This preview shows pages 1–3. Sign up to view the full content.
UNIVERSITY OF CALIFORNIA, BERKELEY
Engineering 7 – Spring 2009
Department of Civil and Environmental Engineering
Instructor: Professor Rector
Lab 9 (Solutions)
Topics
:
Linear Equations
Assigned
:
Monday, 4/13/2009, 8:00 am
Due
:
Monday, 4/20/2009, 12:00 pm (noon)
Type
:
Takehome
1.
Solution of a Set of Linear Equations
Exercise 1 – Truss Systems (5 pts)
A truss is a structure whose components are connected by hinges. Hinges cannot support moments, and the loading
can only be applied on the two ends of any truss component. The internal force in the truss component then is
oriented only along the direction of the component, and is either tensile or compressive.
F ( z )
S
a
S
b
H B
V B
V A
H A
A
C
a
5 m
1 3 . 5 m
2 4 m
b
B
θ
a
c o s
θ
a
=
0 . 6
c o s
θ
b
=
0 . 8
θ
b
In order to determine the internal force of each member of the truss, we can form a system of linear equations and
solve the system. The equations are:
– 0.6 Sa – HA = 0
– VA – 0.8 Sa = 0
0.8 Sb – HB = 0
0 – VB – 0.6 Sb = 0
0.6 Sa – 0.8 Sb = 0
0.6 Sb + 0.8 Sa = – F(z)
(a)
Express the above equations in matrix form, Ax = b, and include them in your report.
(1 point)
A =
0.6000
0
1.0000
0
0
0
0.8000
0
0
0
1.0000
0
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document Lab 10
2
0
0.8000
0
1.0000
0
0
0
0.6000
0
0
0
1.0000
0.6000
0.8000
0
0
0
0
0.8000
0.6000
0
0
0
0
b =
0
0
0
0
0
10
(b) Start a Matlab code for this problem by creating and populating matrix A and array b.
Put your commands in your report.
(1 point)
fz= 10;
% kN
A = [ .6 0 1 0 0 0; .8 0 0 0 1 0; 0 .8 0 1 0 0; 0 .6 0 0 0 1; .6 .8
0 0 0 0; .8 .6 0 0 0 0]
b= [0 0 0 0 0 fz]'
(c)
Check the determinant of matrix A using the Matlab command
det
. Include the answer your report.
(0.5 point) det(A) is 1
(d)
Using the left division operator of Matlab to solve the problem, determine the reaction forces of HA, HB, VA,
VB, and the internal force of members a and b for F(z) = 10 kN. Copy the answer to your lab report.
(0.5 point)
in the order: Sa, Sb, Ha, Hb, Va, Vb
x =
8.0000
6.0000
4.8000
4.8000
6.4000
3.6000
They may use a different order
(e)
Plot Sa vs. F(z) and Sb vs. F(z) for F(z) between 30 and 150 kN at 1kN increments.
(2 point)
They may have one plot with two curves or two plots with one curve.
If it is not written which one is Sa and which one is Sb (either in the title, or the legend, or anywhere), 1, and
don’t check the curves.
If the range is incorrect, or any curve is incorrect, 0.5
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 06/23/2011 for the course ENGIN 7 taught by Professor Horowitz during the Spring '08 term at University of California, Berkeley.
 Spring '08
 HOROWITZ
 Environmental Engineering

Click to edit the document details