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AnOverviewofAnalysisandDesignofaSingle-LayerReticulatedInvertedMonkBowlDome

CONFERENCEPAPER·NOVEMBER2015

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NaveedAnwar

AsianInstituteofTechnology

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PraminNorachan

AsianInstituteofTechnology

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ThaungHtutAung

AsianInstituteofTechnology

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N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 1

An Overview of Analysis and Design of a Single-Layer Reticulated

Inverted Monk Bowl Dome

N. Anwar AIT Consulting, Asian Institute of Technology, Bangkok, Thailand, nanwar@ait.asia,

P. Norachan, AIT Consulting, Asian Institute of Technology, Bangkok, Thailand, pramin@ait.asia

P. Warnitchai, Asian Institute of Technology, Bangkok, Thailand, pennung.ait@gmail.com

T. Htut Aung,

AIT Consulting, Asian Institute of Technology, Bangkok, Thailand, thaunghtutaung@ait.asia

Abstract

This paper provides a broad overview of some of the key factors in the analysis and design of single-layer

reticulated domes to be considered by structural engineers interested in the field of steel space frame structures. The

geometry of the dome which is presented in the present paper is not conventional dome. The dome is “Inverted monk

bowl” in shape with the largest diameter at the quarter height. The dome is used as temple including a tall Buddha

statue inside. It is a single-layer latticed steel dome, resting on the reinforced concrete circular base structure. The

dome is approximately 65 m. in diameter at the base, while the diameter at mid-height is about 86 m. Staged

construction analysis was performed in order to evaluate the performance of the structural components under construction. In this study, wind loads acting on the dome were evaluated based on both conventional design guidelines

and wind tunnel test. The simultaneous pressure measurement on the 1:300 scale model of the dome in the wind tunnel

was conducted to determine the realistic wind pressure. Direct integration approach was employed to find the dynamic

responses of the dome under time-history wind pressures. The response spectrum analysis based on DBE level was

used for earthquake loading assignment. All load cases were combined as load combinations. Finally, the demand

over capacity (D/C) ratios of structural components such as the foundations, columns, beams and steel frames were

carried out to evaluate performances of the structural members. The paper discusses several interesting aspects of the

analysis, design and construction process including development of modular construction and steel modular

connection.

1. Introduction

The use of single-layer reticulated structures has recently increased due to their capacity to

cover large areas with variety of shapes, light weight and without intermediate support. The span

of reticulated domes have increased gradually in recent years. For example, the diameter of the

Formosa plastics storage facility dome in Taiwan is about 122 m. The diameter of the roof of the

Walkup Sky dome in Northern Arizona University is 153 m, and the diameter of Nagoya Dome,

which is supported on the frame column on stands is approximate 187 m [1].

Most of these domes are, however, 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. In this paper, the dome which is presented here is derived from the shape of an

inverted monk's bowl with the largest diameter at about quarter height. The form is neither purely

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 2

spherical nor parabolic, but rather a combination of several forms. The dome is almost no out-of-

plane stiffness available. As a result, the challenge is the main in-plane (primarily tension and

compression) force in the pipes that make up the dome surface. In addition, with the large are in

resisting wind load, it is also important to determine the global and local wind responses for the

overall stability of the structure and for controlling the out-of-plane response. These present a

challenge in terms of the determinations of proper response and designing for the appropriate

demand. An overview of analysis and design of the single-layer super reticulated steel domes with

a large span of 86 m used to cover a tall Buddha statue located in Saraburi, Thailand is presented

in this paper as shown in Figure 1.

