Paper ID #5731

Software Simulations and Project Based Active Learning to Engage Studentsin an Introductory Statics Course

Dr. Abhijit Nagchaudhuri, University of Maryland, Eastern Shore

Abhijit Nagchaudhuri is a Professor in the Department of Engineering and Aviation Sciences at Universityof Maryland Eastern Shore. Dr. Nagchaudhuri is a member of ASME and ASEE professional societiesand is actively involved in teaching and research in the elds of engineering mechanics, robotics and controlsystems; precision agriculture and remote sensing; and biofuels and renewable energy. Dr.Nagchaudhurireceived his bachelors degree from Jadavpur University in Calcutta, India with a honors in MechanicalEngineering in 1983, thereafter, he worked in a multinational industry for four years before joining TulaneUniversity as a graduate student in the fall of 1987. He received his M.S. degree from Tulane Universityin 1989 and Ph.D. degree from Duke University in 1992.

Dr. Rajnish Sharma, University of Maryland Eastern Shore

Dr. Rajnish Sharma is a full-time tenure-track Assistant Professor of Aerospace Engineering in the De-partment of Engineering and Aviation Sciences at University of Maryland Eastern Shore.Dr. Sharmaholds a Ph.D. in Aerospace Engineering from Texas A&M University. He has Bachelors and Mastersof Technology degrees in Mechanical and Aerospace Engineering from Indian Institute of Technology,Kanpur, India. His areas of expertise are Optimal Feedback Control, Flight Dynamics, Space systems,Dynamic Systems and Control. Dr. Sharma has 4 years of teaching experience as faculty member at theUniversity of Alabama. Currently, in addition to the basic core engineering courses such Statics (ENGE260), Dynamics (ENGE 261), and Control system (ENGE 380), he is involved to develop and teachmechanical and aerospace specialization courses such as Space Systems Design (ENAE 389), Space Nav-igation and Guidance (ENAE 412), Design of Autonomous Aerial Systems (ENAE 467), Mechatronics(ENAE/ENME 440) and Robotics (ENME 468).

c©American Society for Engineering Education, 2013

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Software Simulations and Project Based Active Learning to Engage Students

in an Introductory Statics Course

Abstract

In a typical engineering curriculum Statics is the first course offered by engineering faculty that

freshman students in the engineering major take subsequent to fundamental courses involving

basic physics and basic Calculus. While freshman design course has been widely adopted in

engineering curricula throughout the nation to provide a flavor of real world engineering, spark

creativity, incorporate project based active learning and teamwork, and improve student

retention; Statics continues to provide significant challenge to engineering students to

demonstrate that they have mastered the fundamentals to move on to courses such as Dynamics

and Mechanics of Materials that immediately follow in a typical mechanical, aerospace, civil,

biomedical, agricultural and general or integrated engineering curricula. University of Maryland

Eastern Shore (UMES) offers Bachelor of Science degree in engineering with specialization

options in aerospace, computer, electrical, and mechanical areas. All engineering students at

UMES are required to take the basic engineering mechanics sequence including Statics,

Dynamics, and Mechanics of Material.

Statics is offered as a 3 credit lecture course at UMES. Non-uniform preparation levels of

students and logistics associated with credit-hour limitation and student contact hours provide

enormous challenges to faculty to cover all fundamental concepts and assess student outcomes

that demonstrate their readiness to move on to engineering mechanics courses that follow.

Recognizing the difficulty students have in Statics, engineering faculty have discussed about

introducing an additional laboratory hour in the curriculum to motivate students and provide a

physical framework to demonstrate the abstract concepts. While additional contact hours will

certainly enhance learning; credit hour limitation of curricula is also a “realistic constraint”

around which engineering curricula has to be designed. Integration of realistic computer

simulations in and outside engineering classroom enables students to gain hands-on active

learning experiences without expensive laboratory set-ups. Moreover, unlike laboratory set-ups

that can cover only a limited number of physical systems and are available to the students only

for a limited period of time, software tools can simulate an unlimited variety of physical systems

that can be manipulated at will without risk of damage or maintenance and are available for

student use for extended periods of time.

