# ME102: Mechanics I

Unit 3: Bending, Yield, Fracture, Buckling and Creep   You now know how structures will react internally when loaded with basic axial and shear forces.  In this unit, you will take a closer look at the overall reaction of the beam to the application of force.  When beams are loaded with forces, they will bend.  Whenever you enter the second floor of your home, the floor beams bend, if ever so slightly.  When you walk up the stairs, each step changes its shape as you place your weight on it.  This is an important concept, because bending can preclude the fracture of a beam.

This unit will teach you how to determine the maximum bending stress and strain a structure can sustain before it breaks. You will analyze bodies and structure for various failure scenarios, such as fracture, fatigue, creep, and buckling.  These are important concepts, as you need to know how to design products that will not break unexpectedly.

This unit will take you approximately 36.5 hours to complete.

☐    Subunit 3.1: 15.5 hours ☐    Subunit 3.1.1: 2.5 hours

☐    Subunit 3.1.2: 3 hours

☐    Subunit 3.1.3: 4 hours

☐    Subunit 3.1.4: 2 hours

☐    Subunit 3.1.5: 4 hours

☐    Subunit 3.2: 8 hours ☐    Subunit 3.2.1: 3 hours

☐    Subunit 3.2.2: 2 hours

☐    Subunit 3.2.3: 2 hours

☐    Subunit 3.2.4: 1 hour

☐    Subunit 3.3: 13 hours

☐    Subunit 3.3.1: 2 hours

☐    Subunit 3.3.2: 1 hour

☐    Subunit 3.3.3: 1.5 hours

☐    Subunit 3.3.4: 1 hour

☐    Subunit 3.3.5: 3 hours

☐    Subunit 3.3.6: 2.5 hours

☐    Subunit 3.3.7: 1 hour

☐    Subunit 3.3.8: 1 hour

Unit3 Learning Outcomes
Upon successful completion of this unit, the student will be able to: - Identify and explain beam composition, support, and loading configurations. - Compute stresses and strains in simple, composite, and curved elements; explain the underlying mathematics. - Explain and perform basic calculations regarding the experimental and computational determination of strain and stress in model systems. - Categorize, explain, and perform calculations involving material failure scenarios including fracture, fatigue, creep, and buckling; compute quantities such as critical loading, creep rates, and cyclic loading lifetimes.

3.1 Bending Stresses and Deflection   3.1.1 Shear Force and Bending Moment Diagrams   - Reading: Massachusetts Institute of Technology: David Roylance’s “Shear and Bending Moment Diagrams” Link: Massachusetts Institute of Technology: David Roylance’s “Shear and Bending Moment Diagrams” (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

3.1.2 Shear and Bending in Beams   - Reading: Massachusetts Institute of Technology: David Roylance’s “Stresses in Beams” Link: Massachusetts Institute of Technology: David Roylance’s “Stresses in Beams” (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

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
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3.1.4 Curved and Composite Beams   - Reading: The Saylor Foundation’s “Curved and Composite Beams” Link: The Saylor Foundation’s “Curved and Composite Beams” (PDF)

