Bending Moments and Shear Forces in Ships Sailing in Irregular Waves

1981 ◽  
Vol 25 (04) ◽  
pp. 243-251
Author(s):  
J. Juncher Jensen ◽  
P. Terndrup Pedersen
Keyword(s):  
Linear Part ◽  
Vertical Motion ◽  
Bending Moment ◽  
Irregular Waves ◽  
Bending Moments ◽  
Shear Forces ◽  
Strip Theory ◽  
Wave Heights ◽  
Exciting Forces ◽  
Wave Induced

This paper presents some results concerning the vertical response of two different ships sailing in regular and irregular waves. One ship is a containership with a relatively small block coefficient and with some bow flare while the other ship is a tanker with a large block coefficient. The wave-induced loads are calculated using a second-order strip theory, derived by a perturbational procedure in which the linear part is identical to the usual strip theory. The additional quadratic terms are determined by taking into account the nonlinearities of the exiting waves, the nonvertical sides of the ship, and, finally, the variations of the hydrodynamic forces during the vertical motion of the ship. The flexibility of the hull is also taken into account. The numerical results show that for the containership a substantial increase in bending moments and shear forces is caused by the quadratic terms. The results also show that for both ships the effect of the hull flexibility (springing) is a fair increase of the variance of the wave-induced midship bending moment. For the tanker the springing is due mainly to exciting forces which are linear with respect to wave heights whereas for the containership the nonlinear exciting forces are of importance.

Ship Operational and Safety Aspects of Ballast Water Exchange at Sea

1994 ◽  
Vol 31 (04) ◽  
pp. 315-326
Author(s):  
John B. Woodward ◽  
Michael G. Parsons ◽  
Armin W. Troesch
Keyword(s):  
Bending Moment ◽  
Bending Moments ◽  
University Of Michigan ◽  
Bulk Carrier ◽  
Rough Water ◽  
Design Values ◽  
Wave Heights ◽  
Ballast Tanks ◽  
The University ◽  
Wave Induced

A dry bulk carrier, a tanker, and a containership—taken as typical of ships trading to U.S. ports—are analyzed for possible hazards caused by emptying and refilling ballast tanks at sea. Using hydrostatic data furnished by the shipowners, hull bending moments and stabilities are investigated to find the tank-emptying operations that produce the greatest changes in those parameters. As should be expected, bending moment changes do not exceed allowable stillwater values. Changes in GM are insignificant. The worst hydrostatic cases serve as a guide to conditions that should be analyzed in rough water. The University of Michigan SHIPMO program shows that in waves of 10-ft significant height wave-induced bending moments and shears are far below the design values published by the American Bureau of Shipping. On the other hand, in waves of 20-ft significant height, the maximum wave heights that occur occasionally can cause moments or shears that exceed design values. For the 20-ft case, both linear and nonlinear versions of SHIPMO are used.

Estimation of hull girder vertical bending moments including non-linear and flexibility effects using closed form expressions

2009 ◽  
Vol 223 (3) ◽  
pp. 377-390 ◽  
Author(s):  
P T Pedersen ◽  
J J Jensen
Keyword(s):  
Closed Form ◽  
Linear Response ◽  
Bending Moment ◽  
Phase Lag ◽  
Bending Moments ◽  
Hull Girder ◽  
Strip Theory ◽  
Non Linear ◽  
Bow Flare ◽  
Wave Induced

A simple but rational procedure for prediction of extreme wave-induced hull girder bending moment in slender mono-hull displacement vessels is presented. The procedure takes into account main ship hull characteristics such as length, breadth, draught, block coefficient, bow flare coefficient, forward speed, and hull flexibility. The wave-induced loads are evaluated for specific operational profiles. Non-linearity in the wave bending moment is modelled using results derived from a second-order strip theory and water entry solutions for wedge-type sections. Hence, bow flare slamming is accounted for through a momentum type of approach. The stochastic properties of this non-linear response are calculated through a monotonic Hermite transformation. In addition, the impulse loading attributable to, for example, bottom slamming or a rapid change in bow flare is included using a modal expansion in the two lowest vertical vibration modes. These whipping vibrations are added to the wave frequency non-linear response, taking into account the rise time of the impulse response as well as the phase lag between the occurrence of the maximum non-linear load and the maximum impulse load. Previous results for the sagging bending moment are validated by comparison with fully non-linear strip theory calculations and supplemented with new closed form results for the hogging bending moment. Focus is on the extreme hull girder hogging bending moment. Owing to the few input parameters, this procedure can be used to estimate the wave-induced bending moments at the conceptual design phase. Another application area is for novel single-hull ship types not presently covered by the rules of the classification societies. As one application example the container ship MSC Napoli is considered. Further validations are needed, however, in order to select proper values of the parameters entering the analytical form of the slamming impulse.

