DOI QR코드

DOI QR Code

Ultimate strength of initially deflected plate under longitudinal compression: Part I = An advanced empirical formulation

  • Kim, Do Kyun (Ocean and Ship Technology Research Group, Department of Civil and Environmental Engineering, Universiti Teknologi PETRONAS) ;
  • Poh, Bee Yee (Ocean and Ship Technology Research Group, Department of Civil and Environmental Engineering, Universiti Teknologi PETRONAS) ;
  • Lee, Jia Rong (Ocean and Ship Technology Research Group, Department of Civil and Environmental Engineering, Universiti Teknologi PETRONAS) ;
  • Paik, Jeom Kee (The Korea Ship and Offshore Research Institution (The Lloyd's Register Foundation Research Centre of Excellence), Pusan National University)
  • Received : 2018.07.28
  • Accepted : 2018.09.20
  • Published : 2018.10.25

Abstract

In this study (Part I), an advanced empirical formulation was proposed to predict the ultimate strength of initially deflected steel plate subjected to longitudinal compression. An advanced empirical formulation was proposed by adopting Initial Deflection Index (IDI) concept for plate element which is a function of plate slenderness ratio (${\beta}$) and coefficient of initial deflection. In case of initial deflection, buckling mode shape, which is mostly assumed type in the ships and offshore industry, was adopted. For the numerical simulation by ANSYS nonlinear finite element method (NLFEM), with a total of seven hundred 700 plate scenarios, including the combination of one hundred (100) cases of plate slenderness ratios with seven (7) representative initial deflection coefficients, were selected based on obtained probability density distributions of plate element from collected commercial ships. The obtained empirical formulation showed good agreement ($R^2=0.99$) with numerical simulation results. The obtained outcome with proposed procedure will be very useful in predicting the ultimate strength performance of plate element subjected to longitudinal compression.

Keywords

Acknowledgement

Supported by : Ministry of Trade, Industry & Energy (MI)

