Conference Session

Flipped Classrooms in Mechanics

Collection

2015 ASEE Annual Conference & Exposition

Authors

Keri Ryan, University of Nevada, Reno; Adam Kirn, Univeristy of Nevada, Reno

Tagged Divisions

Mechanics

classroom (1 in Section 1 and 4 inSection 2) and students that perceived the flipped classroom took more of their time than atraditional approach (1 in Section 1 and 3 in Section 2).The rate of negative feedback was higher in Section 2 with the graduate student instructor. Asdiscussed above, Section 2 contained more high performers, which could indicate that Section 2was composed of more students that had achieved success under traditional learning techniques,and thus were resistant to the flipped classroom. Upon reflection, we believe that students in bothsections were similarly educated about the benefit of the flipped classroom at the beginning ofthe semester. However, a few students in Section 2 vocally expressed dislike of the approachafter

Conference Session

Computer Tutors, Simulation, and Videos

Collection

2015 ASEE Annual Conference & Exposition

Authors

Moe Tajvidi P.E., Utah State University; Ning Fang, Utah State University

Tagged Divisions

Mechanics

on these characteristics.Visualization characteristics of CSA modules can be associated with cognitive science aspectssuch as schemata; mental and graphic visualization, reflection and debriefing, situated learningor cognition, and cognitive apprenticeship23, 40. Brown40 noted the infrequency of visualizationsintegrated into classroom instruction. He attributed this infrequency to the lack of sufficientteaching tools. Without exposure to them, students could not experience the benefits of usefulCSA tools. In addition, new modules have included more web-based interactive tutoring23, 35, 38.For example, the tutorial package developed by Ong38 could support students with an interactivefeature with the capability of modifying parameters so that

Conference Session

Teaching Mechanics of Materials

Collection

2014 ASEE Annual Conference & Exposition

Authors

Christopher Papadopoulos, University of Puerto Rico, Mayagüez ; Aidsa I. Santiago-Román, University of Puerto Rico, Mayagüez ; Genock Portela-Gauthier, University of Puerto Rico, Mayagüez

Tagged Divisions

Mechanics

problems. On the whole, we believe that our approach is both within reach of students’ abilities andaccelerates their exposure to use of simulation in design. Based on the results thus far, animmediate improvement that the instructors will make is to provide the introductory training inSAP2000 at an earlier stage of the course to allow students more time to adapt to the newmethodology, and hopefully to use it maturely as a design tool. In the long term, we plan totrack student performance of our students in subsequent courses to determine if they outperformother students in design oriented problems and tasks. We also plan to make further improvements in the content of the modules themselves.Further refinements can be made to reflect

Conference Session

Teaching Mechanics of Materials & General Mechanics

Collection

2010 Annual Conference & Exposition

Authors

Robert Freeman, University of Texas, Pan American; Horacio Vasquez, University of Texas, Pan American; Martin Knecht, South Texas College; Taylor Martin, Univ of Texas at Austin; Arturo Fuentes, University of Texas, Pan American; Joan Walker, Long Island University; Araceli Ortiz, Tufts University

Tagged Divisions

Mechanics

activities. In the LC, the following steps are performedand repeated:Look AheadThe learning task and desired knowledge outcomes are described here. This step also allows forpre-assessment and serves as a benchmark for self-assessment in the Reflect Back step.Challenge 1 (shown in Figure 1)The first challenge is a lower difficulty level problem dealing with the topic. The student isprovided with information needed to understand the challenge. The steps shown below representthe remainder of the cycle, which prepares the students to complete the challenge. Note thatformative instructional events can and probably should occur in each step of the cycle. Thefollowing LC steps are to motivate and engage the students: Generate ideas: Students are

Conference Session

New Teaching Pedagogies: Methods and Assessments

Collection

2014 ASEE Annual Conference & Exposition

Authors

Jeffrey F. Rhoads, Purdue University, West Lafayette; Eric Nauman, Purdue University, West Lafayette; Beth M. Holloway, Purdue University, West Lafayette; Charles Morton Krousgrill, Purdue University, West Lafayette

