Download Link: https://sites.google.com/view/varunpratapsingh/teaching-engagements UNIT-5 Stress and Strain Analysis Simple stress and strain: Introduction, Normal shear stresses, Stress-strain diagrams for ductile and brittle materials, Elastic constants, One dimensional loading of members of varying cross section, Strain energy, Thermal stresses. Compound stress and strains: Introduction, State of plane stress, Principal stress and strain, Mohr’s circle for stress and strain. Pure Bending of Beams: Introduction, Simple bending theory, Stress in beams of different cross sections. Torsion: Introduction, Torsion of Shafts of circular section, Torque and Twist, Shear stress due to Torque.

1. STRENGTH OF MATERIAL
UNIT 5
PART-2
(COMPOUND STRESS AND STRAIN)
By
Varun Pratap Singh

2. Generalized Hooke's Law
The generalized Hooke's Law can be used to predict the deformations caused in a given material by an arbitrary combination
of stresses.
The linear relationship between stress and strain applies for

3. In actual Engineering problems combination of stresses will act. The member may be subjected to direct stresses in different
directions. The shear stresses (direct or due to torsion) may also act. A beam is always under bending and shear. A shaft may be
under torque, bending and direct forces. In this chapter we will see the effect of combined/compound stresses. In a three
dimensional stress system, the various stresses acting are shown in Fig.1
In many problems two dimensional idealizations is possible and the general
stress system in such case is shown in Fig. In this book discussion is limited
to two dimensional problems only.

9. The plane on which the normal stress is maximum and shear stresses are absent is known as principal
plane and the corresponding normal stress is principal stress.

10. In general, at any point in a strained material, there are three principal planes mutually perpendicular to each other. Out of
the three planes, the plane carrying maximum normal stress is called major principal plane and corresponding stress as
major principal stress. The plane carrying minimum normal stress is called minor principal plane and corresponding
stress as minor principal stress. In two dimensional analysis, only two principal planes exist.

31. EXAMPLES