Symmetric Response of a Hydroelastic Scaled Container Ship Model in Regular and Irregular Waves

2014 ◽  
Author(s):  
Sheng Peng ◽  
Pandeli Temarel ◽  
S. S. Bennett ◽  
Weiguo Wu ◽  
Zhengguo Liu ◽  
...  
Keyword(s):  
Full Scale ◽  
Irregular Waves ◽  
Container Ship ◽  
Bending Moments ◽  
Segmented Model ◽  
Numerical Predictions ◽  
Hull Structure ◽  
Strip Theory ◽  
Head Waves ◽  
Wave Induced

Wave-induced vibrations, such as whipping and springing, of container carriers have been attracting much attention because of their effects on hull-girder bending moments and fatigue damage. An investigation has been carried out comparing experimental measurements and numerical predictions of symmetric wave-induced loads (i.e. vertical bending moment) of the latest River-sea link container ship design, LPP = 130 m. The dual mission characteristics, namely rivers and open seas, make this type of ship an extremely interesting type of container carrier, particularly in terms of springing and whipping. A backbone beam segmented model is used in the experiments with the focus on springing- and whipping-induced vertical bending moments, for the model travelling at Fn = 0.21 in regular and long-crested irregular head waves, of 2.5m full-scale height or significant wave height. In addition higher order (harmonics) vertical bending moments (VBM) are also extracted from the experiments. The measurements are taken at amidships and the fore and aft quarters. Numerical predictions, for both the full-scale vessel and segmented model, are obtained using the two-dimensional linear hydroelasticity theories, where the hull structure is idealized as a non-uniform beam and the fluid actions evaluated using strip theory. The measured model test results, in relatively moderate conditions based on a particular area of operation for this low-draught vessel, indicate that nonlinear springing accounts for a significant portion of the total wave-induced bending moments in regular and, to an extent, irregular waves and slamming effects are small due to the operational area selected. The numerical predictions in regular waves show that linear hydroelasticity analysis can only predict similar trends in the variation of the VBM and the resonance peak. On the other hand, in long crested irregular waves the linear hydroelasticity analysis provides peak statistics that are commensurate with the measurements. The numerical predictions were obtained for two variants, having L = LPP and L = 0.9 LPP, the latter corresponding to the length of the backbone.

Extreme Response of Very Large Floating Structure Considering Second-Order Hydroelastic Effects in Multidirectional Irregular Waves

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Xujun Chen ◽  
Torgeir Moan ◽  
Shixiao Fu
Keyword(s):  
Second Order ◽  
Irregular Waves ◽  
Bending Moments ◽  
Floating Structure ◽  
First Order ◽  
Fluid Forces ◽  
Principal Coordinates ◽  
Vertical Displacements ◽  
Exciting Forces ◽  
Nonlinear Fluid

Hydroelasticity theory, considering the second-order fluid forces induced by the coupling of first-order wave potentials, is introduced briefly in this paper. Based on the numerical results of second-order principal coordinates induced by the difference-frequency and sum-frequency fluid forces in multidirectional irregular waves, the bending moments, as well as the vertical displacements of a floating plate used as a numerical example are obtained in an efficient manner. As the phase angle components of the multidirectional waves are random variables, the principal coordinates, the vertical displacements, and the bending moments are all random variables. Extreme values of bending moments are predicted on the basis of the theory of stationary stochastic processes. The predicted linear and nonlinear results of bending moments show that the influences of nonlinear fluid forces are different not only for the different wave phase angles, but also for the different incident wave angles. In the example very large floating structure (VLFS) considered in this paper, the influence of nonlinear fluid force on the predicted extreme bending moment may be as large as 22% of the linear wave exciting forces. For an elastic body with large rigidity, the influence of nonlinear fluid force on the responses may be larger than the first-order exciting forces and should be considered in the hydroelastic analysis.

scholarly journals Premature destruction of two-span RC beams exposed to high temperature caused by a redistribution of shear forces

