Structural Design of Cable Stayed Truss of 2002 Chonju World Cup StadiumJong Soo Kim

P.E., President of CS Structural Engineers Inc., 413-4, Togok2-Dong, Seoul, KoreaTel : 82-2-574-2355, Fax : 82-2-578-8786, Web site : http://www.cs.co.kr, E-Mail : cs@cs.co.kr

1. INTRODUCTION2. STRUCTURAL PLAN3. STRUCTURAL ANALYSIS4. MEMBER DESIGN

ABSTRACT

Chonju stadium has 42,000 seats with 260mⅹ160m. All aspects are designed in accordance with FIFA standards. The roof of stadium covers 20,000㎡ that is 87.5% of Stadium area(FIFA requires 60% of Stadium area).

The roof structure is comprised of two major structural systems. One is the cable-stayed truss structure and the other is open-dome structure. A prismatic steel truss(inner ring truss) acts as primary support system to the roof, which is suspended at 28 positions around stadium by φ65.1~84.9 mm front stay cables. The 28 front and back stay cables are suspended by four 63.0m-high masts located at corner of stadium. The ring truss (inner ring) and the perimeter truss (outer ring) supported by A-shaped column make the roof behave as a dome. A system of steel rod bracing in the plane of the roof transfers stability and in-plane forces back to the A-shaped columns.

1. INTRODUCTION

Holding of 2002 World Cup Games gives both Korea and Japan the opportunity to build a lot of large-scaled stadia, and each of it is designed uniquely. The complicated analysis and design processes are applied in order to satisfy the roof-ratio suggested by FIFA. The structural system of Chonju Stadium has particular meaning (Fig. 1). To mention it in detail, the mast signifies the prayer for a peace and a year of plenty in the region, the tensioned cable means the kayakeum(a twelve sprung Korean harp) of Chonju and the arc of the roof presents a hapjoogsun(Korean traditional fan which can be folded). The detailed analyses and designs are performed based on the above concept so that the system of the roof is structurally reasonable and suitable for the construction and the maintenance.

Architectural Firm of this design is Pos-A.C. Seoul Korea. The Structural firm is C·S structural engineers Inc. associated with Pos-Midas Engineering Co. Ltd. in Seoul. The main contractor is Sung-Won Construction Co. Ltd. associated with Dong-Bu Construction Co. Ltd. and Ssang-Yong Construction Co. Ltd.

Figure 1. Chonju World Cup Stadium Figure 2. Plan of the roof structure

2. STRUCTURAL PLAN

2.1 Structural outline

Chonju stadium has about 42,000 seats and the roof surrounds 20,000m2. The roof is again divided into four roofs such as a fan shape and each part is bound with ring truss, branch beam and floor stay cable continued in the four corners as in shown Fig. 2.

The large mast is established by using the dead space in the four corners of the stand, and then roof truss is tensioned. Inside of the stadium can be efficient and free with the aid of these systems.

Because a cable can not resist compression stress, an initial tension stress remained at all cases of external force is introduced in the roof-suspending cables with the truss-like triangular shape. Geometric non-linearity of the cable members is carefully considered in the analysis phase.

To guarantee the stability of the roof structure, it is very important that the structure should behave as a diaphragm. To satisfy this requirement, round-sectioned tubes and tension rods are braced between the main trusses. The tension rods, however, can not resist compression stress like a cable. Initial tension stress is also applied to them.

Base parts of the mast are designed to have hinged joint in all directions in order not to transfer the excessive moments to the foundation structure. This is also advantageous in the construction phase. Details of this joint are elaborately determined so that the hinged joint would not be broken away by earthquake forces.

2.2 Structural Members

Structural members of this project are designed using domestic products as much as possible.

