‘p1’ and ‘p2’ are two equal tensile principal stresses. On the plane AB inclined at 45° to the plane of ‘p1’ as shown in the figure below,
The plane AB is principal plane, and at the principal plane shear stress is zero.
In a Mohr’s circle, the radius of the circle is taken as
For a general two dimensional stress system, what are the coordinates of the centre of Mohr’s circle?
From the above figure coordinates of the centre are
A Mohr’s circle reduces to a point when the body is subjected to
When the normal stresses on the two mutually perpendicular planes are equal and alike then radius of Mohr’s circle will be zero.
Hence Mohr’s circle reduces to a point.
If a body carries two unlike principal stresses, what is the maximum shear stress?
The principal stress given are unlike i.e if one is tensile and other is compressive. Let σ1 be tensile and σ2 be compressive, then
Maximum shear stress in a Mohr’s circle
Radius of the Mohr’s Circle
Maximum shear stress,
∴ Radius of Mohr’s circle is equal to maximum shear stress
In a two dimensional problem, the state of pure shear at a point is characterized by
In a plane stress problem there are normal tensile stresses σx and σy accompanied by shear stres τxy at a point along orthogonal Cartesian co-ordinates x and y respectively. If it is observed that the minimum principal stress on a certain plane is zero then,
Since minimum principal stress is zero, so
State of stress at a point in a strained body is shown in figure.
Which one of the figure given below represents correctly the Mohr's circle for the state of stress?
Mohr’s circle for pure shear stress
Since neither tensile nor compressive stress exists, the Mohr’s diagram is simply a circle of radius τxy and centre at the intersection of the two axes. It can also be verified by transformation of plane formula.
The equivalent bending moment under combined action of bending moment M and torque T is
Maximum principal stress,