Geology 3120 - Geology 3120 - Resolving stresses on a planeResolving stresses on a plane

OutlineOutline

• Resolving stress on a plane

• Determining maximum shear stress

• Class problem

StressStress

Normal and Shear StressesNormal and Shear Stresses

is defined as the angle from horizontal to the plane A’. is defined as the angle from horizontal to the plane A’.

Counterclockwise is positive (+). Counterclockwise is positive (+).

Solving for Shear StressSolving for Shear Stress

Solving for Shear StressSolving for Shear Stress

Solving for Shear StressSolving for Shear Stress

Solving for Shear StressSolving for Shear Stress

Solving for Normal StressSolving for Normal Stress

Solving for Normal StressSolving for Normal Stress

Solving for Normal StressSolving for Normal Stress

Solving for Normal StressSolving for Normal Stress

Solutions for Normal & Shear Solutions for Normal & Shear

StressesStresses

Calculating Maximum Shear StressCalculating Maximum Shear Stress

For what For what value is the shear stress greatest? value is the shear stress greatest?

Calculating Maximum Shear StressCalculating Maximum Shear Stress

For what For what value is the shear stress greatest? value is the shear stress greatest? = 45° or = 45° or //44

//44

FF

A

Class ProblemClass Problem

Find the Find the dip value of the plane such that dip value of the plane such that ss is minimized and is minimized and

n n maximized.maximized.

A

FF

Draw the plane on Draw the plane on

the block figure.the block figure.

Class ProblemClass Problem

A

FF

Draw the plane on a Draw the plane on a

block figure.block figure.

Find the Find the dip value of the plane such that dip value of the plane such that ss is minimized and is minimized and

n n maximized.maximized.

The Relationship Between Stresses and The Relationship Between Stresses and

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 /4/2

n

s

F/A = 1

ReferencesReferences

Slide 1

Twiss, R. J. and E. M. Moores, Structural Geology, W. H. Freeman & Co., New York, 532 p., 1992.