International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 Study on Analysis and Design of Football Stadium Thin Nwe Aye, Zaw Min Htun Abstract—In this study, the main structural elements of the football stadium are presented, with particular emphasis on the steel roof and its interaction with the underlying reinforced concrete structures. The proposed scheme comprised an ellipse shape plan composed of twelve portions with expansion joints. The building is composed of special moment – resisting framed. Dead loads, live loads, impact loads, wind and seismic loadings data are considered based on UBC 97 (Uniform Building Code). ACI 318-99 code is used for R.C grandstand structure and AISC-LRFD 93 code is used for steel structures which is upper part as elliptical steel roof. Wind velocity is taken as 80 mph in this study. In analysing the frames, 28 load combinations are used for all steel members. The grandstand structure is made of reinforced concrete and the roof of structural steel using wide-flanged W-sections and double angles. Structural steel used in the building is A572 Grade 65 steel. Necessary stability checks are carried out. Index Terms— cantilever steel roof, football stadium, grandstand structure I. INTRODUCTION Nowadays, our country, Myanmar is building a new modern developed nation. Development of country’s infrastructure is of vital importance. Infrastructures such as tall buildings, highways, long bridges, modern airports, international standard sport complex, etc are needed. International football stadiums are one of infrastructure. The stadium building itself should be a memorable landmark like many of the architectural achievements of previous eras. Furthermore, people do all types of physical activities to keep healthy or for enjoyment. Football is the most popular sport in Myanmar, which has a population of over 60 millions. Therefore, international standard football stadiums and modern sport complex are needed to construct all over the country. Football stadiums are not only places of emotion and fascination but also places where people celebrate football. Today, football stadiums are being designed to fulfill particularly stringent criteria in terms of comfort, safety and security. In this study, the analysis and design of football stadium with elliptical steel roof truss is proposed. To analyze and design of this study, the base building is structured as a reinforced concrete frame. And the roof is completely designed in steel. Reinforced concrete structure and steel roof are combined as a modern structure. This study is intended to understand the structural analysis and design concepts of football stadium with elliptical steel roof truss. The significant effects of wind and earthquake are considered for the design of proposed stadium. The design of the stadium is done with the aid of computer software program named “ETABS” (Extended Three - Dimensional Analysis of Building Structure). Stadiums are strongly differentiated in shape. The proposed stadium architecture will be of ellipse in plane and of saddle in curved surface. And its long axis of periphery projection line will be 365 m and short axis of 315 m with a total building height of 22.1 m and total building area of 90300 m2. It houses seating for 30,000 spectators. For roof and facade envelope, colorful steel plate and aluminum plate structure will be adopted. Steel plate girder structure will be used for main part of roofing in this study. II. OVERVIEW OF STADIUM Stadium is a vehicle for exploring and expressing the ideas about the role of structure in architecture, and about an architect’s realm of control in a building project. As the ideas developed, the design of stadium tend to be much better-looked than their 20th centuries predecessors. International stadium should be completed the following facilities. Modern stadium should be provided spacious and high-quality dressing rooms and other facilities to ensure that players and match officials can carry out their activities in comfort and safety. The proposed stadium has 147 rooms. A football stadium should be covered to protect spectators from the rain and from the glare of strong sunlight. In those parts of the world where relatively constant sunshine is normal, the shade provided by a roof should be made available to all spectators for at least a certain period of the game. As for roof and facade envelope of proposed stadium, colorful steel plate and aluminum plate structure will be adopted. The shape and type of stadium varies according to the community and types of matches will be held. In