Study on Nonlinear Response of Steel Fixed Offshore Platform Under Environmental Loads

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Arabian Journal for Science andEngineering ISSN 1319-8025Volume 39Number 8 Arab J Sci Eng (2014) 39:6017-6030DOI 10.1007/s13369-014-1148-x

Study on Nonlinear Response of Steel FixedOffshore Platform Under EnvironmentalLoads

Shehata E. Abdel Raheem

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Arab J Sci Eng (2014) 39:6017–6030DOI 10.1007/s13369-014-1148-x

RESEARCH ARTICLE - CIVIL ENGINEERING

Study on Nonlinear Response of Steel Fixed OffshorePlatform Under Environmental Loads

Shehata E. Abdel Raheem

Received: 22 February 2012 / Accepted: 15 June 2013 / Published online: 6 June 2014© King Fahd University of Petroleum and Minerals 2014

Abstract The structural design requirements of a fixed off-shore platform subjected to wave-induced forces andmoments in steel jacket can play a major role in the design ofthe offshore structures. For an economic and reliable design,good estimation of wave loadings is essential. Wave plus cur-rent kinematics are generated using fifth-order Stokes wavetheory. The horizontal components of the wave velocity andacceleration fields are multiplied by a wave kinematics fac-tor that is intended to account for direction spreading andirregularity of the wave profile. The wave and current forcesacting on the member is computed using Morison’s equa-tion, which decomposes the total force into an inertia com-ponent and a drag component. A nonlinear response analy-sis of a fixed offshore platform under wave loadings is pre-sented; the structure is discretized using the finite elementmethod. The dynamic response of fixed offshore structuretogether with the distribution of displacement, axial force,and bending moment along the leg is investigated for regularand extreme conditions, where the structure should keep pro-duction capability in conditions of the 1-year return periodwave and must be able to survive the 100-year return periodstorm conditions. The result of the study shows that the non-linear response investigation is quite crucial for safe designand operation of offshore platform.

Keywords Offshore structures · Nonlinear response ·Finite element analysis · Wave–structure interaction ·Environmental loads

S. E. Abdel Raheem (B)Taibah University, Medina, Kingdom of Saudi Arabia,e-mail: [email protected]

S. E. Abdel RaheemCivil Engineering Department, Faculty of Engineering,Assiut University, Assiut, Egypt

1 Introduction

The total number of offshore platforms in various bays, gulfs,and oceans worldwide is increasing year by year. Most ofthese platforms are fixed jacket platforms located at 100 ft(30 m) to 650 ft (200 m) depth for oil and gas exploration pur-poses. Fixed offshore platforms are subjected to environmen-tal loads during their lifetime; these loads are imposed on theplatform through natural phenomena such as wind, current,wave, earthquake, snow, and earth movement. The analysis,design, and construction of offshore structures compatiblewith the extreme offshore environmental conditions are themost challenging and creative task. Over the usual condi-tions and situations met by land-based structures, offshore

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structures have the added complication of being placed in anocean environment where hydrodynamic interaction effectsand dynamic response become major considerations in theirdesign [1]. Offshore jacket platforms are normally designedusing one of the following offshore design codes: API RP2AWSD [2], API RP2A LRFD [3], or ISO 19902 [4]. APIRP2A-LRFD and ISO 19902 codes are limit state design-based approaches for design of steel jacket platforms. Work-ing Stress Design by American Petroleum Institute uses acommon factor of safety for material. Static nonlinear analy-sis, i.e. pushover analysis, is widely utilized in current off-shore standards such as API, ISO, and DNV [2–6] to evalu-ate nonlinear behavior and ultimate capacity of offshore plat-forms against environmental loads. In this method, the jacketplatform is subjected to the site-specific design wave load andthe corresponding load pattern is increased monotonicallyuntil the collapse of the structure is exhibited.

