machine design, Vol.3(2011) No 1, ISSN 1821-1259 pp. … IĆ, D, Metalne konstrukcije, Građevinski fakultet u Beogradu, Beograd, 1999. Title: Microsoft Word - 041-046.doc Author:

machine design, Vol.3(2011) No 1, ISSN 1821-1259 pp. 41-46

*Correspondence Author’s Address: University of Belgrade, Faculty of Mechanical Engineering, Kraljice Marije 16, 11120 Belgrade, Serbia, [email protected]

Research paper

REDESIGN OF THE TRIBUNE STRUCTURE IN THE BELGRADE ARENA HALL

Zoran PETKOVIĆ1, * - Srđan BOŠNJAK2 - Vlada GAŠIĆ3

1,2,3 University of Belgrade, Faculty of Mechanical Engineering, Belgrade, Serbia

Received (26.02.2011); Revised (19.03.2011); Accepted (28.03.2011) Abstract: Design flaws in the positioning of the tribune supporting structures inside the Belgrade Arena hall prevented adequate usage of internal logistic capabilities. This paper deals with a performed redesign of the tribune supporting structure which resolved the flaws and enabled full functionality of the hall while adhering to safety regulations. Besides FEA, the validation of the tribune structure redesign is also confirmed by a multi-year failure-free tribune usage after the reconstruction. Keywords: tribune structure, redesign, FEM 1. INTRODUCTION Soon after the installation of tribunes and their supports inside the Belgrade Arena hall, the situation showed flaws in the design of the outer/interior vehicle traffic demands. The demand to provide an unobstructed transport way gave rise to the problem of reconstructing the tribune support structure without any change in the capacity of the tribunes.

Fig.1. Belgrade Arena Hall: (a) exterior; (b) interior

(а)

(b)

Fig.2. North tribune: (a) reconstruction zones; (b) detail of zone A

Redesign is required for 2 zones of the south and north tribunes respectively, Fig. 2. Zone A represents the zone of the door which allows the traffic of trucks and zone B corresponds to the entrance of the warehouse door. This paper presents the technology and overview of the tribune reconstruction, as well as the tribune structure validation [1]. 2. THE STATE BEFORE RECONSTRUCTION

2.1. Zone A

Fig.3. Supports of the tribune sections in zone A

Zoran Petković, Srđan Bošnjak, Vlada Gašić: Redesign of the Tribune Structure in the Belgrade Arena Hall; Machine Design, Vol.3(2011) No 1, ISSN 1821-1259; pp. 41-46

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Tribune sections are laid on supports (TS), Fig. 3, consisting of 3 truss columns Fig. 4.

Fig.4. Columns of the TS Columns (C1, C2 and C3 in Fig. 4) consist of sections mounted on top of each other. Main elements of the truss frames are made of square tubes 50x50x4 mm, while diagonal elements are made of square tubes 30x30x3 mm. Proper nivelation of the columns is achieved by adjusting the foot plate, Fig. 5.

Fig.5. Foot plates of the segment basis

Fig.6. Position of the TS with respect to the door

It can be observed, Figs. 2(b), 3 and 6, that trucks can not pass through and reach the center of the hall because of the TS 2 position. In particular, the clearance of 2700 mm, Figs. 2(b) and 3, is not satisfactory for truck traffic. Tribune sections with seats are laid on columns C1 and C2, while sections with floorings are laid on column C3, Figs. 7 and 8. Seats for the audience are mounted on a wooden panel which is connected to the steel frame by bolts , Fig. 9.

Fig.7. Position of the different tribune sections

Fig.8. Structure of the tribune sections with seats 1 – Girder (100 x 40 x 3 mm); 2 –beam (160 x 50 x 3 mm)

(a) (b)

Fig.9. Tribune section with seats

(a) side view; (b) bottom view


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2.2. Zone B

Columns C2 and C3, Fig. 10, disable free opening of the warehouse door (height 3200 mm, width 2100 mm), which results in limited warehouse usage. The support structure of the tribunes corresponds to the structure in zone A. The basic difference between the mentioned structures is the smaller width (560 mm) of columns C1 and C2, Fig. 10 (b).

(a)

(b)

Fig.10. The supp. structure of tribune sections- zone B

3. THE REDESIGN TECHNOLOGY 3.1. Zone A

After disassembling all tribune sections, TS 2 is moved for 1130 mm toward TS 1, Figs. 3 and 11. This achieved a

clearance of 3200 mm which enables(allows) the traffic of trucks. The tribune structure section is reconstructed in such a way that, first, the left end beam is moved for 200 mm, Fig. 12 (a). Then, the square tubes 60x60x5 mm, 3000 mm in length, are welded to the bottom part of the girders, Fig. 12. The structure of the tribunes with flooring is reinforced in the same way, Fig. 13.

