General client
requirements:
The main structural frame had the following requirements:
·
Provide a capacity of 12,000 people in an all
seated configuration.
· Comfortable layout to allow for the accommodation of different amenities required in an Arena (boutique shops, restaurants, cafes, bars, etc.).
· Unrestricted visibility to the centre of the arena stage.
· High acoustic performance.
· Fully capable to cater for the need of disable people.
· Adequate entrances and exits to cater for the 12000+ people in case of emergencies.
· Accessibility of the indoor arena part by emergency vehicles.
· Comfortable layout to allow for the accommodation of different amenities required in an Arena (boutique shops, restaurants, cafes, bars, etc.).
· Unrestricted visibility to the centre of the arena stage.
· High acoustic performance.
· Fully capable to cater for the need of disable people.
· Adequate entrances and exits to cater for the 12000+ people in case of emergencies.
· Accessibility of the indoor arena part by emergency vehicles.
To fulfil these requirements the project trailed the
following stages:
- Final design layout
- Definition of structural loads
- Finite element analysis of the stands section
- Roof static analysis
- Mainframe design and prediction of axial loads transmitted
As it was mentioned earlier the
seating sections were divided in three individual designs that were able to be
replicated around the arena. To further increase the efficiency of the project,
reduce the overall cost, and decrease the self-weight of the structure,
lightweight pre-stressed concrete seating panels were selected for the seating
arrangement. These panels will be supported on beams that are attached on the mainframe
of the building. To predict the behaviour of these sections it was decided that
it was necessary to perform a Finite Element Analysis (FEA) in order to
identify the loads transfer from the seat panels to the main structure. Using
the RFEM v5.02 software the finite element analysis was performed only in
Section 2 which it is the most critical sections of the structure.
Model:
The seating arrangement model of
Finite Element Analysis is consisted by two main parts, the precast lightweight
concrete seating panels and the beam supporting of seating arrangement. This
analysis takes into account a realistic shape for the seating panels which will
be attach to the supporting beams. It was assumed that the seating panel shape
has the following dimensions: 1.6m width and 1.1m height. The supported beam
assumed has 17m length and 8.3m height. At the bottom of the seating supporting
beam there is a 1m wide space that was left for the first row of seats
including a walkway of 0.6m. All the dimensions that were used during the FEA
are presented at Figure 2.14.
Figure 2.14 Model parts for supported beam (A) and seating panel (B)
These parts will be attached to
the final layout of the main structure in order to produce a more realistic
simulation of the loads the supporting beams are taking from the seating area. The
connections between the structural elements (columns & beams) ware
established using connection member function of the RFEM software. The nodal
supports of the main structural frame to the foundations were set as rigid
(fixed). The loadings were applied on seating panels for two different imposed
loads as it was discussed earlier during the structural loading section of this
report. From this analysis the engineering team will extract a uniform load in
z axis for the two different imposed loads and also a separate values for the
self-weight of the seating panel sections alone. These loads will be applied on
the static analysis of the main structure, which follows in the next sections
of this report. The FEA analysis will also produce an initial deflection as
well as a predicted deflected shape for the seating arrangement. This analysis
takes into account the BS EN 1991 loads that were defined earlier as well as
the BS EN 1990 partial safety factors for combined load configurations (Imposed
loads & Self-weight).
In order to correctly configure
the structural model that is presented later in this report the team needed
extract specific loading values from the FEA analysis. The values that needed
to be extracted were: The self-weight load that the panels apply to their
supporting beams, and the loads the two imposed loads are causing to their
supporting beams. A table explaining the extraction values is presented below.
Table 2.10: Extraction values
explanation
Load Case
|
Does
the calculation include self-weight?
|
Extraction
to the structural analysis?
|
Section
type
|
Self – weight
|
YES
|
YES,
Loads due to self-weight of panels that is applied to the supporting beams.
|
Lightweight Concrete seating panel.
|
Imposed loads 1&2
|
NO
|
YES,
Loads due to the live loads that were applied to the panels.
|
Lightweight Concrete seating panel.
|
Combination
|
Includes Self-weight & Imposed loads
multiplied by the necessary safety factors.
|
NO,
this FEA was only perform to access the performance of the seating section
itself.
|
Complete seating section.
|
Section type 2
Section type 2 is used in the long
span of arena and it is replicated twice. The 3D isometric view of the model
that was used to perform the finite element analysis on the seating arrangement
is presented on Figure 2.15.
Figure 2.15: Model geometry
|
Results:
Deflection:
The deflection of the seating panels
of Section 2 was defined for three different cases, self-weight, imposed load 1
and imposed load 2. The allowable self-weight deflection was calculated to be
37.5mm using the equation δmax=span/400. The FEA showed that the maximum
absolute deflections were: 3.9mm, 2.3mm, 1.2mm and 10.2mm for self-weight,
imposed load1, imposed load 2 and Combination respectively. The values of the deflections
that FEA is showing for the combination of all loads are well within acceptable
limits.
