an extension of the 1-D Bar elementin local coordinates (Figure 5).Çk 0 /k 0 Ê u ix Û Ê f ix ÛÈ0 Í Í Í ÍÈ 0 0 0ÙÙ Í uiy Í Í f iy ÍÈ/ k Ë Ü?Ë Ü 0 k 0Ù Íu jx Í Í f jx ÍÈ ÙÉ0 0 0 0Ú ÍÌu jy ÍÝ ÍÌ f jy ÍÝ Page 12.966.7Figure 5. 2-D Truss element as 1-D Bar element Figure 6. Trigonometric transformationsThe stiffness matrix in the global coordinates is obtained with trigonometric transformations(Figure 6)}U ? ]T_}u and }F ? ]T_ }fwhere the transformation matrix [T] can be shown to be Çcos s / sin s
- > x / xK @2 / > x / xw @4 6 EI 2 EI 6 EI 2 EI 24 EI w1 / w0 (10) m0 / > x / xw @ - 5 > x / xm > 3 120 EI ( L / x w ) 6 EIBy letting x = L in Eqs. (9) and (10), we obtain the model formulas for the slope s b and deflec-tion yb at the right end b of the beam ab as follows: Va L2 M a L s b ? sa - - / P ( L / xP ) 2
S, D Q, S, D S, Q, D5.2 Find items under bending5.3 Bending members with commoncross-sections5.4 Feel craft sticks bending5.5 Stress Opticon: Bending stressdistribution S, Q, D5.6 Quantify flexure in a craft stick5.7 Stress Opticon: simple support5.8 Photoelastic beam bending S, D S, Q, DStress Transformation7.1 Directional Strength (Craft Stick) S7.2 Directional Orientation inStructures7.3 Photoelasticity: Beam with holes S, Q, D7.4 Matching loads and failure planes7.5 Brittle and Ductile Failure
24Substituting the above solutions into foregoing equations for EIy¦ and EIy , we write C1 8 w0 L3 8 w0 L3 sA ? y¦(0) ? ? sA ? S EI 3EI 3EI Page 12.1535.5 C2 131w0 L4 131w0 L4 yA ? y (0) ? ?/ yA ? fi EI 24 EI 24 EIIV. Analysis of a Hinge-Connected Beam: Wrong and Right WaysEmploying singularity
conversations withstudents, particularly with those who did very well in the initial assessment; it is plannedto implement this technique in a more formal manner in the next academic year alongwith well instrumented surveys to evaluate the success of DI in a undergraduatemechanics class.1. Tomlinson, C. & Kalbfleisch, L. (1998, November). Teach me, teach my brain: A call for differentiated classrooms. Educational Leadership, 52-55.2. Tomlinson, C.A., & Allan, S. D. (2000). Leadership for differentiating schools and classrooms. Alexandria, VA: ASCD.3. Fischman, B. (as viewed on Jan 17, 2007) http://www.education.pitt.edu/leaders/FAQ/differentiatedinstruc.htm4. Felder, R. M. (as viewed on Mar 7, 2007) http://www.ncsu.edu
1983.9. Dollár, A. and Steif, P.S., “Learning Modules for the Statics Classroom,” 2003 ASEE Annual Conference and Exposition.10. Steif, P.S. and Dollár, A., “A New Approach to Teaching and Learning Statics,” 2003 ASEE Annual Conference and Exposition.11. Crouch, C.H., Fagen, A.P., Callan, J.P., and Mazur, E., “Classroom demonstrations: Learning tools or entertainment?” American Journal of Physics, June 2004.12. Yoder, D.C., Parsons, R., Pionke, C.D., and Weber, F., “Hands-On Teaching of Engineering Fundamentals,” 1998 ASEE Annual Conference and Exposition.13. 80/50 Inc., 1701 S. 400 East, Columbia City, IN 46725, www.8020.net. Page 12.151.12
ce le ge S ad ca H en M le -R tis at ci ol
used as supplementary material in a senior-level vibrations course.The fourth module uses Matlab. Student feedback is included.IntroductionThe advent of student-owned personal computers in the early 1980’s sparked an interest inmotion simulation software. The simple notion is that if students are able to see an animation ofthe systems that they are studying, especially for their choice of conditions, then they are muchmore likely to understand the material. A number of investigators1-5 have worked in this area.The history of the motion-simulation modules presented in this paper dates back to the early1980’s when personal computers were first required for undergraduate engineering students atVirginia Tech. The first efforts by the senior author
analysis.IntroductionThe authors of the National Academy of Science report Rising above the Gathering Storm1 writewith urgency of the need for the United States to strengthen the scientific and technical buildingblocks that lead to economic prosperity. The number of Master’s and Ph.D. degrees awarded inengineering has decreased approximately 7% and 13%, respectively, from 1996 to 20012 and thenumber of Ph.D.’s awarded in mechanical engineering has decreased approximately 19% from1996 to 20043. Engineering dynamics, which encompasses areas such as flight dynamics,vibration isolation for precision manufacturing, earthquake engineering, structural healthmonitoring, signal processing, and experimental modal analysis is naturally affected by thisdecrease in numbers
