equal to the direction of the dynamic nodal
load;
The steps above have been carried out using
Mathcad
(wind
tunnel
results),
Autocad
(areas/direction nodal loads) and Excel (final
parameters of nodal loads and dynamic func-
tions).
6.
The dynamic functions were entered in ESA-
Prima
Win manually, using Time
History
Analysis. Each function in EPW consists out of
two functions. In order to enter the Fourier-
line of 10 sinuses, 5 summarized functions are
needed. Each sinus-function has 4 parameters
(offset, amplitude, frequency and shift). There-
fore, for each situation (wind-direction, num-
ber of towers) an amount of 50x5x2x4 = 2000
numbers had to be entered.
7.
For each nodal load the direction and magni-
tude (x,y,z) had to be entered. For each nodal
load
the
5
applicable functions
were
assigned.
8.
A calculation of Eigen frequencies had to be
done to make dynamic analysis possible.
As a result of the dynamic calculations, the con-
tinuous signal of each node deflection or each
member force could be shown for the one con-
sidered minute.
The other possibility of output has been used
more often to analyse the effects of the wind. For
a group of members a list can be produced of the
maximum deflection, force or
moment
which
occurred in the considered minute. By combin-
ing these output lists, for each member the unity
checks for several
mechanisms were calculated.
From former studies the critical elements
were
known. For these groups of members (e.g. all col-
umn tubes, all end members of a truss), output
lists
were produced in ASCII format. This
was
done for each situation (wind direction, roof
open or closed, 1 or 2 towers). For clarity: these
values are the maximum values of each member
which occurred in the considered minute.
In Excel, these ASCII-files were used to combine
forces and moments for each critical
member or
profile (several
mechanisms, e.g. N+My+Mz for
buckling,
Vy+Vz for shear).
As a result, the maxi-
mum unity check of each
member has been
derived.
These unity checks due to the (dynamic) wind in
the new situation (1 or 2 towers) have been com-
pared with the unity checks due to static wind
load in the old situation (no towers).
Conclusions
For the steel frame structure of the roof of the
Amsterdam ArenA, a comparison has been car-
ried out between a new situation
with one or
two large towers directly next to the stadium and
a situation without large towers.
The wind tunnel tests resulted in an increase of
the static wind loads on the roof of up to 30%
when the tower(s) is(are) added. It is sure that
the existing roof structure can not cope
with
such increased forces.
Using the dynamic analysis, the lack of simultane-
ity of peak loads and the mass inertia of the struc-
ture is incorporated. Consequences of this deci-
sion are that a complex and extended calculation
is necessary. For this
model and these calcula-
tions, ESA-Prima Win 3.50 was chosen. In close
consultation with the people of ESA, the possibil-
ities and optimal
methods were elaborated.
The input of the loads and the processing of the
results required a lot of manual
work and spread-
sheet calculations. This indicates that the chosen
method is really putting ESA to the test. Never
before so many loads and variables were used in
one model.
We have no doubt that in future ver-
sions, the input- and post processing facilities will
be adapted to the always shifting boundaries,
such as this project.
The result of this analysis (dynamic increased
loads) is generally that the unity checks are com-
parable to the ones in the original calculations
(with static, lower loads).
Since the structure has been designed in a way
that left little reserve, only a very small increase of
the unity checks is allowable. The final decision
whether the increase of loads is acceptable, is still
in process at the moment of writing.
Project data
Nodes: 2834
1D macros: 3868
Members: 6428
Types of profiles: 87
Weight of steel: 3098331 kg
Length: 227 m
Width: 177 m
Height: 72 m
95