Tagged Divisions

Mechanical Engineering, Mechanics

complex engineering problems.Apart from the core components highlighted above, there is also considerable ongoingexperimentation within the PMFC with other pedagogy-driven instructional elements. Theseinclude:  Using the Index of Learning Styles (ILS)4-6 to categorize learning style preferences and tailor information delivery. The ILS is a relatively simple measure of how students prefer to receive information. The survey divides learning style preferences into four domains with opposing descriptors, visual-verbal, active-reflective, sensory-intuitive, and sequential-global. Using these domains, it has been established that students tend to prefer visual, active, and sensory modes, despite the fact

Conference Session

Engaging the Online Classroom

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Jacob Matthew Cook, Oregon State University; Thomas W. Ekstedt, Oregon State University; Brian P. Self, California Polytechnic State University, San Luis Obispo; Milo Koretsky, Tufts University

Tagged Topics

Diversity

Tagged Divisions

Mechanics

vectors and graphed parameters. Further work will include analyzing studentsurvey data to explain student perceptions and to determine how student comprehension andlearning compares between remote instruction vs. in-person.AcknowledgementsWe acknowledge the support from National Science Foundation (NSF) through grants DUE1821439 and 1821638. Any opinions, findings, and conclusions or recommendations expressedare those of the authors and do not necessarily reflect the views of the NSF.References[1] J. D. Bransford and A. L. Brown, How People Learn: Body, Mind, Experience and School. Washington, D.C.: Commission on Behavioral and Social Science and Education, National Research Council, 2000.[2] J. Engelbrecht, C. Bergsten, and O. Kågesten

Conference Session

Homework, Learning, and Problem Solving in Mechanics

Collection

2016 ASEE Annual Conference & Exposition

Authors

Julian Ly Davis, University of Southern Indiana; Thomas McDonald, University of Southern Indiana

Tagged Divisions

Mechanics

who do not get facultyinput on homework solutions, may not ever be taught how to present an understandable technicalsolution. There is no doubt that online teaching tools are beneficial and that students perceptionsand interactions are positive.[2] Some students, at the moment of the interview, state that theyprefer online homework systems. However, these students are NOT surveyed at a later date andasked to reflect on their freshman learning experiences. Although many studies have investigated the use of online homework systems in math [3],science [4–6], or engineering [3,7–10] courses, few have assessed the ability of a student to present alogical solution during the course. Authors in these studies usually correlate homework grades

Conference Session

Back to Basics in Mechanics

Collection

2006 Annual Conference & Exposition

Authors

Robert Martinazzi, University of Pittsburgh-Johnstown; Brian Houston, University of Pittsburgh-Johnstown

Tagged Divisions

Mechanics

trulymotivates the students to become active learners.This paper examines a wide variety of alternative quizzing techniques. The title of the paper,“Five Surprises” reflects the quantity of quizzes given per semester and the unannounced natureof the quizzes. Some are formulated by faculty and others recommended by students. Somehave been employed in the classroom; others are being evaluated by faculty for possibleimplementation in the current and future semesters. This paper will highlight some of the bestideas which have been given specific names suggestive of the type of quiz. Overall, ninealternative quiz types have been identified and include names such as “Dante’s Quiz”, “JumpingBeans”, “Who Wants to be an Engine-aire”, and “The Relay”.Introduction

Conference Session

Teaching Dynamics

Collection

2010 Annual Conference & Exposition

Authors

Brian Self, California Polytechnic State University; James Widmann, California Polytechnic State University

Tagged Divisions

Mechanics

candetermine if certain material needs to be covered more in depth, if main issues can be skipped, or Page 15.432.4if supplemental reading material or tutorials need to be provided. The class time can be modified“just-in-time” to reflect student understanding and interest. Seasoned JiTT instructors use actualstudent answers to help build their lecture or explain a theory; they will typically put upoverheads or PowerPoint slides of selected student responses. The class participants recognizetheir own words and feel more ownership of the course.Model-Eliciting Activities (MEAs)MEAs are team-based (usually 3-4 students) assignments where students attempt

Conference Session

Bringing a Different Perspective

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Andrew R. Sloboda, Bucknell University

Tagged Divisions

Mechanics

statistically significant(p=0.056). This increase is unlikely to do with the “dynamics in one week” curriculum, andprobably reflects gains made by students over the course of the entire semester. However, onecould argue that the fact that this change only verges on significance suggests students were in arelatively strong position after only the first week.The student open-ended comments (see Appendix A) complement the quantitative results. Mostof the second week comments focus on details of classroom management/topical coverage orindicate that the pace of instruction seemed fast (definitely true!). However, a few commentsindicate that students appreciated the instructional approach even early on. One student wrote: Honestly, the first week

