COMPARISON OF ANALYSIS OF FOLDED PLATE STRUCTURES BY SIMPLIFIED BENDING THEORY AND ANSYS PROGRAM

International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 1, December 17, pp. 796 83, Article ID: IJCIET_8_1_86 Available online at http://http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=8&itype=1 ISSN Print: 976-638 and ISSN Online: 976-6316 IAEME Publication Scopus Indexed COMPARISON OF ANALYSIS OF FOLDED PLATE STRUCTURES BY SIMPLIFIED BENDING THEORY AND ANSYS PROGRAM Imad R. Mustafa MSc Student of Structural Engineering, Department of Civil Engineering, University of Salahaddin, Erbil, Iraq Dr. Feirushah Salih Assistant Professor of Structural Engineering, Department of Civil Engineering, University of Salahaddin, Erbil, Iraq ABSTRACT Folded plates are a very useful form of structure which has many advantages and several methods are available for the analysis of this type of structure. The simplified bending theory is established in this article to study the mechanical behavior of folded plate structures. The accuracy of the proposed method is validated by computing numerical example, and good agreement is observed between the present results and ones given by ANSYS. The folded plate structure under unsymmetrical load is considered as an example and longitudinal stress and vertical deflections of the structure are compared with numerical result. Key words ANSYS program, Folded plate, Simplified bending theory and Unsymmetrical load. Cite this Article: Imad R. Mustafa, Dr. Feirushah Salih. Comparison of Analysis of Folded Plate Structures by Simplified Bending Theory and ANSYS Program. International Journal of Civil Engineering and Technology, 8(1), 17, pp. 796-83. http://www.iaeme.com/ijciet/issues.asp?jtype=ijciet&vtype=8&itype=1 1. INTRODUCTION 1.1. General Folded plate is one of the most important type of plate structures and it is consists of some flat plates strongly connected together along their edges to produce the structural system capable to support loads without the need for any additional support. In practice folded plate structures use widely in many engineering applications, such as in roofs, floor, wall and in foundation sheet pile. http://www.iaeme.com/ijciet/index.asp 796 editor@iaeme.com

Comparison of Analysis of Folded Plate Structures by Simplified Bending Theory and ANSYS Program 1.. Historical Background In Europe 199 the first folded plate created accidently. After the Second World the folded plate transfer to the United States of America and at short time the folded plate accepted like good structural system because of high performance. In 193 G. Ehlers and H. Craemer published first design method of folded plate. The most popular method to design folded plate structure in the United States of America was wrote by G.Winter and M.Pe. in 1947. In 1954 I.Gaafer was published the first design method considering and including the joints displacement. In 1959 E.Traum introduce the simplified bending theory of the analysis of folded plate structure and this method also permit to analysis unsymmetrically loaded folded plate structure. 1.3. Previous Work Chulsoo Yu performed analytical and experimental study on two-bay folded plate structure. The study investigated symmetrical and unsymmetrical line loading case used two analytical methods, simplified bending theory and beam theory, compared analytically with experimental results in longitudinal stress and ridge deflection for both cases. It was concluded from the study that the simplified bending theory is good to analysis folded plate structure with symmetric and unsymmetrical line loads cases but the beam theory is only suitable for symmetrical case and both methods are unsafe to analysis and design of the outer plates with a free edge [1]. Yung-Ping Wang investigated an analytical study to determine stress distribution and deflection of joints. Analysis based on extension of Gaafar method dependable and satisfactory by the ASCE task committee and the analysis results show good agreements with Yitzhaki slop-deflection method []. Graham presented experimental investigation in 8 aluminum models of varying plate thickness, span and roof slop of the plates loaded until yielding. Also developed and advanced the special theory to analysis of folded plate structure. It was concluded from the study that the analytical study showed accepted result with experimental test results [3]. Bar-Yoseph & Hersckovitz studied the new approximate method based on Vlasov theory of thin-walled beams where the folded plate divided in two longitudinal beams is connected like monolithic structure. The study of the new approach for predicting the mechanical response of folded structure has been introduced. It was concluded from the study that the present model for practical purpose can give good estimates for the displacement and stress fields and the simplicity and computational efficiency of the present method give an important analytical tool for preliminary design of folded plate structure [4]. Bandyopadhyay & Laad studied two computer programs have been developed using the conventional Simpson and Whitney methods. Six different numerical problems solved by earlier investigators are considered to enable easy comparison of numerical results. It was concluded from the study that the maximum variation is approximately3% from those of other methods. Hence these methods can be used for the preliminary analysis of folded plate structures. It is further observed that both of these methods are less satisfactory for spans which are less than twice the width of the plate [5]. http://www.iaeme.com/ijciet/index.asp 797 editor@iaeme.com

