VIRTUAL OUTRIGGERS IN TALL BUILDINGS

Andrew J. Horton

ABSTRACT: As stated by Nair (1998) the conventional outrigger concept is in widespread use today in the design of tall buildings. In this concept, outrigger trusses (or, occasionally, girders) extend from a lateral load-resisting core to columns at the exterior of the building (see Stafford Smith and Coull 1991). It is, in its simplest form, a one-stage, 2-D (planar) concept in the vertical plane. The core may consist of either shear walls or braced frames. Conventional outrigger systems can lead to very efficient use of structural materials by mobilizing the axial strength and stiffness of exterior columns to resist part of the overturning moment produced by lateral loading. There are, however, some important space-planning limitations and certain structural complications associated with the use of conventional outriggers in tall buildings. A variation on the conventional outrigger concept is the offset outrigger concept and associated alternative offset outrigger concept (see Stafford Smith, Cruvellier, Nollet & Mahyari 1996). These are, in their simplest forms, two-stage, 2-D concepts, with the first stage in the horizontal plane and the second in the vertical plane. Offset and alternative offset outriggers can overcome or circumvent many of the problems associated with conventional outriggers. The alternative offset outrigger concept was “re-branded” by Nair (1998) as the “virtual outrigger concept” with respect to the use of belt trusses and belt walls as alternative offset outrigger elements. This was again a two-stage, 2-D concept, first in the horizontal plane and then in the vertical plane. He did however introduce a more specialized development of the alternative offset outrigger concept – the design philosophy of which the present author considers to be a more fitting definition of the virtual outrigger concept – in the use of basement walls as virtual outriggers for tall buildings. This is first a 2-D concept in the horizontal plane (via floor diaphragms) and then a 3-D concept in the vertical plane (transferring the resultant loadings to the basement end walls and their foundation systems – through their connection to the basement side walls – as well as to the basement side walls and their foundation systems). The application of Nair’s virtual outrigger concept for basement walls, as described above, is applied to continuous, perimeter belt trusses or belt walls at outrigger levels in this paper. KEY WORDS: conventional outrigger concept; outrigger trusses; offset outrigger concept;

alternative offset outrigger concept; belt trusses; belt walls; virtual outrigger concept 1. BACKGROUND & INTRODUCTION According to Stafford Smith et al (1996), at the time of writing their paper introducing the offset outrigger and alternative offset outrigger concept, the conventional outrigger concept had already been in use in the design of tall buildings for 30 years. The present author investigated the 10 tallest skyscrapers either completed or expected to be completed in 2010 and discovered that the 7 tallest, along with the 10th tallest, all incorporate the conventional outrigger concept as an integral part of their design, Table 1. The 8th tallest, Willis Tower (formerly Sears Tower) was completed in 1973 and utilized a bundled tube system of construction stepping from 9 bundles at the base to 2 bundles at the top, Figure 1.

The 9th tallest, Guangzhou West Tower (still under construction) is utilizing a twin tube system of construction with the outer tube (perimeter) being comprised of a diagonal grid (diagrid) of 1600 mm diameter concrete filled tubes with ring beams linked back to the inner tube (core) with tie beams, Figure 2.

Table 1: Usage of Conventional Outrigger Concept in Ten Tallest Skyscrapers

# Building City Country Height

(m)

Floors Completed # of

Outrigger

Levels

1 Burj Khalifa Dubai UAE 828 160 2010 5 2 Taipei 101 Taipei Taiwan (ROC) 509 101 2004 11 3 Shanghai World Financial Centre Shanghai China (PRC) 492 101 2008 8 4 International Commerce Centre Kowloon Hong Kong 483 118 2010

(Expected) 4

5 Petronas Tower 1 Kuala Lumpur

Malaysia 452 88 1998 1

6 Petronas Tower 2 Kuala Lumpur

Malaysia 452 88 1998 1

7 Nanjing Greenland Financial Centre Nanjing China (PRC) 450 89 2010 (Expected)

3

8 Willis Tower (formerly Sears Tower)

Chicago USA 442 108 1973 0

9 Guangzhou West Tower Guangzhou China (PRC) 440 103 2010 (Expected)

0

10 Trump International Hotel and Tower Chicago USA 423 96 2010 3

Figure 1: Willis Tower, Chicago, USA

Figure 2: Guangzhou West Tower,

Guangzhou, China

The present author also conducted an investigation to ascertain the usage of the offset outrigger, alternative offset outrigger and virtual outrigger concepts in approved or completed tall buildings to date, Table 2.

