Comparison Between Smooth And Ring Beam Stiffened Cylindrical Shell Roof
Proceedings of 8th IOE Graduate ConferencePeer ReviewedISSN: 2350-8914 (Online), 2350-8906 (Print)Year: 2020Month: JuneVolume: 8Comparison between Smooth and Ring Beam StiffenedCylindrical Shell RoofBharat Niure a , Hikmat Raj Joshi ba, bDepartment of Civil Engineering, Pulchowk Campus, Institute of Engineering , TU, NepalCorresponding Email: a bharatniure@gmail.com, b hjoshi@ioe.edu.npAbstractIn this paper smooth and ribbed spherical is taken for the analysis and the effect on the stresses for increasein span in both shell structure is investigated as it is a prominent factor in optimizing of the cylindrical design.The cylindrical shell roofs can be categorized as smooth cylindrical shell and ribbed stiffened shell roofs.The problem is to compare smooth cylindrical shell roof over ring beam cylindrical shell roof in term of theirmoment, stress and deflection by keeping volume of concrete constant. This paper perform optimisationstudy of ring stiffened cylindrical shell after getting conclusion from comparision. Performance of the ribbedcylindrical shell is higher than smooth cylindrical shell when span of the structure increase. In Spite of theconstruction difficulties and difficulties in the placement of formwork ribbed cylindrical shell might more efficientthan smooth cylindrical shell for a higher span. Thus, the smooth and ribbed cylindrical shell with different riseand span keeping apex angle constant as 120 with different boundary condition has been studied. Furtherfinite element analysis has been performed in SAP 2000 and the stresses are compared with that of thestresses obtained from the theoretical solution for verification.KeywordsSmooth Circular Cylindrical Shell, Ring Stiffened Circular Cylindrical Shell[1, 2], Classical Theory- MATLAB,SAP20001. IntroductionShell structure are plate structures having curvature inone direction or in both direction which can transmitapplied forces by compressive, tensile, and shearstresses that act in the plane of the surface. Shellstructures are also those type of structure which havethree dimensional curved surfaces capable ofspanning long spans without any intermediatesupports i.e. columns. Shell structures, due tocurvatures develops in plane stresses and also somebending stress due to flexure deformations whereasplate structures are flats which develop bending andshear stresses. Thus, shell structures are capable ofresisting load through compression, tension as well asshear stress. So that shell structure perform best loadcarrying capacity having same dead load compare toother type of structures. Because of its structuralconfiguration shell structure are widely used in longspan structures i.e. large buildings, conference halland in stadium. Construction of Shell structure beginsfrom 1920 and are widely used after World War II.Besides that, the shell structures are also used inaesthetically appalling structures like Opera House inSydney, Temple of Delhi etc. are shell structures.The structural analysis of thin concrete shells can beperformed numerically using finite element analysisand/or analytically by using classical theory of thinshells. While FEA analysis is becoming increasinglyprominent way of performing structural analysis thanthe analytical solution procedure. Compared tostructural elements such as beams, slab and walls, thestructural behavior of shells in not easy to predict sothat evaluating the accuracy of the results obtainedfrom FEA of shell structures is a challenging task.Having the knowledge and understanding of theanalytical solution method can provide the basis forthis verification and at the same time give a muchneeded insight into the structural behavior of shells.The cylindrical shell consists of different geometricalconfiguration. For a small span and length of structureit is better to design smooth cylindrical shell, and forlarge span and length ribbed cylindrical shell mayPages: 1081 – 1086
