Skip to main content
SpringerLink
Log in

A simple formulation for predicting the ultimate strength of ships

  • Original Articles
  • Published:
Journal of Marine Science and Technology Aims and scope Submit manuscript

Abstract

The aim of this study is to derive a simple analytical formula for predicting the ultimate collapse strength of a single- and double-hull ship under a vertical bending moment, and also to characterize the accuracy and applicability for earlier approximate formulations. It is known that a ship hull will reach the overall collapse state if both collapse of the compression flange and yielding of the tension flange occur. Side shells in the vicinity of the compression and the tension flanges will often fail also, but the material around the final neutral axis will remain in the elastic state. Based on this observation, a credible distribution of longitudinal stresses around the hull section at the overall collapse state is assumed, and an explicit analytical equation for calculating the hull ultimate strength is obtained. A comparison between the derived formula and existing expressions is made for largescale box girder models, a one-third-scale frigate hull model, and full-scale ship hulls.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A B :

total sectional area of outer bottom

A′ B :

total sectional area of inner bottom

A D :

total sectional area of deck

A S :

half-sectional area of all sides (including longitudinal bulkheads and inner sides)

a s :

sectional area of a longitudinal stiffener with effective plating

b :

breadth of plate between longitudinal stiffeners

D :

hull depth

D B :

height of double bottom

E :

Young's modulus

g :

neutral axis position above the base line in the sagging condition or below the deck in the hogging condition

H :

depth of hull section in linear elastic state

I s :

moment of inertia of a longitudinal stiffener with effective plating

l :

length of a longitudinal stiffener between transverse beams

M E :

elastic bending moment

M p :

fully plastic bending moment of hull section

M u :

ultimate bending moment capacity of hull section

M uh ,M us :

ultimate bending moment in hogging or sagging conditions

r :

radius of gyration of a longitudinal stiffener with effective plating [=(I s /a s )1/2]

t :

plate thickness

Z :

elastic section modulus at the compression flange

Z B ,Z D :

elastic section modulus at bottom or deck

β :

slenderness ratio of plate between stiffeners [= (b/t)(σy/E)1/2]

λ :

slenderness ratio of a longitudinal stiffener with effective plating [=(l/πr)(σy/E)1/2]

σ y :

yield strength of the material

σ yB ,σ′ yB ,σ yD :

yield strength of outer bottom, inner bottom

σ yS :

deck, or side

σ u :

ultimate buckling strength of the compression flange

σ uB ,σ′ uB ,σ uD :

ultimate buckling strength of outer bottom

σ uS :

inner bottom, deck, or side

References

  1. Moan T, Frieze PA, Ganapathy C, et al. (1994) Report of ISSC Committee V.1 on applied design-strength limit states formulations. In: Proceedings of the International Ship and Offshore Structures Congress, vol 2. St. John's, Canada, 12–16 Sep, pp 1–58

    Google Scholar 

  2. Vasta J (1958) Lessons learned from full-scale structural tests. Trans SNAME 66:165–243

    Google Scholar 

  3. Caldwell JB (1965) Ultimate longitudinal strength. Trans RINA 107:411–430

    Google Scholar 

  4. Mansour AE, Faulkner D (1973) On applying the statistical approach to extreme sea loads and ship hull strength. Trans RINA 115:277–313

    Google Scholar 

  5. Viner AC (1986) Development of ship strength formulations. In: Smith CS, Clarke JD (eds) Proceedings of the International Conference on Advances in Marine Structures. Elsevier, London, New York, pp 152–173

    Google Scholar 

  6. Faulkner D, Sadden JA (1979) Toward a unified approach to ship structural safety. Trans RINA 121:1–28

    Google Scholar 

  7. Valsgaard S, Steen E (1991) Ultimate hull girder strength margins in present class requirements. In: Proceedings of the Marine Structural Inspection, Maintenance, and Monitoring Symposium, SSC/SNAME. Arlington, 18–19 March, pp III.B.1-III.B.19

