2.20 Construction of Mohr’s Circle for Two- Dimensional Stress System
29
Fig. 2.14 Simple biaxial stress systems: a compression, b tension/compression, c pure shear
If the shearing stresses on opposite faces of an element would produce shearing
forces that result in a clockwise couple, these stresses are regarded as “positive”.
Procedure for Obtaining Mohr’s Circle
(1) Establish a rectangular co-ordinate system, indicating +τ and +σ. Both stress
scales must be identical.
(2) Locate the centre C of the circle on the horizontal axis a distance
1
2 (σ X + σ Y )
from the origin as shown in the figure above.
(3) Locate point A by co-ordinates σ x , −τ xy .
(4) Locate the point B by co-ordinates σ y , τ xy .
(5) Draw a circle with centre C and of radius equal to CA.
(6) Draw a line AB through C.
An angle of 2θ on the circle corresponds to an angle of θ on the element. The
state of stress associated with the original x and y planes corresponds to points A and
29
Fig. 2.14 Simple biaxial stress systems: a compression, b tension/compression, c pure shear
If the shearing stresses on opposite faces of an element would produce shearing
forces that result in a clockwise couple, these stresses are regarded as “positive”.
Procedure for Obtaining Mohr’s Circle
(1) Establish a rectangular co-ordinate system, indicating +τ and +σ. Both stress
scales must be identical.
(2) Locate the centre C of the circle on the horizontal axis a distance
1
2 (σ X + σ Y )
from the origin as shown in the figure above.
(3) Locate point A by co-ordinates σ x , −τ xy .
(4) Locate the point B by co-ordinates σ y , τ xy .
(5) Draw a circle with centre C and of radius equal to CA.
(6) Draw a line AB through C.
An angle of 2θ on the circle corresponds to an angle of θ on the element. The
state of stress associated with the original x and y planes corresponds to points A and