The dynamic response evaluation is particularly importantfor waves of moderate heights as they make the greatest con-tribution to fatigue damage of offshore structures and havesignificant roles on reliable design and operational safety ofthe offshore structures [7,8], especially recently when suchstudies are motivated by the need to build solid offshore struc-tures in connection with oil and natural gas productions [9].The effects of various wave patterns on offshore structureshave been investigated by numerous researchers in the past[10–14]. The influence of hydrodynamic coefficients in theresponse behavior depends on the wave period and the vari-ation is nonlinear between the different wave heights of thesame wave period [15,16]. Gudmestad and Moe [17] com-pared the API’s and North Sea design practice approachesrelevant to the selection of appropriate values for the coef-ficients used in the calculation of the hydrodynamic loads.Mendes et al. [18] developed a numerical model for the pre-diction of combined wave current loading. Gomathinayagamet al. [19] reviewed methods of determining wind loads onoffshore structures. Sunder and Connor [20] performed asensitivity analysis on jacket platforms considering differ-ent factors including variations in wave height, uncertaintiesin wave period to be associated with wave height, choiceof hydrodynamic force coefficients particularly in the pres-ence of marine growth, changes in deck mass, and hystereticstructural damping. Asgarian et al. [21] discussed a simplifiedmethod for the assessment of the response of jacket offshorestructures using a lumped mass model. A parametric studyis carried out to investigate the effect of different parame-ters on the response of a simplified soil–structure interac-tion model of fixed offshore platform subjected to transientloading due to extreme wave and current loading [22]. Theeffects of sea water level fluctuations on response of jacketare very important and neglecting these effects during pro-cedure of designing jackets could possibly have destructiveeffects especially in seas that are affected by tidal phenom-

enon and the changes in sea water level are very considerable[23–25].

Dynamic responses of offshore structures in random seasto the inputs of earthquake ground motions show that thehydrodynamic damping forces are higher in random seasthan in still water and sea waves generally reduce the seismicresponse of offshore structures. The first passage probabil-ities of response indicate that small sea waves enhance thereliability of offshore structures against earthquakes forces[26]. The characteristics of dynamic responses of the bottom-mounted platform were investigated using the modal analysisand substructure methods for various seismic accelerationsand soil conditions [27]. Based on the generalized wave spec-tral approach, the response of a compliant platform to irregu-lar waves is determined using finite element method [28]. Toprovide a more accurate and effective design, a finite elementmodel is employed to determine the stresses and displace-ments in a steel jacket under combined structural and waveloadings [29].

The finite element method provides a practical and lessexpensive way for studying the dynamic response of offshorestructures; however, experimental programs are necessaryto provide validation for the finite element results. Throughexperimentations, one can reduce the uncertainty of the val-ues of the damping and excitations for offshore structures[30]. Experimental and analytical investigations have beenconducted to evaluate capacities of offshore structures [31].An experimental program to measure wave impact loads ona jacket offshore structure model is described [32]. For anoffshore structure surrounded by severe wave conditions, itis necessary to examine the effects of wave forces on nonlin-ear responses. The nonlinear wave kinematics and the non-linearity due to waves interacting with the structure are themost important factors. The wave-induced loads on a fixedoffshore platform for storm sea states are governed by thenonlinear drag term of the Morison equation [33]. Moreover,the structural responses of fixed jacket platforms subjectedto extreme loads show a nonlinear range of deformationsthat greatly depends on the buckling mode, post buckling,and hysteresis behavior of jacket braces as well as nonlinearbehavior of jacket frame elements. Therefore, results from alinear analysis such as frequency response calculations maybe comparatively easy to obtain, but their validity is usuallylimited to small amplitude motions [34]. Extreme responseand dynamic amplification factors under extreme wave load-ing conditions are presented for the design of jack-up plat-forms [35]. Prediction of the fatigue life of the structuralcomponent is an important factor in extending the lifetime ofjack-up structures. Uncertainty in the load and strength vari-ables of jack-up platform structure can significantly affectthe structural performance and safety, the reliability of jack-up platform is a crucial aspect with regard to the safety ofthe structure during its service time, and possibly beyond the

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predicted lifetime, there is significant demand from the off-shore industry to investigate system reliability of this type ofoffshore structure [36,37].

