Real life examples in mechanics of solids : lesson plans and solutions

44 Pages·2006·0.98 MB·English

by  Eann Alexander Patterson

RReeaall LLiiffee
Examples in
MMeecchhaanniiccss ooff
Solids
Lesson plans and solutions
Eann A Patterson, Editor

Real Life Examples in Mechanics of Solids

Lesson plans and solutions
First edition produced September 2006
Second Edition, 2008
Third [Electronic] Edition, 2011

Real Life Examples in Mechanics of Solids
Lesson plans and solutions

Copyright © 2006, 2008, 2011 Eann A Patterson (editor)

This work is licensed under the Creative Commons Attribution-NonCommercial-
NoDerivs 3.0 Unported License. To view a copy of this license, visit
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The Editor has no responsibility for the persistence or accuracy of URLs for external
or third-party internet websites referred to in this publication, and does not guarantee
that any content on such websites is, or will remain, accurate or appropriate.

Bounded printed copies can be purchased on-line at www.engineeringexamples.org

This edition is distributed free of charge by the ENGAGE project
(www.EngageEngineering.org), which is supported by the National Science Foundation
under Grant No. 0833076.
Real Life
Examples in
Mechanics of Solids

Lesson plans and solutions

Suggested exemplars within lesson plans for Sophomore Solids Courses. Prepared as part
of the NSF-supported project (#0431756) entitled: “Enhancing Diversity in the
Undergraduate Mechanical Engineering Population through Curriculum Change”

Eann A Patterson, Editor

The University of Liverpool, England
[email protected]
This work was developed during the NSF-supported project (#0431756) entitled:
“Enhancing Diversity in the Undergraduate Mechanical Engineering Population through
Curriculum Change”. Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the authors and do not necessarily reflect the views
of the National Science Foundation. The following were members of the project and
contributed to the many discussions which led to this production of this volume:
Ilene Busch-Vishniac Johns Hopkins University (Project leader)
Suzanne Gage Brainard University of Washington
Patricia B. Campbell Campbell-Kibler Associates Inc
Constantin Chassapis Stevens Institute of Technology
Glenn Ellis Smith College
Ashley Emery University of Washington
Darrell Guillaume California State University, Los Angeles
Jeff Jarosz Johns Hopkins University
Susan Staffin Metz Stevens Institute of Technology
Eann Patterson Michigan State University
Pradosh K. Ray Tuskegee University
Helen Ryaciotaki-Boussalis California State University, Los Angeles
Kuei-Wu Tsai California State University, Los Angeles
Horace Whitworth Howard University
Real Life Examples in Mechanics of Solids
CONTENTS
page no.
Introduction and acknowledgements 5
ELEMENTARY STRESS SYSTEMS
1. Stress and strain in unixial solid and hollow bars 6
iPod, suspension bridge, femur, cello
2. Displacement plus deformation in control cables 9
Derailleur gears, yacht rudder
3. Stress in pressure vessel wall 11
Bike pump
STATICALLY INDETERMINATE PROBLEMS
4. Combined use of principles of compatibility and equilibrium 13
iPod, dinosaur display
TORSION
5. Stress and strain due to applied torque 17
Bottle closures
STRAIN ENERGY
6. Conservation of Energy/Energy Methods 19
Slingshot, bungee jumper
7. Helical springs 21
Bicycle suspension, pogo stick
BEAM BENDING
8. Bending moments and shear stress diagrams 24
Skateboarder, unicyclist on plank
METHOD OF SUPERPOSITION
9. Eccentric loading 29
Basketball goal
10. Thermal stress and statically indeterminate loads 31
Rail tracks, jewellery pendant
TWO-DIMENSIONAL STRESS SYSTEMS
11. Mohr’s circle of stress 34
Sausages
12. Combined bending and torsion 36
Wind-up clock, motor
3

Real Life Examples in Mechanics of Solids

INTRODUCTION
These real life examples and supporting material are designed to enhance the teaching of
a sophomore course in mechanics of solids, increase the accessibility of the principles
and raise the appeal of the subject to students from a diverse background. The examples
have been embedded in skeletal lesson plans using the principle of the 5Es: Engage,
Explore, Explain, Elaborate and Evaluate. Such lesson plans were developed by the
Biological Sciences Curriculum Study1 in the 1980s from work by Atkin and Karplus2 in
1962. Today they are considered to form part of the constructivist learning theory and a
number of websites provide easy to follow explanations of them3.
This booklet is intended to be used by instructors and is written in a style that addresses
the instructor, however this is not intended to exclude students who should find the
examples interesting, stimulating and hopefully illuminating, particularly when their
instructor is not utilizing them. In the interest of brevity and clarity of presentation,
standard derivations and definitions are not included since these are readily available in
textbooks which this booklet is not intended to replace but rather to supplement.
Similarly, it is anticipated that these lessons plans can be used to generate lectures/lessons
that supplement those covering the fundamentals of each topic.

Acknowledgements
Many of these examples have arisen through lively discussion in the consortium
supported by the NSF grant (#0431756) on “Enhancing Diversity in the Undergraduate
Mechanical Engineering Population through Curriculum Change” and the input of these
colleagues is cheerfully acknowledged as is the support of NSF. The influence of the
editor’s mentors and peers at the University of Sheffield is substantial and is gratefully
acknowledged since many of the ideas for these examples originate from tutorial
questions developed and used in the Department of Mechanical Engineering in Sheffield
over many years.

1 http://www.bscs.org/library/BSCS_5E_Instructional_Approach_July_06.pdf
2 Atkin, J. M. and Karplus, R. (1962). Discovery of invention? Science Teacher 29(5): 45.
3 e.g. http://www.science.org.au/primaryconnections/constructivist.htm
5
Real Life Examples in Mechanics of Solids

ELEMENTARY STRESS SYSTEMS

1. Principle: Stress and strain in uni-axial solid and hollow bars

Engage:
Take your iPod into class and dangle it by the earphone
cable. Cut open the cable on an old set of earphones to

expose cable and insulation.

Explore:

Pass around class lengths of copper wire and lengths of
empty hollow insulation and invite students to stretch them.
Discuss relative extensions and stiffness. Someone will

probably snap one so talk about ultimate tensile stress. Be

sure have to enough lengths that every student has at least
one to play with while you are talking.

Explain:
Work through the example below:
An iPod, with a mass of 30 grams is dangled from its earplug
cable.

a) Assuming that the copper wire of diameter 0.40mm
inside the cable carries the entire load, evaluate the
stress in the wire due to the weight of the iPod.
b) If the wire in (a) is 1.50m long, by how much will it
stretch?
c) Assuming that the plastic insulation, which fits snugly
over the wire and has an external diameter of 1mm,
carries the entire load, evaluate the stress in the
insulation due to the weight of iPoD.
d) If the insulation is made from uPVC calculate the
extension of the insulation in the circumstances
described in (c).
Solution:
F mg 301039.81
a) Stress,    2.34×106N/m2
A d2 4 0.401032 4
where F, is force applied, A is cross-section area, m is mass, g is gravitational
acceleration, and d is the diameter of the cross-section.
6