integrated statics experiments in the mechanex mini … · integrated statics experiments in the...

“Proceedings of the 2001 American Society for Engineering Education Annual Conference & Exposition Copyright 2001, American Society for Engineering Education”

Session 2468

Integrated statics experiments in the ‘MechANEX’ mini-laboratory

Christine B. Masters, Richard A. Behr

The Pennsylvania State University Abstract ‘MechANEX’ is a mini-laboratory combining comprehensive software analysis modules and matched, bench-scale verification experiments to improve and enrich a sophomore-level engineering mechanics course in statics. Each of the seven statics modules in MechANEX involves a pre-lab exercise combining hand calculations and software analyses, a lab exercise providing a physical connection to analytical techniques discussed in class, and a post-lab exercise promoting a deeper understanding of course concepts through more in-depth, application-oriented software analyses intended to reinforce the practical relevance of targeted course concepts. Throughout, the newly developed MechANEX software enables students to perform analytical and experimental tasks successfully during lab exercises and expedites the solution of multiple versions of the same physical problem during post-lab exercises. Preliminary testing of the seven statics modules is complete, and a rigorous initial assessment of MechANEX is currently under way within multiple sections of the statics course at Penn State in the Spring 2001 semester. This paper introduces the MechANEX laboratory-teaching concept, describes the seven MechANEX modules for a statics course, and summarizes results from preliminary MechANEX assessments in the student user environment. Introduction ‘MechANEX’ is a mini-laboratory combining comprehensive software analysis modules and matched, bench-scale verification experiments to improve and enrich a sophomore-level engineering mechanics course in statics. Developed as an extension of the “AN/EX” (ANalysis and EXperiment) laboratory1,2 used by civil and architectural engineering students in junior-level structural engineering courses, MechANEX combines a newly developed, easy-to-use, statics analysis software package with fully configured experimental setups designed for use with existing AN/EX laboratory equipment. Students begin each MechANEX assignment by using the MechANEX software to check their hand-calculated results for the assigned problem. When the hand calculations and software results match, students perform the associated experiment and compare the resulting experimental data with the existing analytical results. Students complete each MechANEX module by using the MechANEX software to study a more involved problem, varying analytical parameters without the burden of repetitive and lengthy hand calculations. The MechANEX laboratory has four primary pedagogical objectives. (1) Students develop a deeper personal understanding of core course concepts by in-depth study of representative engineering problems using a customize software analysis package. Any mechanics student can gain greater understanding of targeted course concepts by solving additional complex problems or varying parameters and re-solving assigned homework problems. Unfortunately, most students cannot afford the extra time this takes. The

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MechANEX analysis package alleviates much of the mathematical burden these types of studies entail, saving time and allowing for more in-depth conceptual exercises. (2) Students realize that verification of software solutions is essential. While an analysis package can save time and allow for in-depth study, students can easily place too much trust in “black box” computer solutions. Most introductory mechanics courses do not include a formal laboratory component, so the issue of independent verification is not typically addressed. MechANEX allows students to study problems using a three-pronged verification approach, requiring comparison between hand calculations, computer solutions and experimental results. Differences between analytical and experimental results demonstrate that while the analytical models we generate in statics are idealized, they provide good approximations to reality. (3) Students gain insights into their own personal misconceptions. One expectation of the first part of each MechANEX assignment is that hand calculations produce the same results as the MechANEX software solutions. By presenting a series of pertinent intermediate values used to calculate the final answer, each MechANEX module aids students in troubleshooting their hand calculations when results do not match. Even when the discrepancy between software results and hand calculations is nothing more than a sign error, this checking process can help students to recognize fundamental misconceptions they might have with respect to a particular course concept. (4) Students gain a greater appreciation for the multidisciplinary nature of statics. Most students view different engineering disciplines as being stand-alone, rather than overlapping disciplines that share and employ the same fundamental mechanics concepts. The MechANEX analysis package allows students to solve efficiently a greater number of problems from a variety of engineering disciplines, allowing students to experience a wide range of multidisciplinary mechanics applications. The Seven MechANEX Modules for Statics Seven MechANEX modules have been developed around core statics topics: (1) Moment About an Axis; (2) Equivalent Force Systems; (3) Area Moments of Inertia; (4) 2-D Equilibrium; (5) Mechanical Systems; (6) 3-D Equilibrium and (7) Friction. Each of the seven MechANEX modules for statics involves a pre-lab exercise, a lab exercise, and a post-lab exercise. In the pre-lab exercise, students complete a typical ‘homework-style’ problem by hand, which they then check by analyzing the same problem using the windows-based MechANEX software. Each pre-lab exercise serves three purposes: (1) students practice the analytical steps covered in class by solving the problem by hand; (2) students become familiar with the MechANEX software module in an organized, tutorial-like manner; and (3) students are able to identify flaws in their personal understanding of the course topic when their manual calculations and the software computations do not check, compelling them to troubleshoot their own mistakes. Following the pre-lab exercise, each lab exercise provides a physical connection to the analytical techniques discussed in class and introduces students to the reality that analytical and experimental techniques both have their inherent limitations. Each post-lab exercise enables students to develop a deeper understanding of important course concepts by having them perform a more in-depth, application-oriented exercise intended to reinforce the practical relevance of targeted course concepts. Throughout, MechANEX software enables students to P

