Force and Stress

Question 1

Body force vs surface force

Answer 1

Body forces result from action of a field at every point within a body. It can work at a distance and depends somehow on the amount of the material affected. Examples: gravity, magnetic.

 Surface forces act only on surfaces, operate across contact area between adjacent parts of a body, and these forces originate when one body pushes or pulls another. VERY important to
geologists and to deforming rocks.

 Body forces and surface forces are closely related in the earth because body forces give rise to spatial variations or gradients in the surface
forces

Question 2

compressive and tensile forces

Answer 2

compressive push against each other
-positive (in structural geology)

tensile forces pull away from each other
-negative (in structural geology)

Question 3

what is stress on a plane (on a surface) and its vector components

Answer 3

force per unit area
σ = F/A

2 vector components:
 Normal stress (perpendicular to the plane)
 Shear stress (parallel to the plane)

Question 4

Stress state at a point

Answer 4

Stress state
the collection of stress vectors for planes of all possible orientations at the point.

not a vector, but tensor

The stress ellipse is the locus of either the heads or the tails of the stress vectors drawn about their point of action. The stress ellipsoid is the 3-D
equivalent.

Question 5

mohr circle

Answer 5

for stress, won’t do the ones for strain

Stress from two directions (perpendicular to each other) will give you a shear stress in both directions and a normal force in both directions. The total stress will be a combination of all four

Depending on orientation (strike and dip) of the plane, will change the normal and shear stress on the plane

Any dot on the mohr circle plane will give you coordinates for a plane.

X-axis is the normal, y axis is the shear
- equations are tedious, use the coordinates

Important: **Theta is the angle between the normal and the shear stress acting on a plane. **

If two planes are perpendicular to each other, they will plot at 180 degrees (across each other on the circle) from each other because the angle is 2𝛳. Even though they are 90 degrees from each other, based on 2𝛳 then they will be opposites