Table 2: Usage of Offset, Alternative Offset or Virtual Outrigger Concept in

Approved or Completed Tall Buildings

# Building City Country Height

(m)

Floors Approved /

Completed

# of Outrigger Levels

1 Dubai Tower Doha

Doha Qatar 438 90 Approved / Partially Completed /

On Hold

3 (1 Conventional; 2

Mixed Conventional / Alternative Offset)

2 Plaza Rakyat Office Tower

Kuala Lumpur

Malaysia 382 79 Approved / Partially Completed /

On Hold

3 (1 Conventional; 2

Virtual) 3 Aston

Apartments Residential

Tower

Sydney Australia 90 30 1998 2 (1 Alternative Offset; 1

Mixed Offset/Alternative Offset)

A relative dearth of information is available in the literature regarding the offset, alternative offset and virtual outrigger concepts compared to a relative wealth of information regarding the conventional outrigger concept. The following discussion, after laying the ground work for an understanding of the conventional, offset and alternative offset outrigger concepts, seeks to elaborate further on the use of belt trusses and belt walls, as virtual outriggers in tall buildings. 2. DISCUSSION

2.1 Conventional Outrigger Concept

2.1.1 Explanation Stafford Smith et al (1996) stated that up until that point in time, the outrigger concept, speaking of the conventional outrigger system, had been governed mainly by a planar conceptualization of the interactions between the core walls, the outrigger arms and the exterior columns. Summarizing the functioning of this system, in its simplest form, they stated, that when lateral loading acts along the plane of the outrigger bent, the bending of the core rotates the stiff outrigger arms that cantilever from it, inducing tension in the upwind column and compression in the downwind column. These column forces, acting at the extremities of the outrigger arms, form a couple that restrains the bending and deflection of the core, Figure 3 (taken from Stafford Smith and Coull 1991). Stafford Smith and Coull (1991) stated that in addition to those columns located at the ends of the outriggers, it is usual to also mobilize other peripheral columns to assist in restraining the outriggers. This is achieved by including a deep spandrel girder, or “belt” truss, around the structure at the levels of the outriggers, hence the name, “belt-braced structure”, Figure 4. The present author also makes use of this technique in § 2.3.1, § 2.3.3 and Appendix A of this paper.

Figure 3 (a): Outrigger Structure Displaced under Lateral Loading,

(b): Resultant Deflections and (c): Resultant Core Moments.

Figure 4: Conventional Outrigger Structure with Belt Girders

The large, often two-storey, depths of the outrigger and perimeter trusses make it desirable to locate them within the plant levels of the building.