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perform analytical and experimental tasks successfully during lab exercises and expedites the solution of multiple versions of the same physical problem during post-lab exercises. The Moment About an Axis module requires the students to analytically calculate and experimentally measure the moment acting about the hinge axis of a door due to the weight of the door. Students also calculate and measure the cable tension required to counteract this moment and hold the door in place. In the post-lab exercise, students investigate various hinge axis orientations and cable configurations for the installation of an angled exterior basement door. This module helps students to discover the connection between mathematical vector equations and the physical quantities of position, force and moment that these vector equations represent. As a result of this discovery, students should be more capable of applying vector equations correctly, using them with some physical insight rather than treating them solely as abstract mathematical expressions. Through this exercise, students should achieve a better understanding of the abstract concept that moments, as well as forces, can be broken into components, and that the component of moment about a specific axis (e.g., an axle or hinge axis) is often more useful in engineering analysis and design than is the total moment about a point.

Fig. 1 Moment About an Axis In the Moment About an Axis experiment, students first use strain gages to measure the moment about the hinge axis (torque in the rod) caused by the application of the 5-pound weight when the clamp is tightened to prevent rotation. Next, the clamp is loosened to allow rotation of the door and a cable is attached from the force sensor to an eyelet on the door. Students use the force sensor to measure the tension in this cable caused by application of the 5-pound weight.

clamp

force sensor

5-pound weight

cable

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The Equivalent Force Systems module requires students to analytically and experimentally investigate the concept of ‘equivalent loading' (often referred to as the calculation of resultant forces and couples). The pre-lab assignment presents students with a vertical plate supporting several forces and moments applied at various locations. Students calculate by hand, and verify with the software, the magnitude and direction of a force - couple system that can be applied at a single point on the plate to represent an force system that is ‘equivalent’ to the original set of forces and moments (the resultant force – couple system). To experimentally investigate these equivalent loading systems, students first apply the original system of forces and moments to a vertical plate (using a series of weights and pulleys) and measure the reaction force at the roller, which supports the plate. Although at this early point in the semester, statics students have not yet been introduced to the concept of equilibrium equations and support reaction calculations, they have been taught that force – couple systems are ‘equivalent’ if they have the same external effect on a body. One tangible measure of this equivalence is the presence of the same external support reactions under different loading conditions. Hence, the students experimentally verify their equivalent force systems calculations by applying a single force and couple to the plate using the magnitudes and directions calculated by the software, and again measuring the reaction force at the roller support. If the two measured reaction values are comparable, the students can conclude that the force - couple system has the same external effect on the vertical plate as the original set of forces and moments and the two sets of loads are, therefore, equivalent. By completing this MechANEX exercise, students should become proficient at calculating the resultant of a two dimensional system of forces and moments. Through the experimental verification exercise, students will learn that resultants can physically (and not just conceptually) replace a system of forces and moments to produce exactly the same external effects on the body to which they are applied.

