Civil Engineering Reference
In-Depth Information
g(5)
2
g(6)
g(4)
g(2)
g(3)
g(1)
1
Figure 4.20
Node and freedom numbering for 2D beam-rod elements
There are 10 equations and the skyline storage is 40
Node Displacements and Rotation(s)
1 0.0000E+00 0.0000E+00 -0.1025E-02
2 0.3645E-07 -0.8319E-06 -0.9497E-03
3 0.0000E+00 0.0000E+00 0.0000E+00
4 0.6435E-07 -0.6283E-06 0.1774E-02
5 0.0000E+00 0.0000E+00 0.0000E+00
6 0.6435E-07 0.2880E-02 0.1329E-02
Element Actions
1 -0.3038E+02 -0.1975E+02 -0.6000E+02 0.3038E+02 0.1975E+02 -0.5849E+02
2 -0.2325E+02 0.8238E+01 -0.2519E+01 0.2325E+02 -0.8238E+01 0.5195E+02
3 0.0000E+00 0.2000E+02 0.3333E+02 0.0000E+00 -0.2000E+02 0.6670E+01
4 0.7123E+01 0.2080E+03 -0.9497E+01 -0.7123E+01 -0.2080E+03 -0.1899E+02
5 0.3177E+02 0.2610E+02 0.9839E+01 -0.3177E+02 -0.2610E+02 0.1968E+02
6 -0.8513E+01 0.1257E+03 0.1419E+02 0.8513E+01 -0.1257E+03 0.2838E+02
Figure 4.21
Results from first Program 4.4 example
is similar to the pin-jointed frame analysis described in Program 4.2. The first line of data
provides the number of elements (
nels
), the number of nodes (
nn
), the dimensionality
(
ndim
), the number of properties
nprops
and the number of property types
np types
.
In this program, the number of material properties required depends on the dimension-
ality, so the data now includes input to the integer
nprops
which indicates the number of
material properties required for each property type. In a 2D frame problem, there are two
material properties required (
EA
and
EI
), so
nprops = 2
. The material property values
for each type are then read into the two-dimensional array
prop
.
The material property data is followed by the
etype
vector (if needed), the global
nodal coordinates (
g coord
) and the element node numbering (
g num
). The loading on
the nodes is calculated using the equivalent nodal loads approach described previously for
the first example with Program 4.3, and these values are shown for each individual element
in Figure 4.19. There are no
fixed freedoms
in this example. The results shown in
Figure 4.21 indicate that the rotation at node 1 for example is
−
0.001025 (clockwise). The
action
vectors for elements 4, 5, and 6 are correct as printed, however for elements 1,2,
and 3 the equivalent nodal loads must be subtracted, for example
Element 1
=−
+
=−
F
x
1
30
.
38
0
.
00
30
.
38
=−
+
=
F
y
1
19
.
75
60
.
00
40
.
25
