Course: MAE 223
Instructor: Andrej Kosmrlj
F 2020

Description of Course Goals and Curriculum

Modern Solid Mechanics (MAE 223) is an essential course for any student hoping to gain a thorough understanding of the forces at work within solid structures of all kinds, as well as the resulting observable behaviors of these structures. By the end of the course, you will have an intuitive sense for the ways in which solids interact with their environments in your everyday life as well as within complex mechanical and structural engineering systems. The course starts off with an introduction to the basic techniques necessary to isolate forces and torques under the assumption that a system is in mechanical equilibrium, and then builds upon these basic principles to enable analysis of more complex systems. The course is not organized into clearly defined units or sections; rather, the topics covered in each class build successively upon one another and blend into each other. It is impossible to understand many of the later concepts in the class without a thorough grounding in the topics covered early in the semester. By the end of the course, you can expect to solve problems relating to axial and shear stresses and strains, bending, deflection, torsion, statically indeterminate structures, trusses, buckling, structure failure, and elasticity.

Learning From Classroom Instruction

The course is taught through two lectures and one precept per week. The lectures focus on introducing new content, whereas the precepts reinforce and contextualize the content covered in class, providing opportunities to ask clarifying questions about the material. The lectures for this class are taught from PowerPoint slides, which are always uploaded to the class Blackboard page before the start of lecture. Throughout the 80-minute class, the professor refers to and annotates schematics, illustrations, and equations on the slides to introduce new mechanical phenomena, and also writes out examples of these phenomena in real time. It is helpful to download and/or print the slides before the start of lecture so that you can add your own notes during class. Because of the complexity of some of the schematics and drawings on the slides, it is not realistic to copy all of the content by hand during lecture. Many students appreciate the clarity and thoroughness of the lecture slides, and because of this, find it largely unnecessary to refer to the textbook throughout the course. However, when looking for in-depth content review, specific practice problems or examples, the textbook can be a helpful resource. Precepts, usually taught by graduate students, are structured slightly differently; they begin with a 15-20 minute overview of the most recently covered material in class, and then shift to a review of relevant and challenging example problems for the remaining hour or so. Again, it is helpful to download and briefly peruse these example problems from Blackboard before the start of precept, so as to allow for maximum participation in class. All three of these sessions are 80 minutes in length, and the complexity of the computations involved in some of the problems requires strong focus and attention to detail. Although the lectures include a five-minute break halfway through the scheduled time block, precepts do not. The nature of the problems in this course are such that it is essential to follow each step of computation, so it is important to eliminate all distractions and be prepared to ask questions whenever necessary. This last point is particularly important, especially because the professor and preceptors are open to questions at any point, and because many of these concepts are not initially intuitive.

Learning For and From Assignments

This course involves one weekly problem set, a midterm exam, and a final exams. These are the only three components of the grade, and are weighted in the following manner: 40% problem sets, 35% final exam, 25% midterm exam. Though lectures and precepts are clearly important elements of the learning process in this course, most of the actual learning happens during the problem sets. There are usually three to four problems on each assignment, ranging from one to five parts each. To get the most benefit possible out of the assignments, working in a study group is important; collaboration is encouraged in this course. The style of the problems is such that both conceptual and computational mistakes are common, making it essential to bounce ideas off of peers and check each other’s work. Upon individual request, the professor is willing to grant extensions on the problem sets, but the challenging nature of the problem sets makes it important to start them as soon as possible after they are assigned. The midterm and final exams cover content that directly reflects that which appears in lecture, precepts, and problem sets, and are both open book. Before each exam, the professor posts a practice exam to help students get a sense for what will appear on the actual assessment. The practice exams closely emulate what appears on the actual assessments, and the best way to get as much as possible out of them is to complete them under uninterrupted, timed conditions, using only the resources you will have during the actual exam. Logistics aside, the most important aspects of this course are the skills and methods introduced. While understanding the concepts involved in the problems is important, the open-book and timed nature of the exams means that conceptual understanding is secondary to practicing and streamlining the methods and processes involved in problem-solving. Therefore, while group work and attending office hours are important tools utilized by many students in the course, it is always beneficial to attempt problems on one’s own prior to seeking out help, so as to practice the method of breaking down a problem and isolating subsystems within a structure.

External Resources

A large majority of students in the course attend office hours for help with the weekly problem sets, because the concepts and problem-solving methods are not immediately apparent, especially in the first few weeks. The preceptors who run the office hour sessions are happy to answer conceptual questions and walk students through the problem-solving method taught in the course. Office hours are offered throughout the week, but are most highly frequented on Tuesdays and Wednesdays, as the problem sets are due on Thursdays. Making time to attend these sessions is an important part of being successful in this course for many students. In terms of actual tools necessary to complete the work in this course, it is necessary to have a graphing calculator and access to graphing software for deflection, shear, and moment diagrams. The most commonly used graphing software by students in this course was the free website Additionally, although no element of the course requires use of the materials provided in the lab kit, it is extremely helpful to have the styrofoam tubes, rubber I-beam, Kinex building pieces, and other equipment on hand while attending lecture and precept and solving problems. Sometimes the best way to get a grasp of what is happening in the problems is to physically apply torsion, bending, compression, or tension to these objects and observe the results.

What Students Should Know About This Course For Purposes Of Course Selection

Introductory physics (PHY 103) and calculus (MAT 104) are important prerequisites for the course, and it is also helpful (but unnecessary) to have experience in linear algebra (MAT 202) and differential equations (MAE 305 or equivalent) before taking the course. MAE 223 is a fundamental and essential component of both the Mechanical and Aerospace Engineering major and the Civil and Environmental Engineering major, and the topics covered in this class are built upon heavily in later classes, including MAE 206, MAE 222, MAE 224, and beyond. Most importantly, as has already been highlighted, this course teaches a problem-solving method and way of thinking that is essential to tackling more advanced, complex engineering problems of all types.
Modern Solid Mechanics

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