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
Topics
Analysis of rods: uniaxial loading of slender 1D structural elements
Measurable Outcomes
Analyze the structural response of uniaxially-loaded slender elements: rods and bars
Week 16
Topics
- 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
- Euler-Bernoulli beam theory: beam deflections, moment-curvature relation, kinematic boundary conditions. Statically determinate and indeterminate beams
- 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
Measurable Outcomes
n/a
