MDSolids: Software to Bridge the GapBetween Lectures and Homework inMechanics of Materials*

TIMOTHY A. PHILPOTDepartment of Basic Engineering, University of Missouri-Rolla, Rolla, MO 65409±0210, USA.E-mail: philpott@umr.edu

Current educational software for the mechanics of materials course is typically presented astutorials, worksheets, or basic analysis packages. A new software package, called MDSolids,presents an alternative to these types of products. MDSolids is conceived as a tool to help studentssolve and understand homework problems typically used in the mechanics of materials course. Thesoftware is versatile, graphic, informative, and very easy to use. MDSolids is being used at anumber of schools around the world, and feedback from users has been uniformly positive andenthusiastic.

INTRODUCTION

FOR MANY YEARS, computers and particularlypersonal computers have offered the promise of arevolution in the way that traditional engineeringtopics are taught. In some regards, this revolutionhas occurred. Computer-aided drafting and design(CADD) and sophisticated analysis packages havechanged the engineering curriculum, making itpossible for students to analyze and design at alevel of precision impossible to accomplish withhand calculations alone. Much of this improve-ment, however, occurs at the upper-end of theengineering curriculum. At the introductory level,in courses such as mechanics of materials, theimpact of computer software on the teaching offundamental concepts has been less successful.Although educational software has been packagedwith textbooks for a number of years, bookcompany editors assert that book adoptiondecisions are not strongly influenced by the accom-panying software. Therefore, if computers andcomputer software hold such promise as educa-tional tools, why isn't educational software moreeffective at teaching engineering fundamentals?

How do students learn mechanics of materials?In the field of education, Benjamin S. Bloom

proposed a developmental sequence for learning,commonly called the Bloom Taxonomy [1]. Thistaxonomy is comprised of six levels, starting withthe least level of sophistication. The originalBloom taxonomy, followed by typical examplespertaining to the mechanics of materials course, isgiven below.

. Level 1ÐKNOWLEDGE. The student is able toremember by either recognition or recall infor-mation, terminology, phenomena, etc. Example:Define the term elastic limit.

. Level 2ÐCOMPREHENSION. The student isable to know an abstraction well enough so thathe or she can correctly demonstrate its use whenspecifically asked to do so. Example: Computethe normal stress in a rod given the load and cross-sectional area.

. Level 3ÐAPPLICATION. The student is ableto apply the appropriate abstraction withouthaving to be prompted as to which abstractionis correct or to be shown how to use it inthat situation. Example: Determine the elasticmodulus given load-deflection data.

. Level 4ÐANALYSIS. The student is able tobreak down the problem into its constituentparts and to detect relationships among theparts and the way they are organized. Example:Determine the maximum load that a structurecan support given limits on both stress anddeformation.

. Level 5ÐSYNTHESIS. The student is able toput together elements and parts to form a com-plete solution. Relates concepts and processes.Able to adapt knowledge from various sourcesto solve problems. Creative expression withideas being learned and with ideas alreadyknown. Example: Use concepts of statics, shear/moment/deflections diagrams, normal and shearstresses, and combined stress analysis to design abeam.

. Level 6ÐEVALUATION. The student is ableto apply standards and determine levels ofquality. Example: Design concrete beams tobest satisfy several considerations.* Accepted 25 October 1999.

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Int. J. Engng Ed. Vol. 16, No. 5, pp. 401±407, 2000 0949-149X/91 $3.00+0.00Printed in Great Britain. # 2000 TEMPUS Publications.

Students normally enter the introductorymechanics of materials class with diverse back-grounds and differing levels of understanding.After completing the course, students should beable to bring together various skills and conceptsto solve engineering problems, as typified by Level5 in Bloom's Taxonomy. Each student learns at hisor her own rate, and unfortunately, the pace oflecture topics is sometimes faster than the studentfinds comfortable. While the more fundamentallevels of learning (knowledge, comprehension, andapplication) are addressed, the limited time avail-able for lectures requires professors to use in-classexamples and problems to teach analysis andsynthesis skills. Concepts and problem solvingskills that should be firmly in place before pro-ceeding to analysis topics are sometimes absent orunderdeveloped.

Homework assignments are the primary deviceused to develop the student's understanding of themechanics of materials topics. The typical assign-ment can be somewhat lengthy; therefore, onlyselected problems can be assigned. Professorsmay expect (or hope) that their students willwork enough extra problems so that the funda-mentals are firmly grasped, but students sometimesstruggle just to keep up with the homework andexam schedule. To supplement the student's educa-tional development, the self-study potential offeredby software would seem to be the ideal means offilling the gap between the material presented inlectures and the understanding and skills expectedin homework and exams.

