An Overview of Analysis and Design of a Single-Layer Reticulated Inverted Monk Bowl Dome
1. 7th REGIONAL SYMPOSIUM ON
INFRASTRUCTURE DEVELOPMENT
November 5, 2015
Department of Civil Engineering, Kasetsart University, Bangkok, Thailand
An Overview of Analysis and Design of
a Single-Layer Reticulated Inverted
Monk Bowl Dome
Naveed Anwar, Pramin Norachan,
Pennung Warnitchai, Thaung Htut Aung
Dr. Pramin Norachan
Manager, Structural Engineering Unit,
AIT Consulting
9. 9
THE CHALLENGES
• The structural form of the dome is not the most efficient
– Not spherical, not parabolic, but a combination
• The sub structure was already constructed by the time we
were engaged
– The foundations
– The ring columns
• The height is governed by the height of the Buddha
statue, already under construction
• The client had already purchased tones steel pipes of
267.4 dia mm (10 inch) of 4.5 mm thickness
10.
11. 11
INTRODUCTION
Walkup Sky dome:
Northern Arizona University, 502 ft (153 m)
Nagoya Dome:
Nagoya, Japan, 614 ft (187 m)
Most of these domes are conventional and semi spherical forms with large
diameter at the base.
Such forms mostly produce consistent in-plane shell responses and radial tension
at the base.
12. 12
STRUCTURAL GEOMETRY
• The dome is derived from the shape of an inverted monk's bowl with the largest
diameter at about quarter height.
• The form is neither purely spherical nor parabolic, but rather a combination of
several forms.
• This presents a challenge in terms of the determinations of proper response and
designing for the appropriate demand.
13. 13
STRUCTURAL DESIGN CRITERIA
Load Cases Descriptions
Gravity - Consideration of Staged Construction
Wind - The Thai wind design guideline, DPT 1311−50 and ASCE 7−10
- Wind tunnel test
Earthquake - The Thai seismic design guideline, DPT 1302-52
• Finally, all load cases were combined as appropriate load combinations
including both of the critical loading cases for compression-controlled and
tension-controlled actions according to ACI 318 and AISC/ASD.
• The demand over capacity (D/C) ratios of structural components such as the
foundations, columns, beams and steel frames were carried out to evaluate
structural performance of members.
14. 14
FINITE ELEMENT MODELING
RC base structure
Steel dome structure
• The structure was already completed up to columns.
• The RC columns and beams were modelled as linearly
elastic members using frame element.
• The RC slabs were modelled as linearly elastic shell
elements.
• The steel circular pipes were modelled by using frame
elements.
• The cladding areas were modelled by using shell
elements with modification of stiffness in order to
transfer only loads without contributing any stiffness.
15. 15
STAGED CONSTRUCTION
1st Stage 2nd Stage 3rd Stage 3rd Stage (to be continued)
4th Stage 4th Stage (to be continued) 5th Stage 6th Stage
Stages Construction Activities
1 Build RC circular base structure including piles, foundations, columns, beams, and slabs
2 Construct the bottom part of the super steel dome supported by using steel frame shoring
3 Install a set of steel cells until completing the first ring of the top part of the super steel dome
4 Repeat the stage 3 until fishing the top part of the super steel dome
5 Remove the steel frame shoring from the bottom part of the super steel dome
6 Install cladding throughout the super steel dome
16. 16
WIND LOADS
Wind load based on design guidelines
• The structural performances of the dome were firstly checked against the wind loads
obtained from design guidelines before obtaining the wind pressure from the wind tunnel
test.
• The coefficients of external wind pressure for the top part of the steel dome were calculated
based on ASCE 7−10, while those for the bottom part of the dome were obtained from a
research on wind pressure and buckling of cylindrical steel tank.
2
50 25 /
1.0F
V m s
T
17. 17
WIND LOADS
Wind load based on wind tunnel test
To obtain more accurate wind pressure acting
on the dome structure, wind study of the dome
structure was performed by TU-AIT wind tunnel
test.
18. 18
WIND LOADS
• A 1:300 scaled model of the dome was made based on the architectural drawings, and
the simultaneous pressure measurement technique was applied in this wind load
study.
• According to the DPT 1311-50, hourly mean wind speed at the reference height of 10
m is 25 m/s for 50 years return period (Zone 1). However, the hourly mean wind speed
was scaled up to 1,000 year return period with the value of 40.67 m/s (146 km/hr.) at
the height of 40 m.
Wind load based on wind tunnel test
19. 19
WIND LOADS
0
50
100
150
200
0.0 0.5 1.0 1.5
HEIGHT(M)
NORMALIZED MEAN WIND SPEED
MEAN WIND SPEED
open condition
Open-terrain
Suburban
Urban
0
50
100
150
200
0 0.1 0.2 0.3 0.4 0.5
HEIGHT(M)
LONGITUDINAL TURBULENCE INTENSITY
TURBULENCE INTENSITY
OPEN CONDITION
OPEN TERRAIN
SUBURBAN
URBAN
• Simulated mean wind speed profile and turbulence intensity profile well matched with
the wind guideline.
• The wind-induced pressures were measured at 79 pressure tap locations on the dome
surface of the scaled model.
Wind load based on wind tunnel test
20. 20
WIND LOADS
• The scaled model exposed to approaching wind was rotated by direction basis for 36
directions at 10 degree intervals.
• Due to symmetry of the dome geometry, the structural analysis was performed under one
direction of wind.
• The time-history pressure at 79 locations were scaled up and assigned to the finite element
model in SAP2000 for evaluation of the dynamic responses.
• The sample time-history pressures at the different locations on the dome surface are
illustrated in the figure.
Wind load based on wind tunnel test
21. 21
SEISMIC LOADS
• Earthquake load was obtained from the Thai
seismic calculation guideline DPT 1302−52.