Conference Session

Engaging the Online Classroom

Collection

2021 ASEE Virtual Annual Conference Content Access

Authors

Nicolas Ali Libre, Missouri University of Science and Technology

Tagged Divisions

Mechanics

usually last an hour, but theinstructional videos were intentionally short (average ~ 7 min), having been adapted to suitstudents' relatively shorter attention spans while watching educational videos online. To promoteproblem solving skills and higher level thinking, students were required to attempt severalpractice problems after watching the instructional videos. Zhang et. al. [14] reported that studentswho used interactive video content showed 20-30% higher achievement of learning outcomes inpost-gain tests, compared to students who did not use video, or used video without interactionand reflection. This aligns with the observations of this study which indicated that the diversifiedresponsiveness and interactivity of learning tools are

Conference Session

Teaching Statics: What and How?

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Phillip Cornwell, Rose-Hulman Institute of Technology; Amir H. Danesh-Yazdi, Rose-Hulman Institute of Technology; Aimee Monique Cloutier, Rose-Hulman Institute of Technology

Tagged Divisions

Mechanics

all statics problems, including particle problems and rigid body problems; the calculationof internal forces or external forces; and problems involving a frame, a machine, or a truss. Thisapproach is also applicable to solving problems in other courses such as Strength of Materialsand Dynamics. In this approach, the first step in solving any problem is to articulate a “Strategy.”This simple step requires the students to take a few moments to reflect on the problem and writedown a strategy rather than trying to pattern match or “find the right equation.” If the strategy isNewton’s 2nd law, which it often is in Statics, then the next step is for students to “Choose aSystem.” Students are required to define the system by drawing a dotted line

Conference Session

Concept Inventories in Mechanics

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Carisa H. Ramming, Oklahoma State University; Christopher Papadopoulos, University of Puerto Rico, Mayaguez Campus; Eric Davishahl, Whatcom Community College; Brian P. Self, California Polytechnic State University, San Luis Obispo; Sinéad C. MacNamara, Syracuse University; Meredith Silberstein, Cornell University; Joan V. Dannenhoffer P.E., Syracuse University

Tagged Topics

Diversity

Tagged Divisions

Mechanics

this orother process of deeper inquiry.Instructors can also receive useful feedback. Obviously, the results of an initial poll give awindow into what students initially grasp. Later, after repolling, the instructor can view thechange in the students’ responses and reflect upon the effectiveness (or lack thereof) ofadditional comments or explanations. It is indeed humbling for an instructor to experiencenegligible or even “incorrect” changes among students’ responses after “the perfect explanation”has been given. Hopefully, this is part of a formative process in which instructors can betteranticipate what students reasonably can – and cannot – absorb within a certain scope ofconversation or allotted time.Student Feedback:All three cohorts were

Conference Session

Enhancing Mechanics Instruction

Collection

2008 Annual Conference & Exposition

Authors

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

Tagged Divisions

Mechanics

[sic] and discussion ...”Some students had negative comments to make, such as “I did not like the style of solving problems. I can’t see everything I’m going to need right off the bat.” “The “5 steps” half the homework time was wasted Roadmap and discussion rather than learning to problem sole [sic] . . . ”A student, in response to the question “What, if anything, would you change about this course?Please explain.”, stated “Difficult to understand certain problem solving methods [sic].”Despite the presence of negative comments, we wish to remark that the positive and negativeanswers reported above accurately reflect the proportion of positive vs. negative comments weobtained. Therefore, we conclude that the use of a

Conference Session

Teaching Dynamics

Collection

2009 Annual Conference & Exposition

Authors

Robert Hildebrand, Lake Superior State University; Wael Mokhtar, Grand Valley State University; Steve Bryan, Continental Automotive Systems

