V Semester

ADVANCED MECHANICS OF MATERIALS (PROFESSIONAL ELECTIVE-I)

Course Code: 19ME1150 L T P C

3 0 0 3

Course Outcomes: At the end of the course, the student will be able to

CO1: Determine stress and strain transformations and derive constitutive equations in

elasticity

CO2: Calculate fixing moments and support reactions in fixed and continuous beams

CO3: Determine displacements of determinate and indeterminate structures by applying Castigliano’s

theorem and stresses due to torsion of non-circular shafts

CO4: Analyze stresses in curved bars and rotating discs

CO5: Determine shear center in thin walled member and stress distribution in thick cylinders

UNIT- I 10 Lectures

Stress and Strain Transformation: Plane stress transformation, plane strain transformation, principal

stresses and principal strains, strain rosettes.

Theory of Elasticity: Equilibrium and compatibility equations in Cartesian coordinates, Material

property relationships - generalized Hooke’s law, shear and bulk moduli.

Learning Outcomes: At the end of this unit, the student will be able to

1. determine stress and strain transformation for plane stress and plane strain conditions (L3)

2. calculate the strains and stresses using strain rosettes (L3)

3. explain the equilibrium and compatibility equations and their significance (L2)

UNIT- II 10 Lectures

Fixed Beams: Fixing moments for a fixed beam: using moment area method and Macaulay’s method,

effect of sinking support and rotation of support.

Continuous Beams: Analysis of continuous beams using Clapeyron’s three-moment theorem, reactions

at the supports, propped cantilevers.

Learning Outcomes: At the end of this unit, the student will be able to

1. determine shear force and bending moments for fixed and continuous beams (L3)

2. analyze the effect of sinking support in fixed beams (L4)

3. analyze reactions for propped cantilever beams (L4)

UNIT- III 10 Lectures

Energy Methods: Elastic strain energy for various types of loading, Application of Castigliano’s

theorems to statically determinate and indeterminate structures subjected to axial and transverse

loading.

Torsion of Non-Circular Shafts: Concept of Saint Venant’s warping function and Prandtl stress

function, maximum shear stress in solid sections – triangular, square, elliptical, maximum shear stress

in thin walled closed sections.

Learning Outcomes: At the end of this unit, the student will be able to

1. calculate displacements of determinate and indeterminate structures using Castigliano’s

theorems (L3)

2. calculate maximum shear stresses due to torsion in non-circular shafts (L3)

3. determine maximum shear stress due to torsion in thin walled closed sections (L3)

UNIT- IV 10 Lectures

Stresses in Curved Bars: Determination of radius of neutral axis in circular, rectangular and

trapezoidal sections, stresses in crane hook.

Stresses due to Rotation: Stresses in wheel rim, rotating disc of uniform thickness and disc of uniform

strength, permissible speed of a solid disc.

Learning Outcomes: At the end of this unit, the student will be able to

1. discuss the differences between stresses in curved bars and straight bars subjected to bending

(L2)

2. determine stresses in curved bars of circular, rectangular and trapezoidal cross sections (L3)

3. calculate stresses in disc of uniform thickness and uniform strength (L3)

UNIT- V 10 Lectures

Transverse Shear: Shear in straight members, thin walled members, concept of shear center for open

thin walled members.

Thick Cylinders: Lame’s equations, radial and hoop stresses due to internal and external pressures,

compound cylinders.

Learning Outcomes: At the end of this unit, the student will be able to

1. determine shear stress distribution in thin wall members subjected to transverse shear (L3)

2. explain the concept of shear center in open thin walled members (L2)

3. calculate the stresses in thick cylinders (L3)

Text Books:

1. L S Srinath, Advanced Mechanics of Solids, 3rd Edition, McGraw-Hill, 2009. (Unit-I)

2. S S Rattan, Strength of Materials, 2nd Edition, Tata McGraw Hill Education, 2011. (Unit- II to

V)

Reference Books:

1. Gere, Timoshenko, Mechanics of Materials, 2nd Edition, CBS Publishers, 2004.

2. R C Hibbeler, Mechanics of Materials, 9th Edition, Pearson publishers, 2018.

3. B C Punmia, A Jain and Arun Kumar Jain, Mechanics of materials, Laxmi Publications Pvt

Ltd, 2001.

4. S P Timoshenko and J N Goodier, Theory of Elasticity, 3rd Edition, Tata McGraw-Hill Edition,

2010.

5. A Hall, A Holowenko and H Laughlin, Schaum’s Outline of Machine Design, 1st Edition, 2007.