16.20 Schedule and Syllabus, Updated 4/27/2021
Page 1 of 5
16.20 Schedule, Spring 2021
DATE
T
R
F
T
R
F
L= Lecture
R=Recitation
02/16
02/18
02/19
02/23
02/25
02/26
L1
L2
R1
L3
L4
R2
T 03/02
R 03/04
F 03/05
T 03/09
R 03/11
F 03/12
T 03/16
R 03/18
F 03/19
F 03/19
T 03/23
W 03/24
R 03/25
R 03/25
F 03/26
T 03/30
L5
L6
R3
Units Covered
Assignments, Exams
PS = Problem Set
DP = Design Problem
FEBRUARY 2021
1, 2
2, 3
3
4
PS1 out, DP1 out
Design Teams Formed
MARCH 2021
R
F
T
R
F
T
R
F
T
R
F
T
T
R
R
F
04/01
04/02
04/06
04/08
04/09
04/13
04/15
04/16
04/20
04/22
04/23
04/27
04/27
04/29
04/29
04/30
T 05/04
R 05/06
F 05/07
T 05/11
R 05/13
F 05/14
T 05/18
R 05/20
05/24 - 27
5
6
PS1 due, PS2 out
DP1 due, DP2 out
NO CLASS (MONDAY SCHEDULE OF CLASSES)
L7
7
PS2 due, PS3 out
R4
L8
7, 8
PS4 out
L9
8, 9
PS3 due
R5
DP2 due, DP3 out
ADD DATE. Please confirm you are registered for this course.
NO CLASSES (STUDENT HOLIDAY)
None
PS4 due
L10
Canceled for Exam
Evening Exam I (7:30-9:30pm Boston time)
R6
PS5 out
L11
9, 10
APRIL 2021
L12
10, 11
PS5 due, PS6 out
R7
L13
12
L14
13
PS6 due, PS7 out
R8
DP3 due
L15
14
L16
14, 15
PS7 due, PS8 out
R9
NO CLASSES (STUDENT HOLIDAY)
L17
15
R10
PS9 out, DP4 out
L18
Canceled for Exam
Evening Exam II (7:30-9:30pm Boston time)
L19
16
PS8 due
DROP DATE
R11
MAY 2021
L20
17, 18
L21
18
PS9 due, PS10 out
NO CLASSES (STUDENT HOLIDAY)
L22
19, 20
L23
20, 21
PS10 due, PS11 out
R12
DP4 due
L24
22, 23
L25
23, 24
Final Exam (During Finals Week TBA by Registrar)
16.20 Schedule and Syllabus, Updated 4/27/2021
Page 2 of 5
16.20 Syllabus, Spring 2021
The following is a detailed syllabus showing the sections and units within, including suggested
readings. The abbreviation key for the readings is:
R:
Theory and Analysis of Flight Structures, Rivello, McGraw-Hill, 1969.
T&G:
Theory of Elasticity, Timoshenko and Goodier, McGraw-Hill, 1970.
BMP:
Statics of Deformable Solids, Bisplinghoff, Mar and Pian, Addison-Wesley, 1965.
J:
Mechanics of Composite Materials, Jones, McGraw-Hill, 1975.
C:
Understanding Aircraft Structures, Cutler, Granada, 1981.
T:
Theory of Elastic Stability, Timoshenko (and Gere), McGraw-Hill, 1961.
M:
Aircraft Structures for Engineering Students, Megson, Halsted, 1990.
G:
Mechanics of Materials, 4th edition, Gere (and Timoshenko), PWS, 1997.
A:
Materials Selection in Mechanical Design, 3rd edition, Ashby, 2010.
16.20 Schedule and Syllabus, Updated 4/27/2021
UNIT NUMBER, TITLE AND TOPICS
Page 3 of 5
READINGS
SECTION I: REVIEW OF DESIGN CONSIDERATIONS
1.
Introduction and Design Overview
Why structural mechanics? Types of structures; Structural
design process; Factors in cost; The place and role of
(structural) models
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
R:
M:
Ch.1
7.1, 7.3, 7.4
M:
G:
C:
7.2, 12.1, 12.2
1.7
At leisure
SECTION II: GENERAL ELASTICITY
3.
Language of Stress/Strain Analysis (Review)
Definition of stress and strain; Notation; Tensor rules; Tensor
vs. engineering notation; Contracted notation; Matrix notation
4.
Equations of Elasticity (Review)
Equations of elasticity (equilibrium, strain-displacement, 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
strain
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
6.