• The response spectra at the design basis
earthquake level (DBE) for 475 year return
period (10% of probability of exceedance in 50
years) was used in this evaluation with the
importance factor (I=1.25) and the response
modification factor (R=1).
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 1 2 3 4 5 6
SpectralAcceleration,Sa(g)
Period (s)
Map of peak ground
acceleration (PGA), 2% of
probability of exceedance in 50
years
22.
23. 23
MODAL ANALYSIS
• The first two modes are pure translation in horizontal direction, respectively due to
symmetrical configuration of the structure as expected.
• The third mode is vertical vibration, while the fourth mode performs in twisting.
24. 24
MODAL ANALYSIS
• After the fifth mode, it is found that the steel dome structure starts to vibrate with the local
vibration in various patterns.
25. 25
BASE SHEAR
1,577 1,577
1,345 1,345
1,510 1,510
0
500
1,000
1,500
2,000
X Y
BaseShear(kN)
Along Direction
Wind (Design Codes)
Wind (Wind Tunnel)
RS-DBE
• Elastic base shear resulting from wind loads based on the design codes, wind tunnel test
and response spectrum analysis (RSA) at DBE level were compared.
• At the ground level, the computed elastic base shear from wind tunnel test is
approximately 5.7% (1,345/23,613) of the seismic weight (DL+0.25LL = 23,613 kN) in both
X and Y directions.
• It is also found that the elastic base shear obtained from wind tunnel test is slightly lower
than that obtained from wind design codes and from response spectrum.
(5.7%)
(6.7%) (6.4%)
26. 26
DEFORMATIONS AND DIAPLACEMENTS
• The deformation shapes under wind pressure obtained from wind tunnel test at a sample
time step are illustrated in the figure.
• As expected, the results shows that the upward deformation are observed at the top of
the dome due to the suction pressure at this region, while pushing pressure can be
observed at the surface that directly resist wind load.
Deformation of the structure under wind obtained from the wind tunnel test
Suction
Pushing
29. 29
DEFORMATIONS AND DIAPLACEMENTS
• It is found that the maximum lateral displacements is approximate 3.6 cm which is less
than the limit 20 cm (H/200 = 40 × 100/200).
• The maximum vertical displacements at the top of the dome is about 6.1 cm which is
within the limit 17.9 cm (L/480 = 86 × 100/480).
Maximum displacements under lateral and vertical loads
30. 30
PILES AND FOUNDATIONS
• Based on the service load combinations including both the critical loading cases for
compression-controlled and for tension-controlled actions, the maximum and minimum
axial compression forces over pile capacity (D/C) ratios were 0.67 and 0.12, respectively.
• It means that there is no tension occurring in piles. Moreover, the foundation is also safe
to resist the demand forces for both bending moment and shear with the demand over
capacity (D/C) ratio of 0.94 and 0.88 respectively.
31. 31
COLUMNS
• As mentioned in the section of structural design
criteria, the RC columns at the base of the structure
were presently competed, while upper parts of the
structure have not constructed yet.
• The column PMM interaction demands of the
original columns exceeded their capacities limit
with the demand over capacity (D/C) ratio of 1.02
and 1.19, respectively, while the axial and shear
forces are less than their capacities.
• In order to increase the capacities of columns, the
column jacketing approach was proposed.
• After revising the original columns, the maximum
column PMM D/C ratio of the jacketing columns
were less than 1.0. The other demand over capacity
(D/C) ratios of column were also reduced due to
increment of column dimensions and additional
reinforcements.
32. 32
COLUMN DETAILS AT FOUNDATION
0.700.15 0.15
2.70
0.70
0.400.100.10
Elevation
Plan
33. 33
RING BEAMS
Based on the previous structural details, some beams at the roof level of the RC base
structure were not able to resist the demand forces. Thus, these beams were revised by
increasing the amount of reinforcement for both longitudinal and transverse reinforcements.
Moreover, the ring beam which is the main structural component supporting the steel dome
structure was also revised to increase its capacities for both flexure and shear.
34. 34
STEEL CIRCULAR PIPES
• The 267.4 mm (10 inch) steel circular pipes with thickness 4.5 and 6.0 mm were used to be
the primary components of the single-layer steel dome structure.
• The performances of these steel members, such as PMM interaction, axial tension, axial
compression, moment and shear were evaluated against demand forces.
• The member PMM demand over capacity D/C ratio provided the highest value of 0.61
among the other D/C ratios.
• Thus, the steel circular pipes with these sections have sufficient capacities to resist the
demand forces.
35. 35
STEEL DOME SUPPORTS
To avoid the stress concentration and excessive moment at the supports between the steel
dome structure and the ring beam under gravity and lateral loads, the pin-connected
support was presented to release the excessive demand forces.
36. 36
STEEL DOME CONNECTIONS
• At the intersection of the pipes, steel circular joint was proposed in order to make
construction easy and convenient.
• The steel circular joint consists of steel ring plate, inner diaphragm and cover plate. For
building this joint, the first part using three steel pipes are connected with the circular
steel ring and inner diaphragms by welding, while the second part is combined by
welding the other three steel pipes with steel cover plate.
• Finally, both parts are assembled by using bolts.
38. 38
CONCLUSIONS
• A structural system was developed and optimized to fit the tight
constraints of form, existing sub-structure and available materials.
• Wind pressure time histories obtained from wind tunnel test were
applied to determine local wind induced response.
• Construction sequences were carried out to reduce the need for
formwork and shoring.
• Minor retrofitting of columns was needed to accommodate the lateral
loads.
• After revising details of the some structural components, the overall
performances of the structure were improved in terms of global
structural response as well as local member performances under gravity
and lateral loadings.
