AC 2011-1759: A LOW COST PROJECT COURSE TO ENHANCE LEARN-ING IN A STATICS AND STRENGTH OF MATERIALS COURSE

Charles G. Drake, Ferris State University

Professor, Mechanical Engineering Technology Ferris State University Big Rapids, Michigan

MS Mechanical Engineering Michigan Technological University BS mathematics Lake Superior StateUniversity

12 years in Product Development, R & D, Reynolds Metals Company (now ALCOA) Richmond, Virginia

c©American Society for Engineering Education, 2011

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A Low Cost Lab Project Course to Enhance Learning

in a Statics and Strengths of Materials Course

Abstract

A lab-oriented course has been created to supplement lecture instruction in statics and strengths

of materials. The primary goal in initiating the course was to give students more problem

solving experience with a secondary goal of intuition-building hands-on experiences. Over 25

activities have been developed with a limited budget.

Background

Second year students in Mechanical Engineering Technology take a four-credit lecture course in

statics and strengths of materials during their fall semester. Prerequisites for the lecture course

include pre-calculus and college physics. The lecture course includes two-dimensional statics,

stress and deformation for common loadings, and combined loadings with Mohr‟s circle.

Fastener design and column buckling are introduced. Such courses are often challenging due

both to the nature of the subjects themselves and to students being at the beginning of the

development of their aptitudes in mathematics-based problem solving.

Starting as an experimental course in Fall 1999, faculty have created the one-credit lab based

course to provide more problem-solving experience in these very important subjects. Covering

the course material with 4 hours of lecture has always been challenging. The lab was created to

supplement instruction for MET students.

This document covers experience from the first years of the course which were done generally

with low cost/no cost equipment. A sequential paper is planned; the future paper will discuss

equipment enhancements and the continued development of the course.

The text used when this lab course was created was H. W. Morrow‟s Statics and Strengths of

Materials.1

Work by others teaching mechanics includes discussion and student feedback on the integration

of real life examples into a solid mechanics course at Michigan State University. Here students

had a very favorable impression of their learning experience when examples such as skateboards,

basketball hoops, and iPods™ were used to develop key concepts in solid mechanics.2

Pedagogy

The course emphasizes activity learning with generally hands-on equipment experiences

followed by applied computations. The author uses the whiteboard for visual and auditory

explanations. Text is kept to a minimum on author‟s handouts in deference to those who learn

poorly through reading.

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Overview of the Lab-Based Course

As stated, over twenty-five activities have been developed. Nearly all activities include hands-

on experiments using low cost equipment and materials. Each activity included a worksheet for

data, observations, free-body diagrams, and mathematical problem-solving.

The statics portion of the course included activities relating to units, scaling, vectors, concurrent

forces, pulley systems, beam reactions and stability, dry friction, belt friction, trusses, and the

human arm. Low-cost readily-available equipment included engineers‟ scales, protractors,

pulleys, spaghetti, and torque wrenches. Purchased equipment included five high-quality

commercial force gauges with ranges of 100 lb/500 N, 20 lb/100 N, and 176 oz/50 N.

The strength of materials portion of the course involved tensile strength, fastener shear, shear and

tensile modulii, and torsional deformation. Low cost materials used solid aluminum rivets and

foam sponges. A commercial torsional deformation device was purchased; this was

supplemented with two student-build torsional deformation devices. The force gauges

mentioned previously along with a donated universal testing machine were used.

Near the end of the semester instructor led truss and frame design projects were completed.

These thoroughly analyzed projects included stability, frame member selection and analysis,

fastener analysis, and buckling considerations. A load rating for each structure was established.

Finally, a fun hands-on competition and a computer lab session with multiple exercises with

MDSolids™ were used to complete the course.

Nature of Lab Sessions

Lab sessions began with a white board review of principles involved and procedures for the

session‟s experiments. Instructor provided “fill-in” worksheet handouts were used in most

experiments. Students were assigned to small groups for the semester. The instructor

established a rotation for groups to proceed through experiments when equipment was limited.

