Description

Matrix form of equilibrium and compatibility relations; virtual work principles; displacement method; direct stiffness assembly of equilibrium equations; force method; constraints; plastic analysis.

Organization of Course

Assigned work includes required reading and homework. Homework will be assigned weekly on Tuesdays and will be due by 5 pm on Friday of the following week. Late homework will be accepted with reduced credit.

There will be two midterm examinations during the course of the semester. In addition, voluntary weekly quizzes will be conducted during the discussion section to check on the students' mastery of the material. A comprehensive final examination will cover the material from the entire course. Only one single-sided sheet of hand written notes will be allowed in the midterm and final examinations.

Grading will be based on the following weights: Class participation: 10%, Homework: 20%, Midterms: 35%, Final Exam: 35%

Course Objectives

The course emphasizes the principles of modern structural analysis. Its goal is to provide you with a firm foundation for more advanced courses, for research and for practice.

The challenge for the course is that structural analysis in professional practice is conducted with powerful software. In this process most software details remain hidden to the user. Assumptions and limitations of the software package are often easy to overlook. The engineer is responsible for assessing the validity of the computer results. This assessment need not be performed only "by hand". Powerful matrix algebra packages like Matlab© or Mathcad© are available, which also afford the possibility of developing custom solutions with relative ease. Custom solutions are indispensable during concept development in individual studies. The ability to conduct independent checks and of software and, if necessary, develop custom solutions for research or professional practice is an important objective of this course.

By formulating structural analysis methods in matrix form structures of any size can be analyzed. Often this systematic approach with its compact notation reveals relationships that may lie hidden otherwise. Moreover, it encourages clarity and rigor in thinking. Commercial software makes almost exclusive use of the direct assembly of the equilibrium equations based on the displacement method of analysis (also known as the stiffness or equilibrium method). Nonetheless, a solid understanding of structural analysis cannot be obtained without exposure to the building blocks of force equilibrium and geometric compatibility and their combination with appropriate force-deformation relations to form the general displacement method and its counterpart, the force method of analysis (also known as flexibility or compatibility method). The duality of these concepts based on virtual work principles will be used throughout the course. With a firm foundation the extension of these concepts to simple plastic analysis can be achieved with little extra effort. Moreover, these concepts serve as the foundation of more advanced courses in analysis. Limited reference to a few classical analysis methods will be made during the course. Interested students will be referred to other sources for detailed information.

Instructional Software

Software packages that support matrix operations can be of great help with the tedium of repetitive calculations in homework assignments. The most suitable packages for this task are Mathcad© and Matlab©.

Mathcad is relatively easy to learn, has a user-friendly interface and is useful in analysis and design. Its printed output has the look of a word processor and is, thus, suitable for conveying calculations to others. Thus, it is a great tool for documenting analysis and design calculations in professional practice and is widely used in government agencies and in engineering companies. The latest academic release of the product is Mathcad 14, but the earlier release Mathcad 13 is as good and a student license is available from the Scholar's Workstation for $21.99. Mathcad 13 is installed in the CEE instructional computing network in the 3rd floor of Davis Hall.  Many examples and most homework solutions will be prepared with Mathcad.

Matlab's user interface is not as user-friendly as Mathcad's and its documentation abilities are modest. But the impressive collection of built-in array functions, its great plotting capabilities, and its powerful scripting and programming abilities make it ideal for advanced studies and research. It is easy to extend its capabilities with custom functions and modules, as CE220 and CE221 will demonstrate. The latest student version is R2007a which is available from the Scholar's Workstation for $95. The latest release is installed in the CEE instructional computing network. The structural analysis toolbox FEDEASLab is based on Matlab. The toolbox will be used to convey concepts of computer analysis during the course. It is also very useful for checking numerical answers of homework assignments and for further studies of structural response in this and more advanced courses. Starting from an initial set of basic FEDEASLab functions these will be augmented in the course of CE220 and, particularly, in the course on Nonlinear Analysis. The complete set of functions serves as simulation component for instruction and concept development for the Network for Earthquake Engineering Simulation (NEES). It can be found with several examples, some documentation, and a set of handouts describing its architecture and use at a special FEDEASLab website for NEES.

Since you will be asked to write very simple Matlab scripts during the course, the most basic Matlab skills should suffice. Matlab is ideal for creating custom scripts and functions for the solution of numerically intensive structural problems, and will be used extensively in the course on Nonlinear Analysis.
While it is recommended to gain familiarity with both packages, this may be impossible for time limitations. A possible course of action for the novice is to gain rudimentary knowledge of Matlab for the simplest tasks, but learn Mathcad well and use it in the preparation of homework solutions. There is plenty of time later in the course and before the beginning of the next semester to improve Matlab skills for the course on Nonlinear Analysis.

There are two dangers from the use of these packages. First, that the student will sink too much time in mastering one or the other package and will not invest it in learning structural analysis concepts. Secondly, that the student will get used to the power of the software and will forget how to master the art of hand calculations for examinations. While the students are responsible for averting the first calamity, the second will be avoided by suitable selection of homework problems.

The material in CE 220 forms the basis for several courses in the SEMM program, such as CE 221 Nonlinear Structural Analysis , CE 222 Finite Element Methods and CE 225 Dynamics of Structures. In addition, it is used in design courses. More importantly, it appears again and again in Comprehensive, Preliminary and Qualifying Examinations in SEMM. So, if you finally decide not to take this course make sure you have comfortable control of the material.