16.001 | Fall 2021 | Undergraduate

Unified Engineering: Materials and Structures

Calendar

Week 1

Topics

Introduction to aerospace structural mechanics

Measurable Outcomes

Describe a structure, its functions, and associated objectives and tradeoffs.

Week 2

Topics

Introduction to aerospace materials

Measurable Outcomes

Describe the basic mechanical properties of aerospace materials. Describe the general classes of materials used in aerospace and their specific applications.

Week 3

Topics

Three great principles: equilibrium, compatibility, and constitutive material response; equilibrium of a particle, system of particles (free-body diagram)

Measurable Outcomes

Define the “three great principles” of solid mechanics: equilibrium, compatibility, and constitutive material response.

Week 4

Topics:

Planar force systems, equipollent forces

Measurable Outcomes

Determine the relation between applied and transmitted forces and moments, for a particle, a set of particles, and a rigid body in equilibrium. Apply the concept of equipollent force/moment to model and simplify the analysis of force systems.

Week 5

Topics

Support reactions, free-body diagrams, static determinacy

Measurable Outcomes

Represent and use idealizations of structural supports. Draw free-body diagrams for structural systems. Classify mechanical systems according to their state of equilibrium: underdetermined, determinate, or indeterminate. Calculate reactions in determinate systems.

Week 6

Topics

Truss analysis: method of joints, method of sections

Measurable Outcomes

Analyze truss structures using the method of joints and the method of sections.

Week 7

Topics

Statically indeterminate systems

Measurable Outcomes

Define the constitutive relationship for elastic bars. Apply compatibility of deformation in a variety of structural configurations. Analyze statically indeterminate bar and truss systems using the “three great principles.”

Week 8

Topics

Stress: definition, Cartesian components, equilibrium

Measurable Outcomes

Define the concept of stress at a material point and its mathematical representation as a second-order tensor. Describe the state of stress at a point using Cartesian tensorial components, and their meaning as a measure of the local measure of loading at material points in structural systems. Explain stress equilibrium in differential form.

Week 9

Topics

Stress transformation and Mohr’s circle, principal stresses, maximum shear stress

Measurable Outcomes

Explain the basis for transforming stress states between two different Cartesian bases. Transform two-dimensional stress states and compute principal stresses and directions.

Week 10

Topics

Definition of strain, extensional and shear strain, strain-displacement relations

Measurable Outcomes

Define the concept of strain at a material point as the fundamental measure of the local state of deformation and its relation to the displacement field. Describe strain as a second-order tensor, its Cartesian components, and their meaning.

Week 11

Topics

Transformation of strain, Mohr’s circle for strain, principal strains, maximum shear strain

Measurable Outcomes

Explain the basis for transforming strain states between two different Cartesian bases. Transform two-dimensional strain states, and compute principal strains and directions.

Week 12

Topics

Constitutive equations for a linear elastic material; constitutive equations: isotropic and orthotropic elastic materials

Measurable Outcomes

Describe the constitutive relationship between stress and strain for isotropic and orthotropic linear elastic materials.

Week 13

Topics

Engineering elastic constants, measurement, generalized Hooke’s law

Measurable Outcomes

Discuss engineering elastic constants, their measurement, and their relationship to the tensorial description of Hooke’s law

Week 14

Topics

Summary of equations of the theory of elasticity

Measurable Outcomes

Summarize the key equations of the theory of elasticity. Formulate and simplify problems in general elasticity, apply displacement and traction boundary conditions to problems in elasticity, and solve simple cases.

Week 15

Measurable Outcomes

Analyze the structural response of uniaxially-loaded slender elements: rods and bars

Week 16

Topics

1. Analysis of beams: statics, internal forces and their relation to internal stresses; bending moment, shear force and axial force diagrams, concentrated and distributed loads; differential equations of internal equilibrium, kinetic boundary conditions
2. Euler-Bernoulli beam theory: beam deflections, moment-curvature relation, kinematic boundary conditions. Statically determinate and indeterminate beams
3. Cross-section properties: first and second moment of area, center of area, moment of inertia

Measurable Outcomes

Analyze the structural response of transversely-loaded slender elements: beams; internal forces and beam deflections

Week 17

Topics

Analysis of Torsion of slender 1D structural elements: Shafts. Kinematic assumptions, internal torque, constitutive law for the cross-section: torque-rate-of-twist relation, equilibrium; governing equation; solution for various statically- determinate and indeterminate loading cases

Measurable Outcomes

Analyze the stability of slender structural elements subject to compressive loads: buckling loads, mode shapes, effects of imperfections, and eccentric loads

Week 18

Topics

Structural instability and buckling of slender 1D elements subject to compressive loads; analysis of buckling loads and mode shapes for various boundary conditions; effect of imperfections and eccentric loading

n/a

Course Info

Fall 2021
Learning Resource Types
Lecture Notes
Problem Sets with Solutions
Exams with Solutions
Labs
Online Textbook