# Extra Credit Problem Set

#### Summary

This problem set was assigned at the end of the year as a way for the students to get some extra credit and to help them study for the final exam. The problem set has 3 parts: 1) Strain: finding S1 and S3, measuring angular shear, and determining coaxial vs. noncoaxial deformation, 2) Calculating surface stresses on an inclined surface, and 3) Mohr stress circles.

## Context

#### Audience

Required course for undergraduate geology majors.

#### Skills and concepts that students must have mastered

For part 1 they need to be able to measure angular shear and relative line orientations, and know the difference between coaxial and noncoaxial deformation.

For part 2 they need to know what lithostatic stress is, the rules of trigonometry, and they will have to use algebra.

For part 3 they need to know how to calculate max. stress, min. stress, mean stress, differential stress, and deviatoric stress given two of those stresses, and be able to draw Mohr circles and associated failure envelopes, and calculate the equation of the failure envelope and the angles between the fracture plane and sigma-1.

For part 2 they need to know what lithostatic stress is, the rules of trigonometry, and they will have to use algebra.

For part 3 they need to know how to calculate max. stress, min. stress, mean stress, differential stress, and deviatoric stress given two of those stresses, and be able to draw Mohr circles and associated failure envelopes, and calculate the equation of the failure envelope and the angles between the fracture plane and sigma-1.

#### How the activity is situated in the course

This was an extra credit problem set assigned at the very end of the course.

## Goals

#### Content/concepts goals for this activity

Distinguishing coaxial (pure) and noncoaxial (simple) shear.

Deriving normal and shear stress on an inclined surface.

Constructing and interpreting Mohr stress circles.

Deriving normal and shear stress on an inclined surface.

Constructing and interpreting Mohr stress circles.

#### Higher order thinking skills goals for this activity

The only higher order thinking skill is maybe constructing the Mohr-Coulomb failure envelope and interpreting the fracture angles.

#### Other skills goals for this activity

Algebra: in the derivation portion they have to solve equations without any numbers in order to derive general equations for calculating normal and shear stress on any oriented surface.

## Description and Teaching Materials

This exercise was assigned as an extra credit problem set to help students review and prepare for the final exam. It includes 1) measurements of strain: stretching, angular shear, and determination of coaxial vs. noncoaxial deformation, 2) derivation of equations for normal and shear stress on an inclined surface (not quite the full stress equations though), and 3) constructing Mohr stress circles from given data, and determining the equation of the failure envelope and the resultant fracture angles.

End of year problem set (Microsoft Word 2007 (.docx) 151kB May4 12)## Teaching Notes and Tips

In general, my students were very uncomfortable thinking in terms of general quantities, i.e. rho*g*h instead of an actual number for sigma-1, or theta instead of an actual angle. This is something I think is worth gaining comfort and familiarity with.

## Assessment

I just grade this like any problem set, there are clear correct answers so it is pretty easy.