Chapter 2 Compound Stresses and Strains

Prepaired BySANJAY KUMAR

Assistant Professor Department of Mechanical Engineering

YMCA University of Science & Technology, Faridabad

DEPARTMENT OF MECHANICAL ENGINEERINGYMCA UNIVERSITY OF SCIENCE & TECHNOLOGY, FARIDABAD

To derive the transformation equations for stresses in a plane stress system.

To determine the magnitude and nature of stresses on an oblique plane.oblique plane.

To derive the equations for principal stresses and the maximum in plane shear stress, and calculate their magnitudes and directions.

Objectives (Contd…)

To know methods how to draw Mohr circle for a plane stress system.

To determine compound stresses in beams. To determine compound stresses in beams.

To determine combined bending and torsion in shafts.

Types of Stressed Conditions in an Element

Uniaxial direct stress

Biaxial direct stress Biaxial direct stress

General two-dimensional stress

Mohr’s Circle

It can be Drawn for the following Cases

A body in which two mutually perpendicular principal stresses of unequal intensities act.

A body subjected to two mutually perpendicular principal stresses which are unequal and unlike.

A body subjected to two mutually perpendicular principal tensile stresses and a simple shear stress.

Important Concepts and Equations

In a general two-dimensional stress system

pn = cos 2q + q sin 2q

pt = sin 2q – q cos 2q

2 2

x y x yp p p p

2

x yp p

The principal stresses are

p1 =

p2 =

2

2

2

2 2

x y x yp p p pq

2

2

2 2

x y x yp p p pq

Important Concepts and Equations(Contd..)

If ‘q’ is the angle of principal plane w.r.t. the plane of pxmeasured in anticlockwise direction, then

tan 2q =

Center of Mohr’s circle is at

2

x y

q

p p

2

x yp p