CPE 219
Overview Problem
Spring 2014
(Rederive the equations below to test/enhance your understanding of the material we covered this week
in class.)
Problem: Formulate the problem below for the free vibration of the structure below resulting from some
i
Determine and draw the distribution of axial forces in these Statically Determinate 1D structures.
P
a
P
P
P
a
a

P
P
b
3P
P
2P

b
1

b
2.
3.
a
a
2P
a
+
5P
P
P

2P
b
P
b
b
3P
3P
3P
4.
5.
3P
6.
P
P/2
+
x
x
L
8.
P
P
0.75
L
+
L
q(x)=(P/L) .75L<x<1.75l
1
Chapter 11
STRESS AND DEFORMATION
ANALYSIS OF LINEAR
ELASTIC BARS IN TENSION
Figure 11.1:
In Chapter10, the equilibrium, kinematic and constitutive equations for a general threedimensional
solid deformable body were summarized. Special cases were also pr
CPE 219
Homework 1
Spring 2014
1.) Using the appropriate equations for kinematics, compatibility, equilibrium, and
constitutive behavior, verify that the following formulation governs the vertical motion of
the mass shown in the figure below under the cas
CPE 219
1
Spring 2014
1 INTRODUCTION
Look around you and consider any tangible item within your proximity. What purpose does it
serve? From what matter is it composed? How could it fail? Is it efficient? Could it be
improved? The purpose of this course is
CPE 219
1
Spring 2014
How to formulate a problem in Mechanics of Materials
1) Make sure you know what you want to determine. (Either you are trying to determine
forces, displacements, stresses, strains, or all of these things.) If it is not clear at the s
CPE 219
V1
Spring 2014
V Constitutive Behavior
We know how to describe the deformation of materials with our kinematic equations, which
relate strains to displacements. We even know how to ensure that the displacements are
physically reasonable using our
CPE 219
1
Spring 2014
3 Required Previous Knowledge
Given the integrated approach being taken in this course, it is essential for you the student to
effectively utilize your previous knowledge. In this chapter, we will present some of the information
that
CPE 219
5.
Course Overview Problem
5.1 Introduction
In the last chapter, we reviewed a classic problem of physics, projectile motion. We stressed the
importance of applying our skills in physics and math to solve the problem and demonstrated the
utility o
Assorted 1D practice problems:
1. The rod shown below is subjected to three loads of equal magnitude (The loads are applied at the dashed lines.) .
Draw free body diagrams that can be used develop equations that relate the internal forces in the rod to t
Why are manhole covers round?
General Principles
Needed for basic Engineering
Analysis of a Truss
Trusses are a part of the field
Mechanics of Materials
Mechanics of Materials
Statics Force distribution in truss
Strength of Materials response of truss
REVIEW FOR CPE 219
1) You can apply your knowledge of physics, calculus, algebra, and vectors when needed.
2) You understand that all our equations in mechanics of materials can be classified into one
of four types that we are calling: Kinematics, Equilib
Determine and draw the distribution of axial forces in these Statically Determinate 1D structures.
P
P
a
a
a
P
2P
P
b
b
b
1
2.
3.
a
a
a
P
2P
b
P
b
b
3P
4.
5.
3P
6.
x
x
L
L
q(x)=P/L
8.
0.75
L
L
q(x)=(P/L) L<x<2l
10.
L
q(x)=(P/L) sin(x/L)
q(x)=(P/L) (1x/L
1
Uniaxial StressStrain Relations
The modeling of inelastic behavior of solids is a complex and wide ranging subject.
In the rst two parts of this book (Chapters 114), we will nevertheless need only a
few basic facts about the uniaxial stressstrain rela
CPE 219
2014
Practice Exam 1
Spring
Name:_
1) Fill in the appropriate word(s) (15 Points):
a.
_ is the study of the response of matter, materials, and structures
to externally applied loads or imposed deformations.
b.
_ is the study of equilibrium of forc
CPE 219
Practice Exam 1
Spring 2014
Name:_SOLUTIONS_
1) Fill in the appropriate word(s) (15 Points):
a.
_Mechanics_ is the study of the response of matter, materials, and structures to
externally applied loads or imposed deformations.
b.
_Statics_ is the
NOTES for CPE219 2172014
Problem: Determine the displacements of the points x=a and x=2a for the structure subjected to
the load shown below. Determine the minimum and maximum axial stresses in the rod.
q(x)=2P/a
EA
x
a
a
a
Assumptions:
1) Linear elasti
Chapter 6
Continuum Mechanics: One Spatial
Dimension
6.1 Introduction
In the previous chapter we investigated how to model the spatial motion of
objects (cars, molecules, etc.) but omitted the possibility that the objects
exert forces on each other. The o
CPE 219
Chapter 4 A REVIEW PROBLEM
4.1 Introduction
In the last chapter, we reviewed some of the essential prerequisite information that you are
responsible for this course. In the following, we use a classic example from physics to utilize much of
that r
CPE 219 : Some practice short answer problems
1) Define the field of mechanics of materials.
2) What is statics?
3) What is dynamics?
4) List the four classifications of equations used in mechanics.
5) What is the difference between a material and a spati
Determine the Distribution of internal axial forces in the rod shown below and subjected to the
load P.
Structure
FBD
Deformed Structure
Equilibrium:
Since the FBD and equilibrium equation do not change for various values of x, the internal
forces are con
CPE 219 Practice Problems for Constitutive Relations.
1. The graph below is an unlabeled stress strain curve of a material. Label the axes as
stress and strain. Identify the elastic modulus, the yield stress, the ultimate stress, the
stretch and the tensi
Example for spatial and Materials Coordinate systems
Given that (a is a constant) show that the velocity of the material is the same no matter if you
use a material or spatial description of the system. (X = material coordinate, x= spatial
coordinate.)
So
CPE 219: In class Problem (1D structure, Review process of formulating problem in
mMechanics.)
Using Appropriate Engineering Estimations, formulate a problem that represents the free
vibration of the structure given below given an initial displacement. (
CPE 219: Homework 2
Verify that the following expressions adequately describe the forces in the wire (N15) and bar (N24) and
the displacement at the free end of the bar(1). The bar 13 is assumed to be rigid,