Civil Engineering Reference
In-Depth Information
1 kN
1
0.2
1
Pile:
EI= 1.924
×
10
4
kNm
2
0.6
2
Linearly increasing
foundation stiffness
2
1.0
3
'Staircase'
approximation
3
10m
1.4
4
4
1.8
5
5
6
2 kN/m
2
Foundation
stiffness
k(kN/m
2
)
nels nprops np_types
5 2 5
props(ei,k)
1.924e4 0.2 1.924e4 0.6
1.924e4 1.0 1.924e4 1.4
1.924e4 1.8
etype
1 2 3 4 5
ell
2.0 2.0 2.0 2.0 2.0
nr
0
loaded_nodes,(k,loads(nf(:,k))
1
1 1.0 0.0
fixed_freedoms
0
Figure 4.17
Mesh and data for second Program 4.3 example
a linearly increasing soil or foundation stiffness. The pile has a constant flexural stiffness
of
EI
10
4
kNm
2
, and the foundation stiffness increases from zero at the ground
surface to 2 kN/m
2
at a depth of 10 m. The pile is modelled by 5 beam elements, and
the soil stiffness is approximated by a step function based on the stiffness at the mid-
point of each element. The data file provides
nprops=2
to signify the presence of an
“elastic foundation”, and
np types=5
since each element is supported by soil with a
different stiffness value. The composite beam/foundation global stiffness matrix in this
case involves the assembly of the sum of the element stiffness and “mass” matrices,
km
and
mm
respectively.
The remainder of the program follows a familiar course. Forces and/or fixed dis-
placements are read, and, following equation solution, the global nodal displacements and
rotations are obtained. In the post-processing phase, the element nodal displacements
eld
are retrieved, as are the element stiffness and “mass” matrices. The product of
eld
and the
=
1
.
924
×
