16.20 | Fall 2002 | Undergraduate

Structural Mechanics


The following is a detailed schedule, showing the 6 sections and 23 units within these sections, and the topics covered within each unit. The readings assigned for each unit are given as well as the day(s) the unit will be covered in lecture (recitation). The abbreviation key for the reading is given at the end.

Section I: Review of Design Considerations
1; 2 **Unit 1: Introduction and Design Overview
**Why Structural Mechanics? Types of Structures; Structural Design Process; Factors in Cost.
L1; L2 R: Ch.1
M: 7.1, 7.3, 7.4

3; 4 Unit 2: Loads and Design Considerations
Sources of Loads/Deflections; Types of Loads and Environments; Limit and Ultimate Loads; Factors and Margins of Safety; Example, the v-n Diagram; Definition of Failure; FAR’s.
L3; L4, R M: 7.2, 12.1, 12.2
G: 1.7
R-Assessment Exercise
Section II: General Elasticity
4; 5 Unit 3: Language of Stress/Strain Analysis (Review)
Definition of Stress and Strain; Notation; Tensor Rules; Tensor vs. Engineering Notation; Contracted Notation; Matrix Notation.
L4, R; L5 BMP: A.2, A.3, A.6
R: 2.1, 2.2
T&G: Ch. 1
HA1 out; DP1 out
6; 7; 8 Unit 4: Equations of Elasticity (Review)
Equations of Elasticity (Equilibrium, Strain-Displacement, Stress-Strain); Static Determinance; Compatibility; Elasticity Tensor; Material Types and Elastic Components; Materials Axes vs. “Loading Axes”; Compliance and its Tensor; The Formal Strain Tensor; Large Strains vs. Small Strains; Linear vs. Nonlinear Srain.
L6; L7; L8, R R: 2.3, 2.6, 2.8
T&G: 5.1-5.5, 5.8, 5.9, 7.1-7.4, 6.1-6.3, 6.5-6.7
J: 2.1, 2.2 (for

8; 9; 10 Unit 5: Engineering Constants
Engineering Constants (Longitudinal Moduli, Poisson’s Ratio, Shear Moduli, Coefficients of Mutual Influence, Chentsov Coefficients); Reciprocity Relations; Engineering Stress-strain Equations; Compliances and Engineering Constants; Purposes of Testing; Issues of Scale; Testing for Engineering Constants; Variability and Issues in Design.
L8, R; L9; L10 R: 3.1-3.5, 3.9,
M: 1.16
J: 2.3, 2.4, 2.6
HA1 due; HA2 out;
DP1 due;
11; 12; 13 Unit 6: Plane Stress and Plane Strain
Plane Stress; Plane Strain; Applications; Approximations and Modeling Limitations.
L11; L12; L13 T&G: 8-16
J: 2.5
G: 7.2, 7.7, 8.1, 8.2
DP2 out;
HA2 due; HA3 out
13; 14 Unit 7: Transformations and Other Coordinate Systems
Review of Transformations: Direction Cosines; 3-D tensor form (Axis, Displacement, Stress, Strain, Elasticity Tensor); Plane Stress Case (and Mohr’s Circle); Principal Stresses/ Strains; Invariants; Extreme Shear Stresses/Strains; Reduction to 2-D; Other Coordinate Systems (Example: Cylindrical); General Curvilinear Coordinates.
L13; L14 R: 2.4, 2.5, 2.7, 2.9
BMP: 5.6, 5.7, 5.14, 6.4, 6.8, 6.9, 6.11
T&G: 27, 54, 55, 60, 61
J: 2.6
G: 7.3, 7.4

