MAE314 Solid Mechanics Fall, 2003

Dr. Yuan

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GENERAL INFORMATION

INSTRUCTOR

Dr. F. G. Yuan, Research Building II, Rm. 210B, Centennial Campus, 515-5947.

TEXTBOOKS

Mechanics of Materials

Roy R. Craig, Jr., Second Edition, John Wiley& Sons, Inc., 2000.

HOMEWORK

Homework will be assigned on approximately twice of each week, and a due date will be given

with each assignment. No late homework will be accepted.

Homework solutions must be written neatly, on one side of the paper only, and all pages must be

stapled together. Use ink or dark pencil. The following items are not acceptable:

• Very light pencil

• Writing on both sides of the paper

• Untrimmed pages torn from spiral notebooks

• Pages paper-clipped or folded together.

Copy the homeworks from teammates or solution manual is strictly prohibited and will be

penalized.

EXAMS

There will be three one-hour examinations, given in class tentatively on September 17, October

22, November 17, and a final exam. All exams are closed book, closed notes.

GRADING

Grades will be based on homework and exam scores, weighted as follows:

Homework 10%

Exam I 20%

Exam II 20%

Exam III 20%

Final Exam 30%

60-69 - D; 70-79 - C; 80-89 - B; 90-100 - A

*0-*3 '-', *3.1-*6 ' ', *6.1-*9.9 '+'

OFFICE HOURS

To be announced.

MAE314 Solid Mechanics Fall, 2003

Dr. Yuan

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MAE 314

COURSE OUTLINE

0) Units: History of mechanics; SI and USCS units.

1) Introduction to Mechanics of Materials: (1.1-1.5) Fundamental equations of deformable-

body mechanics; problem-solving procedures; equilibrium equations; external and internal forces

and moments; free-body diagrams; support reactions.

2) Stress and Strain; Design: (2.1-2.4; 2.6-2.11) Normal stress, extensional strain, thermal

strain, stress-strain diagram, elasticity & plasticity, Hooke’s law, Poisson’s ratio; shear strain;

single shear and double shear; bearing stress; stress on oblique sections, allowable stresses and

allowable loads.

3) Axial Deformation: (3.1-3.6) Strain-displacement relation (1-D), uniform and non-uniform

axial deformation; statically indeterminate structures; thermal effects.

4) Torsion: (4.1-4.8) Torsion of circular shafts; statically indeterminate torsional members; thin

walled noncircular shafts; transmission of power by circular shafts; design of torsion rods and

shafts; stresses on inclined sections; thin-walled tubes.

5) Equilibrium of Beams: (5.1-5.4) Types of beams, supports and loading; symmetric member

in pure bending; deformation in a symmetric member in pure bending; deformations in a

transverse cross section; sign convention of shear forces, bending moment; relations between

load, shear force, and bending moment; shear-force and bending-moment diagrams; design of

beams.

6) Stresses in Beams: (6.1-6.4 and 6.8) Curvature, normal strain, normal stresses, moment

curvature formulas, flexure formulas; section modulus for different cross sections; shear stress

distributions in rectangular cross-sections, circular section, and I-sections.

7) Deflection of Beams: (7.1-7.4) Differential equations of the deflection curve; Integration of

the moment-curvature differential equation; integration of the load-deflection differential

equation; method of superposition.

8) Transformation of Stress and Strain; Mohr’s Circle: (8.1-8.5) Plane stress; transformation

formulas; principal stresses, maximum shear stresses; Mohr's circle and stress analysis.

9) Pressure Vessels; Stresses due to Combined Loading: (9.1, 9.2 and 9.4) Thin-walled

pressure vessel and combined loading.

MAE314 Solid Mechanics Fall, 2003

Dr. Yuan

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10) Buckling of Columns: (10.1-10.3) Elastic buckling of long slender columns; structural

stability; empirical column analysis and design.

References

1. J. M. Gere, Mechanics of Materials, Fifth Edition, Brooks/Coke, CA., 2001.

2. W. B. Bickford, Mechanics of Solids, Concepts and Applications, Richard D. Irwin, Inc.,

1993.

3. M. A. Eisenberg, Introduction to the Mechanics of Solids, Addison WesleyPublishing

Company, 1980.