2.2.1 Welded sections and tubes

(1) Welded sections Table 2.1. Welded sections

Thick(mm) Sign Yield strength(fy)

~ 40 SM490 B (KS D 3515) 3.3 tonf/cm2

41 ~ 90 SM490 TMC (KS D 3515) 3.3 tonf/cm2

91 ~ SM490 B (KS D 3515) 3.0 tonf/cm2

(2) Steel tubes

SPS 490 (Fy=3.3tonf/cm2, KS D 3566)

The wire ropes used are selected in accordance with the ASTM A603-88, and an A-grade coating is assigned upon them. The minimum elastic modulus of the pre-stretched single rope of A-grade coating is 14,060kgf/mm2. Detailed properties of cables are shown in Table 2.2, and all of them can be offered by domestic producers.

Table 2.2 Detailed properties of the used cables Wire rope

cableconstructionNominal

Diameter(mm)Approx. CrossMetallic

Area (mm2)Minimum Breaking Load (metric tonf)

6×WS(36) + 7×7CFRC 65.1 2198 303.08×WS(36)

+(8×7+1×19)CFRC84.9 3963 529.895.3 4994 671.2100.8 5586 745.7

2.2.3 High-strength steel rods (roof brace)

High-strength steel rods are used as the tension members that are not too much long, and the strengths of rods are varied in two ways according to their use as shown in Table 2.3.

Table 2.3 Strength of rods Diameter Tension test Modulus of

(mm) elasticity(N/ mm2)

Tension strength(N/ mm2)

Yield strength(N/ mm2)

Elongation Percentage (%)

ROA (%)

19~146 min. 610 min. 460 min. 20 min. 45 min. 19×104 19~146 980 830 12 45 19×104

2.2.4 Sockets and Fittings

(1) Cable joints

On the cable joints and on the joints with complicated details, the material for sockets and fittings used for them is cast steel. It is selected according to the KSD4106, SCW550 or ASTM A148 80-50.

(2) Rod joints

Use same material as high-strength rod.

Figure 3. Suspension Figure 4. Arch

Figure 5. Weighted load on Main Truss

Figure 6. Valley Cable Truss

Figure 7. Lateral load on Main Truss Figure 8. Diaphragm

2.3 Structural system of the roof

The roof-suspending structure is composed of two primal structural concepts; One is the suspension system in which the cables suspend the ring truss, which in return, is connected to the main trusses. Another is the dome-like system composed of the perimeter truss and the ring truss. All anticipated forces during the life cycle of the structure can be resisted by two structural systems.

2.3.1 Gravity system

A primary concept is that gravity loads of the ring truss and the main trusses are resisted by tension forces of the cables, and these tension forces are transferred to the base through the mast (Fig. 3); The tension force in the front stay cable introduces compression to the branch beam, which provides additional stiffness to arch action of ring truss (Fig. 4). Gravity loads of the main trusses are resisted in part by the front stay cable assisted by the ring truss and the perimeter truss, and in part by the support of the A-shaped post (Fig. 5).

2.3.2 Lateral system

As stated above, diaphragm effect, which is provided first by the ring truss and the perimeter truss, is fortified by bracing rods between the main trusses (Fig. 8.). Wind load, however, produces not only the lateral force but also the up-lift force on the roof structure. Thus, the front guy is designed to resist this force by tension stress in cooperation with the ring truss and the sub-front guy cable below the main truss (Fig. 6 and Fig. 7).

3. Structural analysis

3.1 Introduction

FEM analysis of the structural model is performed mainly by the commercial program, MIDAS-GEN module. Because Chonju stadium has irregular shape, it is very difficult to ascertain the coordinates of the structure. Thus, the input of the nodal coordinates in FEM modeling is made by reading one of the resulting files from the 3-D CAD program. In this way, not only the consumed time during input of the nodal coordinates of the structural model is reduced but also the configurational difference between the real structure and the structural model is minimized.

A lot of FEM models are simulated to reflect the accurate configurations of each part of the structure ; A large-scaled model is analyzed to check the general behavior of the entire structure, and a string of small detailed model is analyzed to confirm safety of the structurally suspicious parts of the structure. The design of each structural member is performed after checking all of the results in the above simulations.

To express the dynamic modes shapes as accurately as possible, the model for a dynamic analysis is built separately modifying the model for a static analysis.

3.2 Design loads

In the design of the roof structure, the loads written bellow are included and each load is used for the combination.

