Mechanics Of Materials

MAE 231: STRENGTH OF MATERIALS Spring 2009 Instructor: Office: E-mail: Phone: Office Hours: Course Blog:

Dr. Edward Berger A-122 Thornton Hall [email protected] 924-6326 Thursday 2-4 http://people.Virginia.edu/~ejb9z/Weblog

Teaching Assistants: Arun Kailasan [email protected] Office Location: 117 ME Building Office Hours: M, W 2.30 - 5 Class meets:

MWF 12.00-12:50 PM, MEC 339

Review Session:

Occasional, location and time TBD

Catalog Description Stress and strain definitions: Normal stress and strain, thermal strain, shear stress, shear strain; transformations of stress and strain; Mohr’s circle for plane stress and strain; stresses due to combined loading; axially loaded members; torsion of circular and thinwalled closed sections; deformation, strains and stresses in beams; deflections of beams; stability of columns; energy concepts in mechanics. Cross-listed as MAE 231. Detailed Description Strength of materials teaches us about the behavior of materials and solid structures under a variety of load conditions. In this course we will learn and apply the three fundamental keys of mechanics to the study of any solids analysis—EQUILIBRIUM, STRESSSTRAIN RESPONSE and STRAIN-DISPLACEMENT RELATIONS. The course topics will provide the foundation for you to: • Predict the mechanical performance and lifetime of materials and structures whose functions can range from aircraft and bridges to microelectronics and biomedical devices. • Serve as the cornerstone for advanced courses and research into the behavior of materials and structures. We will examine and describe how materials stretch, bend, twist, shake, buckle and break. We will consider the behavior of different materials (ductile vs. brittle). The stress-strain response of different materials will be examined. The stress within externally loaded bodies will be determined at a point. We will cover beam theory with applications to beam deflections and design. Course Objectives and Outcomes By the end of this course you will be able to accomplish the following:

E. J. Berger

A-122 Thornton Hall

[email protected]

MAE 231 Syllabus

Spring 2009

1. Understand the stresses, strains, and deformation response of elastic solids in the presence of external loading. Outcomes: a. define shear and normal stresses and strains b. understand the meaning and use of stress – strain diagrams c. define elastic modulus, shear modulus, and Poisson’s ratio d. describe St. Venant’s Principle e. identify a state of plane stress f. understand the concept of stress transformation 2. Calculate stresses within an elastic solid subject to individual and combined external loading. Outcomes: a. calculate average normal stress and average shear stress b. calculate deflection and reactions for statically determinate and indeterminate: • axially loaded bars • torsionally loaded circular bars c. construct shear and bending moment diagrams for beams subject to bending moments and transverse shear loads d. calculate the normal stress and strain distributions in symmetric beams under pure bending e. calculate the shear stress distribution in a built up beam subject to shear loads f. calculate the deflection of beams from the moment – curvature relationship g. calculate the stress at a point using superposition for the case of simple combined loadings 3. Transform the state of stress in one coordinate system to another. Outcomes: a. construct a Mohr’s circle diagram from a given state of plane stress b. understand the concept of principle stresses and planes c. calculate (from the stress transformation equations or Mohr’s circle) the principle stresses for plane stress d. calculate the maximum in-plane and out-of-plane shear stress for plane stress Prerequisite Courses and Materials APMA 212: Multivariate Calculus (integration, differentiation, vector concepts) CE 230: Statics ( FREE BODY DIAGRAMS , force and moment summation and vectors, truss analysis, point loads and distributed loads, body forces,)

E. J. Berger

309 ME Building

[email protected]