2016 ◽  
Vol 23 (4) ◽  
pp. 431-439 ◽  
Author(s):  
Robert KOWALSKI ◽  
Michał GŁOWACKI ◽  
Marian ABRAMOWICZ
Keyword(s):  
High Temperature ◽  
Cross Sections ◽  
Bending Moment ◽  
Middle Part ◽  
Transverse Reinforcement ◽  
Shear Load ◽  
Bending Moments ◽  
Rc Beams ◽  
Shear Forces ◽  
Load Bearing Capacity

When multi-span RC elements are exposed to fire one usually observes a yielding of span cross-sections while a safety reserve of support cross-sections is still significant. Due to this phenomenon a redistribution of bending moments occurs and the values of sagging moment in span cross-sections decrease while the values of hogging moment in support cross-sections increase. This paper shows the results of tests conducted on two-span RC beams in a situation when only one span has been exposed to high temperature from the bottom. The beams were 12×16 cm in their cross-section. The length of the span was 165 cm. The load has been applied by two forces put on each span. The beams were made of C25/30 concrete with siliceous aggregate. As a result of significant stiffness decrease of the heated span, redistribution of shear forces and bending moment occurs. Due to this redistribution the tested beams were prematurely damaged due to exhaust of the shear load bearing capacity in the middle part of the beam span where there was no transverse reinforcement.

Experimental Assessment of Form Based Approach for Predicting Extreme Value Distribution of Hull Girder Bending Moment in a Ship

2019 ◽  
Author(s):  
Tomoki Takami ◽  
Yusuke Komoriyama ◽  
Takahiro Ando ◽  
Kazuhiro Iijima
Keyword(s):  
Estimation Method ◽  
Bending Moment ◽  
Extreme Value Distribution ◽  
Irregular Waves ◽  
Extreme Wave ◽  
Scaled Model ◽  
Element Analysis ◽  
Hull Girder ◽  
Reliability Method ◽  
Wave Induced

Abstract This paper describes a series of towing tank tests using a scaled model of a recent container ship for validating the First Order Reliability Method (FORM) based approach to predict the maximum response. The FORM based approach is adopted in conjunction with the nonlinear strip method as an estimation method for the most probable wave episodes (MPWEs) leading to the given extreme wave-induced vertical bending moments (VBMs). Tank tests under the pre-determined MPWEs are conducted to evaluate the extreme wave-induced VBMs. Numerical simulations based on the coupled Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA) are also conducted and are compared with the test results under the MPWEs. Furthermore, to estimate the extreme VBM statistics, tank tests under random irregular waves are conducted. A series of validations of the probability of exceedances (PoEs) of the VBM evaluated from the FORM based approach is carried out. The effect of hydroelastic (whipping) vibrations on the extreme VBM statistics are finally discussed.

Steep Wave Effects on Wave Induced Vertical Bending Moment Using a 3D Numerical Wave Tank

2017 ◽  
Author(s):  
Shivaji Ganesan Thirunaavukarasu ◽  
Debabrata Sen ◽  
Yogendra Parihar
Keyword(s):  
Comparative Study ◽  
Incident Wave ◽  
Bending Moment ◽  
Wave Steepness ◽  
Numerical Wave Tank ◽  
Wave Tank ◽  
Strip Theory ◽  
Numerical Wave ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper presents a detail comparative study on wave induced vertical bending moment (VBM) between linear and approximate nonlinear calculations using a 3D numerical wave tank (NWT) method. The developed numerical approach is in time domain where the ambient incident waves can be defined by any suitable wave theory. Certain justifying approximations employed in the solution of the interaction hydrodynamics (diffraction and radiation) enabling the NWT to generate stable long duration time histories of all parameters of interest. This is an extension of our earlier works towards the development of a practical NWT based solution for wave-structure interactions [1]. After a brief outline of the implemented numerical details, a comprehensive validation and verification of vertical shear force (VSF) and bending moment RAOs computed using the linearized version of the NWT against the usual linear results of strip theory and 3D panel codes are presented. Next we undertake the comparative study between the fully linear and approximate nonlinear versions of the present code for different incident wave steepness. In the approximate nonlinear formulation, the ambient incident wave is defined by the full nonlinear numerical wave model based on Fourier approximation method which can generate very steep steady periodic nonlinear waves up to the near wave breaking limit. The nonlinearities associated with the incident Froude Krylov and hydrostatic restoring forces/moments are exact up to the instantaneous wetted surface at the displaced location, but the hydrodynamic diffraction and radiation effects are linearized around the mean wetted surface. The standard S175 container hull is considered for the comparative studies because of its geometric nonlinearities. Numerical simulations are performed for four different wave lengths with increasing wave steepness. It is observed that the computed wave induced VBM amidships from the approximate nonlinear results can be almost 30% higher compared to the results from a purely linear solution, which can be a critical issue from the safety point. Significant higher harmonics are also observed in the approximate nonlinear results which at some times may be responsible for exciting the undesirable whipping/springing responses.