Figure 1: Architectural rendering of the dome structure

2. Structural Design Criteria

Gravity load cases were evaluated based on the nonlinear staged construction analysis

including P-Delta effect. Wind loads acting on the dome were obtained from wind tunnel test and

also evaluated based on the Thai Standard for Calculation of Wind Loads and Responses of

Buildings DPT 1311−50 [2] and ASCE 7−10 [3]. Response spectrum for the design basic

earthquake (DBE) level based on Thai seismic calculation standard DPT 1302−52 [4] was

considered in determination of earthquake load. Finally, all load cases were combined as

appropriate load combinations for evaluating the performance of structural components according

to ACI 318−08 [5]. In addition, the structure is presently constructed up to the columns at the base,

while upper parts of the structure have not constructed yet. Thus, for each structural member, if

the demand forces exceeding their capacities, the member already constructed would be retrofitted,

while the member having not constructed yet would be re-designed.

2.1. Geometry of the structure

As shown in Figure 2, the diameter of the circular RC base structure supporting the steel

dome is 65 m., while the diameter at the middle of the steel dome is 86 m. The total height of the

whole structure is 40 m.

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 3

Figure 2: Overall dimension of the dome

2.2. Staged construction

Staged construction analysis was performed in order to evaluate the performance of the

structure components during construction. The structural components, shoring supports and

construction loads were added and removed following the actual construction sequences to capture

the demand forces under gravity load. The construction stages can be summarized in Table 1 and

Figure 3.

Table 1: The principal activities of construction sequence

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

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 4

1st Stage

2nd Stage

3rd Stage

3rd Stage (to be continued)

4th Stage

4th Stage (to be continued)

5th Stage

6th Stage

Figure 3: Principal activities of construction sequence

2.3. Wind loads

In this study, wind loads acting on the dome were evaluated based on design guidelines

and wind tunnel test.

2.3.1. Wind load based on design guidelines

In order to carry out the preliminary structural design, the structural performances of the

dome were checked against the wind loads obtained from design guidelines before obtaining the

wind pressure from the wind tunnel test. As shown in Figure 4, the coefficients of external wind

pressure for the top part of the steel dome were calculated based on DPT 1311−50 and 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 [6].

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 5

Figure 4: Wind external pressure based on ASCE 7-10

2.3.2. Wind load based on wind tunnel test

To obtain more accurate wind pressure acting on the dome structure, wind study of the

dome was performed by TU-AIT wind tunnel test as shown in Figure 5. A 1:300 scale pressure

model of the dome was made based on the architectural drawings, and the simultaneous pressure

measurement was conducted to determine the wind pressure. The model scale Reynold number of

the wind flow was approximately 1.6×105 and it was greater than the value of 1×105 for buildings

with circular cross-section mentioned in the AWES-QAM-1-2001 [7]. As a result, there was no

effect due to Reynold number. The surrounding area of dome structure was open terrain condition.

Thus, atmospheric boundary layer flow of open terrain condition was simulated in the wind tunnel

by arranging roughness elements and spires through trial and error process. 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, in this work, 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. Simulated mean wind

speed profile and turbulence intensity profile well matched with the wind guideline as shown in

Figure 6.

Figure 5: The 1:300 scaled model in TU-AIT boundary-layer wind tunnel

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 6

Figure 6: Mean wind speed and turbulence intensity

The wind-induced pressures were measured at 79 pressure tap locations on the dome

surface of the scaled model. The average pressure tap density was greater than 1 pressure tap per

200 m2 of building surface mentioned in AWES-QAM-1-2001. This means that the number of

pressure measurement taps which were used were adequate enough to capture the realistic wind

pressure. The scaled model exposed to approaching wind was rotated by direction basis for 36

directions at 10 degree intervals. In this study, 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 [8] for evaluation

of the dynamic responses. The sample time-history pressures at the different locations on the dome

surface are illustrated in Figure 7.

Figure 7: Pressure at the sampling points

0

50

100

150

200

0.0 0.5 1.0 1.5

HE

IGH

T (M

)

NORMALIZED MEAN WIND SPEED

MEAN WIND SPEED

open conditionOpen-terrainSuburbanUrban

0

50

100

150

200

0 0.2 0.4 0.6

HEI

GH

T (M

)

LONGITUDINAL TURBULENCE INTENSITY

T URBULENCE INTENSITY

OPEN CONDITION

OPEN TERRAIN

SUBURBAN

URBAN

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

2000

0 500 1000 1500 2000 2500 3000 3500

Win

d P

ress

ure

(N

/m2 )

Time (s)

Point A

Point B

Point C

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 7

2.4. 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). The DBE elastic response spectra is

illustrated in Figure 8.

