Conference Session

New Teaching Methods in Mechanics

Collection

2014 ASEE Annual Conference & Exposition

Authors

Ruben Pierre-Antoine, Stanford University; Sheri D. Sheppard, Stanford University; Mark Schar, Stanford University

Tagged Divisions

Mechanics

the course4. A concept map is essentially a mental web of connected terms or topics,where the centermost term is the primary learning focus and lines are used to connect relatedconcepts. This results in a web of interconnected concepts that reflect the way studentsassimilate the new information. The three main questions guiding the study reported here are: 1) How can we decode the variety of ideas and structures that students include in their concept maps? 2) How can we use discoveries from this decoding to make lectures and labs more effective? 3) What improvements can be made to the way students are assigned drawing concept maps to further increase the usefulness of concept maps in capturing their learning? The

Conference Session

Flipped Classrooms in Mechanics

Collection

2015 ASEE Annual Conference & Exposition

Authors

Yufeng Hu P.E., Western Michigan University; Javier Martin Montefort P.E., Western Michigan University; Edmund Tsang, Western Michigan University

Tagged Topics

Diversity

Tagged Divisions

Mechanics

poorlyin subsequent courses.Traditionally, Statics has been taught in face-to-face lectures. The traditional lecture formatprevents the students from pausing to reflect and understand what is being explained and theymay often miss important points. A goal of Statics is to have students learn to solve problemsindependently, which is a practice-intensive and time-consuming effort for which the lecture canprovide guidance yet relatively little direct assistance. The traditional lecture is an instructor- Page 26.189.2centered, relatively passive method of learning. While lecturing still remains an effective andimportant way of conveying knowledge, it

Conference Session

Mechanics Classroom Demonstrations

Collection

2016 ASEE Annual Conference & Exposition

Authors

Joel Alejandro Mejia, Angelo State University; Wade H Goodridge, Utah State University; Benjamin James Call, Utah State University - Engineering Education; Steven David Wood, Utah State University

Tagged Topics

Diversity

Tagged Divisions

Mechanics

reflect on their work and analyze theirown problem solving approaches. For instance, some participants were able to use the physicalmanipulative so answer questions very quickly or to reinforce concepts. Some participants wereable to use the physical manipulative without problems, but other felt that the physicalmanipulative was not as intuitive and they required guidance. Although the physicalmanipulative was designed to be very user-friendly, some of the participants required a certaindegree of guidance on how to use the physical manipulative. Some of the participants didn’tknow what to observe or how to detach some of the members in the truss. Thus, theimplementation of the physical manipulative in an engineering mechanics course may

Conference Session

Student Advancement in Mechanics of Materials

Collection

2018 ASEE Annual Conference & Exposition

Authors

Nick A. Stites, Purdue University, West Lafayette (College of Engineering); Charles Morton Krousgrill, Purdue University-Main Campus, West Lafayette (College of Engineering); Jeffrey F. Rhoads, Purdue University-Main Campus, West Lafayette (College of Engineering); Edward J. Berger, Purdue University-Main Campus, West Lafayette (College of Engineering); Jennifer Deboer, Purdue University-Main Campus, West Lafayette (College of Engineering); Angela Goldenstein, Purdue University

Tagged Divisions

Mechanics

materialis based upon work supported by the National Science Foundation under grant number DUE-1519412. Any opinions, findings, and conclusions or recommendations expressed in this materialare those of the author(s) and do not necessarily reflect the views of the National ScienceFoundation.References[1] D. Evenhouse, N. Patel, M. Gerschutz, N. A. Stites, J. F. Rhoads, E. Berger, et al., "Perspectives on pedagogical change: Instructor and student experiences of a newly implemented undergraduate engineering dynamics curriculum," European Journal of Engineering Education, 2017.[2] J. F. Rhoads, E. Nauman, B. Holloway, and C. Krousgrill, "The Purdue Mechanics Freeform Classroom : A new approach to engineering mechanics

Conference Session

Anything New in Dynamics?