15; 16; 17; 18 Unit 8: Solution Procedures
Exact Solution Procedures; Airy Stress Function; Biharmonic Equation; Inverse Method; Semi-Inverse Method; St. Venant’s Principle; Examples: Uniaxiallyloaded Plate, Polar Form and Stress Around a Hole; Stress Concentrations; Considerations for Orthotropic Materials.
L15, R; L16; L17; L18 R: Ch. 4
T&G: 17, Ch. 3, 4, 6
HA3 due; HA4 out;
DP2 due
18; 19; 20; 21; 23 Unit 9: Effects of the Environment
Where Thermal Strains/“Stresses” come from; Coefficients of Thermal Expansion; Sources of Heating; Spatial Variation of Temperature; Self-equilibrating Stresses; Convection, Radiation, Conductivity (Fourier’s Equation); Solution Techniques; “Internal” Stresses; Degradation of Material Properties; Other Environmental Effects; Examples: Moisture; Piezoelectricity.
L18; L19, R; L20; L21; L22 R: 3.6, 3.7
T&G: Ch. 13

HA4 due; DP3 out
22 No Lecture

Evening Exam 1 ; HA5 out
Section III: Torsion
23; 24; 25; 26 Unit 10: St. Venant Torsion Theory
“Types” of Cross-Sections; St. Venant’s Torsion Theory; Assumptions; Considerations for Orthotropic Materials; Torsion Stress Function; Boundary Conditions; Summary of Procedure; Solution; Poisson’s Equation; Example:Circular Rod; Resultant Shear Stress; Other Cross-Sections; Warping.
L22; L23; L24, R; L25 R: 8.1, 8.2
T&G: 10.1, 10.4, 10.5, 10.6
M: 3.1, 3.2
G: 3.1-3.4
HA5 due; HA6 out
26; 27 Unit 11: Membrane Analogy
Membrane Analogy; Uses; Application: Narrow Rectangular Cross-Section; Other Shapes.
L25; L26 R: 8.3, 8.6
T&G: 107-110, 112-114
M: 3.1, 3.3, 3.4

27; 28; 29 Unit 12: Torsion of (Thin) Closed Sections
Thick-walled Closed Section; Special Case – Circular Tube; Shear Flow; Bredt’s Formula; Torsion Summary.
L26; L27; L28, R R: 8.7, 8.8
T&G: 115, 116
M: 8.5
G: 3.10
HA6 due; HA7 out
Section IV: General Beam Theory
29; 30 Unit 13: Review of Simple Beam Theory
Generic types of Loading (review); Review of Simple Beam Theory; Considerations for Orthotropic Materials.
L28, R; L29 BMP: 3.8-3.10
T&G: 120-125
G: 5.1-5.9, 9.1-9.5, 10.1-10.4

30; 31; 32; 33 Unit 14: Behavior of General Beams and Engineering Beam Theory
Geometry Definitions; Assumptions; Stress Resultants; Deformation, Strain, Stress In General Shell Beams; Considerations for Orthotropic Beams; Modulus-Weighted Section Properties; “Thermal” Forces and Moments; Selective Reinforcement; Principal Axes of Cross-Section; Beams with Unsymmetric Cross-Sections; Applicability of Engineering Beam Theory; Transverse Shear Effects; Shear Center; Contribution of “Shearing” Deflection; Limitations of Engineering Beam Theory.
L29; L30; L31; L32, R R: 7.1-7.5, 7.7, 7.8
T&G: 126
M: 2.6, 8.1-8.3
G: 5.10-5.12, 6.1-6.8
DP3 due
34; 35; 36; 38; 39; 40 Unit 15: Behavior (Bending, Shearing, Torsion) of Shell Beams
General loading of a Shell Beam; Semi-monocoque Construction; Skin/stringer Construction; Single Cell “Box Beam”; Bending Stresses; Shear Stresses; Joint Equilibrium; Pure Shear and Pure Torsion Scheme; General Solution Procedure; “No Twist” Condition; Shear Center; Torque Boundary Condition; Deflections; St. Venant Assumption; Section Properties: Bending, Shear, and Torsional Stiffness; Multicell Shell Beams; “Equal Twist” Condition; Open Section Beams; Thick Skin Shells; Effective Width.
L33; L34; L35; L36; L37; L38, R R: Ch.9, 8.7, 7.6
T&G: 126, 127
M: 7.3, 8.2-8.10, 9.3
G: Ch. 12
HA7 due; HA8 (Part A) out (not for hand-in);
HA8 (Part B) due
37 No Lecture

