Courses

In compliance of HB 261 by the State Legislature of Utah, starting in 2025, all course syllabi will be shared below for public access:

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Advanced Mechanics of Materials (ME EN 5300/6300)

University of Utah

Spring 2026

Course Description: Extension of concepts learned in mechanics of materials, along with survey of advanced topics. Includes advanced stress analysis in structural members and prediction of their failure; advanced topics in beam bending; torsion of non-circular cross-sections and thin-walled tubes; inelastic bending and torsion; energy methods; and elastic instability.

Course Outcomes: Assuming appropriate effort, by the end of this course, you will be able to …

evaluate complex states of stress and strain for a variety of loading scenarios
analyze factors influencing material failure and accurately predict its likelihood for complex states of loading
identify limitations of traditional mechanics of materials, or elementary, techniques
utilize solutions from Theory of Elasticity to solve complex problems that can’t be accurately addressed using traditional mechanics of materials techniques (e.g. torsion and bending of non-circular cross-sections, concentrated loads, etc)
apply energy methods to predict multiaxial structural deformation under complex loading
apply fundamental principles of plasticity to predict structural deformation beyond the elastic regime

Class Time:

Office Hours:

Text: Advanced Mechanics of Materials and Applied Elasticity, 5th Ed., A.C. Ugural & S.K. Fenster, Prentice Hall, 2012. (Note that a free online version of this text is available through the Marriott Library website; search for the text, click the “View It” tab, and sign into the service with your university email.)

Prerequisites: For undergraduates (5300): ME EN 2010, ME EN 3310/15, and all ME EN-required Math courses. No Prerequisites (6300) for Master’s and Ph.D. students.

Grading:

Class Participation 5%

Homework assignments 15%

Midterm exam one 15%

Midterm exam two 15%

Midterm exam three 15%

Final exam 35%

No alternative dates for exams are available. Please make sure you can attend all scheduled exams.

Homework

Unless otherwise posted, homework will be due weekly at 11:59 PM on the Thursday following the week where the relevant material was covered in lecture. Late HW will NOT be accepted.
Assignments will be distributed via Canvas and turned in and graded using Gradescope (you’ll be linked to Gradescope via your email address in the Canvas class roster). All work must be submitted in pdf format. It is the student’s responsibility to ensure that work is legible.
To receive credit, solutions must demonstrate the full solution process (answers lacking support will receive no credit).
You are encouraged to work with others and use AI tools to help with the homework, but the work you submit must reflect your own understanding.

Exams

Each midterm exams will be designed to take 80 minutes. The final exam will take 120 minutes.
All exams will be open-book, open-notes, open-computer (no internet), etc.
Do NOT use your phone for any purpose during exams.
You can bring and use any tool that does not need internet connection during the exam.
Internet and any other forms of communication are strictly prohibited during exams.

University Policies

The Americans with Disabilities Act. The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodations in this class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, (801) 581-5020. CDS will work with you and the instructor to make arrangements for accommodations. All written information in this course can be made available in an alternative format with prior notification to the Center for Disability Services.
Addressing Sexual Misconduct. Title IX makes it clear that violence and harassment based on sex and gender (which includes sexual orientation and gender identity/expression) is a civil rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran’s status or genetic information. If you or someone you know has been harassed or assaulted, you are encouraged to report it to the Title IX Coordinator in the Office of Equal Opportunity and Affirmative Action, 135 Park Building, 801-581-8365, or the Office of the Dean of Students, 270 Union Building, 801-581-7066. For support and confidential consultation, contact the Center for Student Wellness, 426 SSB, 801-581-7776. To report to the police, contact the Department of Public Safety, 801-585-2677(COPS).
Campus Safety: The University of Utah values the safety of all campus community members. To report suspicious activity or to request a courtesy escort, call campus police at 801-585-COPS (801-585-2677). You will receive important emergency alerts and safety messages regarding campus safety via text message. For more information regarding safety and to view available training resources, including helpful videos, visit utah.eduLinks to an external site..
Other College / University Policies. See the COE Guidelines (https://www.coe.utah.edu/students/current/semester-guidelines/Links to an external site.; link also provided on Canvas homepage).

