# Measuring Strain

This activity was selected for the On the Cutting Edge Reviewed Teaching Collection

This activity has received positive reviews in a peer review process involving five review categories. The five categories included in the process are

• Scientific Accuracy
• Alignment of Learning Goals, Activities, and Assessments
• Pedagogic Effectiveness
• Robustness (usability and dependability of all components)
• Completeness of the ActivitySheet web page

#### Summary

This activity utilizes randomly oriented strain markers created in Illustrator to estimate strain by measuring angular strain and lengths of lines, calculating shear strain, defining and orienting the principal strain axes, calculating stretching, and creating a Mohr Strain diagram using measurements as well as the strain equations.

## Context

#### Audience

Required course for undergraduate geology majors

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

Students need to have been introduced to the concept of strain and how it is measured (i.e. angular strain, shear strain, stretching). They also need to have heard of a Mohr strain diagram, and they need to be able to use a protractor to measure angles.

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

This is a stand-alone exercise that was meant to be done during a lab period.

## Goals

#### Content/concepts goals for this activity

The goals are to:
Understand the concept of using strain markers to estimate strain.
Understand what shear strain is, and be able identify principal strain axes as directions of zero shear strain.
Learn the concept of relative orientation (orientation of the long axis of a fossil relative to the page).

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

The main higher order thinking skill is for the students to actually use their own measurements of shear strain to determine the orientation of the finite strain ellipse for this deformed sample.

#### Other skills goals for this activity

How to properly use a protractor - originally this was not a goal, but apparently using a protractor is not a skill everyone had mastered

## Description and Teaching Materials

This exercise uses strain markers to estimate strain. The students measure angular shear in 15 strain markers that were in different orientations prior to experiencing homogenous simple shear (done in Illustrator). They also measure the orientation of each strain marker, and lengths of particular lines in the strain markers. They then use this data to determine the orientation of the principal axes of the finite strain ellipse; the lengths of these lines before deformation (assuming plane strain and that all strain markers were the same size originally); and from that they calculate stretching and quadratic elongation and construct a Mohr strain diagram first using their points, and then again using the strain equations with their calculated S1 and S3.

Detailed, step-by-step instructions are found in the downloadable file, which is attached as a Word file as well as a pdf with the deformed 'fossils.'

Measuring Strain pdf with deformed 'fossils' (Acrobat (PDF) 167kB May4 12)
Measuring Strain word document (Microsoft Word 2007 (.docx) 230kB May4 12)
Deformed spirex pdf (Acrobat (PDF) 17kB May4 12)

## Teaching Notes and Tips

I tried to write step-by-step instructions. Most of the confusion was on the measurement of long axis orientation on the page. Specifying that they measure the acute angle between the flat edge of the fossil and a line parallel to the long edge of the page seemed to help, but for many students the very idea of orienting something on the page was confusing.
The next confusing part was how to measure angular strain when they didn't have the originally perpendicular line already drawn in for them. Once we got past that it went pretty smoothly for those who were adept at using a protractor.

## Assessment

Because the fossils are numbered it is pretty easy to grade this exercise because they should all have the same numbers within +/- 5˚.

If their Mohr strain diagram is not roughly circular, they missed something.