Figure 8: Response spectra for DBE earthquake level

Figure 9: Three-dimensional finite element model

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 1 2 3 4 5 6

Spe

ctra

l Acc

ele

rati

on

, Sa

(g)

Period (s)

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 8

3. Finite Element Modelling

As shown in Figure 9, three-dimensional finite element model was created by using

SAP2000 V14.2.4 as analysis tool. For the RC circular base of the structure as shown in Figure

10(a), the foundation system was modelled by using frame elements, while soil springs which

represent piles were assigned below the foundation to include the behavior of soil structure

interaction during the analysis. The concrete rectangular pile with the cross-section area of 40×40

cm2 and the total length of 18 m was used in the construction. The pile was assumed purely end

bearing. Thus, the vertical spring stiffness obtained from the axial properties of the pile was used

with the approximate value of 204,000 KN/m, while the lateral supports were assumed to be fixed

in both directions. The RC columns and beams were modelled as linearly elastic members using

frame element, while the RC slabs were modelled as linearly elastic shell elements. For the steel

dome as shown in Figure 10(b), the steel circular pipes were modelled by using frame elements,

while the cladding areas were modelled by using shell elements with modification of stiffness in

order to transfer only loads to the surrounding steel pipes without contributing any stiffness.

(a) Reinforcement concrete structure (b) Single-layer reticulated steel dome

Figure 10: Structural components

4. Analysis Procedures

Gravity load case was run based on the nonlinear staged construction analysis including

P−Delta effect. Wind load cases were run for both linear static and linear time-history analyses.

Direct integration approach was employed to find the dynamic responses of the structure for the

linear time-history analysis. After trying different values of time-step size to be sure that the

solution was not too dependent on this parameter, the total time step of 27,201 and the time-step

size of 0.133 second were used to capture the wind loads acting on the structure within 1 hour. The

response spectrum analysis based on DBE level with R equal to 1 was used for earthquake loading

assignment. Finally, all load cases were combined as load combinations including both the critical

loading cases for compression-controlled and for tension-controlled actions.

5. Analysis results

This section discusses the structural performances of the dome under the gravity and lateral

loads. Global responses of the structure are presented as follows:

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 9

T1= 0.518s

T2= 0.517s

T3= 0.408 s

T4 = 0.337 s

T5 = 0.295 s

T6 = 0.295 s

T7 = 0.270 s

T8 = 0.270 s

Figure 11: First eight vibration modes

5.1. Modal analysis

Modal analysis was performed to determine the vibration modes of the structure under

dynamic forces as well as to understand the behavior of the structure. A combination of mass from

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 10

100% of dead load and superimposed dead load plus 25% of live load was considered in modal

analysis. Forty modes were considered to achieve more than 90% of the total participating mass

in each orthogonal direction. 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. After the fifth mode, it is found that

the steel dome structure starts to vibrate with the local vibration in various patterns. The modal

participation mass ratios and the modal deformation shapes are shown in Figure 11.

5.2. Base shear

Base shear resulting from different load cases are summarized in Figure 12. Elastic base

shear resulting from wind loads based on the design codes and wind tunnel test as well as that from

response spectrum analysis (RSA) at DBE earthquake 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. The base shear for both

directions are same due to symmetrical configuration of the structure. 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.

Figure 12: Comparison of base shear percentage at the ground

5.3. Deformations and displacements

The deformation shapes under wind pressure obtained from wind tunnel test at a time step

are illustrated in Figure 13. 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. In addition, the maximum

displacements obtained from service load combinations in the lateral and vertical directions are

shown in Figure 14. 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), while 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).