The vertical structural load is essentially a static load whilethe lateral wave loading fluctuates in time domain and isdirectly affected by the incident wave angle. It is significantto study the response for different wave approach angles forbetter understanding of fixed offshore platform behavior inregular wave train. In this study, nonlinear dynamic analysisis formulated for reliable evaluation of fixed jacket platformresponses under environmental loads. A three-dimensionalfinite element model [38] is formulated to determine the dis-placements and stresses in a steel jacket under combinedstructural and wave loadings. The nonlinearities consideredis this study cover the structure system geometrical nonlin-earity (large displacement and P-�), material nonlinearity,and wave nonlinear input. Wave plus current kinematics aregenerated using fifth-order Stokes wave theory. The horizon-tal components of the wave velocity and acceleration fieldsare multiplied by a wave kinematics factor that is intended toaccount for direction spreading and irregularity of the waveprofile. The wave and current forces acting on the member arecomputed using Morison’s equation, which decomposes thetotal force into an inertia component (varying linearly withthe water particle acceleration) and a drag component (vary-ing quadratically with the water particle velocity). The analy-sis considers various nonlinearities produced due to changein the nonlinear hydrodynamic drag force. Numerical resultsare presented for various combinations of typical sea states.Natural periods and corresponding vibration mode shapesof the system are calculated. A parametric study of vary-ing certain parameters of the wave and current loads such ascurrent and/or wave incidence angle is conducted to studytheir effects on the internal forces distribution and platformdisplacement under various combinations of wave loadingconditions.

2 Environmental Loads

The response of offshore platform excited by sea currentand sea surface waves is of great interest to the offshoreindustry. Precise prediction of the dynamic behavior is ofprimary importance; therefore, it is necessary to define allthe significant sources of the environmental loads and theexternal forces. Water forces can be classified as forces dueto waves and forces due to water current. Wind blowing overthe ocean’s surface drags water along with it, thus formingcurrent and generating waves. The forces induced by oceanwaves on platforms are dynamic in nature; however, it isthe accepted practice to design shallow water platforms bystatic approach. As the water depth increases and platformsbecome flexible, dynamic effects become more significant.

The estimation of extreme environments from a relativelyshort oceanographic database is crucial to the calculation ofloads and responses of offshore structures. The loads inducedby extreme storms are critical in the design of offshore struc-tures for location in severe seas. The design environmentalloads such as wind, wave, and current depend on geograph-ical locations. In the absence of site-specific data, regionalinformation is defined in all three codes that give minimumrequirements of the extreme environmental conditions. Forsome areas, substantial database from marine forecastingof the site is becoming available with to establish statis-tics of joint probability of occurrence of wind, wave andcurrent magnitudes and directions. When such a databaseis available, it can be used to develop environmental condi-tions, which provides the true 100-year return period extremeglobal environmental action on the structure.

2.1 Waves and Hydrodynamic Loads

Tides affect the wave and current loads indirectly as usedin platform design, i.e. through the variation of the level ofthe sea surface. The tides are classified as (a) astronomi-cal tides caused essentially by the gravitational pull of themoon and the sun, and (b) storm surges caused by the com-bined action of wind and barometric pressure differentialsduring a storm. The combined effect of the two types oftide is called the storm tide [5,6,39]. Several theories forthe description of the shape and kinematics of regular wavesexist. Regular wave theories used for calculation of waveforces on fixed offshore structures are based on the three para-meters: water depth (d), wave height (h), and wave period(T ) as obtained from wave measurements adapted to differ-ent statistical models, Fig. 1. Wave plus current kinematics(velocity and acceleration fields), Fig. 2, are generated usingfifth-order Stokes wave theory. The horizontal componentsof the wave velocity and acceleration fields are multiplied bya wave kinematics factor that is intended to account for direc-tion spreading and irregularity of the wave profile. The waveforce acting on the member is calculated using Morison’sequation based on hydrodynamic drag and mass coefficients(Cd, Cm) and particle velocity and acceleration obtained bythe chosen wave theory. This description assumes the wave-form whose wave height is small in comparison to its wave-length, L , and water depth. The hydrodynamic force vec-tor is calculated in each degree of freedom. The intensityof wave force per unit length on the structure is calculatedaccording to Morison’s equation. The response analysis isperformed in time domain to solve the dynamic behaviorof jacket platform as an integrated system using the iter-ative incremental Newmark’s Beta approach. Stokes fifth-order wave is defined by providing wave height and periodin the input data with the wave type specified as Stokes in theSap2000 options [40]. Stokes waves were applied as dis-