Collection

2008 Annual Conference & Exposition

Authors

Geoff Rideout, Memorial University of Newfoundland

Tagged Divisions

Mechanics

F34 x ? / F43 x F34 y ? / F43 y F14 ? k SD y SD - RSD v SDywhere negative signs come from the fact that in Figure 5, springs and dampers are defined asbeing positive in extension. Eq’ns (19) reflect the fact that tension forces at point B, forexample, will create negative forces F23x and F23y as drawn on the free body diagrams of Figure6. In Figure 6 all constraint forces have been arbitrarily drawn in positive directions. One mayinstead choose to draw equal and opposite forces on the free body diagrams and remove thenegative signs from Eq’ns (19). If only the equations for bodies 2 and 3 were considered, with jforce F32 omitted, then the resulting equations would

Conference Session

Innovative Mechanics Education Programs and Projects

Collection

2007 Annual Conference & Exposition

Authors

Jean Nocito-Gobel, University of New Haven; Gregory Broderick, University of New Haven; Samuel Daniels, University of New Haven; Michael Collura, University of New Haven; Richard Stanley, University of New Haven

Tagged Divisions

Mechanics

of courses taken by students during their first two years in the traditionalcurriculum reflects a traditional approach to learning mechanics in civil (CE) and mechanical(ME) engineering programs. Students took their first physics course, PH150Mechanics/Heat/Waves, in the traditional curriculum second semester freshman year in whichthey were introduced to basic particle kinematics and kinetics and force resolution. Firstsemester sophomore year, students gained an understanding of the behavior of simple structuresunder various loadings, and investigated stresses and deformations as they relate to the design ofsimple mechanisms and structures in CE205 Statics and Strengths. This 4 credit coursecombined topics from both Statics and Strength of

Conference Session

Internet Delivery of Mechanics Courses

Collection

2007 Annual Conference & Exposition

Authors

Peter Boyle, Saint Mary's University

Tagged Divisions

Mechanics

operational defects did have tobe accommodated.Students purchased the CMS access code, either online or from the campus bookstore. Nearlyall of the students bought both access code and the hardcopy text, reflecting the feeling thathardcopy reading was easier than reading from a screen.Navigating with the CMS was effortless in both instructor and student views, with some minornuisances. Involuntary logoff occurred too rapidly. Making alterations to assigned work createda new assignment which awkwardly coexisted with the old assignment. Exporting from thegrade book to Excel never worked properly. With the publisher’s help, some of these flaws wereeliminated.E-LecturesIn the courses discussed here, about one half of the course lectures were electronic

Conference Session

Statics & Strength of Materials - A nice couple

Collection

2013 ASEE Annual Conference & Exposition

Authors

Jamie Douglas, University of Wisconsin Colleges; Mark H Holdhusen, University of Wisconsin, Marathon County

Tagged Divisions

Mechanics

. Though no calculations were performed in Page 23.433.7this demonstration, students were asked to reflect on their hypothesis from the previousexperiment on creep and consider the design implications with different materials that undergotemperature fluctuations.Lab 6: Stress ConcentrationIn Lab 6 students explored the effects of shape on the concentration of stresses. This lab waslargely a demonstration and observation experiment. Students were given two templates andasked to use those templates to cut out standard shapes (dog-bone and square-edge) of aluminumfoil. Using the same hanging setup as the copper wire tension experiment, students

Conference Session

Teaching Mechanics of Materials & General Mechanics

Collection

2010 Annual Conference & Exposition

Authors

Ing-Chang Jong, University of Arkansas

Tagged Divisions

Mechanics

superposition.IV. Concluding RemarksIn the method of model formulas, no explicit integration or differentiation is involved in applyingany of the model formulas. The model formulas essentially serve to provide material equations(which involve and reflect the material property) besides the equations of static equilibrium ofthe beam that can readily be written. Selected applied loads are illustrated in Fig. 1(a), whichcover most of the loads encountered in undergraduate Mechanics of Materials. In the case of anonlinearly distributed load on the beam, the model formulas may be modified by the user for aspecific nonlinearly distributed load.The method of model formulas is best taught to students as an alternative method, after they havelearned one or more of

Conference Session

Teaching Mechanics of Materials & General Mechanics

Collection

2010 Annual Conference & Exposition

Authors

Edward Anderson, Texas Tech University; Roman Taraban, Texas Tech University

Tagged Divisions

Mechanics

, and reflection as well as the morecommon define, plan, execute and check steps. The McMaster problem solving program uses astructure similar to that of Wankat and Oreovicz and implements it across entire curricula. Page 15.848.2Gray’s structured approach emphasizes pattern-matching that starts with a small number ofgeneral equations that students reduce to fit a given situation. The Mettes problem solvingschema is based upon a flow chart of problem solving steps and a constructionist approach tolearning. Litzinger’s integrated model emphasizes problem representation and the conversionfrom one representation (say problem statement) to another