Tagged Divisions

Mechanics

, reflecting that the instructors felt a strong degree of confidence in the students’abilities. The student confidence level was high in all categories, as well, excepting themaritime/aerospace category; regrettably, practical reasons dictated that the assessmentquestionnaire obtaining this statistic was circulated before instruction on this topic wascompleted in the course, so the low score likely reflects that circumstance.What is lacking here, however, is any external calibration of such data. Tentatively, theonly supporting external data is knowledge that current option graduates are working inmore than one vehicle-related industry (at least one in maritime, and at least one inautomotive, others unknown).6. ConclusionsIt has been demonstrated that

Conference Session

Innovative Teaching Techniques in Mechanics

Collection

2006 Annual Conference & Exposition

Authors

Louis Everett, University of Texas-El Paso; Arunkumar Pennathur; Elsa Villa, University of Texas-El Paso

Tagged Divisions

Mechanics

. Page 11.1280.2Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors anddo not necessarily reflect the views of the National Science Foundation. Support was also from the PACE program(www.PACEpartners.org) and the authors gratefully acknowledge their support.Introduction Student enrollment in the College of Engineering at the University of Texas El Paso is veryhealthy. With student demographics in excess of 70% Hispanics and large class sizes, UTEP isone of the largest producers of undergraduate Hispanic Engineers. UTEP graduates can be foundin the nation’s top graduate schools, in the upper echelons of the nation’s leading corporations, inNational Laboratories and as entrepreneurs. In

Conference Session

Enhancing Instruction in Statics, Dynamics, Mechanics

Collection

2017 ASEE Annual Conference & Exposition

Authors

Rania Al-Hammoud P.Eng., University of Waterloo

Tagged Divisions

Mechanics

session in-class).Towards the end of the term, students were given an online survey to reflect on the effectivenessof the flipped classroom model. The survey was done in both years F15 and F16. On average thesurvey response rate was 42% in F15 and 75% in F16. In both years, students listed thefollowing as the most helpful factors for their learning in the flipped classroom model:  In-class problem solving: covering the material before class allowed them to better participate in the in class problem solving sessions.  Learn at own pace: Having the video resources online allowed some students to learn the material at their own pace.  Students were happy that they had the ability to rewatch the videos whenever they

Conference Session

Learning Environments for Statics, Dynamics, and Mechanics of Materials

Collection

2017 ASEE Annual Conference & Exposition

Authors

Michelle Soledad, Virginia Tech and Ateneo de Davao University; Jacob R. Grohs, Virginia Tech; Jennifer Doggett; Steven Culver, Virginia Tech; Jaime L. Williams

Tagged Divisions

Mechanics

Paper ID #19122Student Perceptions of Learning Experiences in Large Mechanics Classes:An Analysis of Student Responses to Course Evaluation SurveysMs. Michelle Soledad, Virginia Tech and Ateneo de Davao University Michelle Soledad is a doctoral student and graduate research assistant in the Department of Engineer- ing Education at Virginia Tech. Her research interests include faculty development and data-informed reflective practice. Ms. Soledad has degrees in Electrical Engineering (BS, ME) from the Ateneo de Davao University (ADDU) in Davao City, Philippines, where she continues to be a faculty member of the Electrical

Conference Session

Measuring Learning in Statics & Dynamics

Collection

2016 ASEE Annual Conference & Exposition

Authors

Roger G. Hadgraft, University of Technology Sydney; David Lowe, The University of Sydney; Justine Lawson

Tagged Divisions

Mechanics

a resource, how resources are modified by academics and where ina program they might be used 1. For the purposes of this paper, we are looking at resourcesdesigned to assist in the learning and teaching of engineering mechanics.This paper presents the results of a workshop held as part of a project, funded by the AustralianCouncil of Engineering Deans (ACED), to promote curriculum sharing across the 35 universitiesin Australia that teach engineering. It includes a description and analysis of the activities, ananalysis of the workshop evaluation as well as one participant’s reflection on the process.Investigating resource useThe preliminary project investigations mapped the local known in terms of the national andinternational literature and

Conference Session

Computer Tutors, Simulation, and Videos

Collection

2015 ASEE Annual Conference & Exposition

Authors

Matthew G. Green, LeTourneau University; Benjamin W. Caldwell, LeTourneau University; Michael Helms, Georgia Institute of Technology; Julie S. Linsey, Georgia Institute of Technology; Tracy Anne Hammond, Texas A&M University