. Huang, Meirong and Kurt Gramoll, “Online Interactive Multimedia for Engineering Thermodynamics,” ASEE Annual Conf. Proc., Salt Lake City, UT, 20-23 Jun 20045. Ngo, Chean Chin and Kurt Gramoll, “A Web-based Electronic Book (eBook) for Fluid Mechanics,” ASEE Annual Conf. Proc., Salt Lake City, UT, 20-23 Jun 2004.6. Homsy, G. M., Aref, H., Breuer, K. S., Hochgreb, S., Koseff, J. R., Munson, B. R., Powell, K. G., Robertson, C. R., and Thoroddsen, S. T., Multi-Media Fluid Mechanics, Cambridge University Press, 20007. Liggett, J. A. and Caughey, D. A., Fluid Mechanics: An Interactive Text, American Society of Civil Engineers Press, 19988. Philpot, T., "MDSolids," Introduction to Mechanics of Solids, http://www.mdsolids.com/9
applications. In EAS222, students develop an understanding of the basicprinciples and applications of engineering mechanics including the behavior of structures undervarious loads, bending and Mohr’s circle.This paper discusses how the mechanics topics are threaded through this sequence of courses andhow mastery of these topics is being assessed at the disciplinary level in the junior year.Assessment of students’ understanding of mechanics topics includes the following instruments:data drawn from quiz/exam grades and/or particular question(s) on exams/quizzes related tospecific concepts; and faculty observations gathered using a survey tool. Our current dataevaluates the first group of students to reach the junior level in the new curriculum that
conflicting class schedules made it very difficult for students to meet outside of class; and • creating groups where women and minorities are not isolated, when possible.Based on the number of comments suggesting that they be able to choose their own groups,students were allowed in Fall ’06 to specifically request if they wished to work with anindividual or group of students. One request was received from the entire class. Students arealways given the option to suggest students with whom they would rather not work based on pastrelationships. No student has ever taken this option. Table 1 – Individual Student Survey Results F 05 S 06
, if applicable. b) learning unit name/topic, broad statements indicating what the students will learn from the learning unit. c) learning objective(s) , descriptions of measurable outcomes that students should be able to demonstrate upon completion of the learning unit. d) rationale , brief justification of why the students need to learn the topic. e) learning unit content , what is to be taught. Page 12.1118.5 f) instructional procedures , how you will help the students connect with the content. g) evaluation procedures , how you will measure outcomes to determine if the material has been learned. The evaluation
this test were surprisingly accurate, considering the simplicity of the setup.Deflection values agreed with the calculated values to within 1 or 2 mm. It should be noted thatthe students did not find this exercise to be completely straight-forward. Because of the nodenumbering scheme, several made mistakes in assembling the system stiffness matrix or applyingthe boundary conditions. However, these errors provided an opportunity for teaching theimportance of checking the reasonableness of the solution. One common error involved placingthe terms of spring 4’s stiffness matrix in the wrong locations in the system matrix (as if spring 4connected nodes 3 and 4 rather than nodes 4 and 5). In this case, the calculated displacement fornode 5 was zero
rolling asshown in Figure 1. Figure 1. Rolling Wheel Used to Illustrate Various Types of Problems Used to Assess Knowledge of Key Concepts in Dynamics. Page 12.1541.4Traditional ProblemFor the wheel shown in Problem 1, the wheel’s radius is 2 ft, the instantaneous velocity at thecenter of the wheel is 4 ft/s to the right. Express the velocity of points A and B as vectors usingthe coordinate system indicated on the figure.DCI Type ProblemFor the wheel shown in Problem 1, what is the direction of the velocity of point B at the instantshown if the wheel is rolling to the right without slipping?(A) Straight Down (B