Fig.11. Dislocation of TS 2

(a)

(b)

Fig.12. Redesign of the seating tribune section structure

(a) dislocation of the left end beam; (b) side view


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Fig.13. Redesign of the tribune section with walkway seats structure

3.2. Zone B

After the joining of columns C1, C2 and C3, which is achieved over the square tubes, Fig. 14, the base segment as well as the following two segments of column C2 are removed, Fig. 15. These segments are then used to form a new structure C3, Fig. 16. By removing the 3 existing segments of the C3 columns, Fig. 3, the reattachment of the new structure provides an unobstructed opening of the door and entrance to the warehouse, Fig. 18.

Fig.14. Joining of columns

Fig.15. TS 4 side view after removal of C2 segments

Fig.16. The new built-in C3 structure

Fig.17. TS 4 side view after removal of C3 segments

Fig.18. TS 4 side view after reconstruction 4. FEM VALIDATION OF THE REDESIGNED

TRIBUNE SUPPORT(S) STRUCTURE The redesigned structure validations [2] are conducted using the Finite Element Method (FEM). The calculus


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and design check are all perfomed according to the recommendations given in [3-5] and the national regulatives. 4.1. Zone A

Discretization of the original and the redesigned structure, Figs. 19 and 20, is done with beam finite elements, Fig. 21. The maximum stress value in the redesigned structure (3.1 kN/cm2) is lower compared to the value of the original structure (6.1 kN/cm2). Also, the maximum deflection is slightly bigger (value of 0,2 cm compared to 0,12 cm) but certainly lower than the biggest (highest) allowed for this kind of structure.

Fig.19. 3D model of the original structure in zone A

Fig.20. 3D model of the redesigned structure in zone A

(a) (b)

Fig.21. FE model of the original (a) and redesigned

structure (b) in zone A

(a) (b)

Fig.22. Displacement fields of the original (a) and

redesigned structure (b) in zone A

4.2. Zone B

The comparison of the original and the redesigned structure of the tribunes, Figs. 23 and 24, is also done by using the finite element models with discretization of the strucutres with beam finite elements, Fig. 25. The maximum stress value in the redesigned structure (6.6 kN/cm2) is slightly bigger compared to the value of the original structure (6.1 kN/cm2). However, it is much lower than the allowed stress value (16.0 kN/cm2) for the material used in the structure-S235JRG2. The displacement field is also approved for the redesigned structure, Fig. 26.

Fig.23. 3D model of the original structure in zone B


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Fig.24. 3D model of the redesigned structure in zone B

(a) (b)

Fig.25. FE model of the original (a) and redesigned

structure (b) in zone B

(a) (b)

Fig.26. Displacement fields of the original (a) and

redesigned structure (b) in zone B

5. CONCLUSION The redesign of tribune structures enables proper usage of not only the transport ways within the hall but of all the facilities as well, thus achieving complete functionality. Based on the presented results of the numerical analysis of the tribune structure’s stress–strain state, it is conclusive:

stress values in the redesigned structure are lower than the allowed ones;

joint deflections of the redesigned structure lie within the allowed limits.

ACKNOWLEDGMENTS This work is a contribution to the Ministry of Science and Technological Development of Serbia funded project TR 35006. REFERENCES [1] PETKOVIĆ, Z., BOŠNJAK, S., GAŠIĆ, V.,

Redesign of the tribune structure in Belgrade Arena hall, Faculty of Mechanical Engineering, Belgrade, 2007. (in Serbian)

[2] MURRAY-SMITH, D. J., Methods for the External Validation of Continuous System Simulation Models: A Review, Mathematical and Computer Modelling of Dynamical Systems, 4(1), 1998, pp. 5-31.

[3] PETKOVIĆ, Z., OSTIĆ, D., J., Metalne konstrukcije u mašinogradnji, Mašinski fakultet u Beogradu, Beograd, 1996.

[4] PETERSEN , C., Stahlbau, Vieweg, 1990. [5] BUĐEVAC, D., MARKOVIĆ, Z., BOGAVAC, D.,

TOŠIĆ, D, Metalne konstrukcije, Građevinski fakultet u Beogradu, Beograd, 1999.

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machine design, Vol.3(2011) No 1, ISSN 1821-1259 pp. … IĆ, D, Metalne konstrukcije, Građevinski fakultet u Beogradu, Beograd, 1999. Title: Microsoft Word - 041-046.doc Author: