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The other limit states are merely they? We have seen that the two principal attributes stages toward structure collapse. But the converse is not true; the provision of 1. These considerations are of a performance index; in fact, a design cannot be summarized in Table 5. This has to take into assess the degree of seriousness of a failure that account the past experience of ships in service and adversely affects the performance.

Recommended values given by regulatory bod- and vice versa. Also they have different relative ies e. For example, in Canadian Standard Association, A. Design code calibration by comparison with of a mission, and therefore serviceability i. Economic value analysis. The safety indices are vessels. As an example, Based on the review of proposals made by various we herein distinguish three degrees of seriousness, regulatory bodies and analysis of the results of reliabil- which we call extreme, severe, and moderate.

For the attribute get safety indices for hull girder primary , stiffened of safety, the degree of seriousness of a failure cor- panels secondary , and unstiffened plates tertiary responds to its consequences in regard to loss of life modes of failure as well as for fatigue failure. Repair urgent.

Ship out of service for a long period. May be permanent loss e. Loss of some secondary functions. Ship out of service for short period or ship operational but seriously handicapped e. No appreciable risk of fatalities but the Main function unimpaired, some inconven- Moderate structure is weakened e.

It was introduced over a Assuming that the yield stress follows a normal half century ago to deal with hull girder bending of distribution, as shown in Figure 5. This explains even though it is much greater than that of initial why, as shown in Table 5. The members. Therefore, it is likely that the satisfactory experience and better assessment of hull girder ultimate strength criterion that explicitly design loads. Note: In addition, for strength.

Buckling criterion for individual members, a safety index of 4. This is, moreover, the value adopted by More recently, additional requirements on the ulti- Mansour et al. Once the failure modes and limit states are identi- 0. In the following, 0. The Figure 5. For determina- ures has to be assessed on a case-by-case basis, tion of the reliability-based partial safety factors, the depending on their consequences with regard to calibration procedure as described in Section 5. For example, fatigue failures of knuckle can be used. The seriousness of such a fatigue failure is extreme.

To carry out systematic reliability analyses on a wave-induced bending moment. Note: Equation 5. To agree on the reliability procedure to carry out The safety margin with respect to initial yielding these analyses. For example, the following moment. In ment of the ultimate strength of the hull girder. In such a case, the following interaction formula pro- that case, the safety margin may be given by posed by Paik and Thayamballi can be used:. The design equation expressed in terms of the partial safety factors is given by For the limit state considered, the limit state func- tion is 1.

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Axial Compressive Stress For primary members contributing to the longitu- dinal strength, not only the wave-induced pressure Simply Supported Fixed Stiffeners Stiffeners but also the hull girder wave-induced stress has to be incremented and a relationship has to be established Pressure Acting on the Acting on the plating between increments in the wave-induced pressure stiffener side side and hull girder stress for performing the nonlinear analyses. MA and MB end bending moments. A typical 5. The solution of equation 5. For plates with simply supported edges and average initial From equation 5.

Equation 5. The plastic sec- Vy tion modulus Zpm is given by. The safety margin as given by equation 5. The equal to the yield stress: iterative procedure, as described in Section 5. The behavior of the plating may be approxi- mated by the following differential equation: The limit state function may be also expressed as. Uniaxial compression. Biaxial compression. Let us consider the case of biaxial compression of 3.

The safety margin is obtained 4. Biaxial compression and shear. The safety margin is obtained by replacing the of the random variables. They give a taste of how the design parameters in equation 5. Initial yielding. The design equation expressed in terms of the Still-water bending moment.

## IP503811 - Ship Structural Analyses

Laterally loaded plates subjected to in-plane ten- corresponds to a probability of exceed- sile stress acting on the longer sides and shear stress. The actual SWBM of tankers 3. Laterally loaded plates subjected to in-plane can be easily monitored thanks to biaxial stresses and shear stress. Wave bending moment. The random variable 5. Ultimate bending moment. Appendix 5-E. Slamming bending moment. In the sagging condition , that is, for laden 0.

In the hogging condition, that is, for ballast conditions, the forward draught is generally 1.

Yield stress. The probability of failure at time T may be approxi- 0. In addition, for ships subjected to high risk of Calculations of the safety index are performed for corrosion, it may be necessary to take into account the same ships as for initial yielding and according to the degradation with time of the cross-sectional the same procedure. If we assume that oil tankers and properties.

