### Advanced Stress Analysis

#### ME 55000 / 3 Cr. (3 Class)

Studies of stresses and strains in three-dimensional problems. Failure theories and yield criteria. Stress function approach to two-dimensional problems. Bending of non-homogeneous asymmetric curved beams. Torsion of bars with noncircular cross sections. Energy methods. Elastic stability. Introduction to plates. Students may not receive credit for both ME 472 and ME 550.

**Available Online:** No

**Credit by Exam:** No

**Laptop Required:** No

**Prerequisites/Co-requisites:**

P: ME 27200 and MATH 26600.

##### Textbooks

A.C. Ugural and S.K. Fenster, Advanced Strength and Applied Elasticity, Fourth Edition, Prentice Hall, 2003.

##### Goals

The objective of this course is to provide students the tools required for design and analysis of complex problems in mechanics of materials.

##### Outcomes

**After completion of this course, the students should be able to:**

- Explain the concept of elasticity, and the difference between stress and strain [a]
- Explain the terms: isotropic, orthotropic and anisotropic, as applied to materials [a]
- Explain the terms: plane stress and plane strain [a]
- Conduct the transformation of plane stress or plane strain components using Mohr's circle, the method of eigenvalues and eigenvectors, the method of quadratic form of ellipsoids, and the method of stress or strain trajectories [a, e]
- Use the concepts of principal stress and principal strains [e]
- Use the basic tensor notations, the stress, strain and inertia tensors, and their reduction to principal axes [a, e]
- Apply the analytical procedures involved in strain gauge measurements, in particular the transformation equations [e]
- Solve basic problems in two-dimensional elasticity using Airy's stress function [e]
- Evaluate solutions of simple engineering problems using mechanics of material theories [e]
- Use basic stability and yield criteria for elasto-plastic materials [e]
- Apply basic concepts of elastic stability and buckling of elastic [e]
- Using finite difference approximations to solve elasticity problems governed by partial differential equations [e]
- Understand the importance of various yield criteria and material stability.

Note: The letters within the brackets indicate the general program outcomes of mechanical engineering. See: ME Program Outcomes.

##### Topics

- Three-dimensional stress analysis (2 periods)
- Plane stress and plane strain problems (2 periods)
- Stress functions (2 periods)
- Failure criteria (2 periods)
- Bending of curved beams (2 periods)
- Shear stresses (2 periods)
- Shear center (2 periods)
- Torsion (2 periods)
- Thin-walled members (2 periods)
- Statically indeterminate problems (2 periods)
- Elastic stability (2 periods)
- Beams on elastic foundation (2 periods)
- Fourier series (2 periods)
- Energy methods (2 periods)
- Introduction to plates (2 periods)