Evaluating the safety of floating structure under the design sea condition

194 Evaluating the safety of floating structure under the design sea condition Msc Nguyen Tien Cong [1], Dr Le Thanh Binh[2] 1 Shipbuilding Faculty, Vietnam Maritime University, congnt@vimaru edu vn 2[.]

Evaluating the safety of floating structure under the design sea condition

Msc Nguyen Tien Cong [1] , Dr Le Thanh Binh [2]

1 Shipbuilding Faculty, Vietnam Maritime University, congnt@vimaru.edu.vn

2 Shipbuilding Faculty, Vietnam Maritime University, binhlth@vimaru.edu.vn

Abstract This paper shows results from the calculations and analyses of the longitudinal strength of a

multi-purpose floating structure built by Quang Trung Mechanical Enterprise in Vietnam The structure

is concerned under its design sea conditions, using environmental statistical data and spectral theory of ship hydrodynamic in irregular waves The long-term distribution of wave bending moment is approximated to the Weibull distribution based on the results of short-term analyses For analyzing the longitudinal strength, the calculation is taken for different wave propagation directions and in different sea states corresponding to the wave statistical data As a result, the study will give a conclusion about the safety of the structure in terms of longitudinal strength This paper also introduces a reliability based approach for accessing structure’s strength to predict the working safety of floating structures under the real sea conditions

Keywords: shear forces, bending moments, floating structure, longitudinal strength, spectral theory,

reliability based approach

1 Introduction

During the lifetime of ships and floating structures, besides loads from structure’s weight, cargo, etc the structures have to work under loads induced by surrounding environment, for example sea waves, wind and current Wave induced motions and loads on structures are the common topics that are being highly concerned in recent years In the assessment process of longitudinal strength, the most important load is vertical wave bending moment amidships that depends on many factors, for example the loading conditions, the weight distribution, the angle of incoming waves, etc These factors are mostly random and must be taken into account in calculations Because of the randomness, many studies often based

on probabilistic theory and spectral theory using wave statistic data of the navigating area So, the researched structures are then evaluated the safety factor by calculating probability of exceeding extreme values A.P Teixeira & C Guedes Soares [5] presented the reliability based approach to determine the design loads for the remaining lifetime of ships In their study, the probability distribution

of the wave induced loads was obtained by weighting the conditional Rayleigh distribution according

to the probability of occurrence of the various sea states in the ship route, such as significant wave high

Hs, zero up-crossing frequency T0, the ship heading θ, ship speed v and loading condition c, etc The

exceedance probability of the vertical bending moment (VBM) was approximated to the Weibull distribution Using these methods, authors evaluated the longitudinal strength of the studied ship in the period of 20 years, predicted the remaining time of the ship This calculation method was also applied

by C Guedes Soares in the report for “Probabilistic Models for Load Effects in Ship Structures” [6]

In addition, to ensure the safety during working time, the strength of ships are often evaluated through either ships ultimate strength performance or fatigue and fracture analyses For example, J.K Paik et al [9], in 2009, used ALPS/ULSAP code for ultimate strength calculations of stiffened plate structures and ALPS/HULL code for progressive hull collapse analysis The structure in their study is a Suezmax tanker Z Shu & T Moan [10] also presented a study for the “assessment of the hull girder ultimate strength of a bulk carrier using nonlinear finite element analysis”

Regarding the fatigue and fracture analyses, ship structures are often studied in more details, at specific positions which are predicted to occur the fatigue or fracture damages, such as window and door corners

of ship structure studied by Mika Bäckström & Seppo Kivimaa [11], fillet welds at doubler plates and lap joints studied by O Feltz & W Fricke [12], hatch corners studied by Hubertus von Selle et al [13] and hatch cover bearing pad by Kukkanen T and Mikkola T P J [15]

This paper presents an analysis of the longitudinal strength of the multi-purpose floating structure built

by Quang Trung Mechanical Enterprise The structure has the main task as a transhipment terminal of containers for container ships in Vietnam, and as a floating dock for building new ship and ship repairing Because the structure is newly designed with the dimensions exceeding the current upper limit values of Vietnam Register (VR), all the analyses of the structure safety are strictly considered, especially long-term analysis of longitudinal strength The structure is designed to work along the North coast of Vietnam, between Hon Dau and Hon Ngu islands with the sea data are shown in the section 3 later The Response Amplitude Operator (RAO) of shear forces and bending moments (SF/BM) of the structure will be calculated, combined with wave spectra data to get the output spectra of SF/BM From these calculations, the life time of the researched structure will be predicted

