# ME102: Mechanics I

Unit 2: Material Mechanics and Analysis of Solid Objects   *In this unit, we will examine the effects that forces have on solids.  You will understand how forces produce stress and strain and deform bodies, as well as how bodies behave in elastic and plastic regions.  You will study stress developed in bodies due to linear forces and moments in pure tension or compression, bending, and torsion.  We will take a look at centroids, centers of mass, and moments of inertia—structure-specific properties that are related to mass and that help us define how an object will react to an applied force.  We will begin with the simplest objects in order to help you best understand new concepts, such as stress and strain, more easily.  In its most basic terms, stress is defined as the amount of internal force acting on an object, per unit area.  Strain, on the other hand, is used to describe the deformation of an object, or the change in the object’s shape as the result of loading.  More specifically, it describes the structure’s elongation.  For example, imagine putting an orange into a vice and tightening it.  The soft fruit will compress, because there is a lot of stress acting upon it.  It will also change shape; strain often occurs in the presence of stress.  *

This unit will take you approximately 36.5 hours to complete.

☐    Subunit 2.1: 2.5 hours

☐    Subunit 2.1.1: 1.5 hours

☐    Subunit 2.1.2: 1 hour ☐    Subunit 2.2: 10.5 hours

☐    Subunit 2.2.1: 3 hours

☐    Subunit 2.2.2: 2 hours

☐    Subunit 2.2.3: 3 hours

☐    Subunit 2.2.4: 2 hours

☐    Subunit 2.2.5: 0.5 hours

☐    Subunit 2.3: 11.5 hours

☐    Subunit 2.3.1: 2 hours

☐    Subunit 2.3.2: 3 hours

☐    Subunit 2.3.3: 2.5 hours

☐    Subunit 2.3.4: 3 hours

☐    Subunit 2.3.5: 1 hours

☐    Subunit 2.4: 12 hours

☐    Subunit 2.4.1: 2.5 hours

☐    Subunit 2.4.2: 3 hours

☐    Subunit 2.4.3: 2.5 hours

☐    Subunit 2.4.4: 3 hours

☐    Subunit 2.4.5: 1 hour

Unit2 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Identify and explain appropriate formulas for the calculation of the properties of solid bodies including area and mass moments of inertia; perform those calculations. - Compute strain and stress, and describe the relationship of stress and strain for elastic, plastic, and composite bodies. - Compute and describe the relationship betweenstresses and strains in bodies subjected to tension and torsion. - Compute stresses and strains in pressure vessels and composites; identify and explain material properties for such components. - Identify, explain, and perform calculations involving the concept of a stress tensor and the constitutive relationship between strain and stress.

2.1 Properties of Solids   2.1.1 Moments of Inertia: Area   - Reading: University of Nebraska at Lincoln: Mehrdad Negahban’s “Area Moments of Inertia” Link: University of Nebraska at Lincoln: Mehrdad Negahban’s “Area Moments of Inertia” (PDF)

Instructions: Please click on the link above and read the entire article on computation of moments of inertia.

``````Terms of Use: The linked material above has been reposted by the
kind permission of Dr. Mehrdad Negahban and can be viewed in its
original
note that this material is under copyright and may not be reproduced
in any capacity without the explicit permission of the copyright
holder.
``````

Instructions: Please click on the link above and read the entire article.  What is the difference between the mass and area moments of inertia?  What is the radius of gyration?  Be sure to read the examples provided.

Terms of Use: This resource has been reposted by the kind permission of Dr. Mehrdad Negahban and can be viewed in its original form here (HTML).  Please note that this material is under copyright and may not be reproduced in any capacity without the explicit permission of the copyright holder.

2.2 Material Response   2.2.1 Elastic Properties   - Reading: Massachusetts Institute of Technology: David Roylance’s “Introduction to Elastic Response” Link: Massachusetts Institute of Technology: David Roylance’s “Introduction to Elastic Response” (PDF)

`````` Terms of Use: This resource is released under a [Creative Commons
attributed to MIT's [OpenCourseWare](http://ocw.mit.edu/index.htm)
and David Roylance, and the original version can be found
[here](http://ocw.mit.edu/courses/materials-science-and-engineering/3-11-mechanics-of-materials-fall-1999/modules/elas_1.pdf).
``````
• Lecture: Elasticity and Young's Modulus The Saylor Foundation does not yet have materials for this portion of the course. If you are interested in contributing your content to fill this gap or aware of a resource that could be used here, please submit it here.

Submit Materials

2.2.2 Elastic Properties at Atomic Level   - Reading: The Saylor Foundation’s “Testing of Mechanical Properties and Performance of Materials” Link: The Saylor Foundation’s “Testing of Mechanical Properties and Performance of Materials” (PDF)

Instructions: Please click on the link above and read the entire article.  You may wish to peruse the technical data for commercial devices that accomplish the tests described in the document.  This information can be found with an Internet search for terms such as “tensile testing.”

