Structural Analysis and Mechanics of Materials

Course Description

This online course, offered by the MIT Department of Mechanical Engineering, is an in-depth exploration of structural analysis and mechanics of materials. It's designed to equip students with a comprehensive understanding of material behavior under stress, focusing on the principles of continuum mechanics and their applications to three essential types of elastic load-bearing elements: bars in axial loading, axisymmetric shafts in torsion, and symmetric beams in bending.

What Students Will Learn

  • Fundamental concepts of continuum mechanics, including internal resultants, displacement field, stress, and strain
  • Use of free body diagrams to formulate equilibrium equations
  • Identification of geometric constraints to formulate compatibility equations
  • Understanding of stress and strain concepts at a material point
  • Calculation of internal stress and strain fields in loaded elements
  • Prediction of deformation in loaded elements
  • Design of structural elements to prevent failure
  • Use of numerical methods (MATLAB) in structural engineering applications
  • Introduction to Finite Element methods

Pre-requisites

  • Multivariable Calculus
  • Physics: Classical Mechanics
  • Understanding of derivatives, integrals (1D, 2D), vectors, forces, and torques

Course Coverage

  • Introduction to structural analysis and mechanics of materials
  • Review of forces, moments, and integration
  • Introduction to MATLAB
  • Axial loading: equilibrium, free body diagrams, internal forces, stress and strain
  • Torsion: shear stress and strain, internal torque resultants
  • Bending: internal bending moment, curvature, neutral axis, stress and strain distribution
  • Analysis of statically determinate and indeterminate problems
  • Response of inhomogeneous elements with varying cross-sections
  • Numerical methods and Finite Element analysis

Target Audience

This course is ideal for undergraduate-level mechanical engineering students, engineering professionals looking to expand their knowledge, and anyone interested in understanding the principles of structural analysis and mechanics of materials. It's particularly suitable for those who want to gain a strong foundation in predicting structural behavior using analytical methods and calculations.

Real-World Applications

The skills acquired in this course are directly applicable to various fields of engineering, especially mechanical and structural engineering. Learners will be able to:

  • Analyze and design load-bearing structures in construction and manufacturing
  • Predict material behavior under stress in product development
  • Optimize structural designs for efficiency and safety
  • Apply numerical methods to solve complex engineering problems
  • Contribute to the development of innovative materials and structures
  • Enhance safety standards in engineering projects
  • Improve energy efficiency in mechanical systems

Syllabus

Week 1: Introduction and Preliminaries
Week 2: Axial loading I
Week 3: Axial loading II
Week 4: Quiz 1 (Axial Loading)
Week 5: Torsion I
Week 6: Torsion II
Week 7: Quiz 2 (Torsion)
Week 8: Bending I
Week 9: Bending II
Week 10: Quiz 3 (Bending)

Note

This course is the first part of a three-course series, providing a solid foundation for advanced studies in mechanics of deformable structures and multi-axial loading and deformation.