STRENGTH OF MATERIALS-II 

Course Objectives

1. Understand the concepts of strain energy.

2. Understand resilience stress developed due to suddenly applied loads.

3. Understand Castigliano’s & Maxwell theorems.

4. Understand the various theories of failure.

5. Derive equations and graphically represent each of the above.

6. Apply theories of failure to problems in 2D stress systems.

7. Derive the general formula for distribution of shear stress in beams.

8. Apply the above formula to various cross sections of beams.

9. Calculate deflection and reaction of indeterminate beams subjected to various kinds of loads.

10. Draw SF and BM diagrams for each of the above.

11. Derive mathematically Lame’s equation.

12. Compute various type of stresses and strain developed due to internal pressure in types of cylinders.

13. Compute stresses in cranks, rings of various section and chain links.

14. Solve simple numerical problems on the above.

Detailed Contents

1. Strain energy, energy of dilation and distortion, resilience stress due to suddenly applied loads, Castigliano’s theorem, Maxwell’s theorem of reciprocal deflection.

2. Theories of Failure : Maximum principal stress theory, maximum shear stress theory, Total strain energy theory, shear strain energy theory, graphical representation and derivation of equation for each and their application to problems relating to two dimensional stress systems only.

3. Leaf spring, deflection and bending stresses; open coiled helical springs; derivation of formula and application for deflection and rotation of free end under the action of axial load and/or axial couple; flat spiral springs – derivation of formula for strain energy, maximum stress and rotation.

4. Thick Cylinders : Derivation of Lame’s equations, calculation of radial longitudinal and hoop stresses and strains due to internal pressure in thick cylinders, compound cylinders, hub shrunk on solid shafts.

5. Bending of curved beams : Calculation of stresses in crane or chain hooks, rings of circular section and trapezoidal section and chain links with straight sided;

6. Shear stress distribution in rectangular, circular,I,T and channel section and the compression with bending stresses, Importance of shear centre.

7. Rotational stresses in discs and rims of uniform thickness; discs of uniform strength