Fig. 2 Equivalent Force Systems

In the Equivalent Force Systems experiment, students apply several sets of forces and couples to a vertical plate. A force sensor measures the support reaction at the roller for each set of forces and couples. Force – couple systems are ‘equivalent’ when they produce comparable measured reaction forces at the roller support.

forces

couple

roller support (force sensor)

vertical plate

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The Area Moment of Inertia module requires students to calculate the centroidal area moments of inertia for rectangular and wide flange beam cross sections. To provide a physical illustration of the inertial properties, students analytically calculate and experimentally measure the horizontal and vertical deflections of both a rectangular and a wide flange beam. (Since these students have not yet had strength of materials, they simply use their calculated values of inertia in a given formula for beam deflection.) This MechANEX exercise helps students to discover some physical meanings of ’area moments of inertia’ in the context of beam deflections. As a result of this practical discovery, students should be more motivated to learn how to calculate area moments of inertia. The study of beams with nearly identical cross sectional areas demonstrates the dramatic effects that inertial properties can have on physical behaviors such as flexure. Through the post-lab exercise, students will gain insights regarding the design process and performance tradeoffs encountered when optimizing one design parameter at the expense of another. The 2-D Equilibrium module requires students to calculate and measure the support reactions of a model drawbridge under both distributed loads and concentrated loads. Students also determine analytically and experimentally the counterweight magnitude required to raise the drawbridge off one of its supports. Through this MechANEX exercise, students should become more proficient at constructing free body diagrams and employing static equilibrium conditions to analyze support reactions for a rigid body. This exercise also helps students to discover the relationship between mathematical models of distributed loads and typical physical situations that can actually produce distributed loads. By completing the post-lab assignment, students should gain an appreciation of the utility of statics theory in engineering practice by employing static equilibrium calculations to evaluate several combinations of interrelated design parameters. (For this exercise, the students use three different counterweight magnitudes to calculate the corresponding pulley heights necessary to raise the simple drawbridge.)

Fig. 3 Area Moments of Inertia

In the Area Moments of Inertia experiment, students observe the physical effect of cross sectional shape on beam deflections for beam with both rectangular and wide flange cross sections.

vertical displacement

sensor

horizontal displacement

sensor

cantilevered support

rectangular beam

wide flange beam

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The Mechanical Systems module requires students to analyze the internal pin reactions and external clamping force of two different pliers. The first pliers resemble those in a classic ’textbook’ problem with component dimensions and force directions conveniently defined to simplify equilibrium calculations, while the second pliers are commercial pliers in which few of the dimensions and force directions are parallel or perpendicular to each other. Students measure experimentally the clamping force of the commercial pliers. By completing this MechANEX exercise, students should become more proficient at constructing free body diagrams and employing static equilibrium conditions to analyze internal reaction forces in multi-component mechanical systems. By analyzing both the simple and the commercial pliers, students should gain insights into the relative advantages and disadvantages of vector vs. scalar solution techniques. Through the post-lab exercise, students are introduced to the concept of analyzing a mechanism’s parameters individually (using MechANEX software) to determine which parameter(s) has the most significant impact on a particular aspect of a design. For example, in the post-lab assignment students vary the geometric dimensions of the pliers in an attempt to maximize its mechanical advantage (defined here as clamping force divided by force applied at the handle) while keeping the shear force on the internal pins below a pre-specified allowable value.

Fig. 4 Equilibrium 2-D

In the 2-D Equilibrium experiment, students apply several point and distributed loads to a model drawbridge. A force sensor measures one of the bridge support reaction forces for comparison with analytical predictions. Students then apply weights to the drawbridge cable to determine the force required to raise the drawbridge off one of its supports.

drawbridge

cable

force sensor

Fig. 5 Mechanical Systems

In the Mechanical Systems experiment, students apply a gripping force (using a weight with a cable and pulley) to modified commercial pliers. A force sensor measures the resulting clamping force produced by the pliers.