proposed stadium, the grandstand structure is made of reinforced concrete and the roof of structural steel. The stadium has the ability to host 30589 spectators, with its grandstands being completely covered. It has seating capacity of 29788 Nos in ordinary, 393 Nos in VIP, 408 Nos in VVIP. This capacity also meets to hold the international football matches. The stadium is designed to free from unobstructed and complete view of the field of play using sightline quality. The standard formula for calculating the sightline is as follows: D N R R D T Where, C is sightline, D is the horizontal distance from each individual position to the point of focus (the edge of the pitch), N is the riser height of each individual row of seats, R C Manuscript received Oct 15, 2011. Ma Thin Nwe Aye, Department of Civil Engineering, Mandalay Technological University, (e-mail: thinnweaye23@gamil.com). Mandalay, Myanmar, +95 9 402502433, Zaw Min Htun, Department of Civil Engineering, Mandalay Technological University, Mandalay, Myanmar, +95 92038809 , (e-mail: zawmin.t.2012@gmail.com). 1 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 is the vertical height between the persons eye level and the point of focus (pitch level) and T is the depth of each individual row of seats. Because the shape of the stadium is a true ellipse, no row of seats is a straight line. The auditoriums are arranged as in bowl shape to free from unobstructed and complete view of the field play using sightline quality. Modern football stadiums should be designed so that all spectators are safe and comfortable, have a perfect view of the pitch and have easy access to toilets and refreshment facilities. Access and exit to and from the seats, both in normal and emergency situations are carefully planned in this stadium All spectators should be seated. Seats must be individual, affixed to the structure and comfortably shaped, with backrests of a minimum height of one foot to provide support. Seats should be unbreakable, fireproof and capable of withstanding the rigours of the prevailing climate without undue deterioration or loss of color. Seats for VIPs should be wider and more comfortable and should be located at the centre of the field and separated from the rest of the seating areas. To achieve reasonable leg-room, a minimum distance of 85cm from backrest to backrest is recommended. The spectators should be able to find their way easily to their seats. All seats should be numbered in a way that makes them clearly, easily and immediately identifiable. Spectators should not have to stoop to look at obscure, faded and miniscule seat number plates while others wait behind them, impatient and frustrated. It is important that the whole entry process is not stressful or unnecessarily slow. When arriving at an unfamiliar stadium with a ticket for, say, Sector A, Row 11, Seat 9, the spectator should find the route to the seat clearly marked and easily identifiable. Stadium must be provided sufficient toilet facilities consisting of a single WC and sink for both sexes. III. OBJECTIVE OF STUDY The objectives of this study are as follows: (1)To analyze and design the superstructure of football stadium with cantilever elliptical steel roof truss (2)To realize the design concept for reinforced concrete frame football stadium IV. PREPARATION FOR DESIGN CALCULATION A. Structural Framing System This structure is designed based on UBC - 97. It is located in Mandalay area which is UBC seismic zone 4. The stadium has not only 863 ft of long axis of periphery line but also 700 ft of short axis. The grandstand has a total building height of 22.1 m and total building area of 90300m2. ETABS software is used to analyze the superstructure. B. Material Properties of Structure Material properties of structure are as follows: 1) Material Property of Concrete i. Analysis property data - Weight per unit volume of Concrete = 150 pcf - Modulus of elasticity, Es = 3605 ksi - Poisson's ratio = 0.2 - Coefficient of thermal expansion = 5.5x10-6in/in per °F ii. Design property data -Specified concrete compressive strength, f’c -Bending reinforced yield stress, fy -Shear reinforced yield stress, fys 2) Material Property of Steel i. Analysis property data -Modulus of elasticity, Es -Poisson’s ratio ii. Design property data -Minimum yield stress, Fy -Minimum tensile strength, Fu = 4 ksi = 50 ksi = 50 ksi =29,000 ksi = 0.3 = 65 ksi = 80 ksi C. Loading Consideration Loads are forces tending to effect and produce deformations, stresses or displacement in structure. Stadiums are subjected to several types of loads. They are