Evening Exam 2; HA8 (Part B) out
Section V: Stability and Buckling
40; 41; 42 Unit 16: (Review of) Bifucation Buckling
Types of Buckling; Governing Equations for Bifucation Buckling; Application of Boundary Conditions; Euler Buckling Load; Coefficient of Edge Fixity; Geometrical Parameters; Considerations for Orthotropic/Composite Beams; Initial Imperfections; Primary and Secondary Moments.
L38, R; L39; L40 R: 14.1, 14.2, 14.4
M: 6.1, 6.3
G: 11.1-11.4
HA10 out
43; 44 Unit 17: The Beam-Column
Beam-column Definition; Equilibrium Equations; Governing Equations; Solution for Axial Force; Buckling of Beam-Column; Primary and Secondary Moments.
L41; L42, R T: Ch.1
M: 6.4
G: 11.5-11.6
HA9 out
44; 45; 46 Unit 18: Other Issues in Buckling/Structural Instability
Other Issues in Buckling; Squashing; Progressive Yielding; Nonuniform Beams; Plate Buckling; Cylinders; Reinforced Plates; Postbuckling; Curvature Expression for large Deflections; Galerkin Method; Buckling and Failure.
L42, R; L43; L44 R: 14.3, 14.5-14.7, Ch. 15, Ch. 16
T: (Suggested)
J: Ch. 5
M: 6.2, 6.6-6.10

Section VI : Introduction to Structural Dynamics
46; 47 Unit 19: General Dynamic Considerations (Review)
System Response: The Regimes and Controlling Factors; Spring-mass System, Inertial Loads, Governing Equation; Initial Conditions; Damping; Multi-mass System, Matrix Equation Form; (Sources of) Dynamic Structural Loads; Consequences of Dynamic Structural Response.
L44; L45, R

47; 48 Unit 20: Solutions for Single Spring-Mass System (Review)
Single Degree-of-Freedom System; Free Vibration and Natural Frequency; Forced Vibration; Step Function; Unit Impulse, Dirac Delta Function; Arbitrary Force, Duhamel’s convolution) Integral; Sinusoidal Force; Dynamic Magnification Factor; Resonance.
L45, R; L46

HA10 due; HA11 out (not for hand-in)

48; 49 Unit 21: Influence Coefficients
Generalized Forces and Displacements; Flexibility Influence Coefficients; Maxwell’s Theorem of Reciprocity; Examples: Cantilevered Beam; Stiffness Influence Coefficients; Physical Interpretations.
L46; L47 R: 6.6, 6.13, 10.5
M: 4.10, 11.1, 11.2
DP4 due
50; 51 Unit 22: Vibration of Multi Degree-of-Freedom Systems
Governing Matrix Equation; Free Vibration; Eigenvalues and Eigenvectors–Natural Frequencies and Modes; Examples: Representation of Beam as Discrete Mass System; Physical Interpretation of Modes; Orthogonality Relations; Normal Equations of Motion; Superposition of Modal Responses; Forced Vibration.
L48; L49, R

51; 52 Unit 23: Vibrations of Continuous Systems
Generalized Beam-Column Equation with Inertia; Free Vibration; Separation of Spatial and Temporal Solutions; Example: Simply-Supported Beam; Natural Frequencies and Modes; Orthogonality Relations; Normal Equations of Motion; Forced Vibration; Superposition of Modal Responses; Resonance.
L49, R; L50

* R: Rivello. Theory and Analysis of Flight Structures. McGraw-Hill, 1969.

T&G: Timoshenko, and Goodier. Theory of Elasticity. McGraw-Hill, 1970.

BMP: Bisplinghoff, Mar, and Pian. Statics of Deformable Solids. Addison-Wesley, 1965.

J: Jones. Mechanics of Composite Materials. McGraw-Hill, 1975.

C: Cutler. Understanding Aircraft Structures. Granada, 1981.

T: Timoshenko, and Gere. Theory of Elastic Stability. McGraw-Hill, 1961.

M: Megson. Aircraft Structures for Engineering Students. Halsted, 1990.

G: Gere, and Timoshenko. Mechanics of Materials. 4th ed. PWS, 1997.

Course Info

As Taught In
Fall 2002
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Lecture Notes
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