For example, the safety margin with bulk carriers spend half of their lifetime in a sagging respect to initial yielding of the hull girder, as given condition, when fully laden, and half in hogging con- by equation 5. The partial safety Keeping the notations of Section 5. Bpst and Bpw measure the uncer- or, in a more conventional form, tainties in the static and wave-induced pressures. Introducing equation 5. Note: Since calculations are carried out for full tanks, sloshing loads are not considered. Upper The limit state D M function expressed in matrix notation is given by E M 5.

Neutral axis. Inertia of the section. Section modulus. E06 5 E06 0. E06 5. E07 1. E07 4. American Bureau of Shipping. Rules for building Ferry-Borges, J. Structural and classing vessels. Houston, TX: Author. Load Civil. The safety of structure. Chicago: Author. ASCE, Vol. Ang, A.

### 1st Edition

Reliability bases Freudenthal, A. Safety and probability of of structural safety and design. Friis Hansen, P. On combination of slamming and Ang, A. Analysis of wave-induced bending responses. On Structural Engineering, Hong-Kong. Reliability-based load and resistance factor Gordo, J. Approximate design LFRD —guidelines for stiffened panels and load shortening curves for stiffened plates under uni- grillages of ship structures. Naval Engineers Journal, axial compression. Conference on integrity of offshore Vol.

Glasgow: Elsevier. Ayyub, B. Reliability of ship hull structures.

## Analysis and Design of Marine Structures: including CD-ROM

Report Nappi, N, Jr. Methodology No Oslo: Det Norske Veritas. Probabilistic models for load factor design LRFD —guidelines for ship structures. Report UR Trondheim: Naval Engineers Journal, Vol. Hull Technology. Design equation for the com- Netherlands. Asymptotic approximations for mul- initial imperfections. Division, Vol. Guedes Soares, C. Stochastic modeling of maxi- Bureau Veritas. Part B—Hull and Stability, Chapter 5. Research, Vol. Paris: Author. Rationalization of safety moments. Marine Structures, Vol. Probabilistic Report 5. London: Author. Cornell, C. A probability-based structural Marine Structures, Vol.

Reliability of main- Issue 12, — Generalized second-moment reli- Research, Vol. Reliability — Principle of normal tail approxima- corroded elements. Statistical anal- Ditlevsen, O. Structural reli- ysis of still water load effects in ship structures. New York: John Wiley and Sons. Fain, R. SSC, Vol. Mechanics Division, Vol. Faulkner, D. A review of effective plating for use Hess, P. Uncertainties in material strength, geomet- compression. Naval Engineers Journal, Vol. Semi-probabilistic approach to the , Issue 2, — International Symposium Hohenbichler, M.

Non normal on the Extreme Load Response, Trans. SNAME, dependent vectors in structural safety. Ferro, G. Probabilistic analy- Hughes, O. Report SSC Washington, DC: Mansour, A. Assessment of reliability of ship structures. Report of Committee V-I on applied Committee. Geneva: Author. Mansour, A. Consistent code formulation ISSC. Report of Committee V-I on applied for ship structural design.

China: design. China: Author. Elsevier Science. Structural reliability analysis and ISSC.

### Naval architecture and marine engineering

Report of Committee IV-1—design prediction. West Sussex, U. Characteristic still water ISSC. Report of Committee II-1—quasistatic load effect for production ships. Trondheim: The Norwegian Institute of Technology. Nikolaidis, E. Uncertainties in Report of Committee IV-1—design principles stress analysis of marine structures. Trondheim, Norway: Author. Arlington, VA, March. SSC Report Washington, General principles on reliability for structures.

DC: Ship Structure Committee. Revision of IS Paik, J. A new plate Kaplan, P. Conference, San Diego, CA. Ship hull ultimate strength reliability consider- Kaplan, P. Ultimate limit structural loads. Washington, DC: state design of steel plated structures. London: John Ship Structure Committee. Wiley and Sons. Kaplan, P. Pugsley, A. A philosophy of aeroplane strength Other editions.

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## Simple Parametric Ship Structural Analysis in Siemens-NX – Ship Lab

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