4. R. T. Fenner, Mechanics of Solids, Blackwell Scientific Publications, Oxford, 1989.

5. E. P. Popov, Engineering Mechanics of Solids, Prentice Hall, 1990.

6. S. P. Timoshenko, History of Sterngth of Materials, Dover Publications Inc., 1983.

7. A. C. Ugural, Mechanics of Materials, McGraw-Hill Inc.,1991.

8. G. Wempner, Mechanics of Solids, International Thomson Publishing, 1995.

Major Names in the History of Solid Mechanics

Name

Born

Contributions

Euclid 350 B.C. Geometry

Archimedes 287 B.C. Math, Centroids, the Lever

Agrippa 20 B.C. Roman Pont du Gard arched bridge/acqueduct

da Vinci 1452 Inventions, Art

Stevin 1548 Forces are Vectors

Galileo 1564 Dynamics of a Particle, Beam Analysis

Hygens 1629 1656-Pendulum Clock, 1673-Dynamics

Hooke 1635 1678-Hooke's Law, Founder-Royal Society of London

Newton 1642 1669-Calculus, 1687-Principia

Liebnitz 1646 Calculus using differential notation

Bernoulli, Jacob

1

1654 1705-Elastic line for a bent beam

Bernoulli, Johann

1

1667 Virtual work, Gravity=g

Bernoulli, Daniel

2

1700 1726-Motion = trans. + rotation, 1738-Bernoulli's Law

Euler

3

1707 Columns, Math, Hydromech., etc. e i and !

D'Alembert 1717 Modified Newton's third law

Lagrange 1736 Virtual Work

Laplace 1749 Mathematics, "Thus it plainly appears"

Fourier 1768 Math, Fourier's Series

MAE314 Solid Mechanics Fall, 2003

Dr. Yuan

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Young

4

1773 Young's Modulus, Elastic Shear Deformation

Poisson 1781 1811-Poisson's Ratio

Navier 1785 1826-Theory of beams, Hydrodynamics

Cauchy 1789 Stress and Strain, Torsion of Rectangular Sections

Green 1793 Constitutive relations, Fundamental solutions

Saint Venant 1797 Elasticity, Practical Engineer

Clapeyron 1799 Energy Methods, Bridge Designer

Stokes 1819 Hydrodynamics, Elasticity

Rankine 1820 Stress Transformations

Kirchhoff 1824 Plate Theory, Kirchhoff's Laws

Maxwell 1831 Elasticity and Magnetism

Mohr 1835 Graphical methods, Moment-area method

Rayleigh 1842 Vibration Theory

Castigliano 1847 1879-Castigliano's Theorems

Hertz 1857 Elastic Contact, Waves

Love 1863 Text on Elasticity

Timoshenko

5

1878 Text on Elasticity

Von Karman 1881 Inelastic column buckling

Von Mises 1883 Failure theories

Griffith, A. A. 1920 Fracture Mechanics

Muskhelishvili 1891 Complex variable elasticity

Lekhenitskii Anisotropic elasticity

Reissner, Eric 1913 1950-Energy formulation, Plates and Shells

Rivlin 1915 Nonlinear Elasticity, Michelin tires

____________________

1

Jacob and Johann were brothers

2

Johann's son

3

"He became blind due to hard work and the excessive cold of Russia, but kept on working"

4

Deciphered Rosetta Stone

5

Escaped Russian Revolution, brought many concepts to U.S.

Chapter 0. Units

Two units system are to be used in this course; SI (Système International d'Unités) and

the U.S. Customary System (USCS). The SI is based on the seven basic dimensions whose basic

units and unit abbreviations are listed in Table 1.

Table 1

Length meter m

Mass kilogram kg

Time second s

Thermodynamic Temperature kelvin K

MAE314 Solid Mechanics Fall, 2003

Dr. Yuan

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Electric current ampere A

Light intensity candela cd

Molecule substance mole mol

Some useful derived units, and relation to previously listed units are also shown in Table 2.

Table 2

Angle radian rad

Force Newton

N = kg∙m/s

2

Pressure, stress Pascal

Pa = N/m

2

Work, energy Joule J = N∙m

Power Watt W = J/s

Frequency Hz

Hz = s

-1

Customary temperature Degree Celsius

o

C = K - 273.15

The conversion between SI and USCS units is listed in Table 3.

Table 3

Length inch (in.)

foot (ft)

2.54 cm

30.48 cm

Mass slug 14.59 Kg

Force lb

10

3

lb (kip)

4.448 newtons (N)

4.448 KN

Stress pound/inch

2

(Psi or lb/in

2

)

10

3

pound/inch

2

(Ksi)

6895 pascals (Pa)

6.895 kilopascals (KPa)

6.895 magapascals (MPa)

Moment inch x pound

(in.-lb)

11.30 newton-centimeters

(N∙cm)

Power foot-pound/second (ft-lb/s)

horsepower (550 ft-lb/s)

1.356 Watts (w)

745.6 watts (w)

Temperature T(

o

F)

9

5

T(

o

C)+32

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