The two-hour sessions were busy, but most work was completed during the lab times. Write-

ups, on the lab worksheets, were generally collected at the end of the lab period.

A Sampling of Activities

A complete list of activities appears in Table 2. Several of the activities are discussed here.

More information is available on request by contacting the author.

“What‟s a Newton?”: With credit to Associate Professor XXXX, a simple first day

activity was developed to give students an intuitive sense of the force of a newton and do

unit conversions. Initially students determined how many Hersey‟s Kisses™ were in a

newton – and some remembered the figure years later. Other common items could be

used as well. The activity resulted in the equivalent of 2 homework problems.

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Force Table: Workbenches and ordinary classroom tables were made into force tables

with some common hardware as seen in Figure 1. Pulley supports were made in a variety

of ways starting with steel angle braces, eye hooks, and C-clamps. (See Figure 2.)

Students were required to hang different masses on two the three strings shown and bring

the system into equilibrium by pulling on the third string with a force gauge; pulley

positions and masses were adjusted as needed such that the knot was over the table. A

360 degree protractor was then used to identify directions for each string. Starting with a

FBD, students were to add the three applied forces confirm that the net force was zero.

Graphical, trigonometric, and components solutions were required. The set-up presented

some challenges. At first it was noted that students often know nothing about knots!

Lengths of strings often had to be adjusted and knots retied. Masses sometimes hit the

floor or became jammed in pulleys. These issues were worked out. A simple error

analysis was included. The activity required students to do the equivalent of three

homework problems.

Figure 1. Force table. Figure 2. Pulley support.

Spaghetti Truss: This activity was inspired by a university sponsored competition to

build bridges out of spaghetti and hot glue. In this activity trusses were created with

single strands of spaghetti. Note Figure 3. Using hot glue for joints, several king post

trusses were created for the same span but with different heights. The trusses were held

upright while a load was applied at mid-span by a force gauge. With the peak load

captured by the force gauge, students then used the method of joints to determine the load

at failure for each member. A clear plastic restraining fixture was sometimes used to

keep the truss in a vertical plane, but this was later deemed unnecessary. An interesting

observation by the instructor was that it appeared that failure occurred first by buckling of

the diagonal compression members. The tension members usually snapped but

apparently this was initiated by buckling of the diagonals which left the horizontal

members essentially holding the load alone. Bringing discussion and analysis of

buckling into the activity would have been quite premature for the course. The result is

some hands on plus the equivalent of two homework problems.

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Figure 3. Spaghetti truss. Figure 4. Spaghetti truss in test frame.

Belt Friction: This lab presented some rare non-linear phenomena for statics and a good

challenge mathematically. The tension ratio for belt friction is an exponential,

The activity begins with worksheet-aided review of equations of

straight lines, laws of exponents, and a better understanding of logarithms by scaled plots.

This is followed by the development of equations for straight lines on log-log and semi-

log plots. For the experiment, students wrap rope around a horizontal cylinder (Figure 4)

and use a force gauge to determine minimum forces to move and maximum forces to

hold a known weight at several angles of wrap. A semi-log plot is created and a best fit

line is drawn in. From the equation of the line, a coefficient of friction between rope and

cylinder is determined. This is a challenging lab considered the equivalent of 10

homework problems. It is time consuming and not always done. Figure 5 shows a

leather belt apparatus built at the university some time ago. This is used as well.

Figure 5. Belt friction with rope. Figure 6. Belt friction with leather.

Truss and Frame Design Exercises: These were rigorous paper-only design problems

based on a simple roof hoist commonly used in construction. Each design involved

reactions, stability, member selection, and ratings for members and fasteners to arrive at a

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design load. The exercises provided thorough review. Some students complained about

the dry nature of the exercises. The author estimates the truss design problem was

equivalent to 7 homework problems while the frame problem was equivalent to 13

problems.