References

  1. AISC (1964), Specification for the Design, Fabrication and Erection of Structural Steel for Buildings, American Institute of Steel Construction, Chicago, Illinois, U.S.A.
  2. Bortsch, R. (1921), "Die mitwirkende Plattenbreite", Der Bauingenieur, 23, 662-667.
  3. Box, T. (1883), A practical Treatise on the Strength of Materials: Including Their Elasticity and Resistance to Impact, E. & F.N. Spon, London, U.K.
  4. BS 153 (1966), Steel Girder Bridges, Part 4, Design and Construction, British Standards Institution, London, U.K.
  5. BS 499 (1961), The Use of Structural Steel in Building and Addendum, British Standards Institution, London, U.K.
  6. Carlsen, C.A. (1977), "Simplified collapse analysis of stiffened plates", Norweg. Marit. Res., 7(4), 2-36.
  7. Cerik, B.C. (2018), "Ultimate longitudinal compressive strength of steel plates with lateral patch load induced plastic deformation", Thin-Wall. Struct., 122, 416-424. https://doi.org/10.1016/j.tws.2017.10.030
  8. Chilver, A.H. (1953), "The maximum strength of the thin-walled channel strut", Civil Eng. Pub. Works Rev., 48, 1143-1146.
  9. Cox, H.L. (1933), Buckling of Thin Plates in Compression, R&M No. 1554, British Aeronautical Research Committee (ARC), U.K.
  10. Cui, W. and Mansour, A.E. (1998), "Effects of welding distortions and residual stresses on the ultimate strength of long rectangular plates under uniaxial compression", Mar. Struct., 11(6), 251-269. https://doi.org/10.1016/S0951-8339(98)00012-4
  11. Czujko, J. and Paik, J.K. (2015), "A new method for accidental limit states design of thin walled structures subjected to hydrocarbon explosion loads", Ships Offshore Struct., 10(5), 460-469.
  12. DNV (1987), Use of High Tensile Steel in Ship Structures, The Tanker Structure Co-operative Forum Meeting with Shipbuilders, Det Norske Veritas, Paramus, New Jersey, U.S.A.
  13. Dow, R.S. and Smith, C.S. (1984), "Effects of localized imperfections on compressive strength of long rectangular plates", J. Constr. Steel Re., 4, 51-76. https://doi.org/10.1016/0143-974X(84)90035-X
  14. Dwight, J.B. and Moxham, K.E. (1969), "Welded steel plates in compression", The Struct. Eng., 47(2), 49-66.
  15. Faulkner, D. (1975), "A review of effecting plating for use in analysis of stiffened plating in bending and compression", J. Ship Res., 19(1), 1-17.
  16. Frankland, J.M. (1940), The Strength of Ship Plating Under Edge Compression. U.S., Experimental Model Basin Progress Report 469.
  17. Gerard, G. (1957), Part 4-Failure of Plates and Composite Elements, Handbook of Structural Stability, NACA TN 3784.
  18. Gordon, J.M., Teixeira, A.P. and Guedes Soares, C. (2011), Ultimate Strength of Ship Structures, Edited by Guedes Soares C, Garbatov Y, Teixeira AP editors, Marine Technology and Engineering, Taylor & Francis Group, London, U.K.
  19. Guedes Soares, C. (1988), "Design equations for the compressive strength of unstiffened plate elements with initial imperfections", J. Constr. Steel Res., 9(4), 287-310. https://doi.org/10.1016/0143-974X(88)90065-X
  20. Guedes Soares, C., Gordo, J.M. and Teixeira, A.P. (2000), "Design equations for plate subjected to heat loads and lateral pressure", Mar. Struct., 13(1), 1-23. https://doi.org/10.1016/S0951-8339(00)00005-8
  21. Hogstrom, P. and Ringberg, J.W. (2012), "An extensive study of a ship's survivability after collision-a parameter study of material characteristics, non-linear FEA and damage stability analyses", Mar. Struct., 27(1), 1-28. https://doi.org/10.1016/j.marstruc.2012.03.001