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
``````

2.2.3 Composites   - Reading: Massachusetts Institute of Technology: David Roylance’s “Introduction to Composites” Link: Massachusetts Institute of Technology: David Roylance’s “Introduction to Composites” (PDF)

Terms of Use: This resource is released under a Creative Commons Attribution-Non Commercial-Share-Alike 3.0 License.  It is attributed to MIT's OpenCourseWare and David Roylance, and the original version can be found here.

2.2.4 Stress and Strain Graphs   - Reading: Massachusetts Institute of Technology: David Roylance's “Stress-Strain Curves” Link: Massachusetts Institute of Technology: David Roylance’s “Stress-Strain Curves” (PDF)

2.2.5 Materials Response   - Activity: The Saylor Foundation’s “Materials Response” Link: The Saylor Foundation’s “Materials Response” (PDF)

`````` Instructions: Please click the link above and complete all the
quantitative understanding of stress and strain.  If you have
difficulty, you might benefit most from studying the resources,
especially the example calculations contained therein, for subunit

attributed to The Saylor Foundation.
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2.3 Structures Subjected to Tension and Shear   2.3.1 Analysis of Trusses   - Reading: Massachusetts Institute of Technology: David Roylance’s “Trusses” Link: Massachusetts Institute of Technology: David Roylance’s “Trusses” (PDF)

2.3.2 Stresses in Pressure Vessels   - Reading: Massachusetts Institute of Technology: David Roylance’s “Pressure Vessels” Link: Massachusetts Institute of Technology: David Roylance’s “Pressure Vessels” (PDF)

Instructions: Please click on the link above and read the entire article.  Study problems 1 and 2 and the end of the text.

2.3.3 Stresses in Shear and Torsion   - Reading: Massachusetts Institute of Technology: David Roylance’s “Shear and Torsion” Link: Massachusetts Institute of Technology: David Roylance’s “Shear and Torsion” (PDF)

2.3.4 Stress Concentrations   - Reading: The Saylor Foundation’s “Stress Concentration” Link: The Saylor Foundation’s “Stress Concentration” (PDF)

Instructions: Please click on the link above and read the entire article.  After reading, consider where stress may be concentrated in a commonplace item such as a kitchen utensil.

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
``````

2.3.5 Review Activity   - Activity: The Saylor Foundation's “Subunit 2.3.5 Review Activity” Link: The Saylor Foundation’s “Subunit 2.3.5 Review Activity” (PDF)

`````` Instructions:  Please click on the link above and complete all the
questions.  Please consult resources from subunit 2.3 work on the
activity.  After completion, please refer to The Saylor Foundation's

attributed to The Saylor Foundation.
``````

2.4 Analysis of Stress and Strain   2.4.1 Equations for Strain Displacement   - Reading: Massachusetts Institute of Technology: David Roylance’s “Kinematics” Link: Massachusetts Institute of Technology: David Roylance’s “Kinematics” (PDF)

2.4.2 Equilibrium of Stress   - Reading: Massachusetts Institute of Technology: David Roylance's “Equilibrium” Link: Massachusetts Institute of Technology: David Roylance's “Equilibrium” (PDF)

2.4.3 Tensor Concepts   - Reading: Massachusetts Institute of Technology: David Roylance’s “Tensor Transformations” Link: Massachusetts Institute of Technology: David Roylance’s “Tensor Transformations” (PDF)

2.4.4 Constitutive Formulations for Stress and Strain   - Reading: Massachusetts Institute of Technology: David Roylance’s “Constitutive Relations” Link: Massachusetts Institute of Technology: David Roylance’s “Constitutive Relations” (PDF)

2.4.5 Review Activity   - Activity: The Saylor Foundation's “Subunit 2.4.5 Review Activity” The Saylor Foundation's “Subunit 2.4.5 Review Actvity” (PDF)

`````` Instructions: Please click on the link above and complete all the
questions.  Please consult the resources from subunit 2.4 as you
work.  After completion, please refer to The Saylor
Foundation's [“Subunit 2.4.5 Review Activity Answer

attributed to The Saylor Foundation.
``````

The Saylor Foundation's "Unit 2 Assessment"   - Assessment: The Saylor Foundation's “Unit 2 Assessment” Link: The Saylor Foundation's “Unit 2 Assessment”

`````` Intructions: Please click on the link above and complete the
assessment.

You must be logged into your Saylor Foundation School account in
order to access this exam.  If you do not yet have an account, you
will be able to create one, free of charge, after clicking the