1994 Catalog Data:

Stress and strain in elastic solids such as shafts and beams, combined stresses; statically indeterminate beams.

Textbook: Egor P. Popov, Engineering Mechanics of Solids ,Prentice Hall, Englewood Cliffe, 1990.

Coordinator: K. D. Pae, Professor of Mechanical Engineering

Goals:

This course is designed to introduce students to the concept of stress at a point, strain, Hooke's law, and yield theories. It also gives students an opportunity to apply these concepts to solve practical engineering problems; such as calculation of stresses, strains, and deformation in bars, thin-walled pressure vessels, shafts, and beams.

Prerequisites by topic:

1. Engineering Mechanics I, Statics
2. Multivariable Calculus for Engineers
3. Differential Equations for Engineering and Physics

Topics:

1. Stress at a point(2 class)
2. Strain, normal stress-strain relations(1 class)
3. Deformation of bars(1 class)
4. Shear stress and strains; generalized Hooke's law; E, G, and n relation; Bulk modulus(2 classes)
5. Thin-walled pressure vessels(1 class)
6. Torsion of circular bars(2 classes)
7. Bending of beams, deflection of beams(5 classes)
8. Combined stresses; 2-D stress transformation, Principal stress and strain, Mohr's circle(5 classes)
9. Yield theories(3 classes)
10. Tests(2 classes)

Computer usage:

1. Homework may be done by using a computer, but it is optional.

ABET category:

Engineering science: 3 credits or 100%

Prepared by: Professor K. D. Pae Date: March 7, 1994

Catalog description:

Stress and strain in elastic solids such as shafts and beams, combined stresses; statically indeterminate beams.

Textbook:

Egor P. Popov, Engineering Mechanics of Solid

Prentice Hall, Englewood Cliffs, 1990.

Goals:

This course is designed to introduce students to the concept of stress at a point, strain, Hooke's law, and yield theories. It also gives students an opportunity to apply these concepts to solve practical engineering problems; such as calculation of stresses, strains, and deformation in bars, thin-walled pressure vessels, shafts, and beams.

Prerequisites:

14:440:221 Engineering Mechanics, Statics

Corequisites:

01:640:243 Multivariable Calculus for Engineers, or

01:640:244 Differential Equations for Engineering and physics

Course Outline

Lecture 1

Concept of stress at a point in a continuous medium. Stress tensor. Symmetricity of shear stress components. Intrinsic properties of stress components.

Homework problems: 1.1, 1.3, 1.6, 1.8.

Lecture 2

Stress components on inclined planes. Shear stress in bolts. Bearing stress on bolts.

Homework problems: 1.9, 1.13, 1.15, 1.22, 2.1, 2.2.

Lecture 3

Concept of strain. Stress-strain curves. Simple stress-strain relations.

Young's modulus. Isotropy and anisotropy. Homogenous and inhomogeneous materials.

Homework problems: 2.3, 2.11, 2.21, 2.31.

Lecture 4

Deformation of axially loaded uniform and non-uniform bars. Poisson's ratio. Thermal strain and deformation. St. Venant's principle. Stress concentration factor.

Homework problems: 3.2, 3.4.

Lecture 5

Shear stress-strain relationships. Generalized Hooke's law. E, G, and n

relationship. Dilatation of bulk modulus.

Homework problems: 3.5, 3.6.

Lecture 6

Thin-walled pressure vessels. Stresses and strains in cylindrical and spherical pressure vessels.

Homework problems: 3.7, 3.9, 3.11, 3.13.

Lecture 7

Torsion of Circular bars. Torsion of shrink-fitted bars. Torque-HP relationships. Stress distribution in single and shrink-fitted bars.

Design of torsion bars for given HP and rotating speed. Stress concentration in torsion bars.

Homework problems: 4.1, 4.3, 4.5, 4.7.

Lecture 8

Angle of twist in circular torsion uniform and non-uniform bars.

Homework problems: 4.11, 4.15, 4.17.

Lecture 9

Bending of beams. Shear and moment in beams by method of sections. Shear and moment diagrams in beams.

Homework problems: 5.1, 5.3, 5.5, 5.27.

Lecture 10

Differential equation of equilibrium for beams. Variable loading, shear force, and moment relationships.

Homework problems: 5.46, 5.53, 5.57, 5.59.

Lecture 11

Bending of beams. Assumptions made in bending of beams. Bending strain. Bending stress. Bending stress and moment relationship (Flexure formula). Neutral axis.

Homework problems: 6.1, 6.7, 6.9, 613, 6.21.

Lecture 12

Shear stress in beams.

Homework problems: 7.1, 7.3, 7.7, 7.13.

Lecture 14

Combined stresses. Superposition of shear stresses in bending and torsion of a circular cross-section beams.

Homework problems: 7.46.

Lectures 15 and 16

Stress transformation in two-dimensions. Principal stresses. The maximum shear stress.

Homework problems(15): 8.1, 8.3, 8.5, 8.7.

Homework problems(16): 8.17, 8.18, 8.19, 8.21.

Lecture 17

Mohr's circle.

Homework problems: 8.23, 8.24, 8.25, 8.27.

Lecture 18

Transformation of strains in two-dimensions. Principal strains. The maximum shear strains. Mohr's circle for two-dimensional strains.

Strain rosettes.

Homework problems: 8.48, 8.49.

Lectures 19, 20, and 21

Yield theories. The maximum shear theory(Tresca's yield condition).

The maximum distortion energy theory(von Mises' yield condition).

Homework problems: Hand out problems(see Appendix 1).

Lectures 22, 23, and 24

Deflection of beams. Deflections by integration. Governing differential equation. Boundary conditions.

Homework problems(22): 10.1, 10.3, 10.5, 10.9.

Homework problems(23): 10.10, 10.11, 10.14, 10.15.

Homework problems(24): 10.17, 10.35, 10.51.

Administration of the course

1. Attendance is mandatory.

2. Homework is graded

3. 2 hourlies(80 min. each) are given.

4. Final examination(3 hours) covering all subjects studied is given.

Prepared by Professor Kook D. Pae, Date March 10, 1994