Presentation on the Mohr's cirles used to determine rocks strength.

1. SCHOOL OF SCIENCES Group: 1
1. KUORWEL NGANG JACOB 2013/AUG/BPMM/B11865/DAY
2. NYAKATO JUSTINE 2014/AUG/BPMM/B14040/DAY
3. KANDOLE GEORGE 2014/AUG/BPMM/B12982/DAY
4. TUMUSIIME RONALD 2014/AUG/BPMM/B14171/DAY
5. AMPUMUZA JERVIS
a) Discuss what you understand by Mohr tress diagram
b) Discuss the importance/significance of the Mohr stress (MSD) in structural geology
c) Write a detailed notice using sketch diagrams where necessary on the following types of faults
 Normal fault
 Reverse fault
 Strike-slip fault
 Diapirs

2. Introduction
Introduced by Otto Mohr in 1882, Mohr's Circle
illustrates principal stresses (Normal stress) and
stress transformations via a graphical format.
Mohr's Circle was the leading tool used to visualize
relationships between normal and shear stresses.,
and to estimate the maximum stresses before the
hand-held calculators became popular. Even today,
Mohr's Circle is still widely used by engineers all
over the world.

3. Three Fundamental Principles of Mohr Circles
•Directions of planes are always represented by their poles
•Angles on the Mohr Circle are double the corresponding angles in real life.
•Always measure angles in the same sense in both real life and on Mohr Circles
Since angles are doubled on the Mohr Circle, any angles in real life greater than 180 degrees will be
equal to 360 on the Mohr Circle simply because they repeat themselves. Even if you perform stress
calculations for a plane oriented at 180 degrees from the plane, the results remain identical.

5. SYMBOL NO TYPE OF STRESS
1
1= Sigma Maximum Compressive Stress
2
2= Sigma Intermediate Compressive Stress
3
3= Sigma Minimum Compressive Stress
Theta
Angle formed by an inclined plane with the
maximum and minimum compressive stress
directions, and measured from the minimum stress
position.
n n= Normal Stress Oriented perpendicular to a plane
s s= Shear Stress Oriented parallel to a plane in question

6. Given the above diagram, the two principal
stresses are shown in red, and the maximum shear
stress is shown in orange. Recall that the normal
stresses equal the principal stresses when the
stress element is aligned with the principal
directions, and the shear stress equals the
maximum shear stress when the stress element is
rotated 45° away from the principal directions. As
the stress element is rotated away from the
principal (or maximum shear) directions, the
normal and shear stress components will always
lie on Mohr's Circle. A force applied to an area
(stress) may be resolved into a normal force (Fn)
perpendicular to a plane and a shear force (Fs),
parallel to a plane in question.

7. PLOTTING MOHR'S CIRCLE:
Mohr's circle is plotted on two perpendicular axes: The vertical axis (ordinate) depicts
shear stress and the horizontal axis (abscissa) depicts normal stress.
On a Mohr’s Diagram, the following shear conventions apply:
 Sinistral (counter-clockwise) shear is Positive (+)
 Dextral (clockwise) shear is Negative (-).
 Angles theta associated with planes experiencing sinistral shear plotted in the upper
hemisphere as well as planes experiencing dextral shear plot in the lower hemisphere
 Note that the axes of Mohrs diagram do not have a geographic orientation. However,
prior to constructing Mohrs diagram, it is useful to sketch a block diagram of the
orientations of the principal stress axes and the plane in question to ascertain the
relative sense of shear & orientation of principal stress axes.
Two points on the horizontal axis define the diameter of a circle. The Circle is plotted on the
abscissa

8. These points establish a radius (R) whereby:
The center (C) is then plotted:
We can determine the normal and shear stress on
any plane oriented at an angle theta from the
abscissa, as measured counter-clockwise from the
minimum compressive stress direction. Because of
the properties of a circle, the angle between Point
P, the center of the circle and the maximum
compressive stress direction =2 theta, as measured
counter-clockwise from the center of the circle.

9. Importance of Mohr Circle in Structural Geology
Determination of elasticity states for lithospheric stress
Elementary elasticity is appropriate because many in-situ stress measurement
techniques capitalize on the elastic behavior of rocks. Furthermore, many notions
concerning state of stress in the lithosphere arise from the assumption that the upper
crust behaves as a linear elastic body.
Understanding two reference states of stress
Stress generated by plate tectonic processes make the difference in the earth.
Geologically, reference states are those expected in 'young' rocks shortly after
lithification.
Indication of Lithostatic stress. Lithostatic stress will develop if a rock has no
long-term shear strength. Although some rocks such as weak shales and halite have
very little shear strength, experiments suggest that all rocks support at least a small
differential stress

10. Determination of forces. Since
most stresses in structural
geology are compressional, many
workers prefer to define
compression as positive and
tension as negative hence
indicating the direction of forces.
Maximum shear stress occurs on
planes oriented 45O to the
maximum and minimum
compressive stress directions;
thus, these points plot at the top
and bottom of Mohr's Circle as
denoted on the diagram below.
Importance of Mohr Circle in Structural Geology ..Cont..

11. • Determination of stress and strain values.
• Depicts the attitude of planes along which shear stress is the greatest for a
given stress state
• Facilitates a quick, graphical determination of stresses on planes of any
orientation.
• Mohr diagrams are excellent for visualizing the state of stress although
difficult for calculating stress tensors which are used to calculate stress.
• Determination of effective stress & fluid pore pressure
Importance of Mohr Circle in Structural Geology ..Cont..

12. In geology, a fault is a planar fracture or discontinuity in a volume of rock across which there has been significant
displacement along the fractures as a result of rock mass movement. Large faults within the Earth's crust result from the
action of plate tectonic forces form which result in the formation of boundaries between the plates, such as subduction
zones or transform faults. Energy release associated with rapid movement on active faults is the cause of most earthquakes

14. Diapir (from Greek diapeirein, “to
pierce”), geological structure consisting
of mobile material that was forced into
more brittle surrounding rocks, usually
by the upward flow of material from a
parent stratum.

15. Conclusion:
Traditionally, tectonic stresses are associated with stress arising from
the largest-scale natural sources such as plate-boundary tractions,
radioactivity and convection current but cause a lot of deformation
rocks even at the surface.

16. THANK YOU.