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Massachusetts Institute of Technology (MIT) Course/Program Name
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National :15 Dec 
International :15 Dec 

BE Structural Mechanics

Catalog id : 16.20
 Course Level
Bachelors / UG
 Type
Online

 Duration
0 Months
 Start month
September

 Tuition fee

International
48140 USD
National
48140 USD

Application fee

International 75 USD
National 75 USD
Department
Aeronautics and Astronautics
Scores accepted
IELTS (min)7
TOEFL-IBT (min)90
TOEFL-PBT (min)577

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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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