Stafford Smith and Coull (1991) further stated that the degree to which the perimeter columns of an outrigger structure behave compositely with the core depends on the number of levels of outriggers and their stiffness. Multilevel outrigger structures show a considerable increase in their effective moment of resistance over single level outrigger structures. Each additional level of outriggers increases the lateral stiffness, but by a smaller amount than the previous additional level with four or five levels appearing to be the economic limit for a tall building. They found that in any outrigger system it is, perhaps unexpectedly, structurally inefficient to locate an outrigger level at the top of the building and that this should only be undertaken when dictated by other constraints, e.g. a plant floor needing to be located at the top of the building. By making the necessary simplifying assumptions, i.e. the structure is linearly elastic, only axial forces are induced in the columns, the outriggers are rigidly attached to the core, the core is rigidly attached to the foundation, the sectional properties of the core, columns and outriggers are uniform throughout their height and expressing the applied lateral load as a uniformly distributed horizontal load over the full height of the building, Stafford Smith and Coull (1991) used established structural theory, i.e. the moment area method, the moment equation for a vertical cantilever, the deflection equation for a vertical cantilever and various axial and flexural stiffness representations, to develop charts expressing the optimum location of outriggers, for an n-outrigger system (where 1 < n < 4), to minimise top of structure lateral deflections. Generally, by making a further (hypothetical) simplifying assumption, i.e. that the outriggers are flexurally rigid, they found, for the optimum performance of an n-outrigger structure, that the outriggers should be placed at the 1/(n+1), 2/(n+1), up to the n/(n+1) height locations, i.e. for a one-outrigger structure at approximately half-height, for a two-outrigger structure at approximately one-third and two-thirds heights, for a three-outrigger structure at approximately one-quarter, one-half and three-quarter heights, and so on. The present author comments that these findings also hold true for the subsequently discussed offset, alternative offset and virtual outrigger systems under similar simplifying assumptions. It should be noted that the optimum outrigger arrangement for the maximum reduction in drift was not found to simultaneously cause the maximum reduction in the core base moment. For this, the outriggers would have to be lowered toward the base. It was suggested in cases where drift control is not critical, that the design emphasis could change to controlling the core moments by lowering the heights of the outrigger levels from the base until the drift limitations are just satisfied but noted, due to other constraints, that this might only be achievable in reality. Wu and Li (2003) followed up on the above optimum outrigger arrangement work by Stafford Smith and Coull (1991) for the case where the applied lateral load is modelled as both a triangular and uniformly distributed horizontal load over the full height of the building. They found when an outrigger-braced structure is subjected to horizontal triangular loads, the optimum locations of outriggers are 4 – 5% higher than those of the structure subjected to horizontal uniform load. In lieu of any further investigation their findings could be used to give a conservative upper bound for optimum outrigger positions under horizontal trapezoidal loading.

While the conventional outrigger system is very effective in increasing the structures flexural stiffness, it does not increase its resistance to shear, which has to be carried mainly by the core (Stafford Smith and Coull 1991). The present author comments that this principle also holds true for the subsequently discussed offset, alternative offset and virtual outrigger systems. 2.1.2 Examples The 492 m height, 101 floors, Shanghai World Financial Centre, designed by Leslie E. Robertson Associates, completed in 2008 in China, has 8 conventional outrigger levels, Figure 5.

Figures 5 (a) and (b): Model showing the

Building’s Mega-Structure System of

Mega-Columns, Diagonals and Belt

Trusses along with Concrete Core

Walls and Outrigger Trusses

Figure 5 (c): Tie Columns, Diagonals,

Belt Trusses and Outrigger Trusses

Connected to the Concrete

Shear Walls of the

Service Core

The 450 m height, 89 floors, Nanjing Greenland Financial Centre, designed by Skidmore, Owings and Merrill (SOM), presently under construction in China, has 3 conventional outrigger levels, Figure 6.

Figure 6 (a): Outrigger and Belt Truss Configuration, (b): Typical Outrigger Truss –

Continuous through Core and (c): Photograph of Outrigger Truss Construction

The 360 m height, 93 floors, Federation Tower, Tower A, designed by Thornton Tomasetti, presently under construction in Moscow, Russia, has 2 conventional outrigger levels, Figure 7.