  22. Hong, L. and Amdahl, J. (2012), "Rapid assessment of ship grounding over large contact surface", Ships Offshore Struct., 7(1), 5-19. https://doi.org/10.1080/17445302.2011.579003
  23. Hughes, O.F. (1983), Ship Structural Design: A Rationally-Based, Computer-Aided Optimization Approach, Wiley, New York, U.S.A.
  24. ISSC (2012), "Ultimate Strength (Committee III.1)", Proceedings of the 18th International Ship and Offshore Structures Congress, Rostock, Germany, September.
  25. ISSC (2015), "Ultimate Strength (Committee III.1)", Proceedings of the 19th International Ship and Offshore Structures Congress, Cascais, Portugal, September.
  26. Ivanov, L.D. and Rousev, S.H. (1979), "Statistical estimation of reduction coefficient of ship's hull plates with initial deflections", The Naval Archit., 4, 158-160.
  27. Jiang, X.L., Yu, H.Y. and Kaminski, M.L. (2014), "Assessment of residual ultimate hull girder strength of damaged ships", Proceedings of the 33rd International Conference on Ocean, Offshore and Arctic Engineering, San Francisco, California, U.S.A.
  28. John, W. (1987), "On the strains of iron ships", RINA Trans., 18, 98-117.
  29. Kim, D.K., Kim, B.J., Seo, J.K., Kim, H.B., Zhang, X.M. and Paik, J.K. (2014), "Time-dependent residual ultimate longitudinal strength-grounding damage index (R-D) diagram", Ocean Eng., 76, 163-171. https://doi.org/10.1016/j.oceaneng.2013.06.023
  30. Kim, D.K., Kim, H.B., Mohd, M.H. and Paik, J.K. (2013a), "Comparison of residual strength-grounding damaged index diagrams for tankers produced by the ALPS/HULL ISFEM and design formula method", Int. J. Naval Archit. Ocean Eng., 5(1), 47-61. https://doi.org/10.2478/IJNAOE-2013-0117
  31. Kim, D.K., Lim, H.L., Kim, M.S., Hwang, O.J. and Park, K.S. (2017), "An empirical formulation for predicting the ultimate strength of stiffened panels subjected to longitudinal compression", Ocean Eng., 140, 270-280. https://doi.org/10.1016/j.oceaneng.2017.05.031
  32. Kim, D.K., Lim, H.L. and Yu, S.Y. (2018a), "A technical review on ultimate strength prediction of stiffened panels in axial compression", Ocean Eng., Under Revision.
  33. Kim, D.K., Ng, W.C.K. and Hwang, O.J. (2018b), "An empirical formulation to predict maximum deflection of blast wall under explosion", Struct. Eng. Mech., Accepted.
  34. Kim, D.K., Ng, W.C.K. Hwang, O.J., Sohn, J.M. and Lee, E.B. (2018c), "Recommended finite element formulations for the analysis of offshore blast walls in an explosion", Lat. Am. J. Sol. Struct., Accepted.
  35. Kim, D.K., Park, D.K., Kim, J.H., Kim, S.J., Kim, B.J., Seo, J.K. and Paik, J.K. (2012a), "Effect of corrosion on the ultimate strength of double hull oil tankers-part I: stiffened panels", Struct. Eng. Mech., 42(4), 507-530. https://doi.org/10.12989/sem.2012.42.4.507
  36. Kim, D.K., Park, D.K., Park, D.H., Kim, H.B., Kim, B.J., Seo, J.K. and Paik, J.K. (2012b), "Effect of corrosion on the ultimate strength of double hull oil tankers-part II: hull girders", Struct. Eng. Mech., 42(4), 531-549. https://doi.org/10.12989/sem.2012.42.4.531
  37. Kim, D.K., Perdersen, P.T., Paik, J.K., Kim, H.B., Zhang, X.M. and Kim, M.S. (2013b), "Safety guidelines of ultimate hull girder strength for grounded container ships", Safety Sci., 59, 46-54. https://doi.org/10.1016/j.ssci.2013.04.006
  38. Kim, D.K. and Poh, B.Y. (2018), "Ultimate strength of initially deflected plate under longitudinal compression: Part II=reviews on accuracy of existing formulations", Struct. Eng. Mech., Under Review.
  39. Kim, D.K., Yu, S.Y. and Choi, H.S. (2013c), "Condition assessment of raking damaged bulk carriers under vertical bending moments", Struct. Eng. Mech., 46(5), 629-644. https://doi.org/10.12989/sem.2013.46.5.629