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Vibrations (ME EN 5400/6400)

University of Utah

Fall 2025

Lecturer: Pai Wang

Lecture: Tu and Th 12:25 PM – 01:45 PM

Office Hours: Tu and Th 01:45 PM – 02:45 PM

E-mail: Canvas for all correspondence

Web Page: CANVAS

Text: There is no mandatory textbook. The recommendations are the following:

Principles of Vibration, Benson H. Tongue	Undergraduate level
Mechanical Vibrations, S. S. Rao	More comprehensive
Fundamentals of Vibrations, L. Meirovitch	Graduate level
Analytical methods in Vibration, L. Meirovitch	Guru expert level

Description of the Course: Free and forced vibrations of discrete linear systems with and without damping; Lagrange’s equations and matrix methods for multiple-degree-of-freedom systems; isolation of shock and vibrations; and applications.

Course Objective: The purpose is to develop students’ ability to apply mathematical methods, physical understanding, intuitive reasoning, and computational tools to vibration problems. Practical engineering examples will be discussed so students learn to use their knowledge in applications.

Outcomes:
Having successfully completed this course, the student will be able to:

Solve differential equations using complementary (homogeneous) + particular solution method.
Solve differential equations to compute the free vibration of undamped & damped single-degree-of-freedom systems.
Model vibrating systems with several degrees of freedom using Newton’s Law and/or Lagrange’s equations.
Compute the response of single-degree-of-freedom systems experiencing sinusoidal and periodic excitation; understand plots of vibration amplitude and phase vs. excitation frequency.
Compute the matrix eigenvalue problem for a multiple degree-of-freedom system and solve for the natural frequencies and vibration modes (analytically and using Matlab).
Use the orthogonality relations/properties of the vibration modes to reduce the vibration of a multiple-degree-of-freedom system to a set of single-degree-of-freedom systems in terms of modal (also called generalized) coordinates.
Compute the response of multiple degree-of-freedom systems under sinusoidal excitation; understand plots of vibration amplitude and phase vs. excitation frequency for such systems.
Apply vibration analysis and design principles to practical examples.
Use Matlab to numerically calculate vibration response for single and multiple degree-of-freedom systems.
Analyze the vibration of a continuous (or distributed parameter) system such as a string.

Lecture Materials: Outside of class, I will communicate with you via Canvas. The course syllabus, lecture content, assignments, any supplementary materials, and class announcements will be posted in Canvas. While the lecture slides contain important concepts that we will cover in class, I will go into more depth during the lecture, which includes working through example problems on the board. The worked-out example problems from lectures and discussions will not be posted on Canvas. Therefore, it is imperative that you attend lectures or discussions. You can request help or schedule office hours using the messaging system in Canvas.

Homework: Try to work through the homework problems until you understand them well enough that you can teach someone else.

All homework will be due by 11:59 PM on the specified due date and must be submitted to Canvas
Any homework handed in by e-mail or in hard copy will not receive credit at all.
Late homework assignments will not be accepted.

Coding: You are expected to be (or quickly become) proficient in Matlab/NumPy or any other numerical-method-friendly language.

Project: Students will work individually to complete a course project. It will be graded on your technical completeness and your communication techniques, as appropriate. The final deliverables are an oral presentation and a report describing your project in detail.

Exams: There will be a total of 3 exams held during the class lecture time. Each will cover everything we have discussed in the lecture up to that point. No alternative scheduling arrangements will be made for any exam.

Grading: The total course grade is comprised of homework, quizzes, the course project, and exams.
The grading scheme is as follows:

Homework: 30%
In-Class Quizzes: 5%
Lecture Participation: 5%
Exam 01 15%
Exam 02 15%
Exam 03 15%
Term Project: 15%

In-class participation quizzes will only be given during class and cannot be made up outside of class. There will be no way to make up quizzes. The exam dates cannot be rescheduled. Please plan accordingly.

Student Mental Health Resources

Rates of burnout, anxiety, depression, isolation, and loneliness have noticeably increased during the pandemic. If you need help, reach out to campus mental health resources, including free counseling, training, and other support.
Consider participating in a Mental Health First Aid or other wellness-themed training provided by our Center for Student Wellness and sharing these opportunities with your peers, teaching assistants, and department colleagues

Students with Disabilities: The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangements for accommodations. All written information in this course can be made available in an alternative format with prior notification to the Center for Disability Services.