pliers force

sensor

cable

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The 3-D Equilibrium module requires students to determine analytically and experimentally the tensions in two cables supporting a rigid boom with an attached weight. This MechANEX exercise helps students become more proficient at constructing three dimensional free body diagrams. Building upon the 2-D Equilibrium module, students extend their skills at employing static equilibrium conditions to determine support reactions for a rigid body in three dimensions. Because the software illustrates the relationship between the physical dimensions of the problem and each term in both the vector and scalar equilibrium equations, students can use this exercise to examine the correlation between vector and scalar forms of the three dimensional equilibrium equations. As a result, students should become more proficient at performing vector analyses of more complex three-dimensional problems. Through the post-lab exercise, in which students will be required to solve the equations ‘backwards’ to determine an unknown applied load from experimentally measured support reactions, students should be able to apply the principle of static equilibrium with greater confidence to a wider variety of engineering problem contexts. The Friction module introduces students to the reality that several preliminary investigations are normally required to achieve a satisfactory engineering design. In this MechANEX exercise, students are required to select material types, dimensions, and an incline angle for a segment of an industrial production line used to transfer packaged products from floor to floor in a production area. However, before students can successfully determine these aspects of the conveyor belt design, they must determine experimentally the coefficients of static friction between several sets of surfaces and they must understand the relationship between tipping and sliding. Through this process of performing preliminary investigations to determine necessary aspects of a design, students should develop a richer understanding of static friction. They should learn that the coefficient of friction describes the interaction between two surfaces, not an inherent property of any individual material, and that friction force is independent of the area between the contacting surfaces. By studying the deviations found when determining the coefficient of static friction, students will realize that the value for the coefficient used in any analytical calculation represents an AVERAGE (rather than a precise) value describing the

Fig. 6 Equilibrium 3-D

In the 3-D Equilibrium experiment, students hang a known weight from the free end of a rigid boom. The boom is supported by a ball and socket joint at the wall and two cables, each attached to a force sensor. The force sensors experimentally measure the cable tensions for comparison with analytical predictions. In the second experiment, an unknown object is suspended from the end of the boom. By solving the equilibrium equations ‘backwards’, measured string tensions are used to experimentally determine the weight of the object.

cable

cable

rigid boom

weight

force sensors

Ball and

socket

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interaction between two surfaces. By completing this MechANEX exercise, students will be more capable of correctly analyzing statics problems involving friction forces, realizing that friction is a variable force with a maximum limit defined by the coefficient of static friction and the normal force on the contacting surface. (Students will be more likely to avoid the common mistake of setting every friction force they encounter equal to the maximum value defined by the relation f = µN.) This exercise will also enhance the ability of students to predict correctly the impending behavior of tipping vs. sliding for static equilibrium problems. Incorporation of MechANEX into ‘Traditional’ Statics Courses The Accreditation Board for Engineering and Technology (ABET) states quite plainly in it’s Criteria For Accrediting Engineering Programs the need to teach our engineering students to apply their classroom theory to practical problems in a way that emphasizes both analytical and experimental skills:

“The overall curriculum must provide an integrated educational experience directed toward the development of the ability to apply pertinent knowledge to the identification and solution of practical problems … and must include both analytical and experimental studies.”3

The ABET engineering program criterion description goes on to state more explicitly the requirement for both laboratory and computer-based experiences throughout undergraduate engineering programs:

“Appropriate laboratory experience which serves to combine elements of theory and practice must be an integral component of every engineering program. Every student in the program must develop a competence to conduct experimental work such as that expected of engineers in the discipline represented by the program. It is also necessary that each student have “hands-on” laboratory experience.”4

Fig. 7 Friction In the friction experiment, students first measure the coefficient of static friction between the block and several surfaces by measuring the force required to slide the block. Next they tilt the platform using the winch and, using the rotation sensor, record the angle at which the block begins to slide or tip. This experimentally determined incline angle is compared to the analytical angle calculated using the measure friction coefficient or the block dimensions.

bucket for

weights winch

Rotation sensor

platform

block

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“Appropriate computer-based experience must be included in the program of each student. Students must demonstrate knowledge of the application and use of digital computation techniques for specific engineering problems. The program should include, for example, the use of computers for technical calculations, problem solving, data acquisition and processing, process control, computer-assisted design, computer graphics, and other functions and applications appropriate to the engineering discipline. Access to computational facilities must be sufficient to permit students and faculty to integrate computer work into course work whenever appropriate throughout the academic program.”5