Imad R. Mustafa, Dr. Feirushah Salih Lajos KOLL.A..R investigated some special problems in folded plates structure, the static behavior of folded plate under partial vertical and horizontal loads for short and long element folded plates. Also the study investigated the internal force of folded plates under concentrated loads and analysis of plate for buckling [6]. Ruben A. & Gomez, P.E investigated analysis and design of folded plate by hand calculation and computer program the research showed how three dimensional problem modified and solved into two dimensional solution. Used several computer program and hand calculation to reach adequate design principle to engineer in design of folded plates [7]. 1.4. The Present Study The present study investigates the analysis of unsymmetrical folded plate structure by simplified bending theory and ANSYS computer program. A comparison of the simplified bending theory solution with the ones by the finite element structural analysis software (ANSYS) is carried out to demonstrate the accuracy and efficiency. Additionally parametric modelling method using ANSYS is proposed. All parameters of the folded plate can be input in the parametric model and all mechanical quantities can be found.. MATERIAL AND METHODS.1. Method of Analysis Several methods are available for the analysis of folded plate structure. In this study use simplified bending theory to analysis the problem case of folded plate structure. Here the basic assumptions of simplified bending theory to analysis: The material is homogeneous and elastic. The structure is monolithic. Longitudinal stresses vary linearly over the depth of each plate. Individual plates possess negligible torsional resistance. End diaphragms are infinitely stiff in vertical plain, but flexible in horizontal plane [1]... Worked Example A steel plate model, five meter long and.4 meters wide as shown in Figure 1, the analysis is composed of determining the longitudinal stresses and vertical deflections of points A, B, C, D and E. Total load on the model 1KN, Steel material E= GPa =, N/mm. Figure 1 Geometry of folded structure. http://www.iaeme.com/ijciet/index.asp 798 editor@iaeme.com

Comparison of Analysis of Folded Plate Structures by Simplified Bending Theory and ANSYS Program 3. SOLUTIONS AND RESULTS 3.1. Solution by Simplified Bending Theory Sign convention for plate loads is shown in Figure and 3. Figure Sign convention 3 11 N W uniformline load 5mm N mm Figure 3 Unsymmetrical External loading Moment of inertia of a plate: (Thickness=4mm, Width=cos (45)*6=848.5) I pl 3 bd 1 3 8 4 4 848.5 1.365 1 mm Section modulus of a plate (I/(d/), d/= 44.6mm) 8 4 I I.365 1 mm 5 3 Z pl 4.81 mm (1) c d / 44.6mm Moment in plate I or II (M = wx (L-x)/, w = w (1)*cos(45)=1.414N/mm) M ( 1/ ) w L L wl 1.414 ( L ) 8 Free edge stress at centre 55 8 4.4194 1 6 N mm M M 1/ 4.4194 1 S( f. e.) 9.7 N / mm 9.7 Mpa Z 5 5 4.81 4.81 6 () http://www.iaeme.com/ijciet/index.asp 799 editor@iaeme.com

Imad R. Mustafa, Dr. Feirushah Salih Since the longitudinal stresses in two adjacent plates should be the same and there exist an unknown shearing force at each ridge, the free edge stresses are distributed in order to determine the final stresses. The distribution is performed in Table 1. Table 1 Free edge stress distribution After final longitudinal stresses for the top and bottom of the plates are found, the deflections of plates in their own planes are determined by assuming the individual plate deflects just like simply supported beam does. The deflection formula is derived as follows: Moment at center, (1/ ) wl 8 M, stress in top(maximum) wx 3 3 Deflection at center; D x Lx L 4EI S, (3) 4 5wL 5L 5L 5M 1/ L D1/ wl 8M 1/ 384EI 384EI 384EI 48EI 5L IS 5L S 48EI d 48E d Substituting the average of top and bottom stresses for S Sn Sn1 L D S S (4) 1/ 5L 48E d 9.6dE n n1 Substituting Sn-Sn-1 value in Fig. 4. (E=MPa) L 5 D I Sn Sn1 16.651.496mm 9.6dE 3 9.6 848.5 1 Similarly, D II -.189mm, D III.98mm, D IV -.3mm Vertical deflections of ridges are easily calculated. V A cos45 DI DII.496.189.311mm M I y max M I d http://www.iaeme.com/ijciet/index.asp 8 editor@iaeme.com

