Full Paper Proc. of Int. Conf. on Advances in Civil Engineering 2012
Effectiveness of Dome Structures in Reduction of Stresses under Transverse Loadings Ashim Kanti Dey1, Chinmoy Deka2 1
Department of Civil Engineering, National Institute of Technology, Silchar, Assam -10, India Email: ashim_kanti@yahoo.co.in 2 Department of Civil Engineering, National Institute of Technology, Silchar, Assam -10, India Email: cdekanits@gmail.com Abstract— In the present study effectiveness of dome shaped roofing in reduction of deformations under lateral loading is discussed. A comparison was made between a flat roof structure and a dome roof structure on deformations imposed under lateral loading. STAAD Pro software was used to evaluate deformations, bending moments and shear forces under different combinations of loads. For the same column and beam sizes it was observed that deformation in dome roof structure is 30% less than that in flat roof structure. Similar reduction in bending moments and shear forces were also observed. On the other hand, for the same deformation, the sizes of columns were needed to be increased by 40% in the flat roof structure. The present study concludes that a considerable amount of material and money can be saved in choosing a dome shaped roof with a marginal loss in floor area and a total loss of the utility of a flat roof.
transverse loadings in comparison to a conventional flat roof structure. The same seismic load combinations were applied to both the flat roof and dome shaped roof frames using STAAD Pro software [3]. The values of deformation, maximum bending moment and maximum shear force in columns were compared. It was observed that the structure with dome shaped roof was more effective against transverse loads. II. METHODOLOGY A. Dome Shaped Structure Concept Dome shaped structures have been used in ancient times such as the Mughal era with the purpose of lending symmetry and enhancing the beauty of buildings. Research has been carried out on the effect of wind load on dome shaped structures. In a study on the buckling effect of wind load on cylindrical tanks with dome shaped roof, it was seen that there is a low imperfection sensitivity of the tanks for buckling loads associated with wind speeds 45% higher than those specified by the ASCE 7-02 standard [4]. The design and construction method used for a dome subjected to wind loads has been also studied [5]. It was concluded that the pressure coefficients obtained using Fourier series formulation are in close agreement with those obtained by experimental work. However very limited research works have been reported on the possibility of use of dome shape roof to resist transverse loads. The idea behind the present study originated from the fact that a structure may not collapse by virtue of its shape. In this respect a dome shaped structure is more stable than a rectangular frame. During shaking the position of centre of gravity (C.G) of a rectangular structure is shifted whereas there is little shift of C.G of a dome. The outer shell of a dome is under compression in ordinary loading. With a transverse load little or no tension is developed in the shell, whereas, tension is developed in the outer column of the frame structure. Reversal of stresses due to load reversal causes damage and spalling of concrete. Thus a dome shaped roof is supposed to withstand higher loads than a flat roof. With this concept in mind it is proposed to try a structure with dome shaped roof under transverse load. Since the entire structure can’t be made dome shaped because of limitation of space and utility, it is proposed to make at least two/three top floors dome shaped. The present analysis has made a
Index Terms—Dome Shape; Rectangular; Flat Roof; Deformation; Bending Moment; Shear Force; Lateral Load; Transverse Load.
I. INTRODUCTION Most earthquake-related deaths are caused not directly by an earthquake but due to collapse of structures. A structure collapses because of faulty construction, improper design calculation or impractical loading concept. Failure is also due to extent of response of a structure under a seismic loading. It is now observed that a building of moderate height collapses whereas a high rise building does not show any distress although both the buildings are located in the same place. This is because of resonance of frequencies of soil column layer and the building. Since long people are trying to make their buildings earthquake resistant. As a result, various earthquake resistant practices are being followed in different regions of the world. Methods like base isolation [1] and friction damped bracing systems [2] have been studied. Traditionally, the focus of the seismic resistant design of buildings has been collapse prevention with the ultimate aim of saving the invaluable human lives. However, these buildings take enough damage that makes them unfit for further use after an earthquake. The new goal is to build structures that not only avoid collapse, but take no damage when an earthquake strikes and are ready for immediate occupancy with little or no economic loss. Following this philosophy, the present study aimed to find out whether a structure with dome shaped roof would be more resistant to © 2012 ACEE DOI: 02.AETACE.2012.3. 12
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Full Paper Proc. of Int. Conf. on Advances in Civil Engineering 2012 comparison of stresses developed in a conventional five storied frame structure with those developed in a structure of same dimension but the top two floors being dome shaped. The dome was created using curved members of radius half of the smaller dimension of the frame. Fig.1 shows the layout of the two structures.