By its very nature of combining analysis with experimentation, the MechANEX exercises address all three of these program criteria. While statics is only one of many required courses for an undergraduate engineering degree, incorporation of MechANEX into the teaching of introductory statics can aid any undergraduate engineering program in obtaining (or maintaining) ABET accreditation under the new guidelines. The MechANEX modules have been designed with flexibility in mind such that incorporation of the MechANEX laboratory can have as much or as little impact on the lecture component of existing statics courses as desired by a given faculty member. Beyond a brief in-class introduction of the software and hardware, MechANEX can be incorporated into any statics course with very little changes to the current lecture format because students can utilize the laboratory in small groups outside of class. Total student time required to complete the statics course should remain roughly the same by reducing the number of required homework assignments in those areas targeted by the MechANEX modules. Although the MechANEX lab will be assessed initially using all seven modules during the semester, each MechANEX module has been designed to be completely independent such that a given instructor could choose any number (i.e., 1 – 7 ) of the MechANEX modules to incorporate in his/her statics course. In addition to the out of class assignments, MechANEX can be use as an in-class demonstration tool. The hardware is portable, residing on a 2 m x 1 m worktable that can be wheeled directly into the classroom for real time experimental demonstrations. Using the computer projection systems now readily available, MechANEX software can be run in the classroom from a notebook computer or on a college wide network for interactive software demonstrations. Initial Testing and Upcoming Assessment Preliminary testing of the seven statics modules as a supplemental honors option for the general statics course at Penn State was completed successfully during the Fall 2000 semester. Six students participated in the honors option, only two of whom were enrolled in the author’s section of statics. Since the majority of the fall semester statics students (approximately 500 students) were not enrolled in the honors option, no class time was devoted to the MechANEX assignments. All MechANEX assignments were completed outside of class time. The goals of this preliminary testing was threefold: (1) to gather initial feedback on student opinions regarding the prototype MechANEX exercises; (2) to test the hypothesis that MechANEX exercises could be incorporated into traditional statics classes without any change in the structure and format of the course; and (3) to work out any bugs that may be present in the software or assignments in preparation for the rigorous assessment planned for the Spring 2001 semester. P

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Along with some specific suggestions for improving each software module and experiment, students participating in the preliminary testing during the Fall 2000 semester offered a number of positive comments regarding the MechANEX exercises. • “Physical representations of what

we did in class were helpful.” • “The experiment reinforced the

theory learned in class. It is good to see the material in class actually used.”

• “The overall ability to project our class work on paper to a functional lab experiment was most beneficial. My learning was further aided through use of a well designed software program that made it easy to calculate forces and moments.”

• “It (MechANEX) applies very directly to what I am learning in class, what I’m doing for homework, and what I am being tested on.”

• “It was extremely beneficial to have an opportunity to visualize work I had done in class and see what I read in the book. I now have a greater understanding of the relationship of the resultant force-couple system and the resultant only model.”

• “It reinforced the concepts in class and also some more advanced ideas, harder problems.”

• “I feel that using a familiar mechanical system such as the pliers used in this lab was beneficial because we have a preconceived idea on how it works. Testing a simpler known system in this way builds a stronger background for tackling more complex systems.”

• “The ability to check my solutions with the software’s solutions is a good learning tool. The software can show where a mistake was made rather than just giving the correct answer.”

A rigorous assessment of MechANEX will begin in the Spring 2001 semester using four sections of Penn State’s general statics course (EMch 11). All four sections will be given the Mechanics Readiness Test at the beginning of the semester to assess their prior knowledge of geometry and trigonometry. Results from this test, along with group characteristics such as GPA and gender, will be compared to determine group equivalency. Two of the four sections will be presented in the traditional format (control group) while the other two sections will make use of the new MechANEX lab and software technology that is intended to enhance the learning experience (experimental group). (The two different syllabi that will be used during the Spring 2001 assessment are given in the appendix to demonstrate how few changes have been made to the existing statics class to accommodate MechANEX exercises. To balance the student workload,

