DAY #  TOPICS  LECTURES & RECITATIONS  READINGS*  ASSIGNMENTS & EXAMS 

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 vn Diagram; Definition of Failure; FAR's. 
L3; L4, R 
M: 7.2, 12.1, 12.2 G: 1.7 
RAssessment 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, StrainDisplacement, StressStrain); 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: 5.15.5, 5.8, 5.9, 7.17.4, 6.16.3, 6.56.7 J: 2.1, 2.2 (for composites) 

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 Stressstrain 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: 3.13.5, 3.9, 3.11 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: 816 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; 3D 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 2D; 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; SemiInverse 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; Selfequilibrating 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 CrossSections; 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 CrossSections; 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: 3.13.4 
HA5 due; HA6 out 
26; 27 
Unit 11: Membrane Analogy Membrane Analogy; Uses; Application: Narrow Rectangular CrossSection; Other Shapes. 
L25; L26 
R: 8.3, 8.6 T&G: 107110, 112114 M: 3.1, 3.3, 3.4 

27; 28; 29 
Unit 12: Torsion of (Thin) Closed Sections Thickwalled 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: 3.83.10 T&G: 120125 G: 5.15.9, 9.19.5, 10.110.4 

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; ModulusWeighted Section Properties; "Thermal" Forces and Moments; Selective Reinforcement; Principal Axes of CrossSection; Beams with Unsymmetric CrossSections; 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: 7.17.5, 7.7, 7.8 T&G: 126 M: 2.6, 8.18.3 G: 5.105.12, 6.16.8 
DP3 due 
34; 35; 36; 38; 39; 40 
Unit 15: Behavior (Bending, Shearing, Torsion) of Shell Beams General loading of a Shell Beam; Semimonocoque 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, 8.28.10, 9.3 G: Ch. 12 
HA7 due; HA8 (Part A) out (not for handin); 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: 11.111.4 
HA10 out 
43; 44 
Unit 17: The BeamColumn Beamcolumn Definition; Equilibrium Equations; Governing Equations; Solution for Axial Force; Buckling of BeamColumn; Primary and Secondary Moments. 
L41; L42, R 
T: Ch.1 M: 6.4 G: 11.511.6 
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, 14.514.7, Ch. 15, Ch. 16 T: (Suggested) J: Ch. 5 M: 6.2, 6.66.10 

Section VI : Introduction to Structural Dynamics  
46; 47 
Unit 19: General Dynamic Considerations (Review) System Response: The Regimes and Controlling Factors; Springmass System, Inertial Loads, Governing Equation; Initial Conditions; Damping; Multimass System, Matrix Equation Form; (Sources of) Dynamic Structural Loads; Consequences of Dynamic Structural Response. 
L44; L45, R  
47; 48 
Unit 20: Solutions for Single SpringMass System (Review) Single DegreeofFreedom 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 handin) 

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 DegreeofFreedom Systems Governing Matrix Equation; Free Vibration; Eigenvalues and EigenvectorsNatural 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 BeamColumn Equation with Inertia; Free Vibration; Separation of Spatial and Temporal Solutions; Example: SimplySupported Beam; Natural Frequencies and Modes; Orthogonality Relations; Normal Equations of Motion; Forced Vibration; Superposition of Modal Responses; Resonance. 
L49, R; L50 