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CE 3101
Fall 2011
A Simple Truss Exposed
Problem
Consider the simple, statically determinant truss shown in Figure 1. This ﬁgure also presents the externally
applied forces.
[1]
[2]
[3]
1
2
3
2
2
1
2
3
1
1
1
Figure 1: A simple, planar, pinjointed, statically determinant truss. The joint numbers are in the circles,
the member numbers are in brackets. The speciﬁed external loads at the joints are shown with arrows.
Let
M
be the number of members (in this case
M
=
3), and
N
be the number of joints (in this case
N
=
3). Note that this truss satisﬁes the necessary condition for a statically determinant truss
1
M
=
2
N

3
(1)
Using the notation and nomenclature that we have developed in class, this truss problem is fully described
by three matrices.
•
The
(
N
×
2
)
joint geometry matrix
G
=
0
0
1
1
2
0
(2)
•
The
(
M
×
2
)
member connection matrix
C
=
1
2
2
3
3
1
(3)
•
The
(
N
×
2
)
external force matrix
F
=
0
1

3
2
2
2
(4)
1
See, for example,
http://en.wikipedia.org/wiki/Truss#Statics_of_trusses
.
Simple Truss
1
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View Full DocumentCE 3101
Fall 2011
Some Geometric Calculations
It will be convenient to have some basic geometric quantities precomputed. Deﬁne the
(
M
×
2
)
matrix
D
,
where
D
(
m
, 1
)
is the “delta X” for member
m
, and where
D
(
m
, 2
)
is the “delta Y” for member
m
. The code
fragment for computing
D
would look like:
D = G(C(:,2),:)  G(C(:,1),:);
This is very
compact
code (a speciality of
MATLAB
); i.e., there is a lot going on in this one line.
To make sense out of this line of code, we break it into pieces and see what we get for our small example.
Think of every member as having a “FROM” joint and a “TO” joint, with the “FROM” given by the ﬁrst
column of
C
and the “TO” given by the second column of
C
.
C
(:
, 2
) =
2
3
1
(5)
This is nothing more than the second column of
C
; that is the
(
M
×
1
)
matrix of “TO” joint indices. Then
G
(
C
(:
, 2
)
,
:) =
1
1
2
0
0
0
(6)
So, this is the
(
M
×
1
)
matrix of coordinates of the “TO” joints for each member. Similarly,
G
(
C
(:
, 1
)
,
:) =
0
0
1
1
2
0
(7)
is the
(
M
×
1
)
matrix of coordinates of the “FROM” joints for each member. Taking the diﬀerence between
these two gives us the
(
M
×
2
)
matrix of
Δx
and
Δy
for each member (we are denoting this
D
):
D
=
1
1
1

1

2
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 Spring '11
 Barnes

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