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the homework problems in parentheses are optional for the experimental group and one class period has been scheduled as a work day for students to work on each of the seven assignments in class.) Over the course of the semester, three common tests and a common final exam will be administered, and the exam results will be compared between the control and experimental groups. Each of the two instructors involved in this study will teach one control section and one experimental section to eliminate the variable of instructional styles from final comparisons. The experimental group will also be asked to complete questionnaires evaluating their experiences with the MechANEX experiments and software. Summary In summary, MechANEX is a mini-laboratory combining comprehensive software analysis modules and matched, bench-scale verification experiments to improve and enrich a sophomore-level engineering mechanics course in statics. By providing statics students with the opportunity to perform a variety of basic experiments, comparing physical reality to hand calculations and software predictions, the MechANEX mini-laboratory reinforces the need for independent verification of both theory and software. Incorporation of one or all of the MechANEX modules can offer statics students the opportunity for hands-on experience via laboratory experiments and in-depth conceptual study via the software analysis while allowing faculty to keep all the desirable components of an existing statics course. Student feedback from preliminary testing was positive. A rigorous assessment is being conducted during the Spring 2001 semester. Acknowledgments The overall MechANEX development project has been funded primarily by a National Science Foundation ILI-LLD Grant Number DUE9650091. Programming, instructional design and graphic support has been provided by a grant of services from Penn State’s Education Technology Services (ETS) Department, with additional support provided by the following Penn State sources: The Provost’s Office; The Office of Undergraduate Education; The Leonhard Center; and the College of Engineering Division of Undergraduate Studies. The authors would also like to acknowledge the important contributions of Georginna Lucas in developing and testing the experiments, Lisa DeChristopher in developing the instructions and testing the software, and Paul Kremer in providing crucial technical support for the lab and ongoing development efforts. And finally C. Masters would like to thank Dr. Richard McNitt for his gentle guidance and candid discussions on the MechANEX project in particular and on life in general.

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Bibliography 1. “Concurrent Structural Analysis and Experimentation Using the ‘AN/EX’ Mini-Laboratory”, by Richard A.

Behr, Computer Applications in Engineering Education, Vol. 1(3), pp. 213-222, 1993. 2. “Formal Assessment of the AN/EX Structural Engineering Teaching Laboratory”, by A. Belarbi, R.A. Behr,

M.J .Karson and G.E. Effland, Computer Applications in Engineering Education, Vol. 2(2), pp. 109-121, 1994. 3. ABET’s 2000 – 01 Criteria For Accrediting Engineering Programs,

http://www.abet.org/eac/conventional.htm, I.C.3.b. 4. ABET’s 2000 – 01 Criteria For Accrediting Engineering Programs,

http://www.abet.org/eac/conventional.htm, I.C.3.f. 5. ABET’s 2000 – 01 Criteria For Accrediting Engineering Programs,

http://www.abet.org/eac/conventional.htm, I.C.3.g. CHRISTINE B. MASTERS Christine Masters is an Assistant Professor of Engineering Science and Mechanics at The Pennsylvania State University. She received a B.S. degree in Mechanical Engineering from Penn State in 1987 and a Ph.D. from the Engineering Science and Mechanics Department at Penn State in 1992. Since completing her graduate studies, Dr. Masters has worked part time teaching a variety of introductory mechanics courses while raising her four young children. In addition to editorial work on two mechanics textbook solutions manuals, she has been the lead developer on the MechANEX project for the last three years. RICHARD A. BEHR Richard Behr is Professor and Head of the Architectural Engineering Department at the Pennsylvania State University. His research interests include investigating the structural performance and durability of building envelope systems under earthquake and sever windstorm loading conditions. He also continues to develop new laboratory instructional methods and facilities for structural engineering and engineering mechanics at the undergraduate level.