Money Contest: Each student is given a 3 x 5 index card. The challenge is to modify the

card to hold as much money as possible using only specified coins. The instructor starts

by using just the flat card. (See Figure 6.) Nothing may be added to the cards such as

glue, tape, etc. The results required a special fixture be constructed as stacks of coins

would topple over before destroying the structures. While no math was involved here,

students may have developed an intuitive feel for buckling of webs and flanges of

structures. The instructor is pleased that he/she did not promise to pay each student the

amount of money on their card!

Figure 7. "Money Contest" with 3 x 5 index card.

Photographs of some of the other equipment mentioned in Tables 1 and 2 are included

next. This includes custom and purchased items.

Figure 8. Shear modulus/stress foam block. Figure 9. Fastener shear.

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Figure 10. Force gauge to turntable to T-slotted track mount.

Further Development

Equipment for some experiments needed to be improved. The force table arrangement was often

awkward, the stability activity often had contents shifting inside equipment boxes, and students

sometimes waited for equipment. The electronics in the donated universal testing machine in the

lab are dysfunctional; to make the unit functional a process controller with several load cells

were installed to replace the original equipment.

Many additional activities are possible such as buckling and the study shear and bending in

beams with strain gages. A beam with pinned and two-force member support experiment could

be developed. A strain-gaged combined load demonstrator (pressure, torsion, bending, shear)

apparatus was recently developed as a senior project.

As noted above, a follow-up paper on the class is planned.

Assessment

Assessment of the benefits of the course is difficult. One quantifiable measure would be to

compare the number of homework problem equivalents in the lab (94) to the number of

homework problems assigned by the instructor (approximately 200). This imperfect measure

suggests a lot of student involvement. Additionally students have been brought together to work

in their discipline.

The instructor collected activity-by-activity critiques at the end of the semester. Students were

asked to rate each activity on how well it help them understand important concepts with 1 being

low and 5 being high. The results had a lot of scatter, but implied that “What is a Newton?” and

Equations on Linear and Log Plots” were the least effective (3.4 and 3.3 respectively) while

MDSolids™, Pulleys, and Fastener Shear to be the most effective in enhancing learning (4.2,

4.1, 4.1) This assessment is summarized in Table 3. Students cited the hands-on experiences

and “cool applications” a plus. A frequent complaint has been evening labs and not completing

everything within two hours.

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No substantial direct measure of the student comprehension in the subjects of statics and strength

of materials has been done. An ideal direct assessment measure would be to use hourly exams

and/or the final exam to compare results of student learning between students taking the lecture

plus the subject lab class against those taking only the lecture. Originally this was not done in

part due to the effects of different instructors. Another significant variable is students: METs

are in their fourth semester (sophomores) while others taking the lecture course are either juniors

or seniors. However the lecture course in Statics and Strength of Materials generally represents

the first physics based applied engineering course for all. There may be an opportunity for

comparative assessment in the near future.

Conclusions

The enrichment provided by the course, both in physical examples, additional problems, and

time on task, clearly provided additional student engagement in this often difficult subject. The

experience also brought faculty in closer contact with students.

Equipment costs were low at the beginning in part because the lab was a developmental course.

Recommendations

Continue the lab. Enhance equipment. Establish more direct measures to assess the value of the

course.

Bibliography:

1. Statics and Strengths of Materials, H. W. Morrow, 3rd

ed., 1997

2. Kiefer, Scott. Real Life Examples in a Solid Mechanics Course. A paper presented at the

2010 ASEE Annual Conference & Exposition.

3. MD Solids™ Educational Software, version 1.7, Timothy A. Philpott, Wright State

University.

Acknowledgements

The author acknowledges the contributions of his colleagues XXXX and XXXX in the early

development of the course and the recent work of XXXX to further develop the course.