Conference Session

New Teaching Methods in Mechanics

Collection

2014 ASEE Annual Conference & Exposition

Authors

Brian P. Self, California Polytechnic State University; Edward J. Berger, University of Virginia

Tagged Divisions

Mechanics

were to help faculty (quote3): 1) engage in reflection and continuous improvement of learning, both their own and their students 2) facilitate conversations about teaching and learning in the process of building a learning community 3) create a collaborative learning environment with faculty and peers 4) build confidence in curriculum development including designing, guiding, and assessing learning 5) learn with and about technology in the process of improving curriculum, and 6) connect teaching and research and bridge the gap between theory and practice.Recognizing the potential for widespread engagement of engineering educators, an initiative onAdvancing Engineering Education through Virtual Communities of Practice

Conference Session

Teaching Dynamics

Collection

2014 ASEE Annual Conference & Exposition

Authors

Matthew West, University of Illinois at Urbana-Champaign; Geoffrey L. Herman, University of Illinois, Urbana-Champaign

Tagged Divisions

Mechanics

assists in maintaining engagement.However, it remains to be seen whether recruitment of new faculty into the CoP will continue, andwhether the structure is sustainable in the long term.6. Reflections and RecommendationsThe formation of a CoP to reform and improve Introductory Dynamics has provided aproof-of-concept for the effectiveness of the CoP model of education reform. Not only has thecourse improved student and faculty attitudes toward the course, but it has also sparked the reformof additional courses. The reliance on community rather than individuals has sustained thereforms through multiple instructors and multiple semesters

Conference Session

Statics - They can move at constant velocity!

Collection

2013 ASEE Annual Conference & Exposition

Authors

Abhijit Nagchaudhuri, University of Maryland, Eastern Shore; Rajnish Sharma, University of Maryland Eastern Shore

Tagged Divisions

Mechanics

rods 9, 12and 29) on the joint while two of them (corresponding to rods 32 and 35) are “pushing” on thejoint (since forces are “sliding vectors” the arrows along the member forces 32 and 35 have beenextended beyond the joint for visual convenience and it may appear as if these forces are pullingon the “joint X” but a little reflection on the scenario would settle the issue for any insightfulreader, as it did for the students in the taking the course). It is therefore no surprise that the forces Page 23.1075.5on the members are equal to the forces at the joint as displayed in the blocks corresponding toeach block to the left of the

Conference Session

Using Technology to Support Learning in Mechanics

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Anna K. T. Howard, North Carolina State University at Raleigh

Tagged Divisions

Mechanics

learning.Three Small Lessons Learned1) There is a huge value in having someone else look over all your materials, especially someonewho is not an engineer. Being forced to justify the design decisions for a course that I’ve taughtfor almost fifteen years solidified which ones were important.2) It was interesting how resistant I was to the scroll of death. Reflection has shown that myexperience with dial-up internet has lingered in how I see web design. Working with youngerpeople led to a course design that was closer to what my students needed.3) Having a common lexicon with young graphic designers needed intentional communication.We were six weeks into design before we settled on what load, phase, and cycle would mean. (Itwas also very entertaining to

Conference Session

Bringing a Different Perspective

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Eli Broemer, Michigan State University; Geoffrey Recktenwald, Michigan State University

Tagged Divisions

Mechanics

case studies, reflections, portfolios and projects.” [6].The U.S. Military Academy at West Point ended its second chance program, returning to a policywhere cheating results in expulsion from the Academy [7]. Even video game companies aretrying to find ways to stop non-academic cheating. Call of Duty recently banning 60,000 userswho were cheating in its online gaming platform [8]. Cheating, and specifically cheating withChegg, was significant enough to warrant an extensive article in Forbes Magazine titled, “This$12 Billion Company is Getting Rich Off Students Cheating Their way Through COVID” [9].Solutions to the problem of cheating can be daunting. Research suggests that the best cure forcheating is building a culture of strong academic

Conference Session

Enhancing Mechanics Instruction

Collection

2008 Annual Conference & Exposition

Authors

Gary L. Gray, Pennsylvania State University; Francesco Costanzo, Pennsylvania State University