gravity loads and lateral loads. Gravity loads are caused by the gravitational pull of the earth and act in vertical direction. Gravity loads are further classified as dead loads and live loads. The two primary lateral loads on stadiums are wind and earthquakes. Design load combinations are also used. 1) Dead Loads: Dead loads consist of the weight of all material and fixed equipments incorporated into the building. -unit weight of concrete = 150 pcf - 9 " thick brick wall weight = 100 pcf - 4.5 " thick brick wall weight = 55 pcf - superimposed dead load for finishing = 25 psf -weight of aluminium and glass wall = 20 psf -weight of lift = 3 tons 2) Live loads: Live loads shall be the maximum loads expected by the intended use or occupancy. They may be fully or partially in place or not present at all. -live load of handrail and guards = 50 psf -live load on public area = 100 psf -live load on office area = 50 psf -live load on stores = 100 psf -live load on lobbies and similar areas = 100 psf -live load on stair case = 100 psf -live load on landing = 100 psf -live load on stages and platforms = 125 psf -live load on lift = 100 psf -live load on roof = 5 psf 3) Impact Load: Grandstands, stadiums, and similar assembly structures may be subjected to loads caused by crowds swaying in unison, jumping to its feet, or stomping. Designers are cautioned that the possibility of such loads should be considered. -impact dead load on inclined auditorium = 60 psf -impact live load on inclined auditorium = 90 psf 2 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 4) Wind Load: The determination of wind design force on a structure is basically a dynamic problem because a building will be continually affected by gusts and other aerodynamic force. Required Data in designing for wind load: - Exposure type = Type B - Basic wind velocity = 80 mph - Total height of building = 91 ft (up to top of roof) - Method used = Normal Force Method - Windward coefficient = 0.8 - Leeward coefficient = 0.5 - Importance Factor = 1.0 5) Earthquake Load: Nowadays, the structures are designed to resist in an earthquake according to lateral force design. Effects on earthquakes on structures are as follows: (i) Seismic importance factor, I (ii)Seismic zone factor, Z (iii)Soil profile types, S (iv)Seismic source type (v)Near - source factors, Na and Nv (vi)Seismic response coefficients, Ca and Cv (vii) Response Modification Factor, R - Seismic zone = zone (4) - Seismic source type =A - Soil profile type = SD - Structural system = SMRF - Seismic zone factor = 0.4 - Seismic importance factor, I = 1.0 - Response modification factor, R = 8.5 -Seismic response coefficient, Ca = 0.44 Na -Seismic response coefficient, Cv =0.64 Nv - CT value = 0.03 V. Figure1 describes that typical base plan and selected symmetric portions for whole stadium with twelve expansion joints. Three-dimensional view for whole structure analyzing by ETABS software is illustrated in Figure 2. Figure2. Three-Dimensional View of Football Stadium ANALYSIS RESULTS OF FOOTBALL STADIUM The design results of football stadium are carried out (18) types of load combinations based on ACI (318-99) code for grandstand structure and (22) types of load combinations according to AISC-LRFD (93) for cantilever steel roof. The proposed scheme comprised an ellipse shape plan composed of twelve portions with expansion joints. There are five portions for whole stadium to be symmetric. They are portion 1, 2, 3 for other portion and VIP 1, 2 portions for VIP portion. In this paper, the design results for portion 1(one-twelfth), portion 3 (one-twelfth) and VIP 1 portion (one-twelfth) are carried out. Figure3. 3D view of football stadium (portion 1= one twelfth of all) Figure1. Typical Base Plan and Selected Symmetric Portions for Whole Stadium Figure4. 3D view of football stadium (portion 3= one twelfth of all) 3 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 Figure8. Main cantilever truss of VIP 1 portion Figure5. 