Tagged Divisions

Mechanics

other, the Mechanix system has very important contributions to make to learning, some ofwhich are already being realized. Student comments confirmed that Mechanix reinforced theproblem solving process, and offered incremental help throughout that process that studentsvalued (although students did suggest help messages could be more clear.) The software’sindication that a problem was correct up to a certain point helped students focus their learning;they did not have to backtrack to check that an earlier error was propagating to the final answer.Students expressed that this was especially helpful for complicated problems, but for simpleproblems Mechanix was no better than paper and pencil. Students also reflected that while theyfound sketching

Conference Session

Mechanics of Materials

Collection

2015 ASEE Annual Conference & Exposition

Authors

Jenn Stroud Rossmann, Lafayette College; Clive L. Dym, Harvey Mudd College; Lori Bassman, Harvey Mudd College

Tagged Divisions

Mechanics

have developed case studies that reflect the role of national “technologicalculture” in the diverse American and Dutch responses to the risk of flooding (which involvesstudents performing calculations as well as reading and discussion relevant fiction, and builds toan in-class design experience); that consider the capabilities and the complexities of improvedprosthetic designs for competitive athletes; and that describe the interdependence of the historyof aviation, and airplane design evolution, with engineering beam theory. Our approach to theinclusion of professional ethics in technical coursework appreciates the reasoning of Lynch andKline18-19, and focuses on “culturally embedded engineering practice.” Several of the case studiesalso

Conference Session

Alternative Methods of Teaching and Learning Mechanics

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Jillian Schmidt, Missouri University of Science and Technology; Nicolas Ali Libre, Missouri University of Science and Technology

Tagged Divisions

Mechanics

, followed by reflection upon whatthey have done. Bonwell and Eison [1] stated “that in active learning, students participate in theprocess and students participate when they are doing something besides passively listening." Thegoal of active learning activities is to actively involve students in the teaching and learningprocess in order to increase student engagement, performance, and retention [2].Despite the considerable published research in the literature [3-6] showing the advantage ofactive learning approaches in STEM and engineering education and its impact on increasingstudents performance, many instructors still do not implement active learning in their teachingcurriculum. The time required to design, implement and revise an active learning

Conference Session

Teaching Statics: What and How?

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Vimal Kumar Viswanathan, San Jose State University; Josh Taylor Hurt; Tracy Anne Hammond, Texas A&M University; Benjamin W. Caldwell, LeTourneau University; Kimberly Grau Talley P.E., Texas State University; Julie S. Linsey, Georgia Institute of Technology

Tagged Divisions

Mechanics

beginning and end of the study. All error bars show (+ or -)1 S.E.It should be noted that at both schools, participants had difficulties understanding some conceptson the SCI, specifically concepts that were not taught in the class. This understanding led to aminority of students choosing not to fully complete SCI. These attempts were not included in theoverall results, as they did not reflect the overall understanding of students. Some students foundthe SCI to be more difficult than anything that had been taught during the semester and showedless effort overall on this study. Because of the vocal lack of support in the concept Inventories, apossible fix for these major problems has been implemented in the study for other

Conference Session

Grading and Feedback Models in Mechanics

Collection

2020 ASEE Virtual Annual Conference Content Access

Authors

Charles S. White, Norwich University

Tagged Divisions

Mechanics

diversity with only one African-American and one student from Africa.The overall categorization of the Homework problems is shown in Table 2. Note that eventhough 33 students were registered for the course that on any given week only 25 to 30 bothturned in homework and were present to take the quiz. At the university, attendance is taken atclass and the students are allowed to miss lectures totaling 2 weeks’ worth of meetings over thecourse of the semester.The homework breakdown shows some immediate points. The number of homework problemscategorized by the fidelity paid to the published solutions is not constant but varies by problem.For example, the number of problems categorized as 3 (reflecting virtual copying of solutionmanual) varied from a

Conference Session

What's New in the Mechanics of Materials?