  40. Marguerre, K. (1937), "Die mittragende breite der gedruckten platte", Translated NACA Technical Note 833, Original in Luftfahrt Forschung, 14(3), 121.
  41. Metzer, W. (1929), "Die mittragende Breite", Dissertation, er Technischen Hochschule zu Aache (in German).
  42. Ozdemir, M., Ergin, A., Yanagihara, D., Tanaka, S. and Yao, T. (2018), "A new method to estimate ultimate strength of stiffened panels under longitudinal thrust based on analytical formulas", Mar. Struct., 59, 510-535. https://doi.org/10.1016/j.marstruc.2018.01.001
  43. Paik, J.K. (2018), Ultimate Limit State Analysis and Design of Plated Structures, 2nd Edition, Jon Wiley & Sons, Chichester, U.K.
  44. Paik, J.K., Kim, B.J., Jeong, J.S., Kim, S.H., Jang, Y.S., Kim, G.S., Woo, J.H., Kim, Y.S., Chun, M.J., Shin, Y.S. and Czujko, J. (2010), "CFD simulation of gas explosion and fire actions", Ships Offshore Struct., 5(1), 3-12. https://doi.org/10.1080/17445300902872028
  45. Paik, J.K., Kim, B.J. and Seo, J.K. (2008a), "Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part I Unstiffened plates", Ocean Eng., 35(2), 261-270. https://doi.org/10.1016/j.oceaneng.2007.08.004
  46. Paik, J.K., Kim, B.J. and Seo, J.K. (2008b), "Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part II Stiffened panels", Ocean Eng., 35(2), 271-280. https://doi.org/10.1016/j.oceaneng.2007.08.007
  47. Paik, J.K., Kim, B.J. and Seo, J.K. (2008c), "Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part III Hull girders", Ocean Eng., 35(2), 281-286. https://doi.org/10.1016/j.oceaneng.2007.08.008
  48. Paik, J.K., Kim, D.K., Park, D.H., Kim, H.B. and Kim, M.S. (2012), "A new method for assessing the safety of ships damaged by grounding", Int. J. Marit. Eng., 154(A1), 1-20.
  49. Paik, J.K., Kim, D.K., Park, D.H., Kim, H.B., Mansour, A.E. and Caldwell, J.B. (2013), "Modified Paik-Mansour formula for ultimate strength calculations of ship hulls", Ships Offshore Struct., 8(3-4), 245-260. https://doi.org/10.1080/17445302.2012.676247
  50. Paik, J.K., Lee, J.M. and Lee, D.H. (2003), "Ultimate strength of dented steel plates under axial compression loads", Int. J. Mech. Sci., 45(3), 433-448. https://doi.org/10.1016/S0020-7403(03)00062-6
  51. Paik, J.K., Thayamballi, A.K. and Lee, J.M. (2004). "Effect of initial deflection shape on the ultimate strength behavior of welded steel plates under biaxial compressive loads", J. Ship Res., 48(1), 45-60.
  52. Paik, J.K., Thayamballi, A.K. and Yang, S.H. (1998), "Residual strength assessment of ships after collision and grounding", Mar. Technol., 35(1), 38-54.
  53. Park, D.K., Kim, D.K., Seo, J.K., Kim, B.J., Ha, Y.C. and Paik, J.K. (2015a), "Operability of non-ice glass aged ships in the Arctic Ocean-part I: Ultimate limit state approach", Ocean Eng., 102, 197-205. https://doi.org/10.1016/j.oceaneng.2014.12.040
  54. Park, D.K., Kim, D.K., Seo, J.K., Kim, B.J., Ha, Y.C. and Paik, J.K. (2015b), "Operability of non-ice glass aged ships in the Arctic Ocean-part II: Accidental limit state approach", Ocean Eng., 102, 206-215. https://doi.org/10.1016/j.oceaneng.2015.04.038
  55. Raviprakash, A.V., Prabu, B. and Alagumurthi, N. (2012), "Residual ultimate compressive strength of dented square plates", Thin-Wall. Struct., 58, 32-39. https://doi.org/10.1016/j.tws.2012.04.009
  56. Saad-Eldeen, S., Garbatov, Y. and Guedes Soares, C. (2016), "Ultimate strength analysis of highly damaged plates", Mar. Struct., 45, 63-85. https://doi.org/10.1016/j.marstruc.2015.10.006
  57. Schnadel, G. (1930), "Die uberschreitung der knickgrenze dunnen platen", Proceedings of the 3rd International Congress on Applied Mechanics, Stockholm, Sweden.