3.2.1 Dead loads

The 20 percentage of the dead load, the weight of connection and weld of the roof, is added to themselves secondary. And the supplemental loads include purlin, finish, light, speaker and so on.

3.2.2 Live loads

The roof live loads of 60kgf/m2 are applied in accordance with the ANSI regulation hard accessing roof. As snow loads are smaller than live loads, snow loads are replaced by live loads in the load combination.

3.2.3 Wind loads

Chonju City comes under Exposure Category B, but Chonju stadium is included to C. It results from that the stadium is placed at the outside of Chonju City and its surroundings are farms. Consequently wind loads are used 150kg/㎡ in an upward and downward direction and the result by wind tunnel test is analyzed as another load cases.

3.2.4 Seismic loads

Analysis for Seismic design is divided into two parts.

(1) Equivalent static lateral force procedure

Static analysis is used for a regular structure. The system of Chonju stadium is different from the usual and only static analysis cannot be used for considering the structural characteristics. However, it is analyzed by considering the value equivalent to 10% of the dead load as seismic load in the schematic design, as it is difficult to assume the member of a roof structure through dynamic analysis. For the detail, dynamic analysis is done using the former results.

(2) Dynamic analysis

Dynamic analysis is executed for reflecting the dynamic features of the irregular structures. Response spectrum analysis is used for dynamic analysis.

The response for each mode is derived based on response spectrum analysis using design spectrum by each regulation. Then maximum response of the structure is computed by combining modes. For the combination of modes CQC (Complete Quadratic Combination) method is applied in this design.

3.2.5 Temperature loads

Temperature loads are based on meteorological observation datum. The value +20°C for a temperature rise and –30°C for a temperature fall are used. In the steel member of the roof exposed to the direct rays of the sun, the value +45°C is applied.

3.2.6 Pretension forces

The pretension forces in cable make the roof a active structural system forces. These forces are considered as extra loads since the pretension forces are acted as the loads in members except cables

3.3. Load combination

Load combination methods for member design by regulation are as follows.

3.3.1 Long-term loads

- Dead load + Live load + Pretension

3.3.2 Short-term loads

- Dead load + Live load + Wind load + Pretension

- Dead load + Live load + Seismic load + Pretension

- Dead load + Live load + Temperature load + Pretension

- Dead load + Wind load + Temperature load + Pretension

- Dead load + Seismic load + Temperature load + Pretension

- Dead load + Live load + Wind load + Temperature load + Pretension

- Dead load + Live load + Seismic load + Temperature load + Pretension

3.4 Analysis for cables

Since cables possess both material and geometrical nonlinear features, it is difficult to analyze the members by using usual static analysis method. The cable member applied in Chonju stadium is not a suspension cable but a stayed cable. Then it is possible to

analyze by substituting for linear members according to considering the former characteristics. Among the material nonlinear and the geometrical nonlinear, the problem about the geometrical nonlinear must be considered as extra analysis process, while deriving the uniformed modulus of elasticity from pre-stretching work (introduced in manufacturing cables) solves the problem about the material nonlinear. The procedure analyzed linearly by considering the nonlinear of the cables is as follows.

(1) Elasticity of the cables

The problem about the geometrical nonlinear means that the sag resulted from the self-weight of cable members transforms the effective modulus of elasticity of cables. Effective modulus of elasticity in sagging by the self-weight is as follows.

s

(1)

Where, : Effective modulus of elasticity of cables

: Regular modulus of elasticity of cables

: Self-weight per unit length of cables

: Horizontally projected length of cables

: Area of cables

: Member forces

In above form it is represented that effective modulus of elasticity is closely related with member forces in the cables.

After adjusting the length of the cables, sag and member forces by the self-weight take place in the cables. As the loads increase, member forces increase but degree of sag decreases. It means that modulus of elasticity is altered according to more or less of the loads. It will end in behaving nonlinearly.

(2) Analysis procedure

The structural analysis and design of the cables to consider nonlinear features can be obtained by the following procedure.