Figure 2.16 Self-weight deflection
Figure 2.17 Imposed Load 1 case
with 7.5kN/m2
Figure 2.18 Imposed Load 2 (4.0
kN/m2)
Figure 2.19: Deflected shape of the
stands (Combination of self-weight and load cases 1 and 2)
Axial uniform loading:
The aim of this Finite Element Analysis was to define the uniform
distributed loading in z-axis that is applied on the seat supporting beams. The
RFEM software uses a local axis for each member defining the y-axis as the
perpendicular axis of each member. As a result the uniform loading which is
applied on beam due to seating panel loading can be defined by axial loading
per meter in y axis (vy).
The axial uniform loading due to the panels weight was calculated first by hand
using the specific weight of lightweight concrete (γ=19.5 kN/m3) LC60/66 EN, it had a value of 74.45kN/m and the
calculations are presented at Table (2.10). The FEA presented below shows that
the maximum uniform loading due to the self-weight of the panels was between
60-80 kN/m.
Figure 2.20 Self-weight axial
loading per meter on seat support beam.
Table 2.11 Hand Calculations
Cross Section of seat panel (Lightweight Concrete)
|
Seat support beam
|
|||||
Area (m2)
|
Length(m)
|
Specific weight
(kN/m3)
|
Force(kN)
|
Length (m)
|
Number of panels
|
UDL (kN/m)
|
1.4
|
15
|
19.5
|
409.5
|
22.00
|
8
|
74.45
|
The imposed loads 1 & 2 were simulated on
this model in order to define the forces that are produced by the applied
section loads. The simulation gave values of 60-70kN/m and 30-40kN/m for
imposed load 1 and imposed load 2, respectively. The results of Finite Element
Analysis for imposed load 1 and imposed load 2 are presented at Figure 2.21 and
Figure 2.22 respectively.
Figure 2.21 FEA for seat
supporting beam applied imposed load 1.
Figure 2.22 FEA for seat
supporting beam applied imposed load 2.
After the consideration of the Finite
Element Analysis results and the hand calculation checks the structural team
decided to assume that the values of uniform loads which are to be used on the
main structure structural analysis are 74.45kN/m, 75.00kN/m and 35.00kN/m for
self-weight, imposed load 1 and 2 respectively. The values are presented on the
table below.
Table 2.12: UDL's caused by the
seating panels and the imposed loads
Uniform axial load applied on panels sections
|
Value (kN/m)
|
Self-weight
|
74.45
|
Imposed load 1
|
75.00
|
Imposed load 2
|
35.00
|
The roof model of the Arena is
consisted by three main parts, the Brunel truss, the secondary arc and
secondary central trusses, as presented in Figure 2.23.
 |
In order to be possible to
complete the initial simulations it was essential to establish the appropriate
cross sections of structural members to be used. To decide on the appropriate
sections the structural team performed a research in available possible cross
sections that currently exist in industry. The research was focused on cross
sections that can resist: pure compression, tension as well as the combination
of axial loading and bending. Members under compression are expected to be
necessary in the following parts of the roof system: the Brunel‘s top cord, the
top and bottom cord of the secondary central and arc trusses. Tension members
are expected to be on the bottom cord of the Brunel trusses, connections
between top and bottom cord of the Brunel trusses, and bracing of all
structural elements of the roof. In addition, members close to the connections
between top and bottom cords of Brunel trusses are expected to be subjected to
axial loading and bending. For this reason, circular hollow cross sections,
rectangular hollow cross sections, double L shape sections and Universal Beam
cross sections were selected for the initial design. The mention sections were
later refined in order to accommodate any necessary modifications that were
made on the design. The initial structural analysis of the roof was separated
into three main steps, the Brunel truss analysis, the stabilizing side trusses
design and the connections of two Brunel trusses with the central stabilizing
trusses.
1.1.1.1
Brunel truss analysis:
The Brunel trusses serve as the
spinal support of the roof and they were the first members to be design in
order to evaluate their performance. The truss was tested for self – weight to
purely check the stability of the structure and confirm the design. It was
found that it was performing well with 54.2 mm of vertical deformation at the
mid span of the section (Figure 2.24).
As no other external forces were
acting, the sections was confirmed symmetric as no rotation was observed due to
the self-weight of the structure. Stress analysis on Brunel truss also
confirmed that bottom cord is in tension (red colour) and the top cord is in
compression (rest of the colour spectrum), as it is presented at Figure 2.25 in
the following page. Figure 2.25 also shows the critical areas where the
stresses take the maximum values. The lower members of top cord take the
maximum values at the supporting areas.
On the other hand, the upper
members of top cord are taking their maximum value at the middle span of the
Brunel truss. These critical areas of maximum stresses will affect the decision
for the appropriate cross section properties. The combination of two Brunel
trusses connected and stabilize with side and central trusses, will affect
their structural behaviour. Thus it was necessary to model a whole roof
system.
1.1.1.2
Stabilizing the arc truss design:
The secondary arc trusses will be
used to transfer the main loads of the roof to the Brunel trusses and the main
structural framework. After a collaborative agreement of the structural team it
was decided that:
- Arc trusses can
more effectively transfer the axial loadings to the main structural
supporting system of the roof.