In this paper we outline how online tools and simulation software have been utilized to introduce

active and project based learning in Statics course at UMES. The emphasis has been on

mastering important fundamental concepts while encouraging cooperative learning and

teamwork. Learning curve associated with mastering the software environment provides some

challenges, however, motivated students can overcome the initial hurdles by utilizing the faculty

office hours more effectively as they transition from a “teacher-centered” passive learning

framework to a “learner centered” active learning framework.

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1.0 INTRODUCTION

The engineering program at UMES has evolved over the last two decades from a 2 plus 2 feeder

pre- engineering program for University of Maryland College Park (UMCP), to a collaborative

4- year program in 1999 fall (with UMCP) with heavy utilization of the Interactive Video

Network (IVN) system and more recently (2007 fall) into an independent 4-year degree program

offering a bachelor of science degree with specialization options in aerospace, computer

electrical, and mechanical areas. Significant efforts were made to align the Statics course at

UMES to integrate mechanics of material and design aspects following the reform efforts at

UMCP [1]

during the years that UMES offered a 4-year collaborative program with UMES.

While the approach helps to frame Statics in the broader framework of engineering mechanics

with a design emphasis, with the development of the new independent engineering curriculum at

UMES it was decided given the non-uniform preparation level of freshman and sophomore

engineering students at UMES to focus more on the traditional fundamentals emphasizing

mechanics of rigid bodies in Statics following the paradigm outlined in conventional textbooks [2,

3]. However, engineering students are encouraged to continue to spend time using software tools

such as West Point Bridge Designer for motivation, as well as to gain insight into the

engineering design process [4]

when they take the Statics course at UMES. In the last few years

the principal author also utilized the “Engineering Statics” course through Online Learning

Initiative [5]

( Carnegie Mellon University) for initiating the inverted classroom strategy while

following the conventional framework of traditional textbooks in the subject[2,3]

. The online

approach has rich learning outcomes; however, it did not sit very well with majority of the

UMES students. While project based learning in different flavors continue to be emphasized in

teaching Statics and basic engineering mechanics courses at UMES [6]

, this paper is primarily

based on a structured effort to introduce project based active learning using the Working Model

software by Design Simulation Inc.[7]

in the spring 2012 offering of the Statics course by the

principal author. The principal author has worked with a newly hired faculty member (co-author)

who offered the Statics course at UMES in fall 2012 to continue to use the framework introduced

in spring. Formal assessment data was not available for fall 2012 at the time of writing this

paper, but informal discussions with the faculty and anecdotal evidence suggests some of the

motivated students benefited significantly while using the interactive software tools in Working

Model for both visualization and analyses of problems. The rest of the paper is arranged under

the following section headings 2) Course Description, Objectives, and Grading/Assessment

Scheme 3) the “Project Outline” provided to the students in spring 2012, followed by 4)

Discussion on Project 5) Conclusion and 6) Acknowledgment and finally the Bibliography. The

weekly schedule and the entire project assignment for the course in spring 2012 are reproduced

for ready reference in Appendix-I and II respectively,

2.0 Course Description, Objectives, and Grading/Assessment Scheme

The course description, objectives, and grading scheme are provided here for ready reference.

35% of the grade was based on project, class participation and homework and quizzes; and 20%

each on two class tests; and 25% on finals. 85-100 was A, 75-85% - B, 65-75 % -C, 55-65% - D

and below 55% was F with suitable adjustments based on over all class performance and grade

distribution.

Course Description Addition, subtraction, and multiplication of force and moment vectors; equilibrium of particles, planar,

and 3-dimensional rigid bodies under the action of forces and moments; applications of equilibrium

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principles to simple trusses, frames, and machines; introduction to stress, strain and material properties

for design analysis of structural elements. (3 Credits, 3 hours of Lecture)

Course Objectives

To apply knowledge of scalar/trigonometric and vector analysis to forces and moments

To provide fundamental concepts of analysis of 2-D and 3-D rigid bodies in statical equilibrium

with and without friction forces.