Assessment of the Total Ship’s Hull Girder Bending Stresses When Unified Model of Sagging and Hogging Bending Moments is Used

2009 ◽  
Author(s):  
Lyuben D. Ivanov
Keyword(s):  
Life Span ◽  
Bending Moment ◽  
Extreme Value Statistics ◽  
Bending Moments ◽  
Hull Girder ◽  
Section Modulus ◽  
Probabilistic Distribution ◽  
Bending Stresses ◽  
Distribution Laws ◽  
Wave Induced

A method is proposed for calculating the hull girder bending stresses following the procedure in the class rules but in probabilistic terms, i.e. the still water and the wave-induced bending moments; the total hull girder bending moment; the hull girder section modulus and the hull girder bending stresses are treated as random variables with corresponding probabilistic distributions. The still water and wave-induced hull girder hogging and sagging loads are presented in probabilistic format as one phenomenon, i.e. using bi-modal probability density functions. The probabilistic distribution of the total hull girder load is calculated using the rules of the composition of the distribution laws of the constituent variables. After that, the hull girder geometric properties are presented in probabilistic format as annual distributions and distributions for any given life-span. Thus, it becomes possible to calculate both the annual probabilistic distributions and the probabilistic distribution for any given ship’s life span of the hull girder stresses. Individual amplitudes statistical analysis and extreme value statistics are used. Then, the probability of exceeding the permissible hull girder bending stresses in the class rules is calculated. An example is given for 25K DWT bulk carrier.

Influence of Whipping on Long-term Vertical Bending Moment

2004 ◽  
Vol 48 (04) ◽  
pp. 261-272
Author(s):  
Gro Sagli Baarholm ◽  
Jørgen Juncher Jensen
Keyword(s):  
Nonlinear Response ◽  
Extreme Values ◽  
Bending Moment ◽  
Sea Waves ◽  
Short Term ◽  
Strip Theory ◽  
Long Time ◽  
Wave Induced ◽  
Vertical Bending Moment

This paper is concerned with estimating the response value corresponding to a long return period, say 20 years. Time domain simulation is required to obtain the nonlinear response, and long time series are required to limit the statistical uncertainty in the simulations. It is crucial to introduce ways to improve the efficiency in the calculation. A method to determine the long-term extremes by considering only a few short-term sea states is applied. Long-term extreme values are estimated using a set of sea states that have a certain probability of occurrence, known as the contour line approach. Effect of whipping is included by assuming that the whipping and wave-induced responses are independent, but the effect of correlation of the long-term extreme value is also studied. Numerical calculations are performed using a nonlinear, hydroelastic strip theory as suggested by Xia et al (1998). Results are presented for the S-175 containership (ITTC 1983) in head sea waves. The analysis shows that whipping increases the vertical bending moment and that the correlation is significant.

Effect of Heavy Weather Maneuvering on the Wave-Induced Vertical Bending Moments in Ship Structures

1990 ◽  
Vol 34 (01) ◽  
pp. 60-68 ◽  
Author(s):  
C. Guedes Soares
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Decision Rules ◽  
Bending Moment ◽  
Ship Motions ◽  
Bending Moments ◽  
Significant Wave ◽  
Course Changes ◽  
Wave Induced ◽  
Vertical Bending Moment

Statistical data are collected so as to quantify the probability of occurrence of voluntary course changes in heavy weather as well as their dependence on significant wave height and on ship heading. Decision rules are established about when and how to change course, on the basis of the analysis of operational data and of interviews with experienced shipmasters. A Monte Carlo simulation is performed so as to determine how an omnidirectional distribution of initial headings is changed by voluntary course changes depending on the significant wave height. Finally, the effect of the nonuniform distribution of headings on the mean wave-induced vertical bending moment is calculated. It is shown that although heavy weather maneuvering eases the ship motions, it can increase the wave-induced bending moments and thus increase the probability of structural failure.

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