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Appendix COURSE SYLLABUS

(Control Group) E Mch 11 - Section 03

Engineering Mechanics - Statics Spring 2001

Instructor, Dr. Christine Masters Class Day / Date Topic discussed in class Readings Problems Due 1 M 1/8 Mechanics Readiness Test … … 2 W 1/10 Introduction / Vectors 1.1 - 1.3 1.3 b&d, 1.32, 1.33, 1.38 3 F 1/12 Vector Multiplication 1.4 - 1.5 1.41, 1.45, 1.64, 1.66 4 M 1/15 Forces 2.1 - 2.4 2.2, 2.4, 2.6 5 W 1/17 (Continued) … 2.8, 2.16, 2.20 6 F 1/19 Moments about Points 2.5 2.23, 2.28, 2.32 7 M 1/22 (Continued) … 2.33, 2.35, 2.40 8 W 1/24 Moments about Axes 2.6 2.48, 2.51, 2.55 9 F 1/26 (Continued) … 2.58, 2.60, 2.64 10 M 1/29 Couples 2.7 2.68, 2.72, 2.78 11 W 1/31 Force and Couple Systems 2.8 2.83, 2.86, 2.92 12 F 2/2 Resultants 3.1 - 3.5 3.12, 3.24, 3.26 13 M 2/5 (Continued) … 3.32, 3.35, 3.40 14 W 2/7 Distributed Loads 3.6 3.42, 3.46, 3.48 15 F 2/9 (Continued) … 3.52, 3.60, 3.66 16 M 2/12 REVIEW … … Exam 1, Tuesday February 13 6:30 - 7:45 PM 17 W 2/14 Centroids 8.1 - 8.2 8.2, 8.3, 8.15 18 F 2/16 (Continued) 8.3 8.41, 8.52, 8.62 19 M 2/19 Center of Gravity 8.5 8.91, 8.92, 8.93 20 W 2/21 Moment of Inertia of Areas 9.1 - 9.2 9.4, 9.10, 9.18 21 F 2/23 FBD's 4.1 - 4.5 4.6, 4.16, 4.22 22 M 2/26 Single Body Equilibrium 4.6 4.32, 4.38, 4.44 23 W 2/28 (Continued) … 4.46, 4.50, 4.52 24 F 3/2 FBD's / Internal Reactions 4.7 4.53, 4.54, 4.61 Spring Break (March 3 - 11) 25 M 3/12 (Continued) … 4.68, 4.70, 4.72 26 W 3/14 Composite Body Equilibrium 4.8 4.79, 4.84, 4.85 27 F 3/16 (Continued) … 4.86, 4.90, 4.96 28 M 3/19 REVIEW … … Exam 2, Tuesday March 20 6:30 - 7:45 PM 29 W 3/21 Two-Force Bodies 4.9 4.102, 4.106, 4.116 30 F 3/23 Trusses - Method of Joints 4.10 - 4.11 4.132, 4.136, 4.143 31 M 3/26 Trusses - Method of Sections 4.12 4.156, 4.159, 4.177 32 W 3/28 (Continued) … 4.178, 4.184, 4.186 33 F 3/30 3-D FBD 5.1 - 5.6 5.5, 5.22, 5.23 34 M 4/2 3-D Equilibrium Analysis 5.7 5.40, 5.44, 5.53 35 W 4/4 Beams - Internal Forces 6.1 - 6.2 6.3, 6.6, 6.14 36 F 4/6 Friction - Impending Sliding 7.1 - 7.3 7.2, 7.7, 7.8 37 M 4/9 Impending Tipping 7.4 7.28, 7.29, 7.32 38 W 4/11 (Continued) … 7.33, 7.34, 7.38 39 F 4/13 No Class … … 40 M 4/16 REVIEW … … Exam 3, Tuesday April 17 6:30 - 7:45 PM 41 W 4/18 Belt Friction 7.6 7.40, 7.59, 7.62 42 F 4/20 Wedges and Screws 7.5 7.50, 7.56, 7.60 43 M 4/23 Review of Friction … … 44 W 4/25 GENERAL REVIEW … … 45 F 4/27 GENERAL REVIEW … …

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COURSE SYLLABUS (Experimental Group) E Mch 11 - Section 03

Engineering Mechanics - Statics Spring 2001

Instructor, Dr. Christine Masters Lab / Class / Day /Date Topic discussed in class Readings Problems Due

