### 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, 7th Edition.

##### Goals

To teach students basic knowledge of the behavior of various elastic members under different type of loading.

##### 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.
- 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.
- Pure bending of beams, flexure formula, section modulus, shearing stress in beams.
- Shear force and bending moment in beams, method of cross-sections, method of differential relations between load, shear force, and bending moment.
- Analysis of plane stress and plane strain, principal stresses and strains, maximum shear stress, Mohr’s circle.
- 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.
- Buckling of columns, Euler formula for long columns, various supports, secant formula, short columns.
- Special topics: combined stresses, and either statically indeterminate members or pressure vessels.