Civil Engineering Reference
In-Depth Information
(3)
(1)
(n2)
(1)
(3)
(n1)
20000
17500
15000
12500
10000
7500
5000
2500
(n3)
(3)
(n2)
(1)
(1)
(n2)
(n1)
(n3)
(3)
500
2500
(n1)
7500
10000
12500
15000
17500
Figure 4.12
Typical local axis orientation for beam-column elements in Zeus-NL: beam with a T-section to be
modelled (
top
-
left
), two possible orientations of the T-section of the beam (
top
-
right
), the correct position of node
n3 for modelling the orientations (
bottom - left
) and location of non-structural nodes in the fi nite element model of
the SPEAR frame (
bottom - right
)
Fibres form the basis of distributed inelasticity models. The latter are the most reliable formulations
to predict the earthquake response of structural systems. Nevertheless, they may be time-consuming in
practical applications for the analysis of the inelastic behaviour of large structures. Phenomenological
models are employed to simulate the monotonic and hysteretic response of cross sections under different
loading conditions. These are effi cient models but often require tedious calibrations of the large set of
parameters utilized to describe, for example, moment-rotation relationships of steel, RC or composite
sections. Phenomenological models are generally used for lumped inelasticity discretizations of struc-
tural systems. In mechanical models, cross sections are idealized through a discrete number of springs.
These models combine some features of the fi bre method for the construction of the section stiffness
matrix with the basic principles of lumped inelasticity models.
In fi bre-based formulations, the area A of the section is divided into fi nite regions (or fi bres), e.g. a
rectangular grid of lines parallel to cross-sectional principal axes for 2D analysis. Each fi bre is charac-
terized by two geometric quantities, these are its location in the local reference system of the section,
defi ned as 'monitoring point', and the fi bre area dA. Figure 4.13 shows typical subdivision in fi bres for
RC sections. The number of fi bres is dependent on the type of section, the target of the analysis and
the degree of accuracy sought. Refi ned subdivisions with a large number of monitoring points increase
exponentially the computations required in the analysis. For rectangular sections, the number of fi bres
can be determined by subdividing width
B
and height
H
in segments of length equal to 1/10 of
B
and
H
, respectively. At least two lines of fi bres should be used for fl anges and webs in standard metal pro-
fi les. Fibre-based discretizations of RC rectangular and T-shaped sections of the SPEAR frame in Figure
4.2 employ 200 monitoring points. In 3D, subdivision into fi bres along two orthogonal section axes
results in the defi nition of smaller areas with distances of the monitoring points to both axes, as dis-
cussed further below.