2 Theory background

2.1 Wave load on ships and offshore structures

During the working time, there are a number of forces impacting on the structures Generally, these forces include static loads, low-frequency dynamic loads and high-frequency dynamic loads

Static loads are influenced by weights of ship and her contents, static buoyancy of the ship at rest or

moving, thermal loads resulting from nonlinear temperature gradients within the hull, etc

Low – frequency dynamic loads include following components: wave-induced hull pressure

variations, hull pressure variations caused by oscillatory ship motions, inertial reactions resulting from the acceleration of the mass of the ship and its contents

appendages, reciprocating or unbalanced rotating machinery, interaction of appendages with the flow past the ship, short waves induced loads and termed springing

In fact, gathering all aforementioned loads in one study requires much effort and time Kukkanen T et

al [16] gave a summary report of “Nonlinear wave loads of ships”, in which the these wave loads were detailed by using their own numerical calculations and model test results

Generally, depending on the purpose of particular research, one or several loads are often neglected and the calculations will be easier and faster Similarly, this paper will focus on the first type of the aforementioned loads: static loads and low – frequency dynamic loads The low-frequency dynamic loads, loads on ship when neglect dynamic stress amplification are called wave-induced loads

The calculation of these loads requires a previous determination of ship motions induced by waves This is based on the assumptions of linear theory which both waves and ship motion amplitudes are small In addition, the viscous forces are considered as a relatively unimportant forces in vertical loads calculations Thus, the external hydrodynamic force and moment with respect to the neutral axis of a ship are [1]:

⃗( , ) = (− ⃗)

⃗ ( , ) = ⃗ − ⃗ (− ⃗)

(1)

where w is the wave frequency, Sx is the wetted surface partition from stern to the cross-section, p is the summation of the hydrostatic and total hydrodynamic pressures, vector n is the normal vector of the wetted surface pointing towards the fluid field and x0 is the location of considered intersection point X0

on the neutral axis

Figure 1 Bending Moment, Shear Force and Neutral axis

The gravitational force and moment with respect to the intersection point X0are [1]:

⃗( , ) = 0,0, − − ⃗ (0,0, − )

⃗( , ) = ( ⃗ − ⃗) 0,0, − − ⃗ (0,0, − )

(2)

The inertial force and moment with respect to the intersection point X0are [1]:

(3)

where( , , ) is the motion response at the centre of mass of the j-th section, [ ] is the moment

of inertia of the j-th section The summations of all load components in equation (1) and (2) are the total shear force and bending moment on ships The maximum value of shear force and bending moment RAO among all of the calculated wave frequency points at a particular section is called as SF/BM RAO

at that section

2.2 Short-term analysis for longitudinal structure’s strength

The short term analysis is based on the spectral analysis approach developed by Rice (1944) and Wiener-Khintchine theorem that allows us to switch from the time domain to frequency and probability domains Because of stochastic representation, ocean waves are considered to be a Gaussian random process (Rudnick, 1951) so that the wave ordinate follows the normal Gaussian distribution and the wave amplitude follows Rayleigh distribution Using seakeeping program, we can obtain the Response Amplitude Operators (RAO) of the structure motion parameters and forces Thus, the spectra of output response is evaluated by [2]:

where ( ) is the structure’s response spectra, ( ) is wave spectra, and RAO ( ) is the response

amplitude operators corresponding to the output data that we need for analysis Subsequently, the spectra of the shear forces and bending moments (SF/BM) on structures will be calculated from wave spectra following equation:

where ( ) / is the spectrum of the shear forces or bending moments, ( ) / is the RAO

of shear forces, bending moments, respectively

Generally, to study the motions and loads on floating structures or ships, the wave frequency is often considered in the range from 0.2 rad/s to 2.5 rad/s

Regarding the sea spectra, we can describe the sea state as a stationary random process This means that

we can observe the sea at a particular position within a limited time period, from 0.5 to 3 hours This is the short-term description of the sea Two commonly recommended wave spectra are JONSWAP and Pierson-Moskowitz The JONSWAP spectrum is recommended by 17thITTC for limited fetch [3]:

where

= exp − . √ . and

= 0.09 > .