Instructions: Please click on the link above and read the entire article.  Find examples of both curved and composite beams in your everyday life.

`````` Terms of Use: This resource is licensed under a [Creative Commons
attributed to The Saylor Foundation.
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3.1.5 Composite Plates   - Reading: Massachusetts Institute of Technology: David Roylance’s “Laminated Composite Plates” Link: Massachusetts Institute of Technology: David Roylance’s “Laminated Composite Plates” (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.

• Activity: The Saylor Foundation’s “Subunit 3.1.5 Review Activity” Link: The Saylor Foundation’s “Subunit 3.1.5 Review Activity” (PDF)

Instructions: Please click on the link above and complete all the questions.  Please consult resources from the previous subunits as you do so.  You may find it helpful to use the example calculation in the reading for subunit 3.1.3 as a guide.  Upon completion, please refer to The Saylor Foundation's “Subunit 3.1.5 Review Activity Answer Key.

3.2 Computational Stress Analysis   Note: Some of the material in this section may seem especially complex or advanced.  You should not study it as if you need to use it to solve engineering problems in the near future, but rather read in order to gain an appreciation of the phenomena, nomenclature, and technology involved.  To that end, when you read the resource materials assigned in this subunit, you should browse through them at first and then review them for the major points.

3.2.1 Solutions of Stress and Strain in Closed Form   - Reading: Massachusetts Institute of Technology: David Roylance's “Closed-Form Solutions” Link: Massachusetts Institute of Technology: David Roylance’s “Closed-Form Solutions” (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

3.2.2 Solutions of Stress and Strain Experimentally   - Reading: Massachusetts Institute of Technology: David Roylance's “Experimental Strain Analysis” Link: Massachusetts Institute of Technology: David Roylance's “Experimental Strain Analysis” (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

3.2.3 Solutions of Stress and Strain Using Finite Element Analysis   - Reading: Massachusetts Institute of Technology: David Roylance's “Finite Element Analysis” Link: Massachusetts Institute of Technology: David Roylance's “Finite Element Analysis” (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

3.2.4 Review Activity   - Activity: The Saylor Foundation's “Subunit 3.2.4 Review Activity” Link: The Saylor Foundation's “Subunit 3.2.4 Review Activity” (PDF)

`````` Instructions: Please click the link above and complete all the
questions.  Please consult resources from the previous subunits as
you do so.  Upon completion, refer to The Saylor
Foundation's [“Subunit 3.2.4 Review Activity Answer

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

3.3 Material Yield, Fracture, Creep, and Buckling   3.3.1 Yielding and Plasticity   - Reading: Massachusetts Institute of Technology: David Roylance's “Yield and Plastic Flow” Link: Massachusetts Institute of Technology: David Roylance's “Yield and Plastic Flow” (PDF)

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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/yield.pdf).
``````

3.3.2 Fracture Mechanics   - Reading: The Saylor Foundation’s “Fracture” Link: The Saylor Foundation’s “Fracture” (PDF)

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

3.3.3 Material Fatigue   - Reading: Massachusetts Institute of Technology: David Roylance's “Fatigue” Link: Massachusetts Institute of Technology: David Roylance's “Fatigue” (PDF)

Instructions: Please click on the link above and read the entire article.  Then, study problems 1 and 2 at the end of the text.

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.

3.3.4 Buckling   - Reading: The Saylor Foundation’s “Compression and Buckling” Link: The Saylor Foundation’s “Compression and Buckling” (PDF)

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

3.3.5 Creep   - Reading: The Saylor Foundation’s “Creep Deformation” Link: The Saylor Foundation’s “Creep Deformation” (PDF)

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

3.3.6 Cyclic Fatigue   - Reading: The Saylor Foundation’s “Cyclic Fatigue” Link: The Saylor Foundation’s “Cyclic Fatigue” (PDF)

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

3.3.7 Deflections in Complex Systems   - Reading: The Saylor Foundation’s “Structure Failure, Stresses, and Deflections” Link: The Saylor Foundation’s “Structure Failure, Stresses, and Deflections” (PDF)

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

3.3.8 Review Activity   - Activity: The Saylor Foundation's “Subunit 3.3.8 Review Activity” Link: The Saylor Foundation’s “Subunit 3.3.8 Review Activity” (PDF)

Instructions: Please click on the link above and complete all the questions.  Please consult resources from the previous subunits as you do so.  Upon completion, refer to The Saylor Foundation's “Subunit 3.3.8 Review Activity Answer Key”.

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

The Saylor Foundation's "Unit 3 Assessment"   - Assessment: The Saylor Foundation's “Unit 3 Assessment” Link: The Saylor Foundation's “Unit 3 Assessment”

`````` Instructions: 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