1. Mechanical Principles
Mechanical Principles deal with the physical properties of rocks and the significance of these properties in rock deformation.
Force is an explicitly definable vector quantity that changes or tends to produce a change in the motion of a body. Force is defined by its magnitude and direction, hence it may be expressed by an arrow, the length of which is proportional to the magnitude of the force, and the direction of which indicates the direction in which the force is acting.
It is expressed by the equation F = ma
where F is the force, m is mass and a is acceleration.

2. Mechanical Principles
Unbalanced Force: An unbalanced force is one that causes a change in the motion of a body. A body dropped from a high building is subjected to unbalanced force because of the gravitational pull of the earth, and the body accelerates at the rate of approximately 32 feet per second per second.
Balanced Force: Balanced forces exist where no change in motion occurs. If a man pushes against a wall that he cannot move, the wall is exerting a force equal and opposite to that exerted by the man.
Most problems confronting the structural geologist may be analyzed by assuming balanced forces because the velocity of rock bodies is so small that acceleration is negligible. Along faults, however, the motion causing earthquakes may be so rapid that acceleration is important.
Units of Measurement: Two different systems of measurement are commonly used, one, the so called absolute or CGS system, the other the English or Engineer’s system. In CGS systems the unit of force is dyne/cm2 and in English system it is poundal/ft2. Other units are also used, such as atmospheres and bars.

3. Mechanical Principles
Composition and Resolution of Forces: When two or more forces act in different directions at a point, there would be a third force as resultant or equilibrant. O W X Z Y 2 4 6 8 10
scale in pounds
A resultant is the single force that produces the same result as two or more forces, and it may be represented by the diagonal of parallelogram constructed on two arrows that represent two forces.
The equilibrant is the force necessary to balance two or more forces. It is equal to the resultant of the two forces, but acts in the opposite direction.
The process of finding the resultant of two or more forces is called composition of forces.

4. Mechanical Principles
Conversely, the effect of a single force may be considered in terms of two or more forces that would produced the same result.
A single force may thus be resolved into two components, acting in defined directions, by constructing a parallelogram, the diagonal of which represents the given force, and the sides of which have the direction of the components. O Z Y X O X W V 2 4 6 8 10
scale in pounds
The process of finding the components of a single force is called the resolution of forces.

5. Mechanical Principles
The preceding discussion of composition and resolution of forces has been confined to two dimensions, but geology is concerned with three dimensions. X V O Y W Z
In the above figure an inclined force OW lies in the vertical plane OZWV. We can resolve the force OW into two components, one of which – OZ in vertical, the other OV – lies in the horizontal plane OXVY. The OV may inturn be resolved into OX and OY which lies in the horizontal plane and at right angles to each other.
Moreover, any force, regardless of its value and its angle of inclination, may be similarly resolved into three components parallel to X, Y and Z axes.

6. Mechanical Principles
Differential Forces: In many instances, especially in nature the forces acting on a body are not equal on all sides. A body is said to be under differential forces when it is subjected to unequal forces.
Tensional Force: A body is said to be under tension when it is subjected to external forces that tend to pull it apart. It acts on the same straight line directed away from each other.
Compressional Force: A body is said to be under compression when it is subjected to external forces that tend to compress it. It acts on the same straight line and are directed towards each other.
Compression
Tension

7. Mechanical Principles
Differential Forces: In many instances, especially in nature the forces acting on a body are not equal on all sides. A body is said to be under differential forces when it is subjected to unequal forces.
Couple Force: A couple consists of two equal forces that act in the opposite directions in the same plane, but not along the same line.
Torsion: Twisting about an axis, produced by the action of two opposing couples acting in parallel planes.
A rod or plate is subjected to torsion when the ends are twisted in opposite directions.

8. Mechanical Principles
Deformation

9. Mechanical Principles
Pressure: Force per unit area applied to the outside of a body. When a body is immersed in a liquid, the pressure exerted on the body is described as hydrostatic pressure.
Rocks in the lithosphere, because of the weight of whatever rocks lie above them are subjected to similar pressure but not identical kind of pressure.
A small imaginary sphere at a depth of 1 km in the granite would be simulate hydrostatic pressure, but in experimental work this equal, all sided pressure on solids is called the confining pressure.
The lithostatic pressure increases with depth in the earth and reaches tremendous values in the interior.
An increase in confining / lithostatic pressure causes a decrease in the volume of rocks and increase in density. A decrease in confining pressure causes an increase in volume but a decrease in density.
Hydrostatic Pressure
Lithostatic Pressure

10. Mechanical Principles
Stress: Force applied to material that tends to change the material’s dimensions.
In a vertical column of material, let us imagine a horizontal plane, the material above the plane, because of its weight, pushes downward on the material below the plane. Similarly, the lower material pushes upward with an equal force on the upper material. The mutual action and reaction along a surface constitutes a stress.
Two types of stress: (a) Normal Stress
(i) Compressive Stress
(ii) Tensile Stress
(b) Shearing Stress / Tangential Stress

11. Mechanical Principles
Normal Stress: The normal component of applied force to the unit surface perpendicular to it.
Compressive Stress: Results from the normal component of a force if it tends to full apart the material on opposite sides of the plane. It is considered as negative.
Tensile Stress: develops from normal component of a force if it tends to pull apart the material on opposite sides of the plane. It is considered as positive.
Shearing Stress / Tangential Stress: The tangential component of applied force to the unit surface parallel to it.
F (external force)
Tangential Component
Normal Component

12. Mechanical Principles
Strain: Change of dimensions of matter in response to stress. It is the deformation caused by stress.
Two types of strain:
(i) Dilation: which is a change in volume.
(ii) Distortion: which is a change in shape.