Figure 7 (a): Model of

61st Floor Outrigger

Level

Figure 7 (b): 33rd

Floor Outrigger

Trusses linking the Belt Trusses

(Left) to the Central Core

2.2 Offset and Alternative Offset Outrigger Concepts

2.2.1 Explanation Stafford Smith et al (1996) proposed that the outriggers may be located elsewhere than in the planes of the core walls, while retaining all the advantages and mitigating some of the disadvantages of the conventional outrigger system. They proposed to move, or offset, the outrigger arms horizontally within the floor plan, away from the central elevator core, Figure 8. Detailed structural analysis conducted on buildings incorporating such laterally shifted outriggers indicated that, compared to the conventional arrangement – Figure 8 (b) – the offset outrigger concept – Figure 8 (c) – as defined above and compared with the conventional outrigger system, was virtually 100% effective in reducing the building deflections and the core bending stresses resulting from centred wind or earthquake loading (Stafford Smith et al 1996). Moreover, for typical floor slab plan dimensions and thicknesses, they discovered that there was little reduction in the effectiveness of the offset outrigger as it is shifted further from the central core – becoming the alternative offset concept, as represented in Figure 8 (d). For the offset outrigger system to work, it is essential that the floor slabs be effectively rigid and strong enough in their planes to transfer the horizontal plane shears between the outrigger arm and the core. For typical residential and office floor layouts, the slabs will be thick enough and the building dimensions will be sufficient to ensure that this condition is easily met (Stafford Smith et al 1996).

They further noted that it is also necessary for the outrigger arm to be as rigid as possible in flexure across the width of the building (similar to the stiffness requirement for the conventional outrigger). In both cases – offset and alternative offset – there are many ways to achieve adequate stiffness, be it with diagonal bracing (belt trusses) or reinforced concrete in-filled panels (belt walls). Just as in the case of the conventional outrigger system, the outrigger arm in the offset system may also be spread vertically over several stories in order to reduce the obstruction at any individual floor level. Stafford Smith et al (1996) also alluded to studies indicating potentially significant structural benefits arising from the offset outrigger system in terms of the building’s torsional response to off centre loading. The maximum benefit was reported to be obtained by offsetting the outriggers on plan as far as possible from the centre of rotation of the building, i.e. to the perimeter. With the addition of a full-depth of outrigger level, continuous, perimeter belt truss or belt walls to the two remaining horizontal sides of Figure 8 (d) the alternative offset outrigger concept would match the definition provided by the present author of the virtual outrigger concept stated in § 2.3.1 of this paper.

Figure 8 (a): Typical Floor Plan

Figure 8 (b): Conventional Outrigger

Plan

Figure 8 (c): Offset Outrigger Plan

Figure 8 (d): Alternative Offset Outrigger

Plan

In summary the case was made by Stafford Smith et al (1996) that, in terms of structural efficiency, nothing is lost by laterally offsetting outriggers from the plane of the central core walls and that a considerable advantage of this new configuration is greater flexibility of the building floor plan to met functional and aesthetic design requirements.

The relevant load transfer mechanism for the alternative offset outrigger concept shown below in Figure 9 is fully explained in Stafford Smith et al (1996).

Figure 9 (a): Axonometric View

Figure 9 (b): Relative Displacements of

Slabs considering only the Core Wall

Figure 9 (c): Outrigger subject to

Couple from Slabs

Figure 9 (d): Restraining Couple from

Perimeter Columns

Figure 9 (e): Restraining Couple from Perimeter Columns

back through Slabs to Core

2.2.2 Example The 90m height, 30 floors, Aston Apartments Residential Tower, designed by Connell Wagner, completed in 1998 in Sydney, Australia, has 1 alternative offset outrigger level (roof) and 1 mixed offset and alternative offset outrigger level (mid-height), Figure 10 (taken from Dean, Martin, Emery and Chancellor 2001).

The reinforced concrete frame structure with central lift core – quoted as being the first “offset outrigger” building in Australasia – is only 13m wide in the North-South direction resulting in a slender height-to-base ratio of 7:1. The “offset outriggers” – comprising of two storey high shear walls 200 mm thick – significantly reduce building deflections and core bending moments. Core wall thicknesses were able to be limited to 200 mm even in the lower levels (Dean et al 2001).

