

Course Outcomes

• CO1: Understand stress and strain transformation on different plane for combined loading.
• CO2: Analysis and simple design of various riveted and welded joints
• CO3: Apply energy methods to obtain structural deformations.
• CO4: Obtain critical loads for columns with different end conditions.
• CO5: Apply the theories of failure in designing the structures.

CO – PO Mapping

Textbook(s)

• James M Gere, Barry J. Goodno “Mechanics of Materials”, 8^th Edition, Cengage Learning, USA, 2013.
• R.C. Hibbeler “Mechanics of Materials”, 8^th Edition, P P Hall, New Jersey, USA, 2011.

Reference(s)

• James M Gere, Stephen P. Timoshenko ” Mechanics of Materials”, 2^nd Edition,CBS Publishers, New Delhi, 1986
• Srivastava, Gope ” Strength of Materials”, Prentice-Hall of India, 2007
• C. T. Sun, “Mechanics of Aircraft Structures”, Second Edition, John Wiley & Sons, New York, 2006
• Megson,T.H.G., “Aircraft Structures for Engineering Students”, Butterworth-Heinemann, USA, 2007

Evaluation Pattern