To introduce students to analysis of trusses, frames, and machines subject to static loading.

To introduce students to concepts of stress, strain, and material properties related to design

analysis of simple structural members.

Homework and Course Outline

The course content, outline and assignments are provided in Appendix-I for ready reference. The

homework problems are based on the textbook by Hibbeler [2]

used in the course.

Outcomes and Assessment

The course is assessed using formative and summative assessments in the form of homework,

quizzes, tests/finals, term project, project report and presentation. Tests, homework and quizzes

will assess ABET outcomes a, b, and e. Project, project report and oral presentations will assess

ABET outcomes c, d, g, and k. The framework based on Criterion 3 of ABET is outlined

below[8]

:

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3.0 Project Outline (Spring 2012)

Prior to project assignment the students were advised to look over the example projects in the

Statics folder of the Working Model software. Students were also provided basic outline of how

to use the software. The online manual and tutorial was also made available to the students. Also,

selected problems from the text were solved from the earlier part of the course (particle

equilibrium) using Working Model in class to make students comfortable with visualizing the

abstraction of word problems encountered through use of this powerful simulation software. The

students were grouped into teams of three and were instructed to work cooperatively to solve the

problems assigned in the project by hand and verify the solution using Working Model

simulation for various values of the applied forces, weight, spring constant, friction and other

geometric parameters associated with specific problems. It is to be noted that the problems in the

project assignment were selected to enhance basic ideas related to important and fundamental

concepts behind development of free body diagrams for particles /rigid bodies and application of

“Statics” principles to (i) basic rigid body /particle equilibrium problems, (ii) truss problems

amenable to use of method of sections, as well as method of joints, and (iii) rudimentary „Statics‟

problems related to friction.

The complete project outline provided to the students in the Statics (ENGE 260) course in spring

2012 is provided in the Appendix-II at the end of the document. The readers are encouraged to

flip through the appendices before perusing the next section and the rest of the document for

ready reference.

4.0 Discussion of Project

References to the text in the “Project Outline” in Appendix-II are to the 12th

edition of

“Engineering Mechanics: Statics” by R.C. Hibbeler which was the textbook used in the course. It

is to be noted use of textbook problems with the project had an indirect benefit of students

devoting more time to read and understand the textbook. The interested readers are encouraged

to refer to the text for more details. The part (i) of the first project assignment (1(i), see

Appendix –II) is a simulation example developed by the software company which parallels

example problems in the text related to trusses that can be solved easily using “method of joints”.

The readily available simulation example allowed students to change the applied forces observe

the software solution and verify the solutions by hand calculations to have a better grasp of the

concept behind “method of joints” by self directed active learning. The screenshot below shows

the solution of forces related to “joint X” in red arrows which correspond to the five members

(rods 9,32,12,35, and 29 from left to right in the clockwise order) that form the truss “joint X”. It

may be noted that forces on each of the members (rods) forming “joint X” can be displayed on

screen by selecting the member and selecting “Tension” from the pull down menu corresponding

to “Measure” tab on top of the software screen. In the figure below the member/rod 32 has been

selected. It should be noted three of the joint forces are “pulling” (corresponding to rods 9, 12

and 29) on the joint while two of them (corresponding to rods 32 and 35) are “pushing” on the

joint (since forces are “sliding vectors” the arrows along the member forces 32 and 35 have been

extended beyond the joint for visual convenience and it may appear as if these forces are pulling

on the “joint X” but a little reflection on the scenario would settle the issue for any insightful

reader, as it did for the students in the taking the course). It is therefore no surprise that the forces

on the members are equal to the forces at the joint as displayed in the blocks corresponding to

each block to the left of the screenshot and the ones that are “pulling” on the joint (9, 12 and 29)

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are positive indicating the members are in “tension” while the others are negative indicating that

the members 32 and 35 are in “compression”.

The part (ii) of project assignment 1 was to provide an active learning framework to the students

to get a deeper appreciation of method of sections. In this regard the Example 6. 7 solved in the

text [2]

(reproduced below for ready reference) provided a convenient framework. The “Howe

truss” in the part (i) above could be easily manipulated in the Working Model software

environment to develop the “roof truss” in the Example 6.7. Thereafter “slider tools” for force

application and “measurement tools” for determining the member forces could be easily utilized

not only to verify the solution for the specific instance provided below but also for a variety of

other applied force scenarios.

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It should be noted that, although it appears one may obtain the “roof truss” in Working Model

just by eliminating two vertical members and related joints in the “Howe truss” model used for

part (i) of the project assignment, care must be taken to make several adjustments to

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rod/member lengths , additional force application using a “slider tool” for the force at the left

support of the truss, and other minor modifications to get the exact configuration corresponding

to the “roof truss” in Example 6-7 ( part 1 (ii) of the project assignment).

The problem 5-54 of the text (see Appendix –II), which was the basis of the second problem in

the project assignment, exemplifies a basic rigid body equilibrium problem that can be easily

reproduced in Working Model. The solution for the forward

problem of finding the spring stiffness given the weight and

angle of the rod was made available to the student teams,

and they could easily model the configuration to verify the

solution using the “measure” tool in Working Model. The

solution also allowed the students to go over how to draw the

free body diagram of the rod using the forces of the pin

support, the spring, its own weight (as shown), and develop some insight on how to draw free

body diagrams, as well as develop the force and moment equations for rigid body equilibrium

problems in general. However, they soon realized that the analytical solution for the inverse

problem of finding the angle given the weight and spring stiffness posed some difficulty

although the Working Model software could simulate the solution visually from the basic

configuration developed by simply changing the

appropriate parameters and “running”/executing the

program. As it turned out the inverse problem resulted in a

nonlinear moment equilibrium equation in that had to be

solved iteratively to find the solution. Given the fixed

distance of 6 feet between the supports and the rod length

of 3ft. The schematic of the geometry of the configuration

may be represented as in the adjacent figure. The Equations

1, 2 and 3 could be developed by the students easily

following the solution provided using modified weight of 20lb (Fsp is the spring force acting on

the rod. All unknowns in the moment equilibrium equation (Equation 3) can be written in terms

of to get a nonlinear equation in his provided an avenue to discuss “bisection” method of

solving nonlinear equations using Microsoft EXCEL.

Equation 1: Provided the length of the spring

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The Working Model simulation and corresponding and portion of the iterative solution in

EXCEL using the three equations above is shown below which has been reproduced from

student team project report. It is to be noted that significant “air resistance” has to be

introducedto the Working Model solution for the vibrations to dissipate quickly and settle down

to steady state solution.

The third assignment for the project (3(i),(ii) & (iii); see Appendix –II) was selected to enhance

student comprehension of basic concepts related to friction as it applies in a typical statical

equilibrium problem related to a ladder supported by smooth ( or rough) walls and a rough floor.

The students could easily relate to the problem in the real world. Once again given the solution

of an example (reproduced) below in the text, the student teams could study the solution and get

a firm hold on the related free body diagram and analytical solution. This in turn also allowed the

students to set-up and model the configuration in Working Model appropriately and verify the

solution. Once the accurate configuration was developed it was easy to change the weight,

friction coefficient, additional force on the ladder along different lengths of the ladder to

simulate a man climbing the ladder etc. and note when the ladder slipped. Analytical solution

developed by one of the student teams following Example 8-3 with a modified scenario of a 15

lb ladder, smooth wall, and friction coefficient of 0.1 and the corresponding Working Model

solution are reproduced below. As in previous examples the Working Model solution matches

the analytical solution very closely.