Collection

2007 Annual Conference & Exposition

Authors

Andrea Surovek, South Dakota School of Mines and Technology

Tagged Divisions

Mechanics

likely toremember what they see rather than what they hear. The project is extremely visual in nature asit requires first hand observation of an object or structure, and it provides a visual archive of theprocess through photography and diagrams. The act of modeling the structures also requires thestudents to create their own visual representations. While students rarely remember specifichomework problems, they have mentioned specific examples from their project well after Page 12.178.10completing the class.Active and Reflective. Most students learn by actively doing; some learn by introspectivereflection. The project is geared towards active

Conference Session

Dynamics - Wow! They accelerate

Collection

2013 ASEE Annual Conference & Exposition

Authors

Brian P. Self, California Polytechnic State University; James M Widmann, California Polytechnic State University; Michael J. Prince, Bucknell University; Jeffrey Georgette

Tagged Divisions

Mechanics

develop proper conceptual understanding. Ourengineering students seemed motivated by the experiments, and a great deal of good discussioncould be heard as we walked around the room. In future work, we hope to ascertain exactlywhen students seem to understand the concepts, and the exact components necessary to make aneffective inquiry-based learning activity for dynamics.Acknowledgements: Support for this work was funded by the National Science Foundation,NSF 1044282, Using Inquiry-Based Activities to Repair Student Misconceptions in EngineeringDynamics. Any opinions, findings, and conclusions or recommendations expressed in thismaterial are those of the author(s) and do not necessarily reflect the views of the NationalScience Foundation

Conference Session

Teaching Dynamics

Collection

2014 ASEE Annual Conference & Exposition

Authors

James M. Widmann, California Polytechnic State University; Brian P. Self, California Polytechnic State University; Michael J. Prince, Bucknell University

Tagged Divisions

Mechanics

process is beingemployed. An initial mass-pulley demonstration was developed that mimicked question 13 fromthe DCI (DCI – Q13) and was presented to an Intermediate Dynamics Class as a demonstration.Based on initial feedback, the IBLA was finalized and deployed as a hands-on activity tostudents in an introductory Dynamics class. Student learning through the IBLA is supported by ahomework problem assigned during the same week as the activity. Assessment of effectivenesswas provided through pre-post DCI results, in class quizzes, embedded midterm problems andwritten student reflections. At the same time, the authors videotaped individuals from separatecohorts to better understand and identify sources of student misconceptions and how they mightbe

Conference Session

Innovations in Teaching: Statics

Collection

2011 ASEE Annual Conference & Exposition

Authors

Anna Dollar, Miami University; Ronald R. Ulseth, Itasca Community College; Paul S. Steif, Carnegie Mellon University

Tagged Divisions

Mechanics

that informs just-in-time changes of instruction describedbelow.)3.2 Detailed Quiz ReportsWhile an overall quiz grade itself is useful for awarding a grade, for instruction to reflect quizresults in an “inverted-classroom”, the instructor needs to know how students answeredindividual quiz questions, at least in an aggregate way. OLI provides such feedback toinstructors. As an example, an excerpt from the Module 7 Quiz Report is shown in Figure 3. Page 22.291.4 3Fig. 2 Screenshot of Gradebook Page 22.291.5 4Page 22.291.6 5

Conference Session

Innovations in Teaching: Mechanics

Collection

2011 ASEE Annual Conference & Exposition

Authors

David B. Lanning, Embry-Riddle Aeronautical University

Tagged Divisions

Mechanics

, unfortunately, and this is reflected in the rather highrate of mistakes per student.It is ill-advised to draw firm conclusions on the effect of this prerequisite skills testing on finalexam outcomes; however, from this simple analysis there is unfortunately no apparent trend thatshows students achieving a higher level of competency. Page 22.88.8Qualitative evaluationWhile the meager analysis above does not show an obvious quantitative benefit to students, theauthor nevertheless believes there are certain qualitative benefits to administering the PSE,which compel him to continue administering the exam in solid mechanics. First, many studentscome to the

Conference Session

Teaching Statics

Collection

2011 ASEE Annual Conference & Exposition

Authors

Andrea Brose, Hamburg University of Technology; Christian H. Kautz, Hamburg University of Technology

Tagged Divisions

Mechanics

are identified as moments due to a set of several forces, such that the resultant forceis zero while there is a (non-vanishing) resultant moment. Most often one considers two forces ofequal magnitude and opposite direction having different lines of action. The resultant force iszero, but a non-vanishing moment is induced (which can be calculated by adding the momentsdue to each single force with respect to a given point). The non-vanishing moment that arises inthis example is called a couple, or force couple, likely reflecting the fact that it can be thought of Page 22.792.3as the result of two opposing forces whose net moment does not