Instructor: Prof. Carlos E. S. Cesnik E10-105B x2-1518 ccesnik@mit.edu

Teaching Assistant: Ms. Dora Tzianetopoulou TBD tzianet@mit.edu

Course Secretary: Ms. Cathy Chase E10-103 x3-6339 cmchase@mit.edu

Monday, Wednesday, and Friday 10:00-11:00 Rm. 8-205

Recitations: Tuesdays 10:00-11:00 Rm. 26-322

Students graduating from 16.210 will be able to:

1) use energy principles to determine the stress and deformation states of structures comprised of one-dimensional elements (beams, columns, and rods).

2) apply structural discretization techniques to model generic three-dimensional structures under specified loading in order to determine the stress and deformation states.

3) assess the yielding, fracture, and fatigue characteristics of isotropic materials in such structural configurations.

4) assess the applicability of such models and the error introduced in their use.

Students in 16.210 will be introduced to the more advanced concepts and tools used in aerospace structural design. These are the more advanced analysis techniques of energy methods and finite element methods as well as a more in depth treatment of structural materials and structural failure modes. The working objective throughout is to teach students to "ask the right questions," "challenge the assumptions," and figure out what analysis really applies in a particular situation.

Students graduating from 16.210 will be able to:

a) explain the basic considerations of structural design.

b) explain the underlying principles of the finite element approach and the methodology to apply such to generic three-dimensional structures.

c) apply a basic physical intuition for the function and sizing of structural elements and the selection of materials for use in them.

d) calculate generalized displacements and internal generalized forces in one-dimensional structures, such as those listed in (1), using energy principles.

e) calculate the stress and deformation states in beams and membranes by the finite element method

f) design a structural component subjected to different loads and accounting for considerations of yielding, fracture, and fatigue.

g) assess the conditions under which the idealizations listed in (b) and the material failure models listed in (f) cease to be applicable.

Students need a basic statics and mechanics background as provided in (mainly) Unified and 16.20. This includes the ability to use and perform the following:

• Free body diagrams
• The concepts of stress and strain
• Orthotropic constitutive relations
• Transformation of stress and strain
• Basic equations of elasticity: equilibrium, stress-strain, strain-displacement
• Beam theory
• Tensor notation
• Alternate coordinate systems
• Loads analysis
• Design loads in aerospace
• Structural Instability
• Beam Column

Since a core goal of the course is exposure to important aerospace structural design tools and computational techniques, it is also assumed that the students have rudimentary knowledge of computer usage and have Athena accounts. Details on attaching to the course locker and accessing provided programs and Matlab will be provided in Recitation. Students will be expected to become familiar and facile with Matlab during the course of the term.

This is a broad set of topics that you should learn from this course:

• Energy Methods for structural analysis
• Fundamental understanding of the Finite Element method
• Material Types and Characteristics
• Structural Failure Criteria
• Fundamentals of Fracture and Fatigue
• Other Failure Modes
• Design Process for Complicated Structure
• Important Computational Skills
  

The most important reference you will have is your class notes! The material in this class does not correspond to any one available textbook. So be sure to take good notes, and fill any gaps due to missed classes by asking a classmate, or as a last resort, Miguel Ortega-Morales or Prof. Cesnik for the missing notes. Some texts are useful though; here is a rather overdone list:

1. Theory and Analysis of Flight Structures, Rivello, McGraw-Hill, 1969.

2. Statics of Deformable Solids, Bisplinghoff, Mar, and Pian, Dover, 1965.

3. Energy and Finite Element Methods in Structural Mechanics, Shames and Dym, Hemisphere Publishing Corporation, 1985.

4. Theory of Matrix Structural Analysis, Przemieniecki, Dover, 1968.

5. Finite Element Procedures, Bathe, Prentice Hall, 1996.

6. Mechanical Behavior of Materials, Dowling, Prentice Hall, 1993.

7. Engineering Materials 1: Ashby and Jones, Pergammon, 1986

8. Mechanics of Composite Materials, Jones, McGraw-Hill, 1975. (also: Hemisphere, 1988).

9. Theory of Elasticity, Timoshenko and Goodier, McGraw-Hill, 1970.

10. Theory of Elastic Stability, Timoshenko (and Gere), McGraw-Hill, 1961.

11. Material Selection in Mechanical Design, Ashby, Pergammon, 1992.

The first two references ("Theory of Analysis of Flight Structures," and "Statics of Deformable Solids") are the primary text for the first third of the course. The third text ("Energy and Finite Element Methods in Structural Mechanics") has a good overview of the first two thirds of the class, and the fifth text ("Finite Element Procedures") is one of the primary references nowadays for finite elements. The seventh text ("Mechanical Behavior of Materials") is a good reference for the last third of the course.

Some of the texts will be on reserve in the Aero/Astro Library. In addition, Barker has an extensive set of references on structural mechanics including these texts. You are encouraged to seek out additional reading materials to supplement lectures and reading assignments from the primary texts.

