|DAY #||TOPICS||LECTURES & RECITATIONS||READINGS*||ASSIGNMENTS & EXAMS|
|Section I: Review of Design Considerations|
Unit 1: Introduction and Design Overview
Why Structural Mechanics? Types of Structures; Structural Design Process; Factors in Cost.
M: 7.1, 7.3, 7.4
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
|Section II: General Elasticity|
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,
J: 2.3, 2.4, 2.6
|HA1 due; HA2 out;
|11; 12; 13||
Unit 6: Plane Stress and Plane Strain
Plane Stress; Plane Strain; Applications; Approximations and Modeling Limitations.
|L11; L12; L13||
G: 7.2, 7.7, 8.1, 8.2
HA2 due; HA3 out
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.
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
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;
|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
|HA5 due; HA6 out|
Unit 11: Membrane Analogy
Membrane Analogy; Uses; Application: Narrow Rectangular Cross-Section; Other Shapes.
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
|HA6 due; HA7 out|
|Section IV: General Beam Theory|
Unit 13: Review of Simple Beam Theory
Generic types of Loading (review); Review of Simple Beam Theory; Considerations for Orthotropic Materials.
|L28, R; L29||
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
M: 2.6, 8.1-8.3
G: 5.10-5.12, 6.1-6.8
|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
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||
|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
J: Ch. 5
M: 6.2, 6.6-6.10
|Section VI : Introduction to Structural Dynamics|
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|
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)
Unit 21: Influence Coefficients
Generalized Forces and Displacements; Flexibility Influence Coefficients; Maxwell's Theorem of Reciprocity; Examples: Cantilevered Beam; Stiffness Influence Coefficients; Physical Interpretations.
R: 6.6, 6.13, 10.5
M: 4.10, 11.1, 11.2
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|
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|