Civil Engineering Reference
In-Depth Information
6m
6 m
2 m
60
k
N
60
k
N
2m
2m
2m
20 kN/m
2
3
1
2
1
6
4
4
4m
Elements EA(kN) EI(kNm
2
)
1,2,3 5
×
10
9
6
×
10
4
4,5,6 1
×
10
9
2
×
10
4
5m
5
6
3
5
20kN 20kN
60kNm
60kN
60 kN 60 kNm
Equivalent
nodal
loads
6.67 kNm
6.67 kNm
140 kNm
120 kN
120 kN
140 kNm
nels nn ndim nprops np_types
6 6 2 2 2
prop(ea,ei)
5.0e9 6.0e4
1.0e9 2.0e4
etype
1 1 1 2 2 2
g_coord
0.0 0.0 6.0 0.0 6.0 -4.0
12.0 0.0 12.0 -5.0 14.0 0.0
g_num
1 2 2 4 4 6 3 2 3 4 5 4
nr,(k,nf(:,k),i=1,nr)
3
1 0 0 1 3 0 0 0 5 0 0 0
loaded_nodes,(k,loads(nf(:,k))
4
1 0.0 -60.0 -60.0 2 0.0 -180.0 -80.0
4 0.0 -140.0 133.33 6 0.0 -20.0 6.67
fixed_freedoms
0
Figure 4.19
Mesh and data for first Program 4.4 example
The first example analysed by Program 4.4 is shown in Figure 4.19 and is a 2D rigid-
jointed frame subjected to distributed loads and point loads. In 2D, the elements have 6
degrees of freedom as shown in Figure 4.20. At each node there are two translational free-
doms in
- and a rotation (in that order). The nodal freedom numbering associated
with each element, accounting for any restraints, is as usual contained in the “steering”
vector
g
. Thus, with reference to Figures 4.19 and 4.20, the steering vector for element 1
would be [001234]
T
x
-and
y
and for element 2, [234567]
T
, and so on. The data organisation