Figure 2. Columns selected for comparison (dimensions: .23 x .23 m)
deformations shown in Table I. TABLE I. COMPARISON O F D EFORMATION I N SELECTED COLUMNS
(a)
(b)
Figure 1. (a) Flat Roof Structure (b) Dome shaped Roof Structure
The floor height was taken as 3m in each frame. The dimension of the floors in the conventional rectangular portions of the structures was taken to be 10.5 x 7 m. The dimension of the 4th floor of the dome shaped roof structure was kept 9.5 x 7 m. The dimension of the small flat portion at its top i.e. on the roof was kept 1.5 x 3.5 m. B. Loading Considerations A part of the loadings were calculated manually while the rest were generated using load generator in STAAD Pro. The various loading cases considered were self-weight, dead load, live load and seismic load. i. Self weight (SW) from slabs was calculated to be 4.5 KN/m2 by assuming slabs of thickness 180 mm. ii. Uniform dead load (DL) exerted by walls was calculated as 8 KN/m (floor walls) 3.6 KN/m (parapet wall) by assuming thickness of 125 mm. iii. The live load (LL) considered in each floor was 3 KN/ m2 and for the terrace level it was considered to be 0.75 KN/ m2.The seismic load (SL) values were calculated as per IS 1893-2002. The parameters considered were: Zone factor ‘Z’ = 0.36, Response Reduction factor ‘RF’ = 5, Importance factor ‘I’ = 1, Rock and soil site factor ‘SS’ = 1, Damping Ratio ‘DM” = 3, Period in X direction ‘PX’ = 0.6 seconds, Foundation Depth = 3 m and RC Framed Structure. STAAD Pro has a seismic load generator in accordance with the IS code mentioned iv. The structure was analyzed for load combinations considering all the previous loads in proper ratio. Seismic load combination = 1.2 (SW + DL + LL) +SL.
The graphs shown in Fig. 3 compared the deformations along the height of the selected columns. It was observed that a reduction of around 30% in the values of deformation occurred in columns of dome shaped roof.
III. RESULT COMPARISON Analysis was carried out on both the structures. For comparison vertical columns as shown in Fig. 2 were chosen. Some of the findings are discussed below. A. Deformation The selected columns as mentioned above undergo © 2012 ACEE DOI: 02.AETACE.2012.3.12
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Full Paper Proc. of Int. Conf. on Advances in Civil Engineering 2012
Figure 3. Comparison of Deformation in selected columns
B. Bending Moment Table II shows a comparison of maximum bending moments imposed in columns of both the structures under the load combination mentioned above.
Figure 4. Comparison of Bending Moment in selected columns
TABLE II. C OMPARISON OF MAXIMUM B ENDING MOMENT I N SELECTED COLUMNS
Figure 5. Comparison of Bending Moment in selected columns TABLE III. COMPARISON O F MAXIMUM SHEAR FORCE IN SELECTED COLUMNS
The graphs shown in Fig. 4 and Fig. 5 compared the bending moments along the height of the selected columns. It was observed that around 35% reduction in value of maximum bending moment occurred in columns of dome shaped roof.