Comparison between Smooth and Ring Beam Stiffened Cylindrical Shell Roofrequire. In this paper, smooth and ribbed cylindricalshell are analyzed.The specific objective of this paper is to finddifference in the moment,stresses and in deflectionbetween smooth cylindrical shell roof and ringstiffened cylindrical shell roof. Furthermore thisthesis aims to compare the different method ofanalysis done using theoretical methods and finiteelement analysis. The other objectives are:Radius of shell 25 ftThickness 3 inchMaterial PropertiesLinear Elastic homogeneous Isotropic Material withYoung’s modulus 432000000 lb/ft2Poisson’s ratio 0Unit weight of concrete 360 lb/ft3Loading To compare the results obtained from theanalytical method with that of the finite elementmethod. To compare the behavior of both the cylindricalshells on the basis of stresses and deformation.Gravity load 90 lb/ft2 (Uniform load on surface areain –Z direction.)Model 2: After validation of analytical and finiteelement method, this model has been executed as areal problem for this paper. Smooth cylindrical shellhaving following geometry has been selected for thefurther analysis from finite element analysis:2. Detail of ModelTheir are two different model seleted for the analysisof cylindrical shell roof:Geometric PropertiesLength 10 mModel 1: This model is the solved example ofScordelis-Lo barrel roof [3]. This model has beenused to validate the analytical method with finiteelement method.The Scordelis-Lo barrel roof (or vault) is a singlycurved shell structure shown in Figure 1, loaded by itsown weight). This cylindrical shell is supported alongthe curved ends by rigid diaphragms (v w 0) whilethe straight edges are free, meaning that translationald.o.f. parallel to the plane containing the curve areprohibited but translational d.o.f. normal to this planeand all rotational d.o.f. are unrestrained.Semi-circular angle 60 DegreeRadius of shell 2.88 mThickness 80 mmMaterial PropertiesLinear Elastic homogeneous Isotropic Material withYoung’s modulus 25000 N/mm2Poisson’s ratio 0.2Unit weight of concrete 25 KN/m3LoadingLive Load 1.5 KN/m² (as per IS code)By keeping volume constant from model 2[3] ,smooth cylindrical shell[4] convert into the ring beamcylindrical shell by changing thickness of shell.Number of ring for the above geometry has beenvaried by keeping depth to breadth ration of beamconstant with 1.5. so that total 3 number of ringstiffen cylindrical shell having following geometricalparameters different than smooth cylindrical shell areanalyzed:Figure 1: Scordelis-Lo-Barrel Roof geometry andpropertiesGeometric PropertiesGeometric PropertiesThickness 50 mmLength 50 ftSize of Ribbed Beam:Semi-circular angle 40 DegreeHaving 3 Number of Ribbed Beam1082
Proceedings of 8th IOE Graduate ConferenceB 0.258 mD 0.387 mHaving 5 Number of Ribbed BeamB 0.20 mD 0.30 mHaving 7 Number of Ribbed BeamB 0.17 mD 0.253 mFigure 3: Finite Element Modeling of Ring BeamCylindrical Shell3. Analytical MethodAnalytical method has been adopted for the solutionof smooth cylindrical shell roof for the validation ofthe entire work. For the analysis of Smooth cylindricalshell following two theories has been adopted for theAnalytical solution from MATLAB. Schorer Theory K Chandrasekhara Theory[5]4. Finite Element ModelingAnalysis of the smooth and ring beam cylindricalshell are perform by using software packages fromComputers and Structures, Inc. for structural analysisand design, SAP2000 (Version 21).It is a fullyintegrated system for modeling, analyzing, designing,and optimizing structures.All total 144 mess are created as shown in figure 3 forfinite element modeling both smooth and ribbedcylindrical shell roof. It is assumed that the shellthickness throughout the section are constant and is asper geometry.Variable in ribbed beam cylindrical shell is numberof beam, so that according to the number of beamsize of beam are also changed and are modeled infinite element method. Rib network develop in theribbed stiffened cylindrical shell are simple and aren’tconnected with each other.Boundary condition for finite element method: Atcurved edges, the shell body is simply supported. (Uyand Uz are restrained against translation in y and zdirection) and at straight edges the shell body is free.Figure 4: Mess created in finite element analysis forsmooth and ribbed cylindrical shell5. ResultSelected geometry from Model 1 has been modeled byAnalytical method in Matlab and modeling also donefrom finite element method (SAP 2000) and resultfrom both method has been compared with solutionfrom The finite Element Method Fifth Edition Volume2, Solid Mechanics: (Zienkiewicz and Taylor[6]).Further Model 2 having smooth cylindrical shell andring beam cylindrical shell roof has been modeled fromfinite element analysis in SAP 2000. Hence followingresults has observed:Figure 2: Finite Element Modeling of SmoothCylindrical Shell1083