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Fig. 1 Wave coordinate systemand typical wind and tidalcurrent profile

Fig. 2 100-year return period wave/current horizontal velocity

tributed loads to the submerged members of the offshorestructure using normal offshore design procedures. The Cd

and Cm values are considered as per American PetroleumInstitute [2] to be 0.65 and 1.6, respectively. The same val-ues of wave parameters are applied in three directions ±0◦,±45◦ and ±90◦ (X , XY , and Y ) with the associated cur-rent parameters having the same direction of wave applica-tion.

2.2 Current Loads

The wave induces an orbital motion in the water in whichthey travel. However these orbits are closed, they experiencea slight drift forward to wind surface effects. The currentis actually induced by wave. A current in the wave direc-tion tends to stretch the wavelength [1,2]. Typical wind andtidal current profile that shown in Fig. 1 are consider in thisstudy.

2.3 Wind Loads

Wind possesses kinetic energy. When a structure is placedin the path of the moving air so that wind is stopped or isdeflected from its path, all or part of the kinetic energy istransformed into the potential energy pressure. Therefore,wind forces on any structure result from the differential pres-sure caused by the obstruction to the free flow of the wind.These forces are functions of the wind velocity, orientation,and area and the shape of the structural elements. Wind forceson a structure are a dynamic problem but, for design purposes,it is sufficient to consider these forces as an equivalent staticpressure.

3 Jacket Platform Structural Model

A classical steel fixed jacket-type platform [38,41,42] thatwidespread and currently installed in the Suez gulf—Red sea,

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Fig. 3 Fixed steel offshore platform photo in site and finite element model based on as built drawings

Fig. 3, is considered in this study. The offshore structure is afour-leg jacket platform, consisting of a steel tubular-spaceframe. There are diagonal brace members in both verticaland horizontal planes in the units to enhance the structuralstiffness. The platform was originally designed as a four-pile platform installed in 110 feet (110′ = 33.5 m) waterdepth;

The Top side structure consists of Helideck 50′ × 50′ atELevation, EL. (+54′) and Production deck 50′ ×50′ at EL.(+26′); Top of jacket at EL (+12.5′).The Jacket consists of 4 legs with 33 in. outer diameter (33′′O.D.) and 1 in. wall thickness (1′′ W.T.) between EL. (+10′)and EL. (−23′) and (33′′ O.D. × 0.5′′ W.T.) between EL.(−23′) and EL. (−110′).In the splash zone area that is assumed to extend fromEL. (−6′) to EL (+6′) LAT (lowest astronomicaltide).The jacket legs are horizontally braced with tubular mem-bers (8.625′′ O.D. × 0.322′′ W.T.) at elevations (+10′);(10.75′′ O.D. × 0.365′′ W.T.) at elevations (−23′); (12.75′′O.D. × 0.375′′ W.T.) at elevations (−62′) and (14′′ O.D. ×0.375′′ W.T.) at elevations (−110′).In the vertical direction, the jacket is X-braced with tubularmembers (12.75′′ O.D. × 0.844′′ W.T.) from EL. (+10′)to EL. (−23′) and (12.75′′ O.D. × 0.375′′ W.T.) from EL.(−23′) to EL. (−110′). The platform is supported by 4 piles(30′′ O.D. × 1.25′′ W.T.).