EDUCATIONAL BENEFITS UNIQUETO SOFTWARE

Software can help students study mechanics ofmaterials and develop the necessary problemsolving skills in several ways that are not inherentin lectures or customary assignments.

. Correct solution and intermediate results. Whenlearning a new concept, it's very helpful to usethe correct solution as a benchmark. Knowingthat the problem has been solved correctly givesstudents confidence in their problem solvingskills and thereby provides a foundation formore challenging problems. Every textbookprovides answers to selected problems for thisreason. Software can provide the student withthe correct solution for a particular problem, butin addition to the final answer, software canprovide intermediate solutions that can be usedto confirm the calculations along the way. Theseintermediate results can be helpful in trackingdown faults in the problem-solving approach.

. What-if analyses. Observing a cause-and-effectrelationship can be quite helpful to students. Forexample, a student can develop a sense of thecolumn buckling phenomenon without calcu-lating a single number by assuming variousend support conditions and then observing the

effects on the buckled shape. This can helpstudents to develop engineering intuition thatwill help them know what the correct solutionshould be before they calculate a single number.

. Availability. In the evening hours, during week-ends, or when working at home (which may bedistant from the classroom), students don't haveaccess to professors, graduate assistants, orothers who can help them understand thecourse material. Having a versatile softwaretool at hand to supplement the textbook andlecture notes can be a big asset.

. Repetition. Some people must see or performmore repetitions involving a concept before theybegin to fully understand it. Time limits thenumber of examples that can be presented inlectures, and textbooks can present only a fewexamples. With software, students can drillthemselves, trying various numeric combina-tions for a particular problem type until theyfeel confident in their understanding of theconcepts.

. Visualization. Software can depict deformationsor show stress distributions produced in theproblem being considered. Visualization of thematerial's behavior in response to the loadsacting on it can help the student to understandthe relevant theory and to develop engineeringintuition.

CURRENT MECHANICS OF MATERIALSEDUCATIONAL SOFTWARE

Most of the current educational softwaredeveloped for the mechanics of materials coursecan be grouped into three categories: tutorials,worksheets, and basic analysis packages.

. Tutorials direct the student through a series ofprepared screens, each focused on a specificconcept or skill. In this manner, tutorials arelike lectures delivered in a different format.Recent tutorials such as the Multimedia Engi-neering series [2, 3] feature impressive presenta-tion, complete with animation, video clips, andaudio files. Despite excellent presentation, how-ever, tutorial products are limited in appli-cability. The student must follow the sequenceof the tutorial presentation in the same way thatthey would follow along in a lecture. The stu-dent must master the concept presented by thetutorial and then apply that concept to theparticular problems that they are asked tosolve in their homework assignments.

. Worksheets for equation-solving softwaresuch as MathCAD, MATLAB, and TKSolverhave also been developed to supplement themechanics of materials courses [4, 5]. Onedrawback of worksheets is that the studentmust be somewhat familiar with the host soft-ware package in order to use the worksheet. In asense, this disadvantage can also be viewed asan advantage since worksheets encourage the

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student to develop some command of theequation-solving software, and familiarity withthe equation-solving software is a skill that isuseful in later engineering courses. However, tothe student whose immediate goal is learningthe mechanics of materials concepts, the addedburden of gaining proficiency with the equation-solving software can be daunting.

. Basic analysis packages have been included inseveral widely available mechanics of materialstextbooks such as Lardner/Archer [6] and Craig[7]. These programs are useful as tools forassisting students in fundamental skills such asplotting shear and bending moment diagrams orperforming Mohr's circle calculations. Basicanalysis programs may require students todefine nodes and elements and to assign section

properties and material constants to theelements. Input for these programs has typicallybeen text-based, often requiring a user's manualto ensure that the proper data and sign con-ventions are used and to help in interpreting theprogram output. The novice engineer may feeloverwhelmed by the attention to detail neededto set up an analysis model and may havedifficulty visualizing and interpreting theresulting tables of numerical output.

All three categories of educational software aregenerally developed from the professor's point ofview, emphasizing lecture topics or permittingthe student to perform more advanced calcula-tions. While all three software categories arevalid and useful, there is room for another type

Fig. 1. Typical routine pertaining to introductory stress concepts.

Fig. 2. Bolted connections routine.