Figure 10: Frame Perspective – Aston Apartments Residential Tower

2.3 Virtual Outrigger Concept

2.3.1 Explanation Following on from Stafford Smith et al (1996), Nair (1998) coined the phrase “virtual” outriggers to refer to a subset of offset outriggers, previously termed alternative offset outriggers, which were to be located only at the perimeter of the building and which were not to be directly attached to the core, stating that belt trusses and belt walls were well suited for use as “virtual” outriggers. A close investigation, however, of Nair (1998) reveals that, with respect to the belt trusses (or belt walls) at outrigger level, Nair was not considering that the belt trusses (or belt walls) in the plane perpendicular to the action of lateral load could also be mobilised to distribute the resultant tensile and compressive “stresses”, refer to Figure 12 below, to all of the perimeter columns, refer also to § 2.3.3 and Appendix A.

Nair (1998) also used the phrase to refer to a “more specialized development” of the alternative offset outrigger concept – the design philosophy of which the present author considers to be a more fitting definition of the virtual outrigger concept – in the use of basement walls as “virtual” outriggers for tall buildings. This is first a 2-D concept in the horizontal plane (via floor diaphragms) and then a 3-D concept in the vertical plane (transferring the resultant loadings to the basement end walls and their foundation systems – through their connection to the basement side walls – as well as to the basement side walls and their foundation systems), Figure 11 (taken from Nair 1998).

Figure 11. Force Transfer using Basement as Virtual Outrigger System

For the purpose of this paper, the present author would like to define the virtual outrigger concept as being where belt trusses or belt walls are provided, full depth, continuously, around the perimeter of an outrigger level – in a square or appropriately proportioned rectangular on plan building – and act, together with the top and bottom structural diaphragm of the outrigger level, to transfer substantially the same magnitude of overturning moment from the core to the perimeter columns – engaging axially all of the perimeter columns – as could realistically be achieved via the use of conventional outriggers. Leonard (2007), speaking with reference to framed tube structures but equally applicable to virtual outrigger structures, stated that shear lag effects can be reduced by employing additional structural systems which increase the stiffness of the overall structural system, Figure 12. He further stated that belt trusses effectively increase the shear stiffness of framed tube structures by integrating all the columns in the same face of the building. He additionally stated that belt trusses can also be added at multiple levels of a framed tube system. He finally stated that one of the ideas similar to the belt truss system was the offset outrigger system proposed by Stafford Smith et al (1996) and Nair (1998).

Figure 12: Axial Stress Distribution in Box Structure:

(a) Without Shear Lag and (b) With Shear Lag

If the stiffness of the belt truss or belt wall system in the virtual outrigger concept defined by the present author can cause the axial loads on the “flange” perimeter columns to approach what is depicted in Figure 12 (a) above then the capability of the system would better any conventional outrigger system which did not have a belt truss or belt wall system sufficient to spread axial loads along the “flange” and rival any conventional outrigger system which did. 2.3.2 Example The 382 m height, 79 floors, Plaza Rakyat Office Tower, designed by SOM, construction commenced circa 1996, stalled due to the 1997 Asian Financial Crisis and presently still on hold in Kuala Lumpur, Malaysia, has 1 conventional outrigger level at roof height and two virtual outrigger levels, Figure 13. Further information is available in Baker, Brown and Sinn (1997).

Figure 13: Model of Plaza Rakyat Office Tower (taken from SOM)

2.3.3 Finite Element Model (FEM) Investigation A FEM was prepared for purpose of comparison with the results stated by Nair (1998) for his example “75-story steel framed office tower”. The present author noted that the chamfered corners in plan and light bracing in elevation adopted by Nair around these chamfered corners effectively inhibited the full potential of the virtual outrigger concept, as defined by the present author, from being realised. The FEM prepared removed the chamfers, placed “super-columns” at the corners and continued the belt truss bracing around the entire outrigger level. Apart from this modification the FEM compared “apples with apples” based on Nair’s provided information. With the above modification the present author discovered that the onerous and inhibitive measures proposed by Nair as being necessary to “match” the performance of a conventional outrigger system were no longer required. In summary, a 2-fold increase in outrigger diaphragm thicknesses (not a 10-fold increase in stiffness as proposed by Nair) coupled with a 16% increase in belt truss area (not 10-fold increase in stiffness as proposed by Nair) sufficed to enable the virtual outrigger system to perform within 4% of the lateral deflection capacity achieved by the conventional outrigger system. Concrete belt walls were also substituted for the steel belt trusses at outrigger levels to good effect in the FEM and an alternative reinforced concrete structure was also modelled with virtual versus conventional outrigger performance compared. The results of the FEM investigation are included in Appendix A. 3. SUMMARY & CONCLUSION