Tagged Divisions

Mechanics

amount of material that can be taught and that the students’ interest in the material isenhanced.IntroductionTo maintain and enhance our nation’s ability to be on the forefront of technology development,colleges and universities have been called to adopt the most effective teaching practices of Science,Technology, Engineering, and Mathematics (STEM) courses as well as to provide undergraduateswith opportunities to study STEM “as practiced by scientists and engineers as early in theiracademic careers as possible”.1 In fact, the practice of engineering today requires that graduatesbe prepared in a large variety of ways, which are reflected in ABET criteria as well as other recentstudies.2, 3 In addition, as supported by a wide body of literature

Conference Session

Mechanics Education Programs and Projects

Collection

2008 Annual Conference & Exposition

Authors

Christopher Papadopoulos

Tagged Divisions

Mechanics

work of their peersand provide critiques at a draft stage. Out of this process, final work is improved, andcommunications skills are also developed. Cloete5 emphasizes the importance of self-reflection in fostering critical thinking. Although these efforts did not attempt directmeasures of student cognition, perhaps in the future, data can be collected to evaluatestudent cognition in peer review exercises.Longer-term Assessment. To complement direct observation of student reasoning andcognition during problem-solving exercises, how can we determine if students are Page 13.226.10retaining knowledge and problem-solving skills into the future? Most methods

Conference Session

Teaching Mechanics of Materials and General Mechanics Education

Collection

2009 Annual Conference & Exposition

Authors

Henry Christiansen, Brigham Young University; Steven Benzley, Brigham Young University; Spencer Guthrie, Brigham Young Univeristy; Gaurab Paudel, Brigham Young University

Tagged Divisions

Mechanics

Engineering Technology students take bothstatics and mechanics of materials with the engineering students. The College decision to givethe Civil and Environmental Engineering Department this overall responsibility has significantlycontributed to the economy of the resulting program.As shown in the five year average enrollment graph, Figure 1, the average mechanics course sizewas growing modestly but remained under 40 students until in the early nineteen eighties. Then,during the late nineteen eighties and into the early nineteen nineties, the average class size grewto about 100 students per class and has remained approximately at that level. The early growthrate reflected a desire and ability to keep classes small and the average rate of increase

Conference Session

Teaching Dynamics

Collection

2009 Annual Conference & Exposition

Authors

Benson Tongue, University of California, Berkeley

Tagged Divisions

Mechanics

problems can be given. Even so, the number of students complaining of time pressurewill remain non-zero. Although sometimes this complaint is specious (when non amount of timewould help that particular student) at others it reflects the fact that some people approachproblems slowly but truly do understand the material.By eliminating such exams, these problems can be avoided. In the miniquiz format there is only asingle problem and the students are told ahead of time what the area of coverage will be. Hencetheir studying is directed toward that area. Only a fraction of the class time is taken up with thequiz and since there’s only one problem, a goodly amount of time can be allocated to it, reducingthe “no time!” complaints.Since there are many

Conference Session

Dynamic Pedagogies for Engineering Dynamics

Collection

2018 ASEE Annual Conference & Exposition

Authors

William E. Howard, East Carolina University; Jeffry R. Foeller, East Carolina University; Karen A. De Urquidi, East Carolina University

Tagged Divisions

Mechanics

rankings reflect theimprovement of a student’s scores after the first test. The hours per week spent outside of classby quartile are summarized in Table 5. Table 3 Utilization of Resources by Quartiles QUESTION OF THE CLASS SUMMARIES TEXTBOOK DAY Ranked Ranked by Ranked Ranked by Ranked Ranked by by Grade Improvement by Grade Improvement by Grade Improvement Top 55% 47% 37% 38% 20% 13% Quartile Second 48% 47% 46% 42% 13

Conference Session

Curriculum and Instruction in Engineering Mechanics

Collection

2018 ASEE Annual Conference & Exposition

Authors

Javad Baqersad P.E., Kettering University; Yaomin Dong, Kettering University; Arnaldo Mazzei, Kettering University; Azadeh Sheidaei, Iowa State University; Basem Alzahabi, Alghurair University