3D view of football stadium (VIP 1 portion= one twelfth of all) In Figure 3, 4 and 5, three-dimensional view of portion 1, portion 3 and VIP 1 portion are described. Figure 6, 7 and 8show main cantilever truss of portion 1, portion 3 and VIP 1 portion. Sample roof trusses of portion1, portion 3 and VIP 1 portion are described in figure 9, 10 and 11. Figure6. Main cantilever truss of portion1 Figure9. Sample roof truss of portion 1 Figure7. Main cantilever truss of portion 3 Figure10. Sample roof truss of portion 3 4 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 TABLE II DESIGN RESULT OF STEEL ROOF Name Vertical Truss Top, Bottom Chord Truss Member W10x45 W10x54 W10x100 W10x112 W10x88 W10x100 W10x112 W12x120 Material Steel Steel Steel Steel Steel Steel Steel Steel 2L4x3x1/4x3/8SSLB 2L4x4x3/8 2L4x4x5/8 Steel Steel Steel VI. STABILITY CHECKING OF SUPERSTRUCTURE Figure11. Sample roof truss of VIP 1 portion A. Modeling of the structure The proposed superstructure is designed as Special Moment Resisting Frame. Total height = 91 ft (up to top of roof) Length = major axis 863 ft minor axis 700 ft Shape of the structure = elliptical shape Location = zone-4 Type = roofed stadium (with cantilever roof truss) B. Design results of structure The football stadium is constructed with concrete for column(C), beam (B) and slabs. The cantilever steel roof is built with wide-flanged W-sections and double angles for top chords, bottom chords and truss. Wide-flanged W-sections are the most commonly used sections. The wide-flanged shape is designed by the nominal depth and weight per foot. TABLE I DESIGN RESULT OF GRANDSTAND STRUCTURE Name Column Beam Slab Member Material C24′′x24′′ C24′′x28′′ C24′′x48′′ C26′′x26′′ Concrete B9′′x12′′ B12′′x18′′ B12′′x20′′ B12′′x24′′ B14′′x20′′ B14′′x24′′ B14′′x28′′ B18′′x24′′ B18′′x34′′ B18′′x36′′ Aud: slab (7in tk) Other slab ( 6in tk) Roof slab (0.125in tk) Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Concrete Steel plate According to UBC 97, checking for storey drift, checking for P- Δ effect, checking for overturning, checking for sliding, checking for torsion are needed to be safe for the structure. There are five portions to check stability of the stadium. But stability checks of portion 1, portion 2 and VIP1 portion are described as sample in this study. A. Checking for storey drift Story drift is lateral displacement of one level of structure relative to the level below. In UBC-97, for structure having a fundamental period of greater than 0.7 second, the calculated storey drift shall not exceed 0.020 times the storey height. The storey drift shall not exceed 0.025 times the storey height for structures having the fundamental period of 0.7 second or lesser. These limitations are to ensure a minimum level of stiffness so as to control inelastic deformation and possible instability. ΔM= 0.7 R Δs Where, ΔM = Maximum displacement R = Response modification factor= 8.5 Δs = Deformation According to analysis results by ETABS software, the value of storey drifts for proposed portions are within story drifts limitation. Thus, the superstructure is stable. B. Checking for P- Δ Effect According to UBC-97, the resulting member forces and moments and storey drifts included by P- Δ effects shall be considered in the evaluation of overall structural frame stability. In seismic zone 3 and 4, P- Δ effects need not be considered when the storey drift (Δ) is less than or equal to 0.02 hx/R. So, the proposed stadium is located in seismic zone 4. The maximum drift ratio of stadium is satisfied with the limitation, we can neglect P- Δ effect. C. Checking for Overturning Moment Every structure shall be designed to resist the overturning effects caused by earthquake forces. The distributed of earthquake forces over the height of a structure causes to experience overturning moment. The UBC-97 requires that every designed structure be able to resist overturning effect included by earthquake forces. Based on analysis result of stadium, the safety factor is not only 30.25 for X- direction 5 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 but also 14.01 for Y- direction for portion 1. In portion 3, the safety factor of X- direction is 20.72 and that of Y- direction is 12.56. For VIP1 portion, factor of safety for both X and Y-directions are 8.18 and 14.25 respectively. So, the superstructure of stadium is able to resist overturning effect as the safety factors for X and Y directions are greater than 1.5. D. Checking for Sliding Factor of safety for sliding is the ratio of the resistance due to friction to sliding force. From UBC-97, the safety factor of sliding must be greater than 1.5. For the proposed stadium, the factors of safety for sliding in both X and Y- directions are 4.23 and 4.43 in portion1. For portion 3, safety factor for both X and Y-directions are 2.55 and 4.07 respectively. In VIP1 portion, factor of safety in X- direction is 7.35 and that of Ydirection is 8.64. Thus, the structure will be safe for sliding. E. Checking for torsion Accidental torsion that occurs due to uncertainties in the building’s mass and stiffness distribution must be added to the calculated eccentricity. The torsional effect is checked between the most