① Compute the effective modulus of elasticity (E90) to come under 90% of modulus of elasticity (E) of the cables

② Calculate the member forces (T) corresponding to E90 for each cable

③ Obtain the pretension force correspond to E90

④ Get Eeq resulted from step ③ for each cable

⑤ Analyze and design with the pretension force and Eeq obtained from step ③ and ④

3.5 Dynamic analysis

The model for dynamic analysis is varied with the analysis purpose: the model for checking the member of roof and a analyzing the lower part of the structure.

As stated above, a number of models are used for accurate analysis of the structural members assumed through the static analysis in the schematic design. All members of the roof are included in this model and it takes 24 hours to analyze including the dynamic analysis. Therefore, this model is constructed on a large scale.

To estimate the effects for the seismic load, the lower part of the structure is simplified for saving the run-time and analyzing efficiently. It is the simplified system that the area, mass, moment of inertia and torsional rigidity unite together truss elements. Also the propriety of the former analysis is checked with the result of complete model, which is the form using all truss elements in the roof.

In addition the efficiency of the Sub Front Guy is examined by the eigen analysis according to existence of members (Section 3.5.1). The shape of members is decided by analysis as the present shape of the Rear Guy.

(a) 2nd mode (b) 3rd mode (c) 4th mode Figure 9. Mode shape

3.6 Analysis considering the construction courses

The construction process affects the member forces directly. In particular the deviation of the member forces in the same member is getting worse according to construction in the complicated structure. Therefore, Chonju stadium is designed by structural analysis considered the construction process. Its accurate understanding is re-quired. The construction process is subdivided, and then the separated load patterns are applied to the design. The construction courses in each step are as follows.

Step 1: A preparatory stage to build the roof structure

First a temporary shore is installed in the lower end of a Ring Truss. The Jack down device is constructed on the top of the shore. The standard height to erect all the roof structure is determined by the upper level of this device.

Step 2: Installation of the roof truss

The roof truss must be set up rationally by the erection order. Main Truss, Ring Truss and Perimeter Truss are piled one on another. According to the term of work, the former things can be constructed at a time in several places.

Step 3: Installation of the mast

Since the establishment of the mast and branch beam is related with the stability of the whole roof, they must be supported by the temporary cables and members under the construction. Besides the roof brace to bind the roof truss is installed and the length for each is adjusted.

Step 4: Installation of the Front Stay

The upper cable in the front of the roof is constructed.

Step 5: Installation of the Rear Stay and Rear Guy

The cables in the backside of the roof are constructed.

Step 6: Adjust the length of the roof cable / Introduction of the pretension

The pretension is introduced to the roof cable. The whole-inducted pretension capacity is divided into several stages. The examination of excess and deficiency of inducted pretension is performed at the same time as compared with the standard amount in each stage.

Step 7: Jack down the temporary shore

After the appropriate jack-down height is confirmed, Jack down is gradually executed.

Step 8: Installation of the Front Guy

The lower cable in the front of the roof is constructed, and then the necessary pretension force is inducted.

Step 9: Completion of controlling the cable pretension

The last tensioning capacity of each cable is checked and the final stress and displacements are examined.

Step 10: Completion of erection

If the jack down device and temporary support are dismembered, the roof structure erection is completed.

4. MEMBER DESIGN

4.1 Truss design

Table 4.1 Truss member Classification Name Member Length(mm)

MainTruss MT1 ~ MT16

A φ318.5 × 6t ~ φ500.0 × 12t W : 1,200 ~ 2,400 H : 1,500 ~ 3,000 B φ267.4 × 6t ~ φ355.6 × 9t

C φ139.8 × 4t ~ φ216.3 × 7t D φ139.8 × 4t ~ φ267.4 × 9t

Ring Truss RT1~ RT17

A φ700.0 × 25t ~ φ700.0 × 35t W : 2,400 H : 3,000 B φ508.0 × 12t ~ φ508.0 × 16t

C φ267.4 × 6t D φ165.2 × 4.5t ~ φ216.3 × 8t

Perimeter Truss PT1~PT16

A φ355.6 × 9t ~ φ508.0 × 16t W : 1,200 H : 1,500 B φ318.5 × 6t ~ φ355.6 × 12t

C φ165.2 × 4.5t ~ φ216.3 × 8t D φ139.8 × 4t ~ φ165.2 × 7t

(a) Ring Truss (b) Main Truss & Perimeter Truss (c) Roof bracing Figure 11. Truss member and Roof bracing

All member of Truss in the roof structure are designed to use steel pipe. For the construction convenience each member is designed straight. The shapes of the main truss are all the same except cantilever parts from MT1 to MT 16 (Table 4.1).