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of educational software, one developed from thestudent's point of view. Rather than forcing thestudent to solve a problem posed by the software,software can be developed that explains and solvesproblems of specific interest to the student. Tosucceed, this type of educational software must be:

. versatile in the types of problems that can besolved;

. strongly visual to illustrate the behavior ofmaterials;

. informative in explaining how and why thecalculations are performed;

. intuitive and easy-to-use so that the studentis presented with just the right amount ofinformation and analytical power.

THE MDSolids CONCEPT

MDSolidsTM is an educational software packagedevoted to the introductory mechanics of materialscourse. The hypothesis of the MDSolids concept isthat students are most interested in understandingthe specific homework problems assigned by theirprofessors, and that students will use educationalsoftware if it helps them with their immediatecourse concerns. In the process, the software canhelp to develop problem-solving skills by givingstudents an intuitive interface that guides them tothe important factors affecting various problemtypes, helps them visualize the nature of internalstresses and deformations, and provides an easy-to-use means of investigating a greater number ofproblems and variations. Based on this premise,

MDSolids was developed with several objectives inmind:

. Versatility. MDSolids is structured in modulessimilar to typical textbook chapters that can beaccessed in any sequence. Eleven modulespertaining to a wide range of common textbookproblems are presently available: basic stressand strain, beam-and-strut axial problems,trusses, statically indeterminate axial structures,torsion, determinate beams, flexure, sectionproperties, column buckling, Mohr's circletransformations, and general analysis (of axial,torsion, and beam members). Routines withinthe modules enable students to solve problemstypically found in all mechanics of materialstextbooks (for example, see Figs. 1 and 2). Thescope of MDSolids offers routines to helpstudents at all levels of understanding, fromthe most fundamental knowledge-, compre-hension-, and application-type problems tomore complex problems requiring analysis andsynthesis.

. Ease-of-input. Ease-of-input is an essentialaspect in the MDSolids concept. Solving themechanics of materials problems is confusingenough for students. To be effective, educationalsoftware must not add to the confusion. Ideally,the student should be able to define a problemintuitively and directly from a textbook withoutthe need for a user's manual. ThroughoutMDSolids, graphic cues are provided to guideusers in entering data. The illustrations can beeasily adjusted so that the MDSolids inputscreen looks very similar to the textbook illus-tration (Fig. 3). Various units (e.g., stress units,

Fig. 3. Multiple torques applied to a shaft.

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length units) are available and internal conver-sion factors are present to ensure dimensionalconsistency.

. Visual communication. Each MDSolids routinefeatures a picture, sketch, or plot that graphi-cally depicts important aspects of the problem.Sketches are used to show the direction ofinternal stresses, applied loads, and reactionforces (Fig. 4). Plots are given for a number oftopics including critical buckling stress, beam

deflections, and shaft shearing stress. As thecliche goes, `one picture is worth a thousandwords.'

. Correct solution and intermediate results.MDSolids is an `electronic solutions manual,'giving not only the correct solution for aparticular problem but also providing inter-mediate solutions that can be used to confirmthe problem solving approach.

. Text-based explanations. Many of the MDSolids

Fig. 4. Torsion deformation in a hollow shaft.

Fig. 5. Typical context-sensitive explanation of the steps necessary to solve a common mechanics of materials problem.

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modules provide extra explanations to describein words how to perform the calculations(Fig. 5). These explanations can help studentsdevelop the thought processes used in solvingmechanics of materials problems. The textexplanations are dynamic and context-sensitive,tailored specifically to the particular problem interms of the values and units entered for theproblem. Common mistakes in equilibriumequations, unit inconsistencies, and equationmanipulations become obvious when a studentcompares hand calculations with the MDSolidsexplanations.

. Help files. The MDSolids help files containinstructions for using the software, but moreimportantly, the help files contain theoreticalbackground and practical suggestions for solv-ing many types of problems. The help files alsocontain a number of worked example problems.Each example problem describes how to solvethe particular solid mechanics problem by hand,not through the use of MDSolids. Softwareusers can take advantage of MDSolids to get adetailed systematic description of the solutionprocess.

ASSESSING THE EFFECTIVENESS OFMDSOLIDS

MDSolids has been used by students at MurrayState University for four semesters. The softwarewas installed in the departmental student com-puting lab and diskettes were given out so thatstudents could install MDSolids on their homecomputers. Use of the software was encouraged,but the software was not shown or discussedduring lectures and no assignments requiringMDSolids were given. Since students were entirelyfree to choose whether to use the software or not, astatistical assessment of the software effectivenesswas not possible. However, students who tookadvantage of the software did report that theybelieved the software helped them to better under-stand the course material. Furthermore, studentshave reported that they continue to use MDSolids

to help them in subsequent courses such asmachine design and structural steel design.