MAE 231 Syllabus

Spring 2009

Textbook Required: Mechanics of Materials, (7th Edition) by R HIBBELER ISBN: 0132209918. Please note all homework problems and reading assignments are from this book. Useful supplement: Schaum’s Outline on Strength of Materials, William Nash (Amazon). Course Grading Homework (15%): problems and due dates will be announced in class Quizzes (10%): there will be approximately 5 quizzes this semester, announced in advance Project (10%): details will be announced soon THREE midterm exams (15% each): dates, locations, and detailed exam format will be announced prior to their administration Final exam (20%): covers the entire course, Tuesday May 5, 2-5 pm, location TBA Course Policies a. Communication: Check the course homepage on Toolkit as well as the blog page frequently for announcements, handouts, solutions, podcasts, and other downloads. Materials will be updated regularly, so I urge you to subscribe to the RSS feed so that you do not miss any important information. b. Homework: In each homework set, several problems from the text will be assigned but not more than two (2) will be graded in detail. Only the problems to be graded will be collected—you will not hand in each and every problem. Solutions to all homework problems will be posted on the course website. Homework is due AT THE BEGINNING OF CLASS on the stated due date—your homework must be in my hand BEFORE CLASS BEGINS or it is considered late! Late homeworks receive a grade of zero. We have many homework assignments in this course, so we will drop the lowest homework grade from your grade calculation. Note: homework is NOT pledged. c. Attendance: Class attendance is imperative, because we will do many problems and live demos which contribute strongly to your understanding of the material. However, there is no penalty for not attending class (although assignments must be turned in on time, regardless of whether you attend or not). Anecdotally, there is a strong correlation between class attendance and course grade. Moreover, virtually all academic research shows that class attendance is positively correlated with course grade.

E. J. Berger

309 ME Building

[email protected]

MAE 231 Syllabus

Spring 2009

d. Quiz format: each quiz will consist of one question, with a 15-minute time limit. Each will be graded on a 10-point scale. We will NOT drop the lowest quiz grade for the semester from the grade calculation. e. Neatness of Work: success in engineering requires a clear thought process and well-organized problem solving. Your grade will suffer if your assignments are difficult to grade due to sloppiness, scribbles, cross-outs, and an otherwise disorganized and difficult-to-follow solution. f. Grade Appeals: Grade appeals for assignments must be submitted within one week of the return date of the assignment, and must be submitted in writing. You must clearly describe the reason you are requesting a regrade. Requests submitted later than one week after the return date or not submitted in writing will not be honored. g. Emergency Circumstances: Only under unusual, emergency circumstances will late assignments be accepted. You will have plenty of time to complete the assignments, so do not procrastinate. Single-day commitments (i.e., interviews) do not excuse you from the responsibilities of this class. If necessary, you can email your assignment to me. h. Honor System: All exams and quizzes will be administered under the University of Virginia honor system. Students are assumed to be familiar with the honor system and will be bound by it. Homework is not pledged; feel free to work collaboratively. Here is a general statement from SEAS HQ: The Honor System and the School of Engineering and Applied Science The School of Engineering and Applied Science relies upon and cherishes its community of trust. We firmly endorse, uphold, and embrace the University’s Honor principle that students will not lie, cheat, or steal, and we expect all students to take responsibility for the System and the privileges that it provides. We recognize that even one Honor infraction can destroy an exemplary reputation that has taken years to build. Acting in a manner consistent with the principles of Honor will benefit every member of the community both while enrolled in the Engineering School and in the future. If you have questions about your Honor System or would like to report suspicions of an Honor offense, please contact Thad Darden ([email protected]) or Erin Kallman ([email protected]).

i. Cell Phones: Please turn off your cell phone while in class. j. Consultation: I am available during posted office hours, and you can make an appointment with me via email if you cannot attend office hours. Our TA will also be available for consultation, during office hours or by appointment. E. J. Berger

309 ME Building

[email protected]

MAE 231 Syllabus

Spring 2009

k. Problem Sessions: Our T.A. will conduct periodic review and problem sessions every throughout the semester at times and locations TBD. l. Course Project: The course project is going to engage you in the creation of learning materials to share with your peers. Details will be forthcoming, but in the past this project format has been a great success and very popular with students. m. Blogging. All students are encouraged to register a login name on the course blog so that you can post comments and questions about the course, about the homework, or about a specific lecture. You are not compelled to do this, but I strongly encourage you to take advantage of this approach to interaction with the course materials. If you wish to remain anonymous, we can set up confidential screen names. n. University Holidays. MLK Day (Jan. 19), Spring Break (Feb. 28 – March 8), Reading Day (April 29). o. Drop and Withdrawal. The last day to drop the course is Feb. 24, and the last day to withdraw is April 10.