two distant points in a structure. In this stadium, the safety factors for X and Y-directions are 1.17 and 1.09 for portion1, and 1.2 and 1.05 for portion 3 and 1.185 and 1.134 for VIP1 portion. The torsional irregularity can be neglected because the safety factors of stadium are within the limit. Figure 13.Comparison of Storey Drift in X- direction in portion 3 It can be found that storey drift values of SPECY are increased about 44% than that of SPECX in storey 1. But in storey 3, storey drift due to SPECY is a slight drift than that of SPECX. VII. COMPARISON OF STABILITY RESULTS In this study, the design results for members are carried out load combinations based on ACI 318-99 code. The comparisons of structural performance results in response spectrum analysis are graphically described. A. Comparison of Storey Drift in X direction This section discusses the relative story drift value for response spectrum analysis and all these values are graphically represented in Figure 12, 13 and 14. Figure 14.Comparison of Storey Drift in X- direction in VIP 1 portion In Figure 13, maximum storey drift ratio is found in SPECY of storey 1 and minimum storey drift ratio is seen in SPECX of storey 4. B. Comparison of Storey Drift in Y direction This section also discusses the relative storey drift value for response spectrum analysis and all these values are shown in figure 15, 16 and 17. Figure 12.Comparison of Storey Drift in X- direction in portion 1 It can be found that for portion 1, storey drift value for SPEC Y is absolutely five times that of SPEC X. Figure 15.Comparison of Storey Drift in Y- direction in portion 1 6 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 It can be seen that storey drift ratio was considered much less about 5 times for SPECX than the SPECY in all stories. In comparison of storey shear in X- direction, the storey shear in SPECX is less than nearly 4 times than that of SPECY for all stories. Figure 16.Comparison of Story Drift in Y- direction in portion 3 According to Figure 16, storey drift ratio due to SPECY is greater than absolutely 10 times that of SPECX in storey 2, 3 and 4. However, in storey 1, storey drift ratio in SPECX is less than about 6 times of SPECY. Figure 19.Comparison of Story Shear in X- direction in portion 3 In comparison of storey shear in X- direction, maximum value of 715.64 kips is occurred at storey 1 in SPECX. Figure 20.Comparasion of Storey Shear in X- direction in VIP 1 portion Figure 17.Comparasion of Storey Drift in Y- direction in VIP 1 portion Figure 17 can be seen that the storey drift ratio of SPECY is increased over 70% of that of SPECX in all stories. The figure shows storey shear values for response spectrum analysis. Maximum storey shear is occurred at storey 3 and approximately 1100 kips in SPECY. C. Comparison of Storey Shear in X-direction This section shows storey shear for three portions in each storey level and shown in figure 18, 17 and 20. D. Comparison of Storey Shear in Y- direction This section gives storey shear in each storey level for three portions and shown in figure 21, 22 and 23. < Figure 18.Comparison of Storey Shear in X- direction in portion 1 Figure 21.Comparison of Storey Shear in Y- direction in portion 1 7 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 Figure 21 can be seen that maximum storey shear is occurred in SPECY at storey 1 and minimum storey shear is founded in SPECX at storey 2. In comparison of storey moment in X- direction, storey moment values of SPECY is 45243.39 kips-in and it is five times larger that of SPECX. Figure 22.Comparison of Storey Shear in Y- direction in portion 3 Figure 25.Comparison of Storey Moment in X- direction in portion 3 This figure shows comparison of storey shear in response spectrum analysis for portion 3. The values of storey shear for SPECY are sharply increased than that for SPECX. This figure shows storey moment values for portion 3. Maximum value for SPECX of 155637.608 kip-in is occurred at storey 1 and it is twice of SPECY. But storey moment of SPECX is four times greater that of SPECY at remain stories. Figure 23.Comparison of Storey Shear in Y- direction in VIP 1 portion It can be founded that the value of storey shear reached a new peak of just over700 kips on SPECY of storey 3. E. Comparison of Storey Moment in X- direction This section discusses the storey moment value of three portions and it is represented on figure 24, 25 and 26. Figure 24.Comparison of Storey Moment in X- direction in portion 1 Figure 26.Comparison of Storey Moment in X- direction in VIP 1 portion In comparison of storey