The software was made available to theengineering educational community in January1998. In the first year of its availability, over3000 professors, students, and practicing engineersfrom around the world downloaded the software.The software also won a 1998 Premier Award forExcellence in Engineering Education Coursewarein a competition organized by NEEDS, theNational Engineering Education Delivery Systemof the Synthesis Coalition, a National ScienceFoundation Engineering Education coalition.Professors and students from a number of schoolshave contacted the author, and their response hasbeen uniformly positive and enthusiastic. MDSo-lids has been used in engineering, engineeringtechnology, and community college programs.MDSolids is currently available for download atwww.mdsolids.com

CONCLUSIONS

MDSolids has proven to be a valuable addi-tion to the mechanics of materials courses atMurray State University, and it is being used byprofessors and students around the world. Thesoftware was conceived as a tool to help studentsto bridge the gap between topics presented inlectures and the application of that theory insolving problems commonly used in mechanicsof materials homework assignments. UsingMDSolids, students get numerical, visual, andtextual results and details pertinent to a widerange of problems. Since MDSolids is so easy-to-use and because it provides ample feedback,students are encouraged to attempt moremechanics problems and to explore what-if vari-ations. This extra repetition can help studentsdevelop engineering intuition and greater confi-dence in their problem-solving skills. MDSolidshas been a successful supplement to help studentsattain mastery of the knowledge, comprehension,application, analysis, and synthesis levels of thelearning process.

REFERENCES

1. B. S. Bloom, ed., Taxonomy of Educational Objectives, Handbook I: The Cognitive Domain, DavidMcKay, New York, NY (1956).

2. K. Gramoll, R. Abbanat and K. Slater, Multimedia Engineering Statics, Addison WesleyInteractive, Reading, Mass. (1996).

3. K. Gramoll, R. Abbanat and K. Slater, Multimedia Engineering Dynamics, Addison WesleyInteractive, Reading, Mass. (1996).

4. T. C. Evensen, MathCAD supplement, in J. M. Gere, and S. P. Timoshenko (eds), Mechanics ofMaterials, 4th ed., PWS Publishing Co., Boston, Mass. (1997).

5. L. H. Turcotte and H. B. Wilson, Computer Applications in Mechanics of Materials using MATLAB,Prentice-Hall, Upper Saddle River, NJ (1998).

6. T. J. Lardner and R. R. Archer, MECHMAT in Mechanics of Solids: An Introduction, McGraw-Hill, New York, NY (1994).

7. R. R. Craig, MechSOLID in Mechanics of Materials, John Wiley & Sons, New York, NY (1996).

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Timothy A. Philpot is currently an assistant professor in the Basic Engineering Departmentat the University of Missouri Rolla (UMR) and a member of the Instructional SoftwareDevelopment Center at UMR. Dr. Philpot is the author of MDSolids, an educationalsoftware package for the mechanics of materials course in the engineering curriculum.MDSolids won a 1998 Premier Award for Excellence in Engineering Education Coursewarepresented by the National Engineering Education Delivery System (NEEDS). MDSolidsalso appears in one of the leading textbooks in the field: Mechanics of Materials, 2ndEdition by Roy R. Craig, Jr., published by John Wiley & Sons. Prior to joining the facultyat UMR, Dr. Philpot taught civil engineering technology at Murray State University from1986 until 1999. He also held a joint appointment in the Mechanical EngineeringDepartment at the University of Kentucky from 1997 to 1999. He received his Ph.D.from Purdue University in 1992 where his research focused on the structural reliability ofwood structures. He received a Master of Engineering (Civil) degree from CornellUniversity in 1980, and a Bachelor of Science degree in Civil Engineering from theUniversity of Kentucky in 1979. During his academic career, he has taught and developednumerous undergraduate courses in engineering mechanics, structural design, and con-struction. His current research efforts are focused on developing innovative educationalsoftware for engineering mechanics as well as the MDSolids courseware for students in themechanics of materials course. Prior to joining Murray State in 1986, Dr. Philpot workedfor six years as a structural engineer in the offshore construction industry. Much of hisindustrial experience involved the application and development of analytic softwareassociated with the installation of subsea pipelines. He is a member of the AmericanSociety for Engineering Education and the American Society of Civil Engineers. Dr.Philpot is a licensed Professional Engineer.

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