Force
• An example of Force is weight
•
•
•
•
Force = mass x acceleration
Force of gravity F = mg
In SI units, mass m is kilograms
An example of acceleration is g, the
gravitational acceleration.
• IN SI units g = 9.81 meters/second2
• 1 kilogram meters/sec2 is one Newton
Mass Wasting and Hillslopes
• Gravity overcomes Friction
Steep slope
Gd > F
F
3. Gd > F . Boulder
moves downslope
F
Moderate
slope
Gd=F
Gd
G
p
2. Gd = F
W
Boulder on verge
of moving
Gp
W
F
Gd
Gp W
1. Friction force uphill F
is greater than downhill
component of gravity.
Gd. Boulder is
stable
Gd
Gentle
slope
Gd< F
START HERE
Mass x gravity = mg = weight “w”
Downhill force (white) = mass x gravity x sine of angle a
Component of weight along slope (red) Fd = mg sine (a)
Shear Force = Fd = w sine (α)
dip
shear force not shear stress
The downhill force, parallel to the incline,
Is called the shear force. It is the force that
tries to slide the rock down the slope.
a
w
h
Friction and Normal Force
• Friction Force uphill (yellow) is proportional to
Normal Force (green)
• Normal Force is perpendicular to the slope. It is
the component of weight pressing the rock into
the slope.
• Increased water pressure between the surfaces
lifts the rock, and it will slip at a lower dip angle.
dip
a
w
h
Stress
• The Force per unit area is called stress
• Stress has the same units as Pressure
• The term stress is used for solids e.g.
rock, pressure for fluids (liquid e.g. water,
gas e.g. air)
• SI units are Pascals = Newtons/meters2
Stress Sign Conventions
• The “standards”
• The original sign convention is from Physics and Engineering
– For Normal Stress:
Divergence lengthens a solid in that direction and is
therefore positive
– For Shear:
Follow the right–hand-rule
Look at the x-face, up is
positive shear, positive shear
turns the element
Counter-clockwise
All of these conventions vary
All positive stresses, both normal and shear
Stress Sign Conventions
• From your text p47 bottom left”
– “The only ingredient left in our description is a sign
convention. In physics and engineering, tensile stress is
considered positive, and compressive stress negative.
In geology, however, it is customary to make
compression positive and tension negative, ….”
• Even shear has variable sign conventions
• You must be fluent in both conventions, just as you
must be fluent in both English and SI units. We will
start with the engineering convention.
Engineering Convention, tension stress is positive, here positive x-shear is UP
The angle q is measured from
the x-axis x to the normal axis n.
If this direction is clockwise, the
angle is negative, as shown.
q
The angle q is identical to the
angle between the vertical axis
and the fracture.
Problem 1 (worked example)
Engineering Convention, tension stress is positive
Problem 2
Engineering Convention, tension stress is positive
Problem 3
Engineering Convention, tension stress is positive
Problem 4
Engineering Convention, tension stress is positive
Problem 5 for LAB/HOMEWORK
Engineering Convention, tension stress is positive
Problem 6 for LAB/HOMEWORK
Engineering Convention, tension stress is positive
Problem 7 for LAB/HOMEWORK
Engineering Convention, tension stress is positive
Problem 8 for LAB/HOMEWORK
End of part 1
Stress Elements
Part 2
Correctly determining the angle
Homework question 1
Homework question 2
Next Time
Stress Transformation Equations
• Next time I will show you the derivation of the
Stress Transformation Equations.
• These will lead us to a graphical method, the
Mohr’s Circle