1 M 1/8 Mechanics Readiness Test … … 2 W 1/10 Introduction / Vectors 1.1 - 1.3 1.3 b&d, (1.32), 1.33, 1.38 3 F 1/12 Vector Multiplication 1.4 - 1.5 1.41, 1.45, 1.64, (1.66) 4 M 1/15 Forces 2.1 - 2.4 (2.2), 2.4, 2.6 5 W 1/17 (Continued) … 2.8, 2.16, (2.20) 6 F 1/19 Moments about Points 2.5 2.23, (2.28), 2.32 7 M 1/22 (Continued) … 2.33, 2.35, (2.40) 8 W 1/24 Moments about Axes 2.6 2.48, (2.51), 2.55

9 F 1/26 Couples 2.7 2.58, 2.60, (2.64) 10 M 1/29 Work day / pre-lab 1 … 2.68, 2.72, (2.78) 1 11 W 1/31 Force and Couple Systems 2.8 2.83, (2.86), 2.92 12 F 2/2 Resultants 3.1 - 3.5 3.12, (3.24), 3.26

13 M 2/5 Work day / pre-lab 2 … 3.32, 3.35, (3.40) 2 14 W 2/7 Distributed Loads 3.6 (3.42), 3.46, 3.48

15 F 2/9 Centroids 8.1 - 8.3 (3.52), 3.60, 3.66 16 M 2/12 REVIEW … …

Exam 1, Tuesday February 13 6:30 - 7:45 PM 17 W 2/14 Center of Gravity 8.5 (8.2), 8.3, 8.15 18 F 2/16 Moment of Inertia of Areas 9.1 - 9.2 8.41, (8.52), 8.62 19 M 2/19 Work day / pre-lab 3 … (8.91), 8.92, 8.93

3 20 W 2/21 FBD's 4.1 - 4.5 (9.4), 9.10, 9.18 21 F 2/23 Single Body Equilibrium 4.6 4.6, 4.16, (4.22) 22 M 2/26 Work day / pre-lab 4 … (4.32), 4.38, 4.44

4 23 W 2/28 (Equilibrium Continued) … 4.46, 4.50, (4.52) 24 F 3/2 FBD's / Internal Reactions 4.7 (4.53), 4.54, 4.61

Spring Break (March 3 - 11) 25 M 3/12 Work day / pre-lab 5 … 4.68, (4.70), 4.72

5 26 W 3/14 Composite Body Equilibrium 4.8 4.79, (4.84), 4.85 27 F 3/16 (Continued) … 4.86, 4.90, (4.96) 28 M 3/19 REVIEW … …

Exam 2, Tuesday March 20 6:30 - 7:45 PM 29 W 3/21 Two-Force Bodies 4.9 4.102, 4.106, (4.116) 30 F 3/23 Trusses - Method of Joints 4.10 - 4.11 (4.132), 4.136, 4.143 31 M 3/26 Trusses - Method of Sections 4.12 4.156, (4.159), 4.177 32 W 3/28 3-D FBD 5.1 - 5.6 (4.178), 4.184, 4.186 33 F 3/30 3-D Equilibrium Analysis 5.7 5.5, (5.22), 5.23 34 M 4/2 Work day / pre-lab 6 … 5.40, 5.44, (5.53)

6 35 W 4/4 Beams - Internal Forces 6.1 - 6.2 6.3, (6.6), 6.14 36 F 4/6 Friction - Impending Sliding 7.1 - 7.3 7.2, 7.7, (7.8) 37 M 4/9 Impending Tipping 7.4 7.28, 7.29, (7.32) 38 W 4/11 (Continued) … (7.33), 7.34, 7.38 39 F 4/13 No Class … … 40 M 4/16 REVIEW … …

Exam 3, Tuesday April 17 6:30 - 7:45 PM 41 W 4/18 Belt Friction 7.6 (7.40), 7.59, 7.62 42 F 4/20 Wedges and Screws 7.5 7.50, 7.56, (7.60) 43 M 4/23 Work day / pre-lab 7 … …

7 44 W 4/25 Review of Friction … … 45 F 4/27 GENERAL REVIEW … …

(Problems in parentheses are optional.)

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