He acknowledges the contributions of Mr. XXXXX, machine lab technician, and student worker

XXXX for their craftsmanship in manufacturing some test equipment.

And finally acknowledges XXXX for her help compiling survey results.

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Table 1. Material and Equipment with Costs

Special Items Cost Custom Equipment – minor cost

force gage – “fish scale” spring type $15-100 track and swivel bases for force gages

MD Solids™ software none. transparent truss support

torque wrench moment bars

Enhanced Equipment fastener shear test

Shimpo hand held force gauges sponge shear “blocks”

FGE-100x 0-100 lb push/pull $600 belt friction tubes

FGE-200x 0-20 lb push/pull $600 belt friction apparatus (leather)

Shimpo Manual Hand Wheel Operated Test

Stand,

FGS-100H

$900

Extech digital force gage, 0-176 oz/49N

$400

Common Items

calipers/micrometers

engineer‟s scales

rulers

protractors: 180° and 360°

C-clamps

hardware store pulleys, angle brackets,

fasteners

torque wrench(es)

T-slotted mounting track

„Lazy Susan‟ turntables, 4 inch

mechanical or electronic lab scale

kg/lb/N weights

universal testing machine*

*A smaller loading machine such as the

Shimpo Manual Hand Wheel model above

is an option

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Table 2. Summary of Lab Activities

Wk Activity Description Math No.

Problems

Equipment

1 Units Review unit cancellation, force-mass-length-time

relationships.

algebra 1

1 “What is a

Newton?”

For fun, determine the number of Hersey‟s

Kisses™ in a newton.

Evaluate newton weights for accuracy.

w=mg

conversions

algebra

2 mechanical balance

1 Scales Practice with traditional engineering scales and

protractors.

scaling 2 engineers scales,

protractors

2 Triangles Trig review exercise.

Solve triangles for unknowns using drafting, CAD,

and math.

definitions

L. of Sines

L. of Cosines

6 engineering paper, scales,

protractor,CAD program

2 Vector Addition Selected homework problems are solved

graphically

vectors 3 “

3 Force Table/

Concurrent

Forces

Force table exercises are completed. A standard

table with simple pulley supports

equilibrium eqn, trig,

algebra, w=mg

3 angle brackets, C-clamps,

pulleys, masses, string,

360 °protractor

3 High Tension Study loads in ropes at near horizontal orientations

supporting weights.

“

solve graphically,

analytically

7 rope, weights, force,

scale, vertical panel,

protractor

4 Calibration of a

Torque Wrench

(per title) moments of force,

regression

3 torque wrenches, bars

with ¼ in. and ½ in.

square holes, rope,

weights

4 Three Force

System

Complete on paper exercise related to powered

parachutes.

solved 2 ways 2

5 Beam Reactions Determine reactions for beams subjected to

concentrated loads.

equilibrium equations 3 force gages, mounting

board, beam, weights

5 Beam Stability Determine upsetting load for simply supported

overhung beam.

equilibrium equations,

w=mg

2 force gage, beam,

weights, “knife edges”

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Wk Activity Description Math No.

Problems

Equipment

6 Center of

Gravity w/

Moments

Determine the center of gravity of a “mystery box”

by tipping.

moment equation –

solve for position,

w=mg

2 any sturdy box with

square base, ruler, force

gage

6 Spaghetti Truss Build/test/analyze trusses made from single stands

of spaghetti and hot glue

method of joints 2 spaghetti, hot glue, force

gage, transparent support

frame

7 Human Arm On-paper exercise estimates forces from muscles

themselves for push and pull.

moment equation 2 sketch of bone anatomy

of human arm

7 Knots short, fun exercise is basic knot tying rope

7 Pulley Systems Assemble and test pulley systems in equilibrium. FBD, 1-D equilibrium 4 hardware store pulleys,

string, weights, force

gage

8 Coef Friction

/Angle of Frict.

