Vertical Bending Moment Research Articles

Progressive collapse analysis of a bulk carrier hull girder under longitudinal vertical bending moment considering cracking damage

Existence of crack causes reduction of the load carrying capacity of ship hull structural elements and eventually reduces the hull girder strength. Previous numerical and semi-analytical studies by the same authors revealed that in addition to the value of ultimate strength, the deflection shape and plastic collapse mechanism of ship hull structural elements will change due to existence of cracking damage. In this paper results from previous studies are used to investigate the way cracks affect ultimate longitudinal strength of ship hull girder. Progressive collapse analysis of an ISSC2000 bulk carrier is carried out to estimate its ultimate strength considering existence of cracking damages at different locations of the hull girder; namely bottom, double bottom, side and deck structures. For this reason, HULLST software which is based on Smith's method was modified to be able to model specific cracks anywhere in the ship hull girder. Results show that the way cracking damage effects the ultimate strength of the ship depends highly on the ship's collapse modes in hogging and sagging conditions as well as behavior of the ship structural elements.

Application of the Tail Equivalent Linearization Method to wave bending moment and comparison with experimental data

This paper estimates extreme midship wave bending moment of a ship in a specific sea state using First Order Reliability Method (FORM) and the Tail Equivalent Linearization Method (TELM). FORM and TELM are applied to the random vibration analysis of the nonlinear bending moment and results are compared and verified against experimental data obtained from model tests as well as numerical simulations. A case study of an LNG tanker is presented, demonstrating that the proposed methodology yields reasonable results and that the TELM approach provides a fast and computationally efficient way of analyzing nonlinear vertical bending moment of ships in stationary sea states.

A Design Method to Assess the Primary Strength of the Delta-Type VLFS

Very large floating structure (VLFS) is a sustainable concept centered around creating solid platforms at sea. The Delta is a new type of VLFS, designed to withstand open-sea conditions and to form, in addition to a broad deck areas, a sheltered basin of year-round operability. The design of this unique hull relies on direct calculations in order to identify critical load cases and assess their load effects. This study formulates a theoretical procedure for the initial assessment of the primary strength. The procedure analytically integrates the floatation loads while the hull rests at hydrostatic equilibrium on a wave surface and obtains the vertical and horizontal bending moment. This preliminary assessment tool enables a fast review of many load cases and provides the basic insights necessary for a reasonable initial design. Using the procedure, we conducted a primary load assessment for the design of Delta. By calculating the load response to 588 load cases, we identified the critical load scenario and the maximal axial stress. As the stress was too high, we improved the geometry in order to reduce loads and assessed proper scantlings for the critical section. We present the formulation of the procedure, the validation of the results, and the implementation for the structural design of the Delta VLFS.

Method for Prediction of Extreme Wave Loads Based on Ship Operability Analysis Using Hindcast Wave Database

The method for the prediction of extreme vertical wave bending moments on a passenger ship based on the hindcast database along the shipping route is presented. Operability analysis is performed to identify sea states when the ship is not able to normally operate and which are likely to be avoided. Closed-form expressions are used for the calculation of transfer functions of ship motions and loads. Multiple operability criteria are used and compared to the corresponding limiting values. The most probable extreme wave bending moments for the short-term sea states at discrete locations along the shipping route are calculated, and annual maximum extreme values are determined. Gumbel probability distribution is then fitted to the annual extreme values, and wave bending moments corresponding to a return period of 20 years are determined for discrete locations. The system reliability approach is used to calculate combined extreme vertical wave bending moment along the shipping route. The method is employed on the example of a passenger ship sailing across the Adriatic Sea (Split, Croatia, to Ancona, Italy). The contribution of the study is the method for the extreme values of wave loads using the hindcast wave database and accounting for ship operational restrictions.