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5.0 Conclusion

The project assignment promoted cooperative and active learning effectively. Since project

assignments closely resembled text problems, it necessitated the students to spend more time in

reading and understanding. Once the initial hurdle of mastering the fundamentals of the software

tool was overcome it was easy for students to create the models corresponding to the assigned

problems and change significant parameters to set-up different scenarios. In the effort to

establish correspondence between the Working Model solution and the analytical solution for

these different scenarios, it was apparent that the students were moving more into an “active

learning” framework from a more “passive learning” paradigm that they were used to. The

software was made available on all computers in the computing facility for the engineering

students and allowed the students to work on their own time. The stronger students who quickly

mastered the software not only exhibited enhanced understanding of the subject but also helped

their teammates with some of their misconception. During the project presentations students

were encouraged to ask questions to learn from other teams about their approach and seek

clarification of concepts when appropriate. The project assignment also promoted better

utilization of the faculty office hours by some of the students (unfortunately not all!), who

seemed genuinely excited with the software simulations and their correspondence with analytical

solutions. Some students also put additional effort to master the software and devoted time over

and beyond course requirements when they were made aware that the simulation environment

was also suitable for Dynamics (ENGE 261) and Control Systems (ENGE 382) courses to follow

and was likely to be used for project assignments in these courses as well.

The principal author has experimented with different project assignments and online learning

tools in the Statics course to engage students. The percentage of students getting A, B, C, D and

F grades and „withdrawing‟ (W) from the course beyond the initial drop period over the last three

semesters that the principal author has offered Statics is shown below. The student performance

reflects the non-uniform preparation level of the students. Students with „F‟ and „W‟ grades and

some of the „D‟ students have not mastered basic mathematics fundamentals and will be well

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advised to change majors. Moreover, significant numbers of the students who seem to have

mastered basic algebra and trigonometry have trouble with interpreting the problem statements

and setting up the analytical framework for solving the problem. This may well be a

manifestation of how they have taught basic mathematics courses in high school and preparatory

college courses. More outreach efforts for high school mathematics teachers along the

approaches outlined in reference [9]

may have a favorable impact in this regard.

Use of text problems for which solutions were made available as the basic starting point of

project assignments, integrated with software simulations as outlined in this paper, for the spring

2012 offering of the Statics (ENGE 260) course, have had perceptible impact on improved

interpretation of “wording” of the problems resulting in appropriate analytical set-up and

subsequent trigonometric and algebraic manipulation to solve the problems, among students.

The approach has also promoted active and cooperative learning besides providing an avenue for

students to demonstrate their communication skills through written reports and oral

presentations. From improved interaction with the motivated students during office hours, the

authors are convinced the approach has promoted excitement for learning and improved

comprehension. It is difficult to decipher from the student performance bar chart above, the

direct impact of the particular project assignment in spring 2012 in the course as this is related to

several factors, including and not limited to, non-uniformity of student preparation, and non-

uniformity of student recruitment from year to year. Discussions are underway among

engineering faculty and administration to address this issue with due consideration of its mission.

6.0 Acknowledgement

The authors would like to acknowledge the engineering laboratory manager for installing the

software in all the machines in the engineering computing facility at UMES and being available

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to the students when needed. Authors would also like to acknowledge all the students who

actively participated in the project and in-class and out of class-room discussions. Some of the

figures in the paper have been reproduced from the student project reports.

Bibliography

1. Bruck,H.A., Anand,D.K., Fourney, W.L., Chang, P.C., and Dally, J.W., “Development of an Integrated Statics

and Strength of Materials Curriculum with an Emphasis on Design”, Proceedings of the 1999 Annual Conference

and Exposition of American Society for Engineering Education, Charlotte, NC, June 20-23, 1999.

