MECHENG 340 : Mechanics of Materials 2

Engineering

2024 Semester One (1243) (15 POINTS)

Course Prescription

Complex material behaviour and structural analysis, extending capability from two to three dimensions. States of stress and strain at a point in a general three-dimensional stress system. Generalised stress–strain relations for linearly elastic isotropic materials. Failure theories for ductile and brittle materials, elementary plasticity, and fatigue. Analytical techniques and numerical analysis of complex mechanical elements.

Course Overview

The course extends on knowledge provided in Mecheng242, to the analysis of 3D states of stress and strain, with an initial focus on elasticity. Non-linear material behavior is introduced, considering yield and plasticity. Knowledge of material strength is deepened; considering yield theories for ductile materials, fracture mechanics of brittle materials, and fatigue. Application is made to mechanical elements, including complex beams, and axi-symmetric systems (thick walled vessels). Numerical analysis is introduced, students applying Finite Element Analysis to mechanical elements, via a computer based laboratory and an assignment.

Mechanics of Materials
States of stress and strain at a point; analysis of stress under conditions of plane stress and plane strain; strain rosettes; generalised stress-strain relationships for linearly elastic and isotropic materials. Theories of yield.

Introduction to Numerical Methods
Introduction to Finite Element Analysis (FEA), including principles of computation. FEA model development. Results interpretation and validation.

Machine Elements: Beams
Asymmetrical or skew bending. Thin-walled open sections and shear centre.

Machine Elements: Thick-walled Pressure Vessels
Stresses and strains in axisymmetric systems, as applied to thick-walled pressure cylinders. Initial yield and plastic collapse in pressure vessels.

Non-linear Stress-strain Behaviour
Non-linear elasticity. Elementary plasticity, and yield theories for ductile materials.

Fracture in Brittle Materials
Stress concentration due to geometric features. Failure mechanisms in brittle materials. Introduction to linear elastic fracture mechanics; fracture toughness. Crack growth under repeated or cyclic loading.

Fatigue in Ductile Materials
Introduction to material fatigue. Environmental and design influences. Fatigue under uniaxial and multiaxial stress states. Cumulative damage.

Course Requirements

Prerequisite: MECHENG 242

Capabilities Developed in this Course

Capability 1: People and Place
Capability 2: Sustainability
Capability 3: Knowledge and Practice
Capability 4: Critical Thinking
Capability 5: Solution Seeking

Learning Outcomes

By the end of this course, students will be able to:
  1. Analyse three-dimensional states of stress and strain at a point, applying generalised stress-strain relationships, including conditions of plane stress and plane strain for two-dimensional loading situations. Calculation of principal stresses or principal strains in three dimensions, for given loading conditions. (Capability 3.1, 4.2 and 5.1)
  2. Formulate and execute a well-defined structural model for analysis using a Finite Element Analysis (FEA) software package, correctly interpreting results generated by the FEA package. (Capability 3.1, 3.2, 4.2 and 5.1)
  3. Apply the Euler beam theory for the stress analysis of beams, determine the location of the shear centre for thin-walled beam sections, and calculate shear flow and stresses within a section (Capability 3.1, 3.2, 4.1 and 5.1)
  4. Understand and describe several extensions beyond linear elastic behaviour, including nonlinear elasticity, yield and plasticity. (Capability 3.1, 3.2, 4.1 and 5.1)
  5. Understand and apply theories of yield, with application to generalised stress states, and specifically thick-walled pressure cylinders. (Capability 3.1, 3.2, 4.1 and 5.1)
  6. Apply the concept of plane strain fracture toughness to determine critical crack size, for brittle and moderately ductile materials. (Capability 3.1, 3.2, 4.1 and 5.1)
  7. Understand how cracks in components of brittle materials grow under a cyclic stress state, and determine the number of cycles an initial crack requires to grow to critical size. (Capability 3.1, 3.2, 4.1 and 5.1)
  8. Apply the concept of S-N curve to determine the life of a component of ductile materials undergoing uniaxial and multiaxial cyclic stress state. (Capability 3.1, 3.2, 4.1 and 5.1)
  9. Understand and explain environmental conditions and manufacturing methods that contribute to early fatigue failure of ductile materials, or can be applied to extend fatigue life. (Capability 3.1, 3.2, 4.1 and 5.1)
  10. Understand and evaluate the influence of material selection and structural design safety factors on the safety and environmental impact of a product or structure. (Capability 1.1 and 2.1)

Assessments

Assessment Type Percentage Classification
Final Exam 50% Individual Examination
Laboratories 5% Individual Coursework
Tests 20% Individual Test
FEA Assignment 25% Individual Coursework
Assessment Type Learning Outcome Addressed
1 2 3 4 5 6 7 8 9 10
Final Exam
Laboratories
Tests
FEA Assignment

Workload Expectations

This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

For each week in this course, you can expect 3 hours of lectures, a 1 hour clinic, 2 hours of reading and thinking about the content and 4 hours of work on problem sheets, assignments and test and exam preparation.

Delivery Mode

Campus Experience

Attendance is required at scheduled activities including labs to complete credit for components of the course.
Lectures and the clinic will be available as recordings. Other learning activities including labs will not be available as recordings.
The course may include live online events including group discussions and tutorials.
Attendance on campus is required for the tests.
The activities for the course are scheduled as a standard weekly timetable.

Learning Resources

Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).

Please remember that the recording of any class on a personal device requires the permission of the instructor.

Health & Safety

Students are expected to adhere to the guidelines outlined in the Health and Safety section of the Engineering Undergraduate Handbook.

Student Feedback

At the end of every semester students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback and respond with summaries and actions.

Your feedback helps teachers to improve the course and its delivery for future students.

Class Representatives in each class can take feedback to the department and faculty staff-student consultative committees.

Student participation in the 2023 survey was low, being only 15%. Suggestions for improvement were on wide and varied topics, across the students that participated. The most common comments related to the length of the FEA assignment, difficulty level and timing. The content of the assignment will be updated again, and the assessment has been lifted from 20 to 25% for the course.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

Class Representatives

Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.

Inclusive Learning

All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.

Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website http://disability.auckland.ac.nz

Special Circumstances

If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.

If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.

This should be done as soon as possible and no later than seven days after the affected test or exam date.

Learning Continuity

In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.

Student Charter and Responsibilities

The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.

Disclaimer

Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.

In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.