Determine coefficient of friction directly and with

angle of friction F= N, w=mg,

equilibrium equations

3 any mass, tiltable surface,

force gage, protractor

8 Equations for

Log Plots

Paper exercise to determine equations for straight

lines on log-log and semi-log plots.

logarithms, exponent

rules, equations of

lines

5

8 Belt Friction Determine coefficient of friction with belt friction

relationships.

calculus derivation,

logs, equations of

lines on semi-log

plots

5 belt friction apparatus:

rope/pipe, leather

belt/drum

9 Centroids Determine centroids for composite cross-sections. composite area and

moment of area

equations

2 fiberboard, scissors,

engineering paper

9 Tensile Test Determine yield and ultimate strength along with

modulus of elasticity.

def. of stress, strain,

mod. of elasticity,

regression,

4 soft aluminum wire or

plastic, universal testing

machine, ruler, calipers

or micrometers. A rubber

bands were used later.

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Wk Activity Description Math No.

Problems

Equipment

11 Modulii Determine modulii of elasticity and rigidity;

determine Poisson‟s ratio for flexible materials.

definitions of E, G,

and for pure

tension, compression,

and shear

9 sponge like material,

“shear demonstration

blocks,” force gage, ruler,

square

11 Torsion Determine torque, measure/predict angle of twist,

determine shear modulus.

torque, polar mom. of

area, angle of twist, G

from slope of T-

curve

5 torque- angle of twist

device

12 Fastener Shear Determine shear strength of fasteners in single

shear.

def of shear stress 2 universal testing

machine, shear test

fixture, soft rivets,

calipers or micrometers

12 Truss Design On paper bar truss design for a hand-operated hoist

complete with reactions, member sizing for stress,

fastener sizing, buckling.

equilibrium, frame

analysis, bending,

axial, direct shear

7

13-

15 Frame Design On paper frame design consideration for a frame

design similar to above.

last plus bending,

combined

axial/bending, shear

in beam, Euler

buckling

13

15 “Money

Contest”

Modify a 3 x 5 card to hold the max. value of

money (based on a specified coin) over 3 in. span.

develop some

intuition on buckling

beyond column

buckling

- coins or equivalent

weight, 3x5 cards,

support block or tables 4

inches apart

16 MDSolids™ Explore software for statics and strengths of

materials.

5 problems worked by

hand than with MD

Solids™

5 MD solids software

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Table 3. Summary of Student “Critique” of Lab Activities

On the last day of the lab students were

The experiences in this course can be divided into three general categories.

Please rate each activity in terms of usefulness in understanding the subjects of statics and

strengths of materials.

HANDS-ON LABS

RATING

High Low

Avg. COMMENTS (optional)

What is a Newton? 5 4 3 2 1 3.4 min.

Triangles 5 4 3 2 1 3.7

Concurrent Forces 5 4 3 2 1 3.8

Pulleys 5 4 3 2 1 4.1 max.

High Tension Rope 5 4 3 2 1 3.9

Calib. of a Torque Wrench 5 4 3 2 1 3.7

Spaghetti Truss 5 4 3 2 1 3.7

Coef. of Friction 5 4 3 2 1 3.6

Beam Stability 5 4 3 2 1 3.7

Cent. Grav. w/ Moments 5 4 3 2 1 3.8

Belt Friction 5 4 3 2 1 3.7

Equations–Linear & Log. 5 4 3 2 1 3.3 min.

Centroids 5 4 3 2 1

Fastener Shear 5 4 3 2 1 4.1 max.

Torsion 5 4 3 2 1 4.0

Modulii 5 4 3 2 1 3.5

DESIGN PROBLEMS

Human Arm 5 4 3 2 1 3.6

Frame Design 5 5 4 3 2 1 3.9

$ Contest 5 4 3 2 1 3.7

SOFTWARE

MDSOLIDS 5 4 3 2 1 4.2 max.

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