Plane Stress and Plane Strain
Plane stress; Plane strain; Applications; Approximations and
modeling limitations
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
8.
Solution Procedures (Focus on 2D Stress Functions)
Exact solution procedures; Airy stress function; Biharmonic
equation; Inverse method; Semi-inverse method; St. Venant’s
Principle; Examples: uniaxially-loaded plate, polar form and
stress around a hole; Stress concentrations; Considerations for
orthotropic materials
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;
BMP: A.2,A.3,A.6
R:
2.1,2.2
T&G Ch. 1
R:
2.3, 2.6, 2.8
BMP: 5.1-5.5, 5.8, 5.9, 7.1-7.9,
6.1-6.3, 6.5-6.7
T&G: 84, 85
J:
2.1, 2.2 (for
composites)
R:
M:
J:
3.1-3.5, 3.9, 3.11
1.16
2.3, 2.4, 2.6
T&G: 8-16
J:
2.5
G:
7.2, 7.7, 8.1, 8.2,
8.3
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: 13,27,54,55,60,
61,74-83
J:
2.6
G:
7.3, 7.4
R:
Ch. 4
T&G: 17, Chs. 3, 4, 6
R:
3.6, 3.7
T&G: Ch. 13
16.20 Schedule and Syllabus, Updated 4/27/2021
UNIT NUMBER, TITLE AND TOPICS
Page 4 of 5
READINGS
"Internal" stresses; Degradation of material properties; Other
environmental effects; Examples: Moisture; Piezoelectricity
SECTION III: TORSION
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
11.
Membrane Analogy
Membrane analogy; Uses; Application: Narrow rectangular
cross-section; Other shapes
12.
Torsion of (Thin) Closed Sections
Thick-walled closed section; Special case: Circular tube; Shear
flow; Bredt's formula; Torsion summary
R:
T&G:
M:
G:
8.1, 8.2, 8.4
101, 104-106
3.1, 3.2
3.1-3.4
R:
8.3, 8.6
T&G: 107-110, 112-114
M:
3.1, 3.3, 3.4
R:
T&G:
M:
G:
8.7, 8.8
115, 116
8.5
3.10
SECTION IV: GENERAL BEAM THEORY
13.
Review of Simple Beam Theory
Generic types of loading (review); Review of simple beam
theory; Considerations for orthotropic materials
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;
General comments on Shell Beam Analysis
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
BMP: 3.8-3.10
T&G: 120-125
G:
5.1-5.9, 9.1-9.5,
10.1-10.4
R:
T&G:
M:
G:
7.1-7.5, 7.7, 7.8
126
2.6, 8.1-8.3
5.10-5.12, 6.1-6.8
R:
T&G:
M:
G:
Ch.9, 8.7, 7.6
126, 127
7.3, 8.2-8.10, 9.3
Ch. 12
SECTION V: STABILITY AND BUCKLING
16.
(Review of) Bifurcation Buckling
Types of buckling; Governing equations for bifurcation buckling;
Application of boundary conditions; Euler buckling load; Coefficient
of edge fixity; Geometrical parameters; Considerations for orthotropic
beams; Initial imperfections; first and second moments
R:
M:
G:
14.1, 14.2,
14.4
6.1, 6.3
11.1-11.4
16.20 Schedule and Syllabus, Updated 4/27/2021
Page 5 of 5
UNIT NUMBER, TITLE AND TOPICS
READINGS
17.
T:
M:
G:
Ch.1
6.4
11.5-11.6
R:
T:
J:
M:
14.3, 14.514.7, Ch. 15,
Ch. 16
At leisure
Ch. 5
6.2, 6.6-6.10
A:
At leisure
R:
M:
6.6, 6.13, 10.5
4.10, 11.1, 11.2
The Beam-Column
Beam-column definition; Equilibrium equations; Governing
equations; Solution for axial force; Buckling of beam-column;
Primary and secondary moments; Solutions
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
SECTION VI: (INTRODUCTION TO) MATERIALS
SELECTION AND STRUCTURAL DYNAMICS
19.
Materials Selection in Design
Materials selection formalism; Ashby Charts; Use of Ashby Charts
20.
General Dynamics 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
21.
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
22.
Influence Coefficients
Generalized forces and displacements; Flexibility influence coefficients;
Maxwell's theorem of reciprocity; Examples: Cantilevered beam;
Stiffness influence coefficients; Physical interpretations
23.
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
24.
Vibrations of Continuous Systems
Generalized beam-column 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