what they had gained, comments now include: “More problem solving techniques, taking what I know and applying to a problem that I have never seen or thought of working.”Additionally, some do begin to enjoy the material, as evidenced by comments such as:“I truly enjoyed the course and loved learning about dynamics of structures.”AcknowledgmentsThe authors want to thank the Zachry Department of Civil Engineering for providing support fora peer teacher used in this class. Also, the generous support provided by the National ScienceFoundation is acknowledged (Award Number 0536834).References:1. ABET (2000) Criteria for Accrediting Engineering Programs. Engineering Accreditation Commission.2. Barron, B. J. S. (1998). Doing with
10Performance on Final Exam. Each semester the department offers between eight and tensections of Statics and either seven or eight sections of Mechanics of Materials. All studentstake the same final exam at the same time during final exam week. Grading is divided so that thesame faculty member will grade the same problem(s) on the final for all students taking the finalexam. That is, faculty member A may be assigned to grade problems 1 and 2 for all studentstaking the final exam that semester. This insures that all of the finals are graded consistently.Performance on the common final is a good indicator of how well the students learned thematerial taught in the class. An average is generated each semester for each section of the class,and an overall
universities use the proposed approach and provide feedback.Besides the topic under consideration, the proposed approach can also be used when the subjectof strains analysis in two dimensions is presented in class. Once the equations for straintransformations have been obtained, identical steps to the ones presented here can be followed toderive the expressions for the in-plane principal strains, the maximum magnitude of the in-planeshear strain and their corresponding orientations. Page 12.76.13References1. Seely, F.B., Resistance of Materials, Second Edition, John Wiley & Sons, 1934.2. Timoshenko, S. and MacCullough, G.H., Elements of
better prepared for each class to some extent; thus theytook less time to solve problems as a group, if not correctly all the time. Some times thestudents are asked to show only the methodology and steps for solving the problem. Theywere then asked to complete the solution as group homework. Some times the data in thesame problems is changed for each group (for example the magnitude of a load or theangle of application of a load), so that their results can be plotted on the board as trendlines. Those who get wrong answers fall out of bounds of the trend line(s) and theyimmediately realize their mistakes. Careful design of classwork problems seems to helpstudents to a great extent as they learn the problem solving techniques just in time. Thefeed
AC 2007-117: ELECTRONIC COURSE PACKAGING FOR STATICS ANDDYNAMICS: A REVIEW OF EFFORT, REWARD AND POTENTIALPeter Boyle, Saint Mary's University W. Peter Boyle holds B.Sc. and Ph.D. degrees in Mechanical Engineering from The Queen's University of Belfast, is Professor of Engineering at Saint Mary's University, Halifax, N. S., and was previously Lecturer in the Department of Mechanical Engineering at the University of Cape Town. He is the author of a McGraw-Hill textbook on introductory fluid mechanics, and about forty publications in a variety of topics in mechanical engineering. A current interest is in the search for superior cost and time effective course delivery methods
integral was introduced by Gottfried Leibniz in 1675. The integral Page 12.806.5symbol he used, " ", was derived from an elongated letter S, standing for summa (Latin for "sum"or "total"). Newton was at times a very nasty man. Following the death of Leibniz, Newton isreported to have declared that he had taken great satisfaction in "breaking Leibniz's heart."Newton seemed to be characterized by a lack of publishing for much of his life. This may havebeen due to the fact that he was very sensitive to criticism. For example, the conflict he had withRobert Hooke over optics resulted in his ceasing all publications until after the death of Hooke