2. Hibbeler, R.C., Engineering Mechanics:Statics, Pearson/Prentice Hall , 12th

. Ed., 2010

3. Bedford, A.M., and Fowler, W., Engineering Mechanics:Statics, Pearson/Prentice Hall, 5th

ed., 2008

4. West Point Bridge Designer (2013), Online : http://bridgecontest.usma.edu/download.htm

5. Steif,, P.S., and Dollár,A.,”Web-Based Statics Course Used In An Inverted Classroom”; Proceedings of the

American Society for Engineering Education Annual Conference & Exposition, Austin, Texas, June 2009

6. Nagchaudhuri, A. and Yilmaz, E., “Design Experience Using Software Tools in Undergraduate Engineering

Mechanics Courses”, Paper # IMECE2008-69242, Proceedings of IMECE’08, 2008 ASME International

Mechanical Engineering Congress and Exposition, Oct.31- Nov. 6, Boston, Massachusetts, USA.

7. Working Model 2D, http://www.design-simulation.com/wm2d/index.php

8. ABET Criteria 3(Student Outcomes), Online http://www.abet.org/DisplayTemplates/DocsHandbook.aspx?id=3149

9. Nagchaudhuri, A., and Seaton, D., “An Experimental Mathematics Course for Middle and High School

Mathematics Teachers”, Proceedings of 2005 ASEE Annual Conference, June 12-15, Portland, CD ROM.

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Appendix –I

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Appendix II

STATICS PROJECT ( Spring 2012)

Project report and presentation due on last week of classes. DO problem 1 and any one from 2 and 3

Email electronic versions to anagchaudhuri@gmail.com when completed.

1. (i) The snap shot shown below is a Working Model 2D simulation of a HOWE Truss when loaded as shown. The

simulation is available as a demo within the Working Model 2D software. In a typical installation you will find the

demo file named “Howe Truss.wm2d” in the location “C:\Program Files\Working Model 2D\Simulations\Statics”.

As the first step in your project work find the demo file and run it for joint loads of -2000N as shown and also for

each load of -1000N . Obtain tensions on the members ( red arrows) for which the forces at the joint are shown by

selecting the member and measuring tension/ compression. Values should correspond to the joint forces. Verify

these values by hand calculations using method of joints.

1(ii) After completing part (i) use select all and copy and paste the Howe Truss.wm2d in a new Working Model 2D

window. It can be relatively easily modified to recreate the roof truss of Example 6.7 in page 285 of your text book

as shown in the snap shot from Working Model 2D Window shown below. Note you will need to add a new force

and slider control for it and modify some of the truss members. By measuring tension/compression in the rods

corresponding to members ED, EF and EB show that Working Model provides a solution very close to the one

calculated in page 285 of your text when the loads applied are same as in the example (shown below). For additional

credit change the loads to 1000N, 1000N, 500 N and 1000 N and obtain the tensions/compressions in rods ED,EF,

and EB using Working Model as well as hand calculations using method of sections following the approach

followed in Example 6.7 ( page 285)

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2. Study the solution for problem 5-54 ( pg 2-34) of your text as reproduced below thoroughly. Verify that the angle

is indeed 30 deg. solution using Working Model when spring stiffness is inputted as K = 11.2 lb/ft. (i) Change

the spring stiffness to 15lb/ft and calculate the angle without using working model and verify the result using

working model ( as shown in the snap shot below).(ii) Also obtain the solution by hand when the weight of the rod

AB is changed to 20 lbs and the stiffness of the spring is changed to 10 lbs/ft. Verify the solution using Working

Model 2D

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3. (i)Study example 8.3 ( page 397) of your text and recreate the problem in Working Model as shown in

the snapshot below. Different friction values can be inputted by double clicking on the wall and floor

(orange and green). The weight of the ladder can be changed also as required. The ladder of appropriate

length and can be placed at various angles to obtain the solution.(ii) Obtain the solution when coefficient

of friction of the wall (orange) is changed to 0.1 and weight of the ladder is 15 kg. Solve the problem by

hand as well as working model.(iii) For extra credit simulate a person climbing the ladder by adding a

vertical force of 50 kg at different vertical distances on the ladder and determine when and if the ladder

slips if it is placed at an angle of 60 degree with the horizontal. Verify by hand calculations. Start with

coefficient of friction at the wall and floor as 0.3. Explore the effect of reducing wall and floor friction

coefficients

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