### Mechanics of Materials

#### ME 27200 / 3 Cr. (3 Class)

Analysis of stress and strain; equations of equilibrium and compatibility; stress/strain laws; extension, torsion, and bending of bars; membrane theory of pressure vessels; elastic stability; selected topics.

**Available Online:** No

**Credit by Exam:** No

**Laptop required:** No

**Prerequisites/Co-requisites:**

P: ME 27000.

##### Textbooks

F.P. Beer and E.R. Johnston, Jr., Mechanics of Materials, McGraw Hill, Fourth Edition.

##### Goals

To teach students basic knowledge of the behavior of various elastic members under different type of loading. In the laboratory portion of the course, students perform basic experiments related to the theoretical part of this course.

##### Outcomes

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

- Employ the strength of materials theory as a tool to approximately solve the complex stresses and deformations in members of structures and machine elements. [a]
- Use the factor of safety in design of machine components and structures to compensate for the unforeseen factors and stress concentrations. [a]
- Analyze tensile and compressive stresses and deformations in bars subject to axial loads. [a]
- Analyze shear stresses and deformations in circular bars subject to torques. [a]
- Analyze bending stresses in beams subject to transverse loads. [a]
- Analyze shear forces and shear stresses in beams due to transverse loadings. [a]
- Analyze deflection of beams due to transverse loads. [a]
- Identify the instability of long bars under compressive forces, and thus use the theory of columns in design of structures and machine components. [a]
- Employ theory of combined stresses to find maximum tensile, compressive, and shear stresses in an element in design of machine components and structures. [a]

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

##### Topics

- Stress and strain in axial loading, Hooke’s law, displacement, Poisson’s ratio, shear stress and shear strain, generalized stress-strain relationship, strain energy. (6 classes)
- Torsion of bars of solid or hollow circular cross-sections, determination of shear stresses and angle of twist of such members and torsion of thin-walled hollow members. (3 classes)
- Pure bending of beams, flexure formula, section modulus, shearing stress in beams. (3 classes)
- Shear force and bending moment in beams, method of cross-sections, method of differential relations between load, shear force, and bending moment. (2 classes)
- Analysis of plane stress and plane strain, principal stresses and strains, maximum shear stress, Mohr’s circle. (3 classes)
- Deflection of beams, method of differential equation, boundary conditions for various types of support, introduction to singularity functions and their applications in deflection of beams, moment area method. (4 classes)
- Buckling of columns, Euler formula for long columns, various supports, secant formula, short columns. (3 classes)
- Special topics: combined stresses, and either statically indeterminate members or pressure vessels. (3 classes)
- Exams. (3 classes)