## MEC E 480 - Advanced Strength of Materials II **Subject & Number:** [MEC E 480]{.mark} **Title:** [Advanced Strength of Materials II]{.mark} **Course Career** **Units**: 3 **Approved Hours:** 3-0-0 **Fee index:** [8]{.mark} **Faculty:** [Faculty of Engineering]{.mark} **Department:** Mechanical Engineering **Typically Offered:** either term or Spring/Summer ### Calendar Description Special topics for beams, torsion, pressure vessels, plane stress and strain, stability, fracture mechanics. Prerequisites: MEC E 360, 380, MATH 300. ### Course Objectives & General Content The subject known as 'Advanced Strength of Materials' is primarily concerned with the prediction of stresses and strains (deformation) in engineering structures subjected to a given set of loading conditions. There are two principal objectives: 1\. To maximize the efficiency and effectiveness of the structure by using the optimal combination of material properties, geometry and loading configurations. 2\. To identify critical conditions under which the structure will fail. This is an essential part of the engineering design process and requires a thorough understanding of the mechanisms and procedures used to make these predictions. In essence, these 'mechanisms and procedures' involve both practical/experimental tests of the structure as well as the use of mathematical models. Both work together, symbiotically, to produce the best possible results for the design engineer. This course builds on the foundations of the subject presented in Mec E 380 focusing on the development and analysis of mathematical models used in a number of different types of stress analysis problems that arise in practical applications. ### Learning Outcomes: By the end of this course, students should be able to: 1\. Apply advanced concepts elasticity and stress and strain fields to engineering applications 2\. Determine the stresses andstrains in problems including torsion of structures with non-circular cross-section, and the bending of flat plates 3\. Determine the stresses andstrains in plane stress or plane strain problems including thick-walled pressure vessels, shrink fit problems, rotating disks and composite pipes 4\. Identify material and structural features that influence the propagation of cracks in a material 5\. Assess the stability of structures including beams under torsion, rings and flat plates 6\. Construct and analyze mathematical models of real-world problems in solid mechanics ### Text and References [Recommended:]{.underline} Ansel C. Ugural and Saul K. Fenster, Advanced Mechanics of Materials and Applied Elasticity, Prentice Hall, 5th Ed., 2012. J.P. Den Hartog, Advanced Strength of Materials, Dover Publications, 1987. ### Assessment Details --------------------------------------------------------------------------- **Activity** **(A)Synchronous** **Due/Scheduled** **Weight** --------------------- -------------------- ------------------- ------------ Homeworks Asynchronous 30% Quizzes Synchronous 30% Final Exam Synchronous April 17 35% Course Participation 5% --------------------------------------------------------------------------- ### Course Schedule **Jan 6 - Course Introduction (1 Lecture)** **Jan 9 - Review of Stress and Strain (7 Lectures)** • Stress Analysis • Displacement and Strain • Constitutive Relations **Jan 25 - Torsion of Prismatic Beams (9 Lectures)** • Bars of circular cross section • Bars of arbitrary cross section • Prandtl's stress function • Torsion of a narrow rectangular cross section • Kelvin's fluid flow analogy and stress concentrations • Arbitrary thin-walled members **Feb 15** **- Bending of Thin Flat Plates (7 Lectures)** • Geometry of Curved Surfaces • Kirchho-Love Theory • Simple Solutions • Boundary Conditions General Solution for Simply Supported Plates **Feb 20** - **Bending of Thin Flat Plates (7 Lectures)** - • Geometry of Curved Surfaces - • Kirchho↵-Love Theory - • Simple Solutions - • Boundary Conditions - • General Solution for Simply Supported Plates **Mar 10 - Buckling (6 Lectures)** • Review of Elastic Energy • Buckling of Beams Buckling of Thin Flat Plates **Mar 24 - Introduction to Fracture Mechanics (6 Lectures)** - • Griffith's Theory - • Plastic Yielding - • Stress Intensity Factors - J-Integrals **Apr 7 & 10 - Good Friday and Easter (no class)** **Apr 12 - Last Day of Classes** **Apr 17 - Final Exam 2:00 PM** ASSIGNMENT, QUIZ AND EXAM DATES Jan. 6 - Quiz 0 (in class) Jan. 9 - Homework 0 Due Jan. 18 - Homework 1 Due Jan. 20 - Quiz 1 (in class) Feb. 1 -- Homework 2 Due Feb. 3 - Quiz 2 (in class) Feb. 15 - Homework 3 Due Feb. 17 - Quiz 3 (In class) Mar. 1 - Homework 4 Due Mar. 3 - Quiz 4 (In class) Mar. 15 - Homework 5 Due Mar. 17 - Quiz 5 (In class) Mar. 29 - Homework 6 Due Mar. 31 - Quiz 6 (In class) Apr. 12 - Homework 7 Due Apr. 17 - Final Exam 2:00 PM **Assignments:** Students are encouraged to discuss homework problems with their peers. However, each student should submit their own solutions to homework problems and copying of solutions will result in a grade of zero for all parties involved. Assignments are to be scanned or typed and submitted electronically through eClass by 6:00 PM MT (Edmonton time zone). Late assignments will not be accepted. However, the lowest assignment grade for each student will be dropped when final grades are calculated. **Quizzes**: Quizzes are designed to provide frequent feedback to students on their understanding of course material. The quizzes are open note, which means lecture notes and homework assignments may be used, but no other resources (e.g. text books, online solution guides, google, your classmates) are allowed. Quizzes must be scanned and submitted electronically through eClass before the end of the class period (11:50 AM MT). **Quiz Corrections**: Graded quizzes can be corrected for up to half of the missed points on a quiz (e.g. if the initial score were 10/20, submitting perfect quiz corrections would result in a score of 15/20). To receive full marks on the corrected quiz, the correct solution showing all steps must be submitted along with a written description of the "sticking point" (the step or steps that were unclear or incorrect) in the initial quiz and what new knowledge has alleviated the confusion. Final Exam: The final exam will be administered online at the official scheduled time and will cover all course material.