Full-scale test on seismic performance of circumferential joint of shield-driven tunnel

A shield-driven tunnel is deformed along the longitudinal direction when subjected to seismic loadings; the circumferential joint is the key position of the shield-driven tunnel when such longitudinal deformation occurs. In this study, the variations of the internal forces (including both axial forces and bending moments) in the longitudinal direction of the tunnel are analyzed through a numerical method based on the longitudinal equivalent continuous model (LECM). The results show that the internal forces of the tunnel are mainly an axial force caused by longitudinal excitation, and a vertical bending moment caused by transverse excitation. Based on the stress distribution of the circumferential joint, a full-scale test is conducted, and the test results are compared with those obtained by a refined numerical model with 16 segmental rings. It is shown that the variation of the opening and bolt strain of the circumferential joint follows that of the internal force. When the tunnel is subjected to longitudinal tensile forces or bending moments, the distribution rules for the bolt stress at the position of the largest opening are essentially the same. Moreover, the distribution characteristics of the concrete strain on the segment surface at the position of the largest opening are essentially the same. The maximum tensile strain appears on the outer surface of the sleeve side segment. However, the maximum compressive strain appears on the inner surface of the hand hole side segment. The maximum principal stress and damaged plasticity of the segment generally appear near the sleeve and hand hole, and have a limited influence on the segment surface. Finally, a failure test shows that the segment becomes damaged before the bolt yield, with more severe damage occurring in the sleeve side segment.

Residual ultimate strength of stiffened box girder with coupled damage of pitting corrosion and a crack under vertical bending moment

In this paper, the residual ultimate strength of stiffened box girder with coupled damage of pitting corrosion and a crack subjected to vertical bending moment was numerically investigated. Influences of the bending mode, crack length, angle and position as well as pit diameter, depth and density on the strength reduction characteristics were discussed. According to the finite element results, the ultimate strength decreases significantly with the increase of crack length when it is located in the primarily compressed area or destroys the connection of the panel and stiffener. Corroded volume loss is also a critical factor leading to the linear decline of ultimate strength. Superimposed strength reduction as a result of the pit and crack as they exist independently almost equals to the reduction induced by the coupled damage, indicting their effects can be simply composed. Four predictions as a function of actual/projected crack lengths and corroded volume loss were proposed to assess the residual strength of the girder with coupled damage.

Vertical and horizontal bending moments on the hydroelastic response of a large-scale segmented model in a seaway

Wave-induced vertical bending moment (VBM) and horizontal bending moment (HBM) on a large-scale segmented model with a box-type backbone beam in short-crested irregular seas are systematically analyzed using sea trial measurement data. New insights into the relationship between nonlinear VBM and HBM of the ship sailing in short-crested sea waves are explored and presented. The results indicate that the HBM significantly contributes to the total sectional loads when the ship is sailing in a seaway and the HBM has a strong correlation with VBM in both magnitude and tendency. Therefore, design loads of HBM and the corresponding lateral structural strength issues should also be concerned in addition to VBM at the ship design phase.

Simulation based calculation of ship motions in extreme seas with a body-exact strip theory approach

For all design phases of naval vessels, the fidelity of seakeeping calculations in extreme seas is open to discussion due to the inadequacy of the linear theory of ship motions. Currently the computer-generated time series of ship responses and wave height (the real time computer experiments) are utilized to calculate the distribution of the vertical distortion, shear force and bending moment by means of “ship hydroelasticity theory”. Inspired by these studies a simulation based calculation of symmetric ship motions is performed in long crested irregular head seas, in addition with a body-exact strip theory approach. The scope of this study is limited to the ship motions only. Verification is achieved utilizing the spectral analysis procedure which contains the discrete Fourier transform (DFT) and the smoothing algorithms. The results are compared with the experimental data, and the ANSYS AQWA software results. The simulation results provide adequate data for the extreme responses. This state-of-the-art method in addition with a “body-exact strip theory approach” ensures the consistent assessment of the seakeeping performance in extreme sea condition. As a result, it is evaluated that this calculation method can be used in the design stages of naval platforms.