The virtual outrigger system, as defined by the present author, is found to be capable of providing comparable performance to the conventional outrigger system. The virtual outrigger system thus employed would eliminate the need to attach outrigger members to the core for square or appropriately proportioned rectangular on plan buildings. Additionally, when utilizing the virtual outrigger system, outrigger levels could be placed at optimum levels up the height of the building, as the virtual outrigger members, i.e. belt trusses or belt walls, are positioned on the perimeter of the building. Furthermore, the adoption of the virtual outrigger system, with its full depth, continuous, perimeter belt trusses or belt walls at outrigger levels would result in a reduction in potential “shear lag” type effects in the perimeter columns of the building. Finally, the virtual outrigger system would also dually offer the building enhanced torsional resistance and reduced susceptibility to the differential shortening effects encountered by the conventional outrigger system.

REFERENCES

Baker, W. F., Brown, C. D. and Sinn, R. C. (1997). Structural Analysis and Design of the World’s Tallest Reinforced Concrete Building. E & FN Spon. Multi-Purpose High-Rise Towers and Tall Buildings, 333–346. Dean, B., Martin, O., Emery, D. and Chancellor, P. (2001). Tall Building Design Innovations in Australia. Tall Buildings and Urban Habitat, Cities in the Third Millennium, 6

th World Congress of

the Council On Tall Buildings and Urban Habitat, Melbourne, 26 February to 2 March 2001. Planning and Architecture, 393–394. Leonard, J. (2007) Investigation of Shear Lag Effect in High-Rise Buildings with Diagrid Systems. Degree of Master of Engineering in Civil and Environmental Engineering. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology. Nair, R. Shankar (1998) Belt Trusses and Basements as “Virtual” Outriggers for Tall Buildings. American Institute of Steel Construction. Engineering Journal, Fourth Quarter, 140–146. Stafford Smith, B. and Coull, A. (1991) Tall Building Structures: Analysis and Design. John Wiley and

Sons, Inc. Chapter 14, Outrigger-Braced Structures, 355–371. Stafford Smith, B., Cruvellier, M., Nollet, M-J. and Mahyari, A. T. (1996) Offset Outrigger Concept for Tall Building Structures. Council on Tall Buildings and Urban Habitat. Tall Building Structures – A World View, 73–80. Wo J. R. and Li, Q. S. (2003) Structural Performance of Multi-Outrigger-Braced Tall Buildings. Published online in Wiley InterScience (www.interscience.wiley.com). DOI:10.1002/tal.219. The Structural Design of Tall and Special Buildings 12, 155–176.

ABOUT THE AUTHOR

Andrew J. Horton, BE(Hons), MIPENZ(Structural), CPEng, IntPE(NZ), Structural Design Manager, Hyder Consulting Middle East Ltd, Global Design Centre – Manila, Philippines. Email: andrew.horton@hyderconsulting.com.

ACKNOWLEDGEMENTS

Francis O. Macatingrao, B.S. C.E., Graduate Structural Engineer and Carlos Alfonso V. Fabie, B.S. C.E., Assistant Structural Engineer, Hyder Consulting Middle East Ltd, Global Design Centre – Manila, Philippines. Email: francis.macatingrao@hyderconsulting.com and carlos.fabie@hyderconsulting.com. Milan Petrovic, dipl.inž., Senior Structural Engineer, Hyder Consulting Middle East Ltd, Dubai, UAE. Email: milan.petrovic@hyderconsulting.com. Marie-José Nollet, ing., Ph.D., Département de génie de la construction, École de technologie supérieure, 1100, rue Notre-Dame ouest, Montréal, Qc, H3C 1K3, Canada. Email: marie-jose.nollet@etsmtl.ca.

