Civil Engineering Reference
In-Depth Information
Table 4.3
Displacement Scheme
Global
Figure 4.10b
Element 1
Element 2
Element 3
v
(1)
1
1
U
1
0
0
(1)
1
2
U
2
0
0
v
(1)
2
v
(2)
1
u
(3)
1
3
U
3
(1)
2
(2)
1
4
U
4
0
v
(2)
2
5
U
5
0
0
(2)
2
6
U
6
0
0
u
(3)
2
7
U
7
0
0
Table 4.4
Element-Displacement Correspondence
Global Displacement
Element 1
Element 2
Element 3
1
1
0
0
2
2
0
0
3
3
1
1
4
4
2
0
5
0
3
0
6
0
4
0
7
0
0
3
is subjected to bending loads, so the assumptions of the bar element do not apply to this
member. On the other hand, the vertical support member is subjected to only axial load-
ing, since the pin connections cannot transmit moment. Therefore, we use two different
element types to simplify the solution and modeling. The global coordinate system and
global variables are shown in Figure 4.10b, where the system is divided into two flexure
elements (1 and 2) and one spar element (3). For purposes of numbering in the global
stiffness matrix, the displacement scheme in Table 4.3 is used.
While the notation shown in Figure 4.10b may appear to be inconsistent with previ-
ous notation, it is simpler in terms of the global equations to number displacements suc-
cessively. By proper assignment of element displacements to global displacements, the
distinction between linear and rotational displacements are clear. The individual element
displacements are shown in Figure 4.10c, where we show the bar element in its general
2-D configuration, even though, in this case, we know that
v
(3)
1
=
v
(3)
2
=
0
and those dis-
placements are ignored in the solution.
The element displacement correspondence is shown in Table 4.4. For the beam
elements, the moment of inertia about the
z
axis is
bh
3
12
=
40(40
3
)
12
213333 mm
4
I
z
=
=
For elements 1 and 2,
207(10
3
)(213333 )
300
3
EI
z
L
3
=
=
1635
.
6N/mm