The graphs shown in Fig. 6 compared the shear forces along the height of the selected columns. It was observed that around 35% reduction in value of maximum shear force occurred in columns of dome shaped roof. IV. PARAMETRIC STUDIES B. Shear Force
It is known that thicker columns undergo less deformation when subjected to loadings. The same principle was applied to the analysis and the columns of the rectangular structure were made larger. An attempt was made to achieve
Table III shows a comparison of maximum shear forces imposed in columns of both the structures under the load combination mentioned above. Š 2012 ACEE DOI: 02.AETACE.2012.3.12
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Full Paper Proc. of Int. Conf. on Advances in Civil Engineering 2012 TABLE IV. C OMPARISON OF MAXIMUM D EFORMATION I N SELECTED COLUMNS (AFTER INCREASE)
Figure 7. Comparison of deformation in selected columns (after increase)
1. The shape of the dome encloses the maximum amount of space with the least surface area. And because a dome’s surface area requires a much smaller quantity of expensive building materials, the cost savings and efficiencies are substantial. 2. The construction of steel reinforced concrete domes is quick, regardless of weather conditions. The process takes place within an air-inflated form that covers equipment and stockpiled materials, allowing construction to continue regardless of weather conditions. 3. Domes are ideally suited for structures where open spaces are required: They are open span and therefore no columns intrude on or interrupt valuable available space. Steel reinforced concrete domes provide unprecedented flexibility, especially in buildings requiring a large amount of open space. The designer has total flexibility in the layout of rooms. Virtually any size and number of rooms are possible.
Figure 6. Comparison of Shear Force in selected columns
the same deformation after increasing the column size. Accordingly, the section was increased from 230 x 230 mm to 270 x 270 mm (around 40 mm increase). Table IV shows a comparison of maximum deformation imposed in selected columns between flat roof structure with larger column section and dome roof structure. Fig. 7 shows comparison of deformation along the height of the selected columns after larger column section was considered in conventional flat roof structure. V. CONSTRUCTION AND ADVANTAGES New age dome construction applies a patented process known as airforming [6]. The advantages of such construction are : Š 2012 ACEE DOI: 02.AETACE.2012.3.12
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Full Paper Proc. of Int. Conf. on Advances in Civil Engineering 2012 CONCLUSIONS
ACKNOWLEDGMENT
A comparison study was carried out between a conventional flat roof structure and a dome shaped roof structure on the deformation, maximum bending moment and maximum shear force. These were followed by some parametric study whereby the column section of the flat roof structure was increased to obtain the same deformation. The following conclusions were drawn from the present study: There was a significant reduction in terms of deformation, maximum bending moment and maximum shear force when the top two floors of the rectangular framed structure [G+4] were given a dome shape. The average percentage reduction was nearly 30%, 34.5% and 35% in deformation, maximum bending moment and maximum shear force respectively. i. The column section of the flat roof structure was needed to be increased by 40 mm to get the same deformation value as obtained in the dome roof structure for a G + 4 storied frame. ii. There was a loss of approximately 1.2 % floor area in the dome roof structure in comparison to that of the rectangular framed structure.
The authors wish to thank National Institute of Technology, Silchar. This was carried out as a project under its Summer Research Fellowship’12 program.
© 2012 ACEE DOI: 02.AETACE.2012.3.12
REFERENCES [1] Kelly, James. M. 1997. Earthquake-Resistant Design with Rubber. 2nd ed. Berlin and New York: Springer-Verlag. [2] Ciampi, V., De Angelis, M., Paolacci, F.1995. Design of yielding or friction-based dissipative bracings for seismic protection of buildings. Engineering Structures Volume 17, Issue 5, June 1995, Pages 381–391. [3] STAAD Pro, Getting Started and Tutorials STAAD Pro Manual, Research Engineers International, 2005. [4] Portela, G., Godoy, L.A. 2005. Wind pressures and buckling of cylindrical steel tanks with a dome roof. Journal of Constructional Steel Research Volume 61, Issue 6, June 2005, Pages 808–824. [5] Montes, P., Fernandez, A. 2001.Behaviour of a hemispherical dome subjected to wind loading. Journal of Wind Engineering and Industrial Aerodynamics Volume 89, Issue 10, August 2001, Pages 911–924. [6] Maximilliaan J. Dykmans. 1992. Multi-purpose dome structure and the construction thereof, Patent: US5094044.
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