UNIVERSITY OF CALIFORNIA, BERKELEY
Engineering 7 – Spring 2009
Department of Civil and Environmental Engineering
Instructor: Professor Rector
1
Lab 09 [15 pts]
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
HB
VB
VA
HA
A
C
a
5m
13.5m
24m
b
B
θ
a
cos
θ
a
= 0.6
cos
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.
(b)
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 Spring '08
 Patzek
 Numerical Analysis, Matrices, Environmental Engineering, Elementary algebra, Complex number

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