Civil Engineering Reference
In-Depth Information
3
t
1
B
1
3
3
1
2
2
1
2
1
t
w
t
w
t
2
B
D
B
2
Figure 4.11
Typical sections implemented in the non-linear fi nite element code Zeus-NL
4.5.2 Sections
Cross sections are modelled by defi ning geometric and material properties of their components. Com-
prehensive section libraries are generally included in FE programs for different materials of construction
as shown, for example, in Figure 4.11 . It suffi ces to defi ne only certain sectional dimensions, e.g. width
and height for rectangular sections, because the remaining properties, such as cross- section area
A
,
effective areas for shear (
A
vy
and
A
vz
), fl exural (
I
y
and
I
z
) and torsional (
J
) moments of inertia, are
computed automatically. Sections with non-standard shapes can be modelled by defi ning manually all
geometric and mechanical properties. The number of properties required is a function of the problem
under consideration. For example, to analyse plane structures, it is required to specify
A
,
A
vz
and
I
z
,
where
z
is the axis perpendicular to the plane.
Depending on the type of section employed, e.g. steel, RC or composite, a different number of mate-
rial properties is specifi ed. These are a function of the model adopted for the material(s) as illustrated
in Section 4.5.1. For RC and composite sections, it is necessary to specify the area and location of steel
reinforcing bars, which are located with reference to the local axes of the section. These axes generally
coincide with the section principal directions, e.g. axes labelled ' 1 ' and ' 3 ' in the sections shown in
Figure 4.11. The correct orientation of local axes should always be thoroughly checked before running
analyses as it is a common source of errors in FE modelling of structures. Sections with different
moments of inertia about the principal directions (e.g. sections with a T- shape in Figure 4.11 ) may be
oriented incorrectly. Modern software packages employ user-friendly graphical environments that
render checks at the sectional level easy to perform. For example, Figure 4.12 shows how the section
local axes 1-2-3 relate to the global axes X- Y - Z in beam -elements implemented in Zeus- NL (Elnashai
et al
., 2003). Nodes n1 and n2 are the end nodes of the element. The element local 2-axis lies on the
line defi ned by them, i.e. n1-n2. However, n1 and n2 give no information for the T-section in the fi gure
and its orientation. Node (3) is thus required to defi ne the (local) 2-3 plane and can be a non- structural
node. It is possible, and advisable, to use one non-structural node as the third node for all the beam
elements that lie on the same plane of the model; this is also shown for the sample SPEAR frame in
Figure 4.12, where non-structural nodes are indicated by dark markers.
Three basic formulations can be used for section analysis with FEs:
• Fibre (or fi lament) models;
• Phenomenological (or mathematical) models;
• Mechanical (or sectional spring) models.