Three-dimensional finite element analysis on the flexural behavior of composite beams under linear displacement

This paper presents a three-dimensional finite element model for reinforced concrete beams to study their flexural behavior under linear displacement with different mesh sizes. The model was assessed in terms of failure modes and ultimate strength of composite beams with three different mesh sizes. This was found to be accurate in taking the linear displacement of the specimens. The analysis was further carried out to study various parameters like the percentage of horizontal and vertical web reinforcement, bending moment, shear strength, compression damage, and tension damage. Based on the results of this study optimum mesh size was proposed for further analysis.

Investigation of Non-Linear Ship Hydroelasticity by CFD-FEM Coupling Method

With the increase of ship size, the stiffness of the hull structure becomes smaller. This means that the frequency of wave excitation tends to be closer to the natural frequency of the hull vibration, which in turn makes the hydroelastic responses more significant. An accurate assessment of the wave loads and motion responses of hulls is the key to ship design and safety assessment. In this paper, the coupled CFD (Computational Fluid Dynamics)-FEM (Finite Element Method) method is used to investigate the non-linear hydroelasticity effect of a 6750-TEU (Twenty-foot Equivalent Unit) container ship. First, by comparing the heave, pitch, and vertical bending moment at midship section (VBM4) against experimental results reported in the literature, the validity of the numerical method in this paper is illustrated. Secondly, the ship responses under different wave length–ship length ratio, wave frequency-structure natural frequency, wave steepness, and ship speeds are studied. It is found that the wave length–ship length ratio has a more important influence on the hydroelastic response than that from wave frequency-structure natural frequency ratio, and the effect of wave non-linearity will behave differently under different wave length–ship length ratio. The increase of rigid body motion caused by forward speed will not correspondingly increase the non-linearity of the hydroelastic response.

Resarch on Calculation Method of Pile Horizontal Response under Combined Loads

The main function of the pile foundation is to bear the vertical load, but in actual engineering, the pile foundation usually bears combined loads which contain vertical load, lateral load and bending moment. Under combined loads, due to the P-Δ effect, the calculation of the bearing capacity and deformation of the pile foundation is very complicated. The small deformation superposition principle recommended by the current pile foundation codes fails to consider the resistance of the soil around the pile under the combined loads, and it is difficult to accurately evaluate the influence of P-Δ effect on the bearing capacity and deformation of pile foundation. In view of this, this paper firstly starts from the potential energy equation of the pile-soil system and deduces the calculation formula for the horizontal displacement of the pile considering the P-Δ effect, and it is verified in conjunction with related calculation examples. Then the factors affecting the P-Δ effect are discussed in detail, and the results show that the larger the load ratio is, the more obvious the P-Δ effect will be; when the pile top is fixed under the same load condition, the P-Δ effect will be significantly weakened.

Cyclic behavior of wood-frame shear walls with vertical load and bending moment for mid-rise timber buildings

In light wood-frame buildings, the gravitational and lateral force-resisting systems are composed of floor diaphragms and shear walls. During an earthquake, these walls are subjected to the simultaneous action of in-plane vertical force, shear force, and in-plane bending moment. In a mid-rise building, these internal forces can reach large magnitudes, especially on the lower stories, and could have an important influence on the lateral behavior of the walls. The historical use of light wood-frame construction has been in low-rise buildings. Consequently, few investigations have analyzed the effects of high gravitational forces or in-plane bending moment on the lateral behavior of wood shear walls designed for multi-story buildings. This paper presents an investigation of the cyclic lateral behavior of light wood-frame shear walls, designed for mid-rise buildings, subjected to large axial compressive load and in-plane bending moment. Eight wall specimens were experimentally tested with a cyclic lateral displacement protocol, a constant compressive load, and a cyclic in-plane bending moment. The effects of axial compressive load and in-plane bending moment were analyzed. Also, the wall length and the spacing of sheathing nails were varied to study the effects of these variables on the response. A numerical study was performed to show how these effects could influence the response of mid-rise timber buildings. An improvement in the lateral performance of the walls was observed compared to walls tested without compressive force nor bending moment, showing an increase in stiffness, load-carrying capacity, and dissipated energy.