Comparison between Smooth and Ring Beam Stiffened Cylindrical Shell RoofFigure 5: Comparison of Analytical method, FEMMethod and Zeinkiewicz and TaylorAbove figure 5 is the graphical comparison betweenthree solution made for only one problem. Thisgraphical representation gives result for Model 1.First method adopted to solve Scordelis-Lo barrel roofis Analytical method, second is finite element andthird is solve example from Zienkiewicz andTaylor[6]. First graph gives result for longitudinaldisplacement ’w’ of support and second graph givesresults for vertical displacement ’v’ of center. Bycomparing three solution,we only find thediscrepancies of less than 5 % so that this two graphillustrates the validity of methods we adopted andanalysis process.Figure 6: Mx at Support SectionFigure 7: My at Support, at L/4 and Center SetionFigure 8: Mxy at Support Section1084
Proceedings of 8th IOE Graduate ConferenceFigure 9: Mxy at L/4 SectionFigure 11: Vertical Displacement at support , L/4 andat center sectionFigure 6 to figure 11 compares different outputparameter between smooth cylindrical shell andrinned stiffened cylindrical shell having three, five andseven rib beam. Comparing Mx from figure 6 it seemsthat difference between smooth and ribbed beamcylindrical shell are noticeable. There is hugedifference between smooth and seven ribbed beam incomparison with Mx. Similarly with compared to My,Mxy and Smax their is significant difference betweensmooth and ribbed cylindrical shell roof for sameFigure 10: Maximum Stress at support,at L/4 and atcenter section1085
Comparison between Smooth and Ring Beam Stiffened Cylindrical Shell Roofvolume of concrete.From figure 11, deflection of ribbed cylindrical shellare negligible in compare to smooth cylindrical shellat support section and L/4 section. Similarly at centralsection deflection of smooth cylindrical shell os about3 times greater than ribbed cylindrical shell.6. Conclusion and further scopeThis paper gives a distinct figures for the selection ofribbed cylindrical shell over a smooth cylindrical invariation of span to length of the shell. And it alsoaims to find out the effect on increasing number ofribbed in the same ribbed shell. This might beconcluded that the ribbed cylindrical shell is morestable and suitable because of its moment and stressresisting capacity. Furthermore because of thebulkling phenomenon in large cylindrical shell roof itwould be better to design ribbed stiffen cylindricalshell rather than smooth cylindrical shell.This paperdelivers further conclusions: Moment stresses Mxx and Myy for smoothcylindrical shell is higher than the ribbedcylindrical shell so that moment carryingcapacity of ribbed cylindrical shell is higherthan of smooth cylindrical shell hencepercentage of reinforcement for ribbedcylindrical shell will be much lesser thansmooth cylindrical shell. Maximum Plane normal stresses for smoothcylindrical shell is higher than the ribbedcylindrical shell .1086 Vertical deflection for smooth cylindrical shellis much higher than ribbed cylindrical shell andit is about 3 times higher than ribbed cylindricalshell so that this may prevent pre and postbukling phenomenon on shell surfaces .Furthermore optimisation of ringed stiffen cylindricalshell with the variation of span and number of circularring will be perform in the continuation of this paperand optimisation on the ring beam will be carried onthe basis of this paperReferences[1] Wei Li, Anzong Zheng, Lihua You, Xiaosong Yang,Jianjun Zhang, and Ligang Liu. Rib-reinforced shellstructure. In Computer Graphics Forum, volume 36,pages 15–27. Wiley Online Library, 2017.[2] Nikolaos D Lagaros, Michalis Fragiadakis, andManolis Papadrakakis. Optimum design of shellstructures with stiffening beams. AIAA journal,42(1):175–184, 2004.[3] Paweł Foryś. Optimization of cylindrical shellsstiffened by rings under external pressure includingtheir post-buckling behaviour. Thin-Walled Structures,95:231–243, 2015.[4] Ahmad Bazgir. The behaviour of steel fibre reinforcedconcrete material and its effect on impact resistance ofslabs. PhD thesis, City University London, 2016.[5] K Chandrashekhara and DVTG Pavan Kumar.Assessment of shell theories for the static analysis ofcross-ply laminated circular cylindrical shells. Thinwalled structures, 22(4):291–318, 1995.[6] Olgierd Cecil Zienkiewicz, Robert Leroy Taylor,Robert Leroy Taylor, and Robert Lee Taylor. Thefinite element method: solid mechanics, volume 2.Butterworth-heinemann, 2000.
Comparison between Smooth and Ring Beam Stiffened Cylindrical Shell Roof Figure 5: Comparison of Analytical method, FEM Method and Zeinkiewicz and Taylor Above figure 5 is the graphical comparison between three solution made for only one problem. This graphical representation gives result for Model 1. First method adopted to solve Scordelis-Lo .
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