Safe U: The University of Utah values the safety of all campus community members. To report suspicious activity or to request a courtesy escort, call campus police at 801-585-COPS (801-585-2677). You will receive important emergency alerts and safety messages regarding campus safety via text message. For more information regarding safety and to view available training resources, including helpful videos, visit safeu.utah.edu

Indigenous Land Acknowledgement Statement: We acknowledge that this land, which is named for the Ute Tribe, is the traditional and ancestral homeland of the Shoshone, Paiute, Goshute, and Ute Tribes. The University of Utah recognizes and respects the enduring relationship that exists between many Indigenous peoples and their traditional homelands. We respect the sovereign relationship between tribes, states, and the federal government, and we affirm the University of Utah’s commitment to a partnership with Native Nations and Urban Indian communities through research, education, and community outreach activities.

College of Engineering (COE) Guidelines:

Please visit the link below to familiarize yourself with the COE guidelines pertaining to this semester.

https://www.coe.utah.edu/semester-guidelines

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Advanced Mechanics of Materials (ME EN 5300/6300)

University of Utah

Spring 2025

Course Outcomes: Assuming appropriate effort, by the end of this course, you will be able to …

evaluate complex states of stress and strain for a variety of loading scenarios
analyze factors influencing material failure and accurately predict its likelihood for complex states of loading
identify limitations of traditional mechanics of materials, or elementary, techniques
utilize solutions from Theory of Elasticity to solve complex problems that can’t be accurately addressed using traditional mechanics of materials techniques (e.g. torsion and bending of non-circular cross-sections, concentrated loads, etc)
apply energy methods to predict multiaxial structural deformation under complex loading
apply fundamental principles of plasticity to predict structural deformation beyond the elastic regime

Class Time: Tu/Th 9:10-10:30 AM; WBB 617

Office Hours: Tu/Th 10:30-11:30 AM; WBB 617 (Or send an email for appointments at other time)

Prerequisites: For undergraduates (5300): ME EN 2010, ME EN 3310/15, and all ME EN-required Math courses. No Prerequisites (6300) for Master’s and Ph.D. students.

Grading:

Class Participation 5%

Homework assignments 15%

Midterm exam one 15%

Midterm exam two 15%

Midterm exam three 15%

Final exam 35%

No alternative dates for exams are available. Please make sure you can attend all scheduled exams.

Homework

Unless otherwise posted, homework will be due weekly at 11:59 PM on the Thursday following the week where the relevant material was covered in lecture. Late HW will NOT be accepted.
Assignments will be distributed via Canvas and turned in and graded using Gradescope (you’ll be linked to Gradescope via your email address in the Canvas class roster). All work must be submitted in pdf format. It is the student’s responsibility to ensure that work is legible.
To receive credit, solutions must demonstrate the full solution process (answers lacking support will receive no credit).
You are encouraged to work with others on the homework, but the work you submit must reflect your own understanding.

Exams

Each midterm exams will be designed to take 80 minutes. The final exam will take 120 minutes.
All exams will be open-book, open-notes, open-computer, etc.
Do NOT use your phone for any purpose during exams.
You can bring and use any tool that does not need internet connection during the exam.
Internet and any other forms of communication are strictly prohibited during exams.

University Policies

The Americans with Disabilities Act. The University of Utah seeks to provide equal access to its programs, services, and activities for people with disabilities. If you will need accommodations in this class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, (801) 581-5020. CDS will work with you and the instructor to make arrangements for accommodations. All written information in this course can be made available in an alternative format with prior notification to the Center for Disability Services.
Addressing Sexual Misconduct. Title IX makes it clear that violence and harassment based on sex and gender (which includes sexual orientation and gender identity/expression) is a civil rights offense subject to the same kinds of accountability and the same kinds of support applied to offenses against other protected categories such as race, national origin, color, religion, age, status as a person with a disability, veteran’s status or genetic information. If you or someone you know has been harassed or assaulted, you are encouraged to report it to the Title IX Coordinator in the Office of Equal Opportunity and Affirmative Action, 135 Park Building, 801-581-8365, or the Office of the Dean of Students, 270 Union Building, 801-581-7066. For support and confidential consultation, contact the Center for Student Wellness, 426 SSB, 801-581-7776. To report to the police, contact the Department of Public Safety, 801-585-2677(COPS).
Campus Safety: The University of Utah values the safety of all campus community members. To report suspicious activity or to request a courtesy escort, call campus police at 801-585-COPS (801-585-2677). You will receive important emergency alerts and safety messages regarding campus safety via text message. For more information regarding safety and to view available training resources, including helpful videos, visit utah.eduLinks to an external site..
Other College / University Policies. See the COE Guidelines (https://www.coe.utah.edu/students/current/semester-guidelines/Links to an external site.; link also provided on Canvas homepage).