1,577 1,577

1,345 1,345

1,510 1,510

0

500

1,000

1,500

2,000

X Y

Ba

se S

he

ar

(kN

)

Along Direction

Wind (Design Codes)

Wind (Wind Tunnel)

RS-DBE

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 11

Figure 13: Deformation of the structure under wind obtained from the wind tunnel test

Figure 14: Maximum displacements under lateral and vertical loads

6. Design Review of Structural Members

According to the strength design approach based on ACI 318−08, the force demands (D)

were obtained from the load combinations including load factors, while the design strength of

structural components (C) were multiplied by strength reduction factors. 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.

6.1. Piles and foundation

Based on the 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.

6.2. Columns and beams

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

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 12

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.

The details of column jacketing is illustrated in Figure 15(a).

After checking the performances of beams based on the previous structural details, it found

that some beams at the roof level of the RC base structure were not able to resist the demand forces.

In order to increase the beam capacities, 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. The details of the revised RC ring beam is illustrated in

Figure 15(b).

(a) Details of RC jacketing column (b) Details of revised RC ring beam

Figure 15: Details of Column and Beam

Figure 16: Steel pipe section used for the dome structutre

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 13

6.3. Steel circular pipes

As illustrated in Figure 16, 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. Based on the results, 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.

Figure 17: Steel dome support

Figure 18: Steel circular joint with inner diaphragms

6.4. Steel dome supports and connection

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. The details of the pin-connected support is

shown in Figure 17. At the intersection of the pipes, steel circular joint was proposed in order to

make construction easy and convenient. As shown in Figure 18, the steel circular joint consists of

N. Anwar, P. Norachan, P. Warnitchai, and T. Htut Aung 14

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.

7. Conclusions

Based on the analysis, the overall performance of the global structure was generally

acceptable under gravity, wind and earthquake loads. The elastic base shear obtained from wind

design codes and from response spectrum analysis was higher than that obtained from wind tunnel

test. The maximum displacements under the gravity and lateral loads were also within the

acceptable limit. In addition, the design review of structural components were also carried out.

Both piles and foundations were safe to resist the demand forces. To increase the capacities of

columns, the column jacketing approach was proposed. All beams seemed to have sufficient

capacities to resist the demand forces after revision. For the steel structure, the steel circular pipes

had sufficient capacities to resist the demand forces. To avoid the stress concentration and

excessive moment at the supports under gravity and lateral loads, the pin-connected support was

presented to release the excessive demand forces at the supports. Moreover, steel circular joint was

proposed at the intersection of the pipes in order to make construction easy and convenient. Finally,

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.

8. Acknowledgements

This conference paper was made possible through the help and support from many staff

members of AIT Consulting, Asian Institute of Technology, Thailand.

9. References

[1] Anuj C., “Analysis and Design of Steel Dome using Software”, International Journal of Research in

Engineering and Technology; Vol. 3, No 3, 2014, pp. 2321-7308.

[2] DPT 1311−50, Thai Standard for Calculation of Wind Loads and Responses of Buildings, Department

of Public Works and Town & Country Planning, 2007.

[3] ASCE 7−10, Minimum Design Loads for Buildings and Other Structures, American Society of Civil

Engineers, Reston, VA, 2010.

[4] DPT 1302−52, Thai Standard for Design of Buildings Resisting Earthquakes, Department of Public

Works and Town & Country Planning, 2009. [5] ACI 318-08, Building Code Requirements for Structural Concrete (ACI 318−08) and Commentary.

American Concrete Institute: Farmington Hills, MI, 2008.

[6] Portela G., and Godoy L.A., “Wind Pressure and Bucking of Cylindrical Steel Tanks with a Dome

Roof”, Journal of Constructional Steel Research; Vol. 61, 2005, pp. 808-824. [7] AWES-QAM-1, Quality Assurance Manual for Wind-Engineering Studies of Buildings. Australasian

Wind Engineering Society, 2001.

[8] SAP2000, Version14, Linear and nonlinear static and dynamic analysis and design of three-dimensional structures. Computers and Structures Inc., Berkeley, CA, 2011.