moment in X- direction in VIP1 portion, storey moment value of SPECY is increased approximately 13 times that of SPECX. F. Comparison of Storey Moment in Y- direction This section represents the storey moment value for response spectrum analysis for each storey and it is shown in figure 27, 28 and 29. Figure 27.Comparison of Storey Moment in Y- direction in portion 1 8 All Rights Reserved © 2012 IJSETR International Journal of Science, Engineering and Technology Research (IJSETR) Volume 1, Issue 1, July 2012 This figure can be founded that storey moment of SPECX is decreased about 5 times that of SPECY. Figure 28.Comparison of Storey Moment in Y- direction in portion 3 We can be seen in this figure 28 that the values of storey moment of SPECX are increased significantly to each storey at 15 times that of SPECY. stability of the superstructure are within the limitation, so the structure is stable. Firstly, the proposed stadium is analyzed with static analysis. If the static condition is satisfied, the model is also analyzed with response spectrum analysis for dynamic approach. In comparison of analysis results, maximum storey drift ratios due to SPECX and SPECY can be found at storey 1 in all portions for both directions. Maximum storey shear among all portions is occurred at storey 3 of VIP 1 portion and approximately 1100 kips due to SPECY in X-direction. In comparison of storey shear for Y- direction, it can be founded that the value of storey shear reached a new peak of just over700 kips on SPECY of storey 3among all portions. The minimum storey moment among all portions can be seen at storey 2 of portion1 and nearly 700 kips-in due to SPECX in X- direction. The maximum storey moment in Y-direction can be seen at storey 4 for portion1 and at storey 1 for portion 3 and VIP 1 portion. It is hoped that the study here will get some knowledge to build a safe economical structure. ACKNOWLEDGMENT Figure 29.Comparison of Storey Moment in Y- direction in VIP 1 portion In figure 29, storey moment in SPECY has almost 15 times as many as storey moment in SPECX for all stories. <<, Firstly, the author thanks her parents for educating her from her childhood till now. The author is very thankful to, Dr. Myint Thein, Rector, Mandalay Technological University and Dr. Kyaw Moe Aung, Associate Professor and Head of Civil Engineering Department, Mandalay Technological University, for her kind advice and permission to carry out this paper. The author would like to express her special appreciation to her supervisor, Dr. Zaw Min Htun, Lecturer, Department of Civil Engineering, Mandalay Technological University. The author also wishes to reveal her thanks to all teachers from Civil Engineering department at Mandalay Technological University who guided and helped during the preparation of the study. Moreover, the author thanks to Max Myanmar Construction Group which helped in collecting data required for this study. The author also wishes to thank all her friends for their helps and advices on her studying. Finally, the author would like to express grateful thanks to all teachers for their supports, kindness and unconditional love. VIII. DISCUSSIONS AND CONCLUSIONS In this study, the stadium with reinforced concrete grandstand structure and cantilever steel roof is analyzed and designed for the superstructure by ETABS software, ACI (318-99), AISC-LRFD 1993.The design of superstructure for wind speed 80 mph was done. As the structure is located in high seismic risk zone 4, dynamic analysis is considered in the proposed stadium according to UBC- 97. Wide-flanged W-sections and double angles are used for top chords, bottom chords and truss of cantilever roof. In this study, both of bolted connection and welded connection were used for cantilever roof. To make the structural analysis, preliminary estimation of the member sizes were chosen as a first step. Cross sections were chosen to meet the design requirements according to the design procedure. P- Δ effect, story drift, overturning and sliding, torsion were also checked in the design calculation. All the checking carried out for the REFERENCES [1] [2] [3] Anonymous: Football Stadiums, Technical Recommendation and requirements, FIFA, Fe'de'ration Internationale de Football Association, 4 th Edition, Switzarland, 2007. Uniform Building Code, Volume 2. "Structural Engineering Design Provisions". 1997, 8th Ed. International Conference of Building Officials. Charles G. Salmon, John E. Johnson, "Steel Structures Design and Behavior”, 3rd Edition, Harper Collons Publishers, 1986. 9 All Rights Reserved © 2012 IJSETR