18AU34 Mechanics of Materials syllabus for AU

Stress and Strain:

Introduction, Hooke’s law, Calculation of stresses in straight, Stepped and tapered sections, Composite sections, Stresses due to temperature change, Shear stress and strain, Lateral strain and Poisson’s ratio, Generalized Hooke’s law, Bulk modulus, Relationship between elastic constants.

Analysis of Stress and Strain:

Plane stress, Stresses on inclined planes, Principal stresses and maximum shear stress, Principal angles, Shear stresses on principal planes, Maximum shear tress, Mohr circle for plane stress conditions.

Cylinders:

Thin cylinder: Hoop’s stress, maximum shear stress, circumferential and longitudinal strains, thick cylinders: Lames equations.

Shear Forces and Bending Moments:

Type of beams, Loads and reactions, Relationship between loads, shear forces and bending moments, Shear force and bending moments of cantilever beams, Pin support and roller supported beams subjected to concentrated loads and uniformly distributed constant / varying loads.

Stresses in Beams:

Pure bending, Curvature of a beam, Longitudinal strains in beams, Normal stresses in Beams with rectangular, circular, ‘I’ and ‘T’ cross sections, Flexure Formula, Bending Stresses, Deflection of beams (Curvature).

Torsion:

Circular solid and hallow shafts, Torsional moment of resistance, Power transmission of straight and stepped shafts, Twist in shaft sections, Thin tubular sections, Thin walled sections.

Columns:

Buckling and stability, Critical load, Columns with pinned ends, Columns with other support conditions, Effective length of columns and Secant formula for columns.

Strain Energy:

Castigliano’s theorem I and II, Load deformation diagram, Strain energy due to normal stresses, Shear stresses, Modulus of resilience, Strain energy due to bending and torsion.

Theories of Failure:

Maximum Principal stress theory, Maximum shear stress theory.

Course Outcomes:

At the end of the course the student will be able to:

• Explain the basic concepts of stress, strain, behaviour of engineering materials under different loading conditions.
• Calculate principal stresses using analytical and graphical methods, shear force and bending moments, deflection and slop of beams, critical loads for different type of columns using euler’s and rankine’s equations.
• plot shear force and bending moment diagrams for beams carrying different types of loads, and various support conditions.
• Determine deflection and slope of beams subjected to various type of loads.
• Compare solid and hollow shafts subjected to torque.

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub- questions) from each module.

Textbook/s

1 Strength of Materials James M Gere, Barry J .Goodno, Cengage Learning, 2009

2 Strength of Materials S. S. Bhavikatti Vikas publications House -1 Pvt. Ltd. 2006

Reference Books

3 Strength of Materials- S. S. Rattan, , Tata McGraw Hill 2009

4 Mechanics of Materials K.V. Rao, G.C. Raju, Suhas stores, Bangalore 2007

5 Strength of Materials R Subramanian, Oxford 2005