Tensors
CEE 501
Notes
A common operation in vector analysis is to determine the component of one vector in the direction of
another. For example, in the figure below we wish to determine the component of the vector b along the
direction of the vector a, d

Variational Calculus
CEE 501
Supplemental Handout
The calculus of variations is a collection of techniques and theorems making it possible to extend the
methods and results of ordinary calculus (which treats functions of scalar variables) to the case of f

CEE 379
Beam Analysis
Notes
This handout presents the various ingredients of generalized beam analysis using a stiffness-based approach. It is assumed that the basics of beam analysis are familiar from other coursework such as statics
and mechanics of mat

Plane Frame Elements
CEE 379
Notes
Frame elements can be thought of as combining the characteristics of beam and truss elements, and our
task here is to work through the details of forming this combination. As usual, once we have characterized
the behavio

Truss Analysis
CEE 379
Notes
Trusses belong to the class of structural systems in which the principal load carrying mechanism is axial
tension and compression. An idealized truss model typically assumes all joints act like pins and all loads are
applied a

1-D Elasticity
CEE 501
Notes
This handout presents the basic concepts and analytical framework associated with engineering solid
mechanics considered in the simple context of 1-Dimensional systems. Although this is not a particularly
useful class of model

CEE 501
1-D Spring Characterization
Supplemental Notes
This handout presents a classical matrix structural analysis derivation of the force-displacement relation
for a simple 1-D spring, illustrating the consistent combination of kinematics, equilibrium,

CEE 379
1-D Structural Analysis
Notes
The majority of the basic concepts and issues associated with structural analysis can be considered in
the simple context of 1-Dimensional structural systems, i.e., structural systems in which all members are
aligned

1D Elasticity Example
CEE 501
Notes
This short document contains a transcript of the simple 1D-elasticity approximate solution example done in
class using Mathematica.
In[1]:=
n[x ] := x * (x L)
In[2]:= n[1]
Out[2]= 1 L
In[3]:= Q1 := Integrate[n[x] * sin[