Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Chapter 4
Vector Spaces
4.1
Vectors in Rn
Homework: [Textbook, 4.1 Ex. 15, 21, 23, 27, 31, 33(d), 45, 47, 49,
55, 57; p. 189].
We discuss vectors in plane, in this section.
In physics and engineering, a vector is represented as a directed
segment. It is
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Calculations
1. Water content of samples
Container Label
222
210
214
219
228
YRC
82.340
Falling Cone
1
2
3
Water Content (%)
35%
36.6%
30.1%
33.8%
23%
24.9%
23.2%
30.7%
30.9%
31.8%
2. Plot the liquid limit data twice, once for the Casagrande method and on
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Purpose and Principles
The purpose of the plastic limit test, the Casagrande liquid limit device test, and the
fall cone liquid limit device test are to determine the plastic and liquid limits of a
finegrained soil. The plastic limit is the water content
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Name
Poseidon
Orestes
Zeus
Aigisthos
Polyphemos
Kalypso
Athene
Telemachos
Nestor
Phemios
Penelope
Antinoos
Eurymachos
Eurykleia
Agamemnon
Menelaos
Who?
God of the sea
Holds a grudge against Odysseus
Makes sea journey difficult
Murdered Aigisthos, Zeus def
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Theogony
What did Hesiods scepter do?
Which of the Muses corresponded with
Hesiod the most?
How did Zeus rule?
How did kings rule?
How were the connections between
kings and Zeus?
What are the major themes of Theogony?
What is the succession myth?
What do
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Problem 2
Part A
The analytical model (MASTAN) of this structure had assumptions. I assumed that there it is a 1 st
order elastic analysis of a planar frame. This was assumed so that the structure would be stable
on MASTAN. An analysis on a space frame wo
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Question 1
(a) The midspan vertical displacement from the truss model of the
Cooper River Bridge is 1556 inches downward (or 129.67 feet). The
midspan vertical displacement from the frame model of the Cooper
River Bridge is 1554 inches downward (or 129.5
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Problem 1 Explanation of Results
Idealizing the bridge as a truss, we need to check for its static determinacy. If the
bridge is not statically determinate as a truss model, for learning purposes, we have to
make it statically determinate. To do this, we
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Procedure
We did not deviate from the procedure specified in the lab manual. Gauges 1 and 2
are full bridges and gauges 3, 4 and 5 are half bridges. Remember to take this into
account when doing calculations. For full bridges, the measured strain is doubl
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Procedure:
The lab experiment was done on Machine #1. The red button indicates
the X, and the white button moves the pen. Make sure the reset is
marked. We do not want sweeping to occur; we do not want it to be
time dependent. Put it in lock mode. This pr
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
%Inputs
%Generate an ntuple of 10 equispaced points covering [1,1].
n=10;
interval=[1,1];
t_10=linspace(interval(1),interval(2),n);
for i=1:n
y_10(i)=(t_10(i)^3;
end
%Generate an ntuple of 100 equispaced points covering [1,1].
nn=100;
t_100=linspace
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
%Inputs
%The length of ntuples_t must be the same as the length of ntuples_y. In
%other words, [t1,.,tn] must have n terms. [y1,.,yn] must have n terms.
t=input('Input the ntuples of tj, like [t1,.,tn]');
y=input('Input the ntuples of yj, like [y1,.,yn]
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
%Inputs
%Generate an ntuple of 10 equispaced points covering [1,1].
n=10;
interval=[1,1];
t_10=linspace(interval(1),interval(2),n);
for i=1:n
y_10(i)=(1+25*t_10(i)^2)^1;
end
%Generate an ntuple of 100 equispaced points covering [1,1].
nn=100;
t_100
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
%Generate an ntuple of 100 equispaced points covering [1,1].
n=length(t);
nn=100; %Evaluate at 100 equispaced points
t_100=linspace(t(1),t(length(t),nn);
%Set initial condition.
product=ones(n,1);
for s=1:nn %Overlay the polynomial, evaluating on 100 po
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
clear all
%Inputs: values of f(xk) at x1,.,xn1 and boundary data a and b
x=input('Input x1,.,xn1, like [x1,.,xn1]');
f=input('Input f(x1),.,f(xn1), like [f1,.,fn1]');
a=input('Input initial boundary condition, like [x1,a]');
b=input('Input end bounda
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
clear all
n=10;
while n<=1000
%Inputs: values of f(xk) at x1,.,xn1 and boundary data a and b
a=0;
b=1;
x=linspace(a,b,n+1);
f=4*pi^2*sin(2*pi*x);
%Create the matrix of the linear system.
h=1/n;
for i=1:n1
for j=1:n1
if i=j
M(i,j)=2
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
clear all
n=10;
while n<=1000
%Inputs: values of f(xk) at x1,.,xn1 and boundary data a and b
a=0;
b=1;
x=linspace(a,b,n+1);
f=cos(exp(3*x);
%Create the matrix of the linear system.
h=1/n;
for i=1:n1
for j=1:n1
if i=j
M(i,j)=2;
elseif
Special Topics in Civil and Environmental Engineering
CEE 3090

Fall 2015
Can you distinguish gods vs. humans?
Who is the protagonist of The
Odyssey?
Who was he held captive by?
When was the story taking place?
Where was Odysseus trying to return
to?
What was happening back home
during his capture?
What is Odysseuss flaw?
The O