Tagged Divisions

Mechanics

havebeen generally positive. The authors will use results of future surveys to assess the success ofthis project and to improve student engagement. AcknowledgmentsThe research presented in this paper is partly supported by the Kern Family Foundation grantentitled “Implementation of Innovation and Entrepreneur Mindset Concept into Mechanics ofMaterials”. We would like to acknowledge and appreciate the supports by Dr. Massoud Tavakoliand Dr. Mohammad Torfeh, principal investigators of the grant at Kettering University. Anyopinions, findings, and conclusions or recommendations expressed in this material are those ofthe author(s) and do not necessarily reflect the views of the sponsoring organizations. References[1] J. Baqersad, P. Poozesh

Conference Session

Mechanics Division Technical Session 5

Collection

2019 ASEE Annual Conference & Exposition

Authors

Amitabha Ghosh, Rochester Institute of Technology

Tagged Divisions

Mechanics

and understand theconventions and math principles. I really appreciate how Dr. Ghosh focuses on making sure youunderstand the physical reasons behind the math and formulas.I think his grading appropriately reflects his teaching/testing style, which I like. Dr. Ghosh wants peopleto understand his material on an intimate, conceptual level which requires tests and quizzes be moredifficult because you cannot simply rely on knowing formulas. He therefore is quite lenient with gradingand awarding points to wrong answers that he believes were conceptually on the right track. He asks alot from his students but does not punish a more difficult style of teaching/learning with harsh grading, ifthat makes sense…References[1] E. C Hensel and A. Ghosh, “A

Conference Session

Mechanics Classroom Demonstrations

Collection

2016 ASEE Annual Conference & Exposition

Authors

Aldo A. Ferri, Georgia Institute of Technology; Bonnie H. Ferri, Georgia Institute of Technology

Tagged Divisions

Mechanics

done withoutopportunities for reflection and metacognition have missed the opportunity to create deeperunderstanding [17]. Shavelson, et al. [20] refer to four different types of knowledge: declarativeknowledge (“knowing that”), procedural knowledge (“knowing how”), schematic knowledge(“knowing why”), and strategic knowledge (“knowing when, where, and how our knowledgeapplies”). This framework provides a useful way of evaluating laboratory experiences; what istypically termed “inquiry based laboratory exercises,” are ones that reach the higher levels of theknowledge taxonomy [12]. Pre-labs and other types of preparation are also important as identifiedin Kolb’s experiential learning cycle [21] and [18]. Without “just in time” lectures and pre

Conference Session

Teaching Mechanics of Materials

Collection

2014 ASEE Annual Conference & Exposition

Authors

William E. Howard, East Carolina University; Odis Hayden Griffin Jr. P.E., East Carolina University; Ihab Ragai, East Carolina University

Tagged Divisions

Mechanics

from an Internet sourceand write a reflection summarizing the article and relating it to their careers. We have foundMachine Design magazine’s website12 in particular to be an excellent source for this type ofarticle. For outcome i, we found a white paper on non-linear analysis from SolidWorksCorporation13 to be appropriate. After completing the non-linear analysis assignment, we gavethe students the assignment as follows: In this assignment, we used tabulated results that have been available for many decades along with non-linear software that was not readily available to engineering graduates of only a few years ago. Without a doubt, you will need to keep learning throughout your career. Besides formal classes, trade

Conference Session

Teaching & Learning Statics and Mechanics of Materials

Collection

2016 ASEE Annual Conference & Exposition

Authors

Andrew Lee, Arizona State University; Haolin Zhu, Arizona State University; James A Middleton, Arizona State University

Tagged Divisions

Mechanics

University Dr. Haolin Zhu received her PhD in Solid Mechanics and Computational Science and Engineering from Cornell University. She is currently part of the engineering education team in the Ira A. Fulton Schools of Engineering at Arizona State University. Currently she focuses on designing the curriculum for the fresh- man engineering program as well as the NAE Grand Challenge Scholars Program. She also designs and teaches courses in mechanical engineering at ASU. Her interests include innovative teaching pedagogies for increased retention and student motivation, innovations in non-traditional delivery methods, as well as structured reflective practices throughout the engineering curriculum.Prof. James A Middleton

Conference Session

Active Learning & Laboratories in Statics, Dynamics, and Mechanics

Collection

2016 ASEE Annual Conference & Exposition

Authors

John W. Sanders, University of Illinois, Urbana-Champaign; Matthew West, University of Illinois, Urbana-Champaign; Geoffrey L Herman, University of Illinois, Urbana-Champaign