APPENDIX A

STEEL FEM SUMMARY

Ratio of Lateral Displacement at Top for Outrigger Type i Versus

Lateral Displacement at Top without Outriggers (SLS Wind)

Type of Outrigger From Present FEM Analysis From Literature

(%) (%)

Conventional Outrigger 22.2 23.3

Belt Truss as Virtual Outrigger 25.7 34.2

Ratio of Σ Total Outrigger Moment Type i at Base Versus

Σ Total Moment at Base

Type of Outrigger From Present FEM Analysis

(%)

Conventional Outrigger 56.9

Belt Truss as Virtual Outrigger 52.0

As shown in the following table, in the Steel FEM Analysis an equivalent 100mm thick continuous perimeter concrete belt wall may be used to replace the above continuous perimeter steel belt truss system – holding everything else constant – to achieve the same lateral performance. Moreover, the performance of the structure may be further enhanced by thickening these concrete belt walls.

Using Concrete Belt Walls as Virtual Outriggers

Thickness Lateral Displacement at

Top due to SLS Wind (m)

Reduction in Lateral Displacement at Top compared with Steel Belt

Truss (%)

100mm 0.620 0.9

200mm 0.565 8.6

300mm 0.543 13.0

CONCRETE FEM SUMMARY

Type of Outrigger

Ratio of Lateral Displacement at Top for Outrigger Type i Versus

Lateral Displacement at Top without Outriggers (SLS Wind)

(%)

Conventional Outrigger 29.2

Belt Wall as Virtual Outrigger 27.2

Type of Outrigger

Ratio of Σ Total Outrigger Moment Type i at Base Versus

Σ Total Moment at Base

(%)

Conventional Outrigger 54.0

Belt Truss as Virtual Outrigger 52.0

MODELLING ASSUMPTIONS

1. The structural diaphragms were assumed to have no out of plane stiffness. 2. SLS Wind Combinations and Wind Loads were as per ASCE 7-05 code provisions.

ADDITIONAL FEM ANALYSIS Subsequent modifications to the steel belt truss system were performed in the Steel FEM in order to achieve the same lateral performance as the conventional outrigger system. This is summarized in the tables below. Before any modifications were made the following table shows the results:

Type of Outrigger

Lateral Displacement at Top due to SLS Wind

(m)

Without Outrigger 2.386

Conventional Outrigger 0.529

Virtual Outrigger 0.614

The ratio of virtual outrigger to conventional outrigger displacement is approx 16.1%. The following modifications were then made to the steel beam truss virtual outrigger system:

Modifications to Belt Truss System (Normal-Weight Concrete)

SLS Deflection (m)

Comparison to Performance of Conventional Outrigger

(% Difference)

1.6 x Increase in Outrigger Diaphragm Thicknesses 0.599 13.2

2.0 x Increase in Outrigger Diaphragm Thicknesses 0.592 11.9

Increase Bracing Size in Belt Trusses from W14x730 to W36x848 (Increase in Area by 15.8%) without Increasing

Outrigger Diaphragm Thicknesses 0.593 12.1

Combined 2.0 x Increase in Outrigger Diaphragm Thicknesses and Increase in Bracing Size from W14x730

to W36x848 0.552 4.3

The above table shows that an increase in outrigger diaphragm thicknesses alone has no significant effect on the lateral performance of the structure. An increase in bracing size alone, likewise exhibits similar behaviour. A combination of increased outrigger diaphragm thicknesses and bracing size are required in order to achieve a comparable lateral performance with the conventional outrigger system. However, this is not considered to be a cause for concern since the required structural system can be designed economically to meet the necessary demand.