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2.080

Structural Mechanics

4-0-8 units · Graduate

Applies solid mechanics fundamentals to the analysis of marine, civil, and mechanical structures. Continuum concepts of stress, deformation, constitutive response and boundary conditions are reviewed in selected examples. The principle of virtual work guides mechanics modeling of slender structural components (e.g., beams; shafts; cables, frames; plates; shells), leading to appropriate simplifying assumptions. Introduction to elastic stability. Material limits to stress in design. Variational methods for computational structural mechanics analysis.

Fall 2013

Topics

  • Overview of the Subject, Applications, Reconstruction of Famous Structural Accidents
  • Vector and Tensor Analysis; Review of Static Equilibrium
  • Concept of Strain
  • Concept of Stress
  • Stress / Strain Transformation, Mohr’s Circle
  • Multidimensional Elastic Stress-Strain Relations for Beams, Plates, and Shells; Elastic Strain Energy
  • Principle of Minimum Total Potential Energy, Principle of Virtual Work
  • Exact Solutions of the Differential Equation for Beam Deflections
  • Energy Method of Solving Beam Problems
  • Shear Stress in Beams and Shafts
  • Material Characterization
  • Moderately Large Deflection of Beams
  • Methods of Experimental Mechanics and Discussion of Lab Test
  • Concept of Stability of Elastic Structures, Rayleigh-Ritz Quotient
  • Solutions of Typical Column Buckling Problems
  • Distinction Between Buckling and Equilibrium Solutions, Imperfect Columns, and Columns with Eccentric Load
  • Elastic Plate Buckling, Buckling Loads, and Buckling Modes
  • Buckling of Sections, Stiffened Plates
  • Examples of Plate Buckling
  • Yield Condition and Limit Analysis
  • Application of Plasticity to Beams, Plates and Shell Problems
  • Mechanics in Cyclindrical Coordinate System (Thin and Thick Cylinders)
  • Solutions to Plasticity Problems
  • Formulation and Solution of Dynamically Loaded Beams and Plates
  • Fracture of Materials and Structures
  • Implosion of Cylinders and Submarine Safety
  • Case Studies: Columbia Space Shuttle and BP Deepwater Horizon
  • Estimation of Damage of Collision and Grounding of Ships
  • Energy Absorption and Crashworthiness of Vehicles

Readings

Prerequisites & course information

Same subject as 1.573[J] Prereq: 2.002 G (Fall) 4-0-8 units

Sources