V V V V Comparison of Analysis of Folded Plate Structures by Simplified Bending Theory and ANSYS Program D cos45 DII DIII.189.988.1979mm B cos45 DIII DIV.98.3.856mm C cos45 DI.1765mm E cos45 DIV -.14mm Check for Rotation Finding Perpendicular deflection p II = D II - D III =.496-.98=.1588 mm D P III = III D IV =.98-.3=.66 mm R II = p II /d=.1588/848.5=.18 R III = P III /d=.66/848.5=.71 r (5) r=.8*1-5 R II =X*r X=6 R III =Y*r Y=.5 Values of X and Y are not small, therefore the Rotation should be considered in the design of plate. 3.. Solution by ANSYS Program Figures 4 to 7 show the results of analysis by ANSYS program. Figure 4 FE Model Figure 5 Vertical deflection distribution http://www.iaeme.com/ijciet/index.asp 81 editor@iaeme.com

Imad R. Mustafa, Dr. Feirushah Salih Figure 6 Vertical deflection at ridges Figure 7 The longitudinal stress at ridges (MPa) 3.3. Results and Discussion After found deflections and stress distributions in folded plate structure by simplified bending theory and ANSYS program, the results show good agreements between ANSYS program and simplified bending theory. In Table and 3 showed compared results of deflections and stress distribution in folded plate. Table Deflection of Folded Plate Ridge Simplified theory ANSYS A D B.311 mm.1979 mm.856 mm.394 mm.89 mm.785 mm Table 3 Stress Distribution in Folded Plate Ridge Simplified theory ANSYS A D B 7.714 Mpa 4.64 Mpa 1.313 Mpa 7.563 Mpa 4.45 Mpa 1.31 Mpa http://www.iaeme.com/ijciet/index.asp 8 editor@iaeme.com

Comparison of Analysis of Folded Plate Structures by Simplified Bending Theory and ANSYS Program 4. CONCLUSIONS This study investigated the analysis of unsymmetrical folded plate structure by simplified bending theory and ANSYS program. The stress distribution and deflections found during analysis process. The following conclusions and findings can be reached from this study: The simplified bending theory is suitable for design unsymmetrical folded plate structure, during the analysis process it can be found the effect of rotation. The simplified bending theory showed good agreement results compared by ANSYS program solution. The maximum deflection and stress distribution located at the part of plate which load is applied. REFERENCES [1] Chulsoo Yu, J.B.: Investigation of a two-bay Folded Plate Structure, (196) [] Yung-Ping Wang: Analysis of continuous folded plate roofs, (1965) [3] Graham, F.: The behavior of a folded plate roof system. Retrosp. Theses Diss. (1966) [4] Bar-Yoseph, P., Hersckovitz, I.: Analysis of folded plate structures. Thin-Walled Struct. 7, 139 158 (1989). doi:1.116/63-831(89)916-5 [5] Bandyopadhyay, J.N., Laad, P.K.: Comparative analysis of folded plate structures. Comput. Struct. 36, 91 96 (199). doi:1.116/45-7949(9)918-o [6] Lajos KOLL.A..R: Some problems of static analysis of folded plate structures, (1993) [7] Ruben A., Gomez, P.E.: Design of Folded Plates, (13) [8] Narendiranath Babu T, Prateek Parmeshwar, Arth Bel adiya and Akshay Bhabhra, CFD analysis and comparison using A NSYS and STAR-CCM+ of model aerofoil Selig 13, International Journal of Mechanical Engineering and Technology 8(11), 17, pp. 31 318. [9] Rajesh Prabha N, Edwin Raja Dhas J and Ramanan G, Finite Element Structural Analysis of Connecting Rod of Aa775-Tic Composite Using ANSYS, International Journal of Mechanical Engineering and Technology 8(7), 17, pp. 11 111. [1] Pawan Kumar Singh, Dr. L. P. Singh, Vicky Lad and A nil Kumar Vishwakarma, Modelling of Crankshaft by Cad Tool and Finite Element Analys is Using Ansys Software. International Journal of Mechanical Engineering and Technology, 7(4), 16, pp. 5 11. http://www.iaeme.com/ijciet/index.asp 83 editor@iaeme.com