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National :15 Dec

International :15 Dec

National :15 Dec

International :15 Dec

Catalog id : 16.20

Course Level

Bachelors / UG

Bachelors / UG

Type

Online

Online

Duration

0 Months

0 Months

Start month

September

September

Application fee

International
75 USD

National
75 USD

Department

Aeronautics and Astronautics

Scores accepted

IELTS (min)

7

7

TOEFL-IBT (min)

90

90

TOEFL-PBT (min)

577

577

WeMakeScholars initiative is supported by the Govt. of India; associated with 10+ public/private banks & NBFCs.

About this course

Applies solid mechanics to analysis of high-technology structures. Structural design considerations. Review of three-dimensional elasticity theory; stress, strain, anisotropic materials, and heating effects. Two-dimensional plane stress and plane strain problems. Torsion theory for arbitrary sections. Bending of unsymmetrical section and mixed material beams. Bending, shear, and torsion of thin-wall shell beams. Buckling of columns and stability phenomena. Introduction to structural dynamics. Exercises in the design of general and aerospace structures.

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Eligibility Criteria

**Graduate Record Examination**

Most MIT departments require the Graduate Record Examination (GRE) General Test

and an appropriate Subject Test. Please check the departmental listings beginning on

page 4 of this booklet for information on the department to which you intend to apply.

The fee for the GRE ranges approximately from $160 to $190 US

**International English Language Testing System**

IELTS exam measures ability to communicate in English across all four language skills

– listening, reading, writing, and speaking – for people who intend to study or work

where English is the language of communication. Most departments now require this

test. Please check the departmental listings beginning on page 4 of this booklet for

information on the department to which you intend to apply.

**Test of English as a Foreign Language**

Students whose native language is not English may take the Test of English as a

Foreign Language (TOEFL). A minimum score of 577 (233 for computer-based; 90

for internet-based) is required for visa certification. Many departments have higher

score requirements. See departmental information beginning on page 4 of this booklet.

The fee for the TOEFL ranges approximately from $150 to $225 US.

Check further details on University website

Course Modules

**Section I: Review of Design Considerations**

- 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
- 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 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,
- 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: 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.

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How to Apply

http://ocw.mit.edu/courses/

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