MAE314 Solid Mechanics Fall, 2003

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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



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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



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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