Problem Sets: Problem sets (a total of approximately 8) will be handed out generally on a weekly basis. (For planning purposes, this will likely be on Monday.) They will be due, on average, one week later in class. Late submission of problem sets is discouraged. Maximum credit on late problem sets will be degraded by 33% per class day. After 3 class days, a zero will automatically be recorded. This policy may be changed if necessary to get solutions out in a timely fashion before a test or other event.

Exams: The date for the term-time exam is currently Wednesday, 19 March, in lecture room during regular class hour. The department actively seeks to avoid major conflicts/pile-ups between exams in different courses, so these may move. Check the on-line schedule for the latest information. The final exam will be during the final exam period as scheduled by the Registrar. It will be a comprehensive exam, with emphasis on the last half of the course material.

Design Project: The course will contain a design project work on teams of approximately four students. This will run for about 6 weeks, starting 03 April. The project will consist of teamwork on the design of a structural component progressing from the conceptual design phase to the detailed design of the component. There will be a final written report and presentation of the Final Design. Since team work is part of the object of this exercise, Dr. Donna Qualters will come to give a lecture on the dynamics of groups, and she will be available to support the groups during those 6 weeks. Evaluation on the group performance (non-technical) will be responsible for 10% of the final Design Project grade.

The final grade will be calculated as follows:

Problem sets 35%

Project 30%

Midterm Exam 15%

Final Exam 20%

_____

100%

Attendance, participation, general evaluation ±5%

The letter grades are based on absolute performance and are not subject to a curve. All problems (except pop quizzes) will be graded on a letter basis according to the MIT definition of grades:

A - Exceptionally good performance, demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge and a skillful use of concepts and/or materials.

B - Good performance, demonstrating capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the subject.

C - Adequate performance, demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field.

D - Minimally acceptable performance, demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

F - Unsatisfactory performance.

Plusses and minuses will be used in conjunction with the letters in grading term-time work. The final grade will also include plusses and minuses, which, in accordance with the new MIT policy, will not appear on external transcripts or be used to evaluate students' GPA.

The Syllabus for the course and the schedule of expected dates of lectures are attached to this document. In addition the course calendar including critical dates is attached.

The important dates during the term are:

• Midterm Exam March 19 (in Lecture)
• Final Project May 5 (in Lecture) (Report Due and Final Presentation)
• Final Exam: During finals week (to be scheduled by the Registrar)
  

Tests will be open note (anything you wrote by hand, including "cheat sheets") but closed book (including things other people wrote, including "bibles"). Calculators, including programmable ones, are OK, but no laptop computers. Tests will be written such that students will not get much of an advantage from written materials beyond notes and summary sheets, or calculating power beyond that of simple calculators.

The pertinent policy with regard to homework and design problems is basically the same as you are familiar with from Unified. The fundamental principle of academic integrity is that you must fairly represent the authorship of the intellectual content of the work you submit for credit. In the context of this course, this means that if you consult with others in the process of completing homework, you must acknowledge their contribution in a way that reflects their true ownership of the ideas and methods you borrowed.

Discussion among students to understand the home problems or to prepare for quizzes is encouraged. Some exercises will be deliberate team exercises, in which one cooperative piece of work will be handed in. Even in cases where individual answers are expected, collaboration on homework is allowed so long as all references (both literature and people) used are named at the end of the assignment. Word-by-word copies of someone else's solution or parts of a solution handed in for credit will be considered cheating unless there is a reference to the source for any part of the work which was copied verbatim. Failure to cite another student's contribution to your homework solution will be considered cheating. Official Institute policy regarding academic honesty can be found in the current Bulletin under "Academic Procedures and Institute Regulations". Cases of academic dishonesty are a severe breach of the student's and engineer's code and will be treated appropriately.

Study Group Guidelines: Study groups are considered an educationally beneficial activity. However, at the end of each problem on which you collaborated with another student, you must cite the students and the interaction. The purpose of this is to acknowledge their contribution to your work. Some examples follow:

1. You discuss concepts, approaches, and methods that could be applied to a home problem before either of you start your written solution. This process is encouraged. You are not required to make a written acknowledgment of this type of interaction.

2. After working a problem independently, you compare answers with another student which confirms your solution. You should acknowledge that the other student's solution was used to check your own. No credit will be lost if the solutions are correct and the acknowledgment is made.

3. After working a problem independently, you compare answers with another student which alerts you to an error in your own work. You should state at the end of the problem that you corrected your error on the basis of checking answers with the other student. No credit will be lost if the solution is correct and the acknowledgment is made.

4. You and another student work through a problem together exchanging ideas as the solution progresses. You both should state at the end of the problem that you worked together jointly. No credit will be lost if the solutions are correct and the acknowledgment is made.

5. You copy all or part of a solution from a reference such as a textbook or a bible. You should cite the reference. No credit will be lost assuming the solution is correct and pertinent to the problem statement. You receive credit because you showed the judgment to look in the literature for solutions to the problems. However, doing this without understanding the solution is unwise!

6. You copy verbatim all or part of a solution from another student. This process is strongly discouraged. You will lose credit for verbatim copying from another student when you have not made any intellectual contribution to the work you are both submitting for credit.

7. Verbatim copying of any material which you submit for credit without reference to the source is considered to be academically dishonest. At the least, you will receive no credit for the problem set or test in question.