Assessment of wave induced higher order resonant vibrations of ships at forward speed

An efficient nonlinear time domain method computed higher order springing induced vertical bending vibrations of ships in waves. A weakly nonlinear time domain approach obtained the hydrodynamic response of the elastic hull girder, and a linear finite element model based on Timoshenko’s beam theory calculated its structural response. Coupling of the fully nonlinear stationary forward speed problem with the weakly nonlinear elastic body seakeeping problem constituted the major progress. We demonstrated that accounting for the nonlinear stationary forward speed problem significantly affected the prediction of springing-induced vibrations. Rigid body motions were computed via a nonlinear equations of motion. Elastic vibrations were computed using the modal superposition technique based on linear elastic motion equations. Radiation forces of the moving and vibrating hull structure (rigid body and elastic) were computed via convolution integrals, and Froude–Krylov and hydrostatic forces were combined and integrated over the instantaneous wetted surface. A waterline integral accounted for nonlinear effects of radiation and diffraction forces due to the changing wetted surface. A two-way coupling algorithm ensured accurate convergence. Comparisons of the numerically calculated midship vertical bending moment of a large container ship with experimental results showed good agreement. Investigations of the subject container ship advancing at forward speeds of 15 and 22kn in regular head waves focused on second, third, and fourth order springing.

The effect of spatial correlation of sea states on extreme wave loads of ships

ABSTRACT The purpose of the study is to include a spatial statistical correlation between sea states that ship encounters during a voyage to improve wave scatter diagram for the analysis of ship structures. The methodology consists of computation of system reliability of a series of partially correlated events, representing sea states that ship encounters along the sailing route. The North Atlantic wave scatter diagram is modified to account for such spatial correlation and new scatter diagrams for partially correlated sea states are constructed. Based on such “correlated scatter diagrams”, long-term distribution of vertical wave bending moments is performed and compared to the results following from an “uncorrelated scatter diagram”. It was found that a spatial correlation may considerably reduce extreme vertical wave bending moments. Verification of the methodology is performed by simulating shipping route in the North Atlantic using ERA5 wave database.

Risk-based ultimate strength design criteria for very large floating structure

Very large floating structures (VLFSs) are novel offshore structures without direct reliability design criteria available currently. Target reliability, as a critical safety indicator, could be used to evaluate the ultimate strength reliability of VLFSs. Therefore, it is necessary to establish acceptable risk criteria to determine the structural design target reliability of VLFSs and to calculate partial safety factors (PSFs) for use as ultimate strength design criteria. This paper developed a reliability assessment process in order to achieve the ultimate strength design criteria of VLFS. A reasonable target reliability range for VLFS was determined by risk assessment methods and principles considering the structure failure probability and consequences. The longitudinal ultimate strength for the typical sections of VLFS was calculated by applying the simplified progressive failure method. The vertical extreme wave bending moments and their uncertainties for the corresponding typical sections of VLFS were analysed based on wave scatter diagram of the South China Sea. Finally, the ultimate strength reliability was assessed based on the reasonable target reliability range established within this paper. Results have shown that the reasonable target reliability range is found to be applicable for identifying the weak structural components of VLFS and some typical sections of VLFS should be redesigned to satisfy the criteria. This paper can provide a reference for the safe design and compilation of relevant guidelines for VLFS.

Flexural Response of Reinforced Concrete Beam on Elastic Foundation under Vertical Load and Bending Moment: Review of Existing Methods and Proposed New Method

AbstractThis work examined the behavior of a RC beam on a soil foundation subject to concentrated vertical loads and bending moment in both the elastic and the plastic phases. Some of the simplifie...