  58. Schuman, L. and Back, G. (1930), Strength of Rectangular Flat Plates Under Edge Compression, NACA Technical Report 356, National Advisory Committee for Aeronautics, Washington, U.S.A.
  59. Sechler, E.E. (1933), The Ultimate Strength of Thin Flat Sheets in Compression, Guggenheim Aeronautical Laboratory Publication 27, California Institute of Technology, Pasadena, California, U.S.A.
  60. Smith, C.S., Davidson, P.C., Chapman, J.C. and Dowling, P.J. (1988), "Strength and stiffness of ship's plating under in-plane compression and tension", Tran RINA, 130, 277-296.
  61. Sohn, J.M., Kim, S.J., Kim, B.H. and Paik, J.K. (2013), "Nonlinear structural consequence analysis of FPSO topside blastwalls", Ocean Eng., 60, 149-162. https://doi.org/10.1016/j.oceaneng.2012.12.005
  62. Soreide, T.H. and Czujko, J. (1983), "Load-carrying capacity of plates under combined lateral load and axial/biaxial compression", Proceedings of the 2nd International Symposium on Practical Design in Shipbuilding, Tokyo, Japan.
  63. Teixeira, A.P., Ivanov, L.D. and Guedes Soares, C. (2013), "Assessment of characteristics values of the ultimate strength of corroded steel plates with initial imperfections", Eng. Struct., 56, 517-527. https://doi.org/10.1016/j.engstruct.2013.05.002
  64. Timoshenko, S. (1936), Theory of Elastic Stability, 1st Edition, McGraw Hill, New York, U..SA.
  65. Ueda, Y., Yao, T., Nakacho, K. and Yuan, M.G. (1992), Prediction of Welding Residual Stress, Deformation and Ultimate Strength of Plate Panels, Engineering Design in Welded Constructions, Pergamon Press, Oxford, U.K.
  66. Ueda, Y., Yasukawa, W., Yao, T., Ikegami, H. and Ominami, R. (1975), "Ultimate strength of square plates subjected to compression effects of initial deflection and welding residual stresses (1st report)", J. Soc. Naval Archit. Jap., 137, 210-221.
  67. von Karman, T. (1924), "Die mittragende Breite (The effective width), Beitrage zur technischen Mechanik (in German).
  68. Wijaya, C. and Kim, B.T. (2011), "FE analysis of unstiffened and stiffened corrugated panels subjected to blast loading", J. Mech. Sci. Technol., 25(12), 3159-3164. https://doi.org/10.1007/s12206-011-0825-x
  69. Winter, G. (1940), Stress Distribution in and Equivalent Width of Flanges of Wide Thin-Wall Steel Beams, NACA Technical, Note 784.
  70. Witkowska, M. and Guedes Soares, C. (2015), "Ultimate strength of locally damaged panels", Thin-Wall. Struct., 97, 225-240. https://doi.org/10.1016/j.tws.2015.09.025
  71. Xu, M.C. and Guedes Soares, C. (2013), "Assessment of residual ultimate strength for side dented stiffened panels subjected to compressive loads", Eng. Struct., 49, 316-328. https://doi.org/10.1016/j.engstruct.2012.11.019
  72. Xu, M.C. and Guedes Soares, C. (2015), "Effect of a central dent on the ultimate strength of narrow stiffened panels under axial compression", Int. J. Mech. Sci., 100, 68-79. https://doi.org/10.1016/j.ijmecsci.2015.06.008
  73. Yao, T. and Fujikubo, M. (2016), Buckling and Ultimate Strength of Ship and Ship-like Floating Structures, Elsevier Inc., New York, U.S.A.
  74. Youssef, S.A.M., Faisal, M., Seo, J.K., Kim, B.J., Ha, Y.C., Kim, D.K., Paik, J.K., Cheng, F. and Kim, M.S. (2016), "Assessing the risk of ship hull collapse due to collision", Ships Offshore Struct., 11(4), 335-350. https://doi.org/10.1080/17445302.2014.993110
  75. ANSYS (2014), User's Manual Version 13.0, ANSYS Inc., Canonsburg, Pennsylvania, U.S.A.

Cited by

  1. Optimum design of stiffened plates for static or dynamic loadings using different ribs vol.74, pp.2, 2018, https://doi.org/10.12989/sem.2020.74.2.255