Tagged Divisions

Mechanics

was supported by the College of Engineering at the University of Illinois atUrbana-Champaign. This work was also supported by the National Science Foundation undergrants DUE-1347722 and CMMI-1150490. The opinions, findings, and conclusions presented inthis paper do not necessarily reflect the views of the National Science Foundation or the authors’institution.Bibliography [1] M. M. Lombardi. Making the grade: The role of assessment in authentic learning. EDUCAUSE Learning Initiative, 2008. [2] J. Reeve. Why teachers adopt a controlling motivating style toward students and how they can become more autonomy supportive. Educational Psychologist, 44:159–175, 2009. [3] F. Marton and S. Booth. Learning and Awareness. New York: Lawrence

Conference Session

Learning Environments for Statics, Dynamics, and Mechanics of Materials

Collection

2017 ASEE Annual Conference & Exposition

Authors

Jakob C. Bruhl, U.S. Military Academy; James Ledlie Klosky, U.S. Military Academy; Todd Mainwaring P.E., U. S. Military Academy; Joseph P. Hanus, U.S. Military Academy

Tagged Divisions

Mechanics

get a better indication of student opinion about theeffectiveness of these activities, a survey was administered at about the mid-point of the course.Students agreed (4.2 / 5.0, n = 95) that the hands-on learning activities completed to that pointwere contributing to their learning. As shown in Figure 9, student opinion increased slightly (4.3/ 5.0, n = 227) by the end of the term when the same question was asked again on the course-end-feedback survey. Figure 9 Student feedback on value of hands-on learning activities (1-strongly disagree, 2-agree, 3-neither agree nor disagree, 4-agree, 5-strongly agree)Many of the student comments on the mid-term feedback survey reflected a positive opinion ofthe hands-on activities. A few

Conference Session

New Teaching Pedagogies: Methods and Assessments

Collection

2014 ASEE Annual Conference & Exposition

Authors

Benjamin W. Caldwell, LeTourneau University; Colleen M. Halupa, LeTourneau University

Tagged Divisions

Mechanical Engineering, Mechanics

longer enough to ensure success of the majority ofstudents in the educational environment today. Professors must evaluate techniques and methodsthat can assist in meeting the multiple learning styles of the students in their classes. For thestudent, transformation includes reflection, practice, and creating personal relevancy andmeaning in the learning process. This is the framework of this pilot study on an onlineEngineering Statics class.Literature ReviewOnline courses were created and deployed in numerous fields throughout the 1990s and 2000s.Online engineering courses lagged behind because of the difficulty of converting face-to-facemathematics and science courses to an online format.1 The technology was not advanced enoughto deploy these

Conference Session

Teaching Statics

Collection

2014 ASEE Annual Conference & Exposition

Authors

Paul S. Steif, Carnegie Mellon University; Levent Burak Kara, Carnegie Mellon University; Luoting Fu

Tagged Divisions

Mechanics

toassociate any equations with a specific subsystem. Admittedly, students in statics do sometimeswrite down equations of equilibrium without specifying the subsystem or drawing its free bodydiagram. This design feature of the tutor reflects a trade-off between granting the user latitude tosolve freely vs constraining the user. The task of interpreting a bundle of equations, eachunclearly associated with a free body diagram, seemed likely to result in false errors. Note alsothat by clicking on ΣFx = 0, for example, the user signals to the tutor that the equation should bejudged by comparison with the correct summation of forces in the x-direction for that subsystem,in terms of the variables and constants as they appear in its free body diagram.The

Conference Session

Teaching Mechanics

Collection

2011 ASEE Annual Conference & Exposition

Authors

Ing-Chang Jong, University of Arkansas; William T. Springer, University of Arkansas

Tagged Divisions

Mechanics

understanding the deflection ofbeams, and students favor this method in solving the problems. (a) Quiz result on using MoI (b) Quiz result on using MoMF (overall average = 69.1%) (overall average = 79.7%) Fig. 14. Students’ performance in using MoMFIV. Concluding RemarksIn the method of model formulas, no explicit integration or differentiation is involved in applying Page 22.1380.15any of the model formulas. The model formulas essentially serve to provide material equations(which involve and reflect the material property) besides the equations of static equilibrium ofthe