(6)

T1is the mean wave period defined as:

where

(7)

H1/3is defined as:

The Pierson-Moskowitz spectrum is a special case for fully developed long crested sea The spectral ordinate at a frequency (in rad/s) is [3]:

( )

where

= 2 ( ) /

T1 = 1.086.T2 T0 = 1.408.T2

(10)

Equation (6) satisfied equation (8) is only true for a narrow-banded spectrum and when the instantaneous value of the wave elevation is Gaussian distributed

Following IACS Recommendation No.34, [4] with the assumption that the process is narrow banded,

amplitudes of the vertical wave bending moment (MW) in short-term sea state follows Rayleigh distribution Thus, the probability function for the maxima (peak values) MWcan be obtained following equation:

, = − (11) Where process variance is calculated as area below response spectrum:

Where Pshis the probability that wave induced bending moment on ship exceeding the given peak value

of the bending moment MW; SRis the spectral of response

2.3 Long-term analysisforlongitudinal structure’s strength

Long-term probabilities of the vertical wave induced bending moment exceeding given values are calculated by combining the short-term probabilities with the probabilities of sea state and other factors such as ship headings, ships speeds and loading conditions Long-term distribution is given in [5]:

where , , is the relative number of response cycles in each short-term sea state, p(H1/3,T2) is the

probability of occurrence of sea state

In long-term analysis, the probability distribution of VBM exceeding the given value MWfollows the

Weibull distribution FVBM(MW) [6]:

Subsequently, probability of the VBM exceeding the given value Mwis calculated as following function:

Where k and w are parameters calculated from the fitting of ( ) to 1 − ( )

3 Long-term safety evaluation of the multi-purpose floating structure

3.1 Parameters of the structure

To evaluate long-term safety of the investigated floating structure, the details of the structure parameters

as well as structure’s working environment must be provided Table 1 shows the summarization of the structure’s parameters Because the structure is newly designed, then all load conditions data during the life time of the structure are still unknown So, in this study, the load conditions of the structure are supposed to include three main cases: Full load, Ballast load and Partial load, with the corresponding time consuming proportions are 0.4, 0.4 and 0.2 (of the structure’s working time), respectively

Table 1 Main parameters of the structure

Main parameters

amidships [m3] 4.476 Neutral axis [m] 4.600

Parameters in particular load conditions Full load Partial load Ballast load

3.2 Working area data

The structure is designed to work along the North coast of Vietnam, between Hon Dau and Hon Ngu islands shown on Figure 2

Figure 2 The design working area of the structure

In 2014, Supott Thammasittirong (AIT), Sutat Weesakul (AIT), Ali Dastgheib (UNESCO-IHE) and Roshanka Ranasinghe (UNESCO-IHE) [14] presented a report of their study on “Climate Change Driven Variations in the Wave Climate along the Coast of Vietnam” This report included statistical wave data of sea area along the North coast of Vietnam, between Hon Dau and Hon Ngu islands The report also shown that during the period of time from 1981 to 2000, the mean wave height at the above sea area ranged from 0.4 m to 1.0 m; the mean wave period ranged from 4.0 s to 6.5 s and the main wave direction was South-East These data are well fitted with the data from the National Centre for Hydro - Meteorological Forecasting [7] which are given on the Table 2 below

Table 2 gives basic data for the short-term calculations for the structure strength With the results gained from the short-term calculations, strength of structure will be evaluated in given periods of time, such

as 1 years, 5 years, 10 years, and 20 years

Table 2 Annual statistical data of the design sea area

T0[s] 3.5 4.5 5.5 6.5 7.5 8.5 9.5 >10.5 SUM

3.3 Results and discussion

The structure is supposed to work in its design sea wave environment with different wave frequencies and propagation directions These frequencies range from 0.2 rad/s to 2.5 rad/s The wave propagation angles range from -180oto +180o( = 30o) with the corresponding probability of each is 1/12, [3] We also suppose that the weight distribution in each load condition is fixed, the liquid’s sloshing in tanks are neglected, and the structure will generally have 1 month docking for small renovation each year, 3

÷6 months docking for big renovation every 5 years of working Figure 3 shows examples of the calculated bending moment RAO at mid-section of the structure in different wave propagation directions