Uncertainty analysis of hydroelastic responses and wave loads for different structural modeling and potential methods

Different modeling methods and potential flow methods have substantial influences on the prediction results of wave loads and hydroelastic responses of ships traveling in waves, so it is of great importance to carry out uncertainty analyses for relevant aspects. For a very large bulk carrier, the 1D Euler–Bernoulli beam and 3D FEM are used to build the dry structure model, and 3D methods in the frequency domain and time domain are used to predict the wave loads. The influences and uncertainties of the structure modeling method on the hydroelastic response and wave load are assessed, which indicates that the 1D Euler–Bernoulli beam model overestimates the resonant frequencies. Furthermore, the hydroelastic responses and wave loads are analyzed using three-dimensional methods in the frequency domain and time domain for a 205,000 DWT bulk carrier, a 500,000 DWT ore carrier and a 156,800 m3 LNG carrier. Furthermore, a comparison is conducted between the numerical prediction results and experimental data measured from the see-keeping basin; meanwhile, the error principles of the numerical analysis are investigated, which infers that the vertical bending moment and horizontal bending moment have smaller numerical prediction errors, while the torsional moment has the largest error.

A numerical method to compute global resonant vibrations of ships at forward speed in oblique waves

Resonant wave-induced vibrations of a ship hull girder, known as “springing”, is an important issue when addressing fatigue aging of the steel structure. To compute resonant wave-induced vibrations, fluid-structure interactions and associated structural and hydrodynamic properties need to be addressed. This paper introduces a time-domain numerical method that predicts higher-order springing taking into account forward speed. Structural dynamics were computed based on a beam element approach that considers vertical and horizontal bending as well as nonuniform torsion. Furthermore, mass and stiffness matrices accounted for strong coupling effects between hull girder bending and torsion. The hydrodynamic solver coupled the fully nonlinear stationary free surface flow with the oscillatory flow and considered geometrical nonlinearities caused by the changing wetted surface due to the incident waves, nonlinear rigid body motions and linear elastic vibrations. Numerical predictions were validated against model tests of a post-Panamax containerships at forward speed. Dry and wet natural frequencies and midship vertical bending, horizontal bending and torsional moments induced by higher order springing vibrations compared favourably to experimental measurements.

Load calculation and strength analysis of floating garbage cleaning equipment

In order to alleviate the problem that there is increasingly floating garbage pollution on the sea, this paper proposes a new design of floating garbage cleaning equipment. This equipment is a slender structure, and whether its structural strength can meet the design requirements requires special attention. In order to ensure the rationality and safety of the design, load calculation and strength analysis are carried out based on the design wave method. The calculation results show that the longitudinal torque load of this equipment is the largest, which is 2.5 times of the second largest vertical bending moment. At the same time, there are three large stress areas in the floating structure, which are the connection between the pontoon and the connecting buntons, the connecting buntons intersecting with the Y axis and the pontoons on both sides. For the abovementioned high-stress areas, a structural strengthening plan is proposed. After the improvement, the stress in the high-stress areas of the structure is significantly reduced, with a maximum reduction of 52%. The strength of the improved structure meets the design requirements. The research results of this paper can provide relevant references for the development of floating garbage cleaning equipment in the future.

Probabilistic time series prediction of ship structural response using Volterra series

This study targets to develop a computational procedure to predict the structural response of a ship voyaging through irregular seaways taking into account the relevant uncertainties from probability perspective. To achieve the goal, ship structural response under random wave excitation was assumed to be linear one and represented by linear Volterra series, which is expanded by linear combination of Laguerre polynomials. Then the unknown Laguerre coefficients were treated as random variables, the probability of which was sought by solving Bayesian linear regression model using prepared data sets. For the validation of the proposed methodology, a single DOF linear oscillator model with artificial damping uncertainties was introduced and time series of the system response was predicted probabilistically. For more practical and realistic application, 400,000 DWT VLOC model ship experimental data was analyzed and vertical bending moment time series were probabilistically predicted using the proposed method. On top of probabilistic time series prediction of model ship, the fatigue damage was also estimated based on the stochastic time series obtained using predicted probabilistic time series data.