4.2 Cable design

The design strength of cables is based on the load combination about the tension of cables specified in UBC(1994). The construction processes are under consideration in the design of cables. The results are listed in Table 4.2.

Table 4.2 Cable Design

CableName

NominalDia.(mm)

E90(t/cm2)

TE

(ton)T1

(ton)Tmax

(ton)Tmin

(ton)Tnor (ton)

Enor (t/cm2)

Tallo

(ton)Ratio

FSC1 65.1 1260 34 - 49.5 34.8 45.8 1336.9 303.0 0.16 FSC2 65.1 1260 29 - 66.5 29.3 49.9 1368.9 303.0 0.22 FSC3 84.9 1260 44 - 143.0 44.1 84.8 1379.2 416.4 0.34 FSC4 2×84.9 1260 72 - 283.6 76.9 142.1 1379.6 681.3 0.42 FSC5 2×84.9 1260 72 - 285.9 82.5 142.6 1379.8 681.3 0.42 FSC6 65.1 1260 24 - 73.8 26.6 46.2 1378.2 303.0 0.24 FSC7 65.1 1260 29 - 58.7 33.2 48.7 1368.0 303.0 0.19 RSC 6×100.8 1260 126 17001274.

4568.4824.7 1399.4 2388.

60.53

RGC 6×100.8 1260 222 17001667.5

738.11066.9

1398.6 2388.6

0.70

FGC1 84.9 1260 28 60 204.3 29.5 29.6 1284.4 416.4 0.49 FGC2 84.9 1260 28 60 165.7 28.8 28.8 1275.2 416.4 0.40 SSC1 65.1 1260 14 53 53.5 16.9 34.5 1389.1 303.0 0.18 SSC2 95.3 1260 32 172 177.4 118.8149.1 1398.4 487.1 0.36 SGC1 65.1 1260 13 53 71.5 18.5 50.8 1397.1 303.0 0.24 SGC2 95.3 1260 30 172 181.3 151.0171.2 1399.1 487.1 0.37 FRSC1 84.9 1260 30 88 45.6 31.9 41.0 1341.6 416.4 0.11 FRSC2 84.9 1260 30 88 45.6 31.9 41.0 1341.6 416.4 0.11 ※ 1) E90 : 90% of modulus of elasticity of the cables 2) Enor : Modulus of elasticity in Tnor 3) TE : Member force for E90

4) T1 : Pretension required for 90% of the laboratory elastic modulus of the

cables

5) Tmax : Maximum cable tension force (in case of the final considering

pretension)

6) Tmin : Minimum cable tension force (in case of the final considering

pretension) 7) Tnor : Cable tension force (in case of norminal operation condition)

8) Tallo : Allowable strength of the cables (Breaking strength × 0.5 : a short

term)

9) Ratio : Tmax / Tallo

4.3 Rod design

The Rods are used in the short tension members like the brace, which comprises the diaphragm of the roof. The standardized Rods by the domestic production are applied. The Steel Rods used as the brace of the roof are consisted of the members shown in Table 4.3.

Table 4.3 Steel Rod

Sign Nominal Diameter(mm) Pretension(ton)FBR3, FBR4 φ76 24

FBR7 φ64 24

FBR5 φ76 18FBR6 φ64 18

FBR1, FBR2, FBR8, FBR9 φ30 4

4.4 Mast design

The total length of the mast is 64m and the branch beam in height of 19.6m supports it laterally. The mast has a tapered section for the architectural requirement. The Mast is divided into seven parts in its design for the transport, the number of the stiffener, and the transformation of its thick. The diameter is 3000mm and the thickness is 20mm in the most convex part. It becomes the tapered section which has the diameter of 1000mm and 45mm-thick in the minimum diameter.