E. J. Berger

309 ME Building

[email protected]

MAE 231 Syllabus

Spring 2009

Detailed Course Agenda: Date 1

1/13

2

1/14

3

1/16

4

1/21

5

1/23

6

1/26

7

1/28

8

1/30

9

2/2

10

2/4

11

2/6

12

2/9

13

2/11

14

2/13

15

2/16

16

2/18 **** 2/20 2/23 2/25 2/27

17 18 19 20

E. J. Berger

Topic Introduction Equilibrium of a Deformable Body Stress Average Normal Stress in an Axially Loaded Bar Average Shear Stress Allowable Stress Deformation Strain The Tension and Compression Test The Stress – Strain Diagram Stress – Strain Behavior of Ductile and Brittle Materials Hooke’s Law Strain Energy Poisson’s Ratio The Shear Stress – Strain Diagram Saint – Venant’s Principle Elastic Deformation of an Axially Loaded Member Principle of Superposition Statically Indeterminate Axially Loaded Member The Force Method of Analysis for Axially Loaded Members Thermal Stress Thermal Stress Stress Concentrations Torsional Deformation of a Circular Shaft The Torsion Formula Power Transmission Angle of Twist Statically Indeterminate Torque – Loaded Members Solid Noncircular Shafts Thin – Walled Tubes Having Closed Cross Sections Stress Concentrations Shear and Moment Diagrams TEST #1 on Chapters 1 – 5 (date TBA) Bending Deformation of a Straight Member The Flexure Formula Unsymmetric Bending Composite Beams

309 ME Building

Reading Due 1.1 – 1.2 1.3 1.4 1.5 1.6 2.1 2.2 3.1 3.2 3.3 3.4 3.5 3.6 3.7 4.1 4.2 4.3 4.4 4.5 4.6 4.6 4.7 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 6.1 6.3 6.4 6.5 6.6

[email protected]

MAE 231 Syllabus

Spring 2009

21 22 23

3/9 3/11 3/13

Shear in Straight Members The Shear Formula Shear Stresses in Beams

7.1 7.2 7.3

24 25 26 27

3/16 3/18 3/20 3/23

28

3/25

Shear Flow in Built – up Members Shear Flow in Thin – Walled Members Combined Loading in Thin – Walled Vessels State of Stress Caused by Combined Loadings Plane – Stress Transformation General Equations of Plane – Stress Transformations Principal Stresses and Maximum In – Plane Shear Stress Mohr’s Circle – Plane Stress Mohr’s Circle – Plane Stress Stress in Shafts Due to Axial Load and Torsion Absolute Maximum Shear Stress Absolute Maximum Shear Stress Plane Strain General Equations of Plane – Strain Transformation TEST #2 on Chapters 6 – 9 (date TBA) Basis for Beam Design Prismatic Beam Design The Elastic Curve Slope and Displacement by Integration Slope and Displacement by Integration Method of Superposition Method of Superposition Statically Indeterminate Beams and Shafts Final Review FINAL EXAM 2-5 pm (location TBA)

7.4 7.5 8.1 8.2 9.1 9.2

29

3/27

30

3/30

31

4/1

32 33 34 35 36

4/3 4/6 4/8 **** 4/10 4/13

37

4/15

38 39 40 41 42

4/17 4/20 4/22 4/24 4/27 5/5

E. J. Berger

309 ME Building

9.3 9.4 9.4 9.5 9.7 9.7 10.1 10.2 11.1 11.2 12.1 12.2 12.2 12.5 12.5 12.6

[email protected]