    Google Scholar 

  8. Frieze PA, Lin YT (1991) Ship longitudinal strength modelling for reliability analysis. In: Proceedings of the Marine Structural Inspection, Maintenance, and Monitoring Symposium, SSC/SNAME. Arlington, 18–19 Mar, pp III.C.1-III.C.20

    Google Scholar 

  9. Rutherford SE, Caldwell JB (1990) Ultimate longitudinal strength of ships: a case study. Trans SNAME 98:441–472

    Google Scholar 

  10. Paik JK, Song JY, Kim CW (1993) Development of ultimate longitudinal strength standard for ships, phase I: Prediction method for ultimate collapse strength of a ship's hull. Korean Register of Shipping, Report No. OR-04(1)-93

  11. Smith CS (1977) Influence of local compressive failure on ultimate longitudinal strength of a ship's hull. In: Proceedings of the International Symposium on Practical Design in Shipbuilding (PRADS). Tokyo, 17–21 October, pp 73–79

  12. Mansour AE (1986) Approximate formulae for preliminary design of stiffened plates. In: Proceedings of the 5th International Symposium on Offshore Mechanics and Arctic Engineering. Tokyo, 16–20 April, pp 427–434

  13. Ueda Y, Rashed SMH, Paik JK (1995) Buckling and ultimate strength interaction of plates and stiffened panels under combined inplane biaxial and shearing forces. Mar Struct 8:1–36

    Google Scholar 

  14. Mansour AE (1980) Ultimate strength of a ship's hull girder in plastic and buckling modes. Ship Structures Committee, report no. SSC-299

  15. Paik JK, Lee JM (1995) An empirical formulation for predicting ultimate compressive strength of plates and stiffened plates. Submitted for publication in J of Ship Research

  16. Dowling PJ, Moolani FM, Frieze PA (1976) The effect of shear lag on the ultimate strength of box girders. In: International Congress on Steel Plated Structures. Imperial College, London, 20–21 July, pp 108–147

    Google Scholar 

  17. Nishihara S (1983) Analysis of ultimate strength of stiffened rectangular plate (in Japanese). J Soc Nav Archit Jpn 154: 367–375

    Google Scholar 

  18. Mansour AE, Yang JM, Thayamballi A (1990) An experimental investigation on ship hull ultimate strength. Trans SNAME 98: 411–440

    Google Scholar 

  19. Dow RS (1991) Testing and analysis of a 1/3-scale welded steel frigate model. In: Smith CS, Dow RS (eds) Proceedings of the International Conference on Advances in Marine Structures. Elsevier, London, New York, pp 749–773

    Google Scholar 

  20. Jensen JJ, Amdahl J, Caridis PA et al. (1994) Report of ISSC Committee III.1 on ductile collapse. In: Proceedings of the International Ship and Offshore Structures Congress, vol 1. St. John's, Canada, 12–16 Sep, pp 299–387

    Google Scholar 

  21. Paik JK (1993) ALPS/ISUM: a computer program for nonlinear analysis of large plated structures using the idealized structural unit method. Pusan National University, Pusan

    Google Scholar 

  22. Mansour AE, Lin YH, Paik JK (1995) Ultimate strength of ships under combined vertical and horizontal moments. In: Proceedings of the International Symposium on Practical Design of Ships and Mobile Units (PRADS'95). Seoul, 17–22 Sep, pp 2.844–2.851

  23. Paik JK, Kim DH, Bong HS et al. (1992) Deterministic and probabilistic safety evaluation for a new double-hull tanker with transverseless system. Trans SNAME 100:173–198

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Naval Architecture and Ocean Engineering, Research Institute of Mechanical Technology, Pusan National University, 30 Jangjeon-Dong, Kumjung-Ku, 609-735, Pusan, Korea

    Jeom K. Paik

  2. Department of Naval Architecture and Offshore Engineering, University of California at Berkeley, 94720, Berkeley, CA, USA

    Alaa E. Mansour

Authors
  1. Jeom K. Paik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alaa E. Mansour
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Paik, J.K., Mansour, A.E. A simple formulation for predicting the ultimate strength of ships. J Mar Sci Technol 1, 52–62 (1995). https://doi.org/10.1007/BF01240013

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01240013

Key words

Search

Navigation