The mast supports the 60% of the total roof load. Therefore its behavior affects decisively overall stability of the structure. The cable and the branch beam prevent from the lateral buckling.

The combination of the concentrated load and moment is given to the mast of the tapered steel pipe. The elastic buckling load considering the tapered section, the inelastic buckling load considering material inelasticity and the stress combination to the moments are included in the design.

4.5 Post design

The form of the post member is like A shape, which supports the main truss and perimeter truss (Figure 13). The plate and the shear stud fix the anchor of the post. The steel plate of SM490 is used to pass the shear forces (Figure 14).

Figure 13. Elevation of Main Truss, Post

Figure 14. Detail of the Post Anchor

4.6 Design of the connected part

4.6.1 Branch joint of the pipe

The truss connection needs for the detailed design. Each connection is checked with the design standards for the steel pipe construction and the guide for construction (1997, The Architectural Institute of Korea).

Figure 15. Design of Pipe branch joint

Figure 16. Analysis and picture(the low of the mast)

4.6.2 Connection in the low of the mast

In this case, compression forces from the mast and tension forces from the cable are given to the member at the same time. This member transmits the resultant loads to the frame. Therefore these parts are checked with magnified analysis (Figure 16).

Design of Anyang City Gymnasium, Korea

▶ Introduction ▶ Shape▶ Analysis and structural system ▶ Material ▶ CONCLUSION ▶ REFERENCES

SUMMARY: The Anyang City gymnasium has 6000 seats for handball, basketball and volleyball. It is designed with a steel truss roof and columns. The roof trusses are covered with sandwich metal panel and the truss columns are exposed to the air. This article shows how the design of the roof and column effectively use the concept of the structure.Keywords: Lattice columns, Korea, metal sandwich panels, pin base connections, stadia roof, steel roof trusses.

Introduction

The gymnasium is located in Anyang City near Seoul, Korea (Fig. 1). The Architect is Hang-Lim Architects Inc., Seoul in association with Anderson & OH Inc., an architectural firm in Chicago, Illinois, USA. The structural consultant is C.S Structural Engineers INC., Seoul in association with Tylk, Gustafson and Associates, Inc., Chicago, Illinois. The contractor is Doosan Construction INC., Seoul. The construction period is from September 1997 to October 2000.

Shape

The shape is an elliptical roof supported with 12 trusses, the eaves height is GL+15.22m and the maximum height of roof truss is GL+24.33m (See Figs 2 and 3).The dimensions of the roof are 94.50m log and 72.00m transverse. The roof trusses consist of an inverted triangle pipe truss, 1.30m deep at the centre and 3.00m at the eaves end(see Figs 4 and 5).The supporting column is a triangle lattice column with a pin base (see Fig. 6).

Analysis and structural system

The dead load (DL), the live load (LL), the wind load (WX, WY), the snow load (SL) and the temperature load (TL) are considered for the analysis and combined for the worst case, as follows:

1. DL + LL2. 0.76 * (DL + WX)3. 0.75 * (DL + WY)4. 0.76 * (DL + SL)5. 0.75 * (DL + TL)

The portal shaped one-way trusses carry the roof loads to the lattice columns and foundations in the transverse direction of the ellipse roof. For horizontal stability, the bridging trusses are connected to each portal frame in the middle and the eaves truss are connected to each lattice column at the eave of the roof truss.

Material

The yield strength of pipe truss and lattice pipe column is 3300 Kg.f/cm2 and the strength of purlin and bridging pipe truss is 2400 Kg.f/cm2. The 28-day cylindrical compressive strength of the foundation concrete is 240 Kg.f/cm2.

CONCLUSION

The 12 portal truss frame whose lattice columns are exposed to the air are very sophisticated and very effective for supporting the roof. The total quantity of steel including the main frame and purlins is 71 Kg/m2. The bridging and eaves trusses act for the wind loads and the vertical loads effectively.

REFERENCES

1. The code of steel structures, The Architectural Institute of Korea.2. Manual of steel construction, 10th edition, AISC.