- Each secondary
truss was individually designed to have the centre of gravity as closer to
the support as possible in order to resist some of the rotational moments
with its own self-weight.
- The arc shaped
roof design results in a higher angle of pitch which will be more
effective in absorbing loads and will also reduce the build-up of the snow
volume on the roof top compared to a conventional flat roof.
- The catenary arc
type trusses will have their vertex close to their connections with the
Brunel trusses.
- There are twenty
six (26) points of connection between the Brunel truss and main framework
of the building which will be located 2.5m above the last seating
arrangement of the upper level.
- Circular hollow
cross section were selected to be used due to the compression and tension
states
1.1.1.3
Roof system:
The roof system model was created
using the Brunel and the stabilizing arc and central trusses, as it is
presented in Figure 2.27.
The roof system model simulation
was performed by applying imposed loads on all the main parts of the model. The
stabilizing trusses were uniformly loaded with a value of 15kN/m and the main
Brunel trusses with 2.5kN/m as well as 4 point loads of 7.5kN. Applying these loadings on roof system will
affect each the deformation of each component, especial the Brunel trusses. The
deflection of roof truss under its self-weight is presented in Figure 2.28.
From
Figure 2.28 the deformation of the structure was found to be 50.5mm located at
the bottom cord of Brunel trusses. The highest deformation was found to be
present within the central stabilizing trusses at the mid-span of the roof
section. A similar observation can be seen in the combination of self-weight
and imposed load analysis as it is presented at Figure 2.29.
The
maximum deformation observed from the combination loading figure was found to
be 112.9mm. The maximum allowable deformation is more complicated to calculate
into 3D problems. For this reason, the team made the assuption that it is
necessary to check the maximum allowable deformation in both major roof axis (x,y).
The maximum allowable as well as the predicted roof deformations are presented
at Table 2.13.
Table 2.13 Maximum allowable deformation for both major roof axis.
Axis
|
Maximum
span (m)
|
Maximum
deformation (mm)
|
x
|
120.00
|
300.0
|
y
|
97.64
|
244.1
|
Predicted max. deformation (mm)
|
112.9
|
|
As it can be observe from the Table above the
predicted deformation was less than half the value of the minimum allowable.
This prediction took into account the combination loading with the partial
factors (γc,γQ) accounting for a safer roof structure.
1.1.1.4
Structural observations:
From
previous simulation performed it was evident that the roof structure tents to
rotate which causes torsion at the Brunel trusses. This effect distablizes the
roof, increases the shear stresses as well as the absolute deformation of the
structure. In order to reduce this effect, the structural team decided to use
diagonal bracing opposing the direction of the torsional forces. This
configuration was used along the full span of the two Brunel trusses and it
successfully reduced the torsional phainomenon.
By
observing the presented figures in this section it is clearly evident that the
structure, even under maximum deformation tents to hold its designed cross
sectional shape. This was not the case in previous performed simulations
without the diagonal bracing. In the following Tables 2.14 and Figures 2.30 the
differences between diagonal bracing and no bracing models are presented.
Table 2.14 Differences in deformations.
Load Case
|
Diagonal Bracing
|
Max. deformation (mm)
|
Self-weight
|
No
|
259.9
|
Self-weight
|
Yes
|
50.5
|
Imposed load
|
No
|
225.6
|
Imposed load
|
Yes
|
39.3
|
By observing all the above data
the benefits of diagonal bracing system are clearly evident. Both models are
featuring the same cross section configuration and the deflected shapes are
presented using the same factor of deformations (100). The non-braced system
was unable to complete the analysis for the combination of loading conditions.
In this situation the team identified two possible solutions: Solution 1:
Increasing the diameter and/or the cross sectional area of the individual
member(s), Solution 2: Using diagonal bracing along the Brunel trusses opposing
the torsional stresses. The structural team identified that solution 1 would be
un-economical and also greatly increase the self-weight of the structure, for
this reason solution 2 was selected to eradicate the problem.
After analysing the bracing system of the roof it was
following observations were made:
·
The side stability trusses are mainly in
compression.
·
The top cord central stability trusses are in
compression while the bottoms in tension.
·
The behaviour of Brunel trusses remains along
the same lines as it was discussed earlier.
·
The connections between the central and the side
stability trusses are in compression.
·
Negative moments at the y-axis can be observed
in post part of the roof structure apart from the members close to the
supports.
·
The location of changing between the negative
and positive moments defines the border lines of the deflected shape of the
structure.
·
The structure tends to deform inwards due to the
negative moments.
1.1.1.5
Roof supports loadings
After the initial roof analysis the team extracted the axial support
loads that are going to be applied to the main structural analysis of the
arena. As it was mentioned earlier the team assumed that only axial forces are
going to be transferred from the roof to the mainframe of the structure, this
was done to simplify the analysis and perform a basic stability check of the
whole structure.
Photos using Revit 2015 Student Edition:
