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					                                                                                       Ver. 5, 12/05/06

                             MECHANICS OF SOLIDS
Catalog description
This course builds on the fundamentals of solid mechanics taught in MEAM210 and addresses more
advanced problems in strength of materials. The students will be exposed to a wide array of
applications from traditional engineering disciplines as well as emerging areas such as biotechnology
and nanotechnology. The methods of analysis developed in this course will form the cornerstone of
machine design and also more advanced topics in the mechanics of materials.

The course is intended as an intermediate course in mechanics of solids to fill the gap between a
sophomore level statics course (MEAM 210) and a more advanced (senior/graduate level) treatment
which includes elasticity(MEAM 454).


Prashant Purohit

Text book

Mechanics of materials by Beer, Johnston and DeWolf (4 th edition)

Target audience
Juniors and seniors across the school of engineering.

Weekly homeworks, quizzes, midterm and final exam. Possibly an FEM and/or design project.

MEAM 210 or equivalent, BE200 or permission of instructor


Credit Units
This is a 1 unit course with 3 hours of lectures each week.

Syllabus (not in the order taught in class)
WEEK #1& #2
  - Statically indeterminate problems
  - Strain-displacement relations
  - Compatibility equations
    - Linear-elastic isotropic stress-strain relations
    - Elastic perfectly plastic material behavior

WEEK #3 & #4
  Review of beam theory
  - Stress and deformation in symmetrical beams with pure bending
  - Stress in beams with bending and shear
  - Shear flow in thin walled open sections: Shear center
  - Calculation of deflections by integrating the beam equation

  Stability of beam columns
   - How stability is related to the second variation of energy
   - Stability of flexible columns
   - Critical loads for different boundary conditions
   - Eccentric loads

WEEK #6 & #7
  Torsion of bars
   - Stress and deformation in twisted circular shafts
   - Torsion of hollow circular shafts
   - Determining the spring constant of elastic springs
   - Problems with combined bending and torsion

  Energy methods
  - Strain energy of a solid
  - Simple impact problems
  - Principle of minimum potential energy
  - Castigliano’s theorems

WEEK #9 & #10
   Introduction to approximate methods of solution
   - Rayleigh-Ritz method
   - Finite elements introduced through one-dimensional axial problems

WEEK #11
  Membrane stresses in axisymmetric shells
   - Meridional and circumferential stress
   - Pressure vessels

WEEK #12
  Principal stresseses and failure criteria
   - Mohrs circle for 2D plane stress and plane strain
   - Prinicipal stresses as eigenvalues of the stress matrix
   - Maximum shear stress expressed in terms of principal stresses
   - Tresca and von-Mises yield criteria

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