4 Finite Element Analysis Procedures

A three-dimensional model had been generated based onbuilt-up drawings for a classical steel platform [38,41,42].A finite element analysis is carried out under different typesof wave loadings. The hull of jack-up is relatively stiff com-pared to legs, so the structural model concentrates on theaccurate description of load deformation characteristics ofthe legs. The legs are modeled by equivalent beam elements.For the present analysis, dead loads include all fixed items inthe platform deck, jacket, and bridge structures. Live loadsare defined as movable loads and will be temporary in nature.A uniformly distributed live load intensity of 50 psf “0.245t/m2” is applied to Helideck area; 200 psf “0.978 t/m2” isapplied to production deck area and cellar deck area. Thewater depth in the location of installed platform is110′ (33.5 m).

The first edition of API RP 2A [2] which used the work-ing stress design was issued in 1969. Structural design hasevolved over the years and 22 editions of the code have beenpublished. Prior to the 7th edition (1976), return period of thewave was not specified and both 25- and 100-year waves wereused. After the 7th edition, a 100-year wave became standardpractice. The 20th edition (1993) introduced a new wave for-mulation and recommended using 100-year load condition.These changes with higher recommended drag coefficientshave led to design loads that are 2–4 times higher today thanwhat they were for early generation platforms [43].

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5 Numerical Results and Discussion

The stress distribution within such a large structure is a dom-inant factor in the design procedure of an offshore struc-ture. To provide a more accurate and effective design, thefinite element analysis package, SAP2000 computer soft-ware package [40], is employed herein to determine the inter-nal forces and displacements in an offshore leg under com-bined structural and wave loadings. The vertical structuralload is essentially a static load, while the lateral wave load-ing fluctuates in time domain and is directly affected by theincident wave angle. A three-dimensional model had beengenerated based on built-up drawings for a classical steelplatform. Secondary members that are not expected to con-tribute much to the structure strength are not included in themodel simulation (i.e. ladders, grating, etc.) but their loadswere reflected to the model. The right-hand Cartesian sys-tem is used with the Z -axis vertically upwards and the ori-gin is located at the Mean Water Level (MWL) as shown inFigs. 3 and 4.

Application of the statistical process of extreme analysisto the hindcast data at specific sites yields the design criteria(e.g. 1- and 100-year return period significant wave periodand height) required by structural engineers. A wave height of1- or 100-year return period is the commonly used design cri-terion, which was extended by employing the combination ofthe 100-year wave with the 100-year wind. A formula givenby American Petroleum Institute [1,2] is used to calculate

Fig. 4 Finite element model and selected nodes for measured response

wind force on offshore structures. The 100-year return periodsustained wind at 30 ft above LAT shall be 70 mph (mile perhour); the wind may act in any direction. The wind speed istaken to be varying with height according to the power law. A1-year return period wave with a height of 17 ft and a periodof 6.5 s and a 100-year return period wave with a height of26 ft and a period of 8 s were selected for the analysis that isnormally used for safety checks in operation and storm con-ditions, respectively. Table 1 lists the wave loading parametervalues for 1-year return period wave for operating conditionsand for 100-year return period wave for safety conditions.

5.1 Natural Vibration Analysis

The natural periods and corresponding vibration mode shapesare computed by Eigen values analysis; the first three dom-inant vibration modes are shown in Fig. 5 and the naturalperiod values and corresponding vibration mode for the firstsix vibration modes are listed in Table 2. The first and sec-ond modes are sway modes in y- and x-directions with slightdifferent natural periods. The three first vibration modes pre-sented predominance of displacements in the steel jacket sys-tem. In the first vibration mode there is a predominance oftranslational displacements towards the “y” axis in the finiteelement model. In the second vibration mode a predominanceof translational effects towards the axis “x” of the numeri-cal model was observed. The third vibration mode presentedpredominance of torsional effects on the steel jacket systemwith respect to vertical axis “z”. While the higher modes fromfourth to sixth are local vibration modes of bracing or couplehigher-order global sway model with local bracing vibrationmode.

5.2 Geometrical Nonlinearity Effects

The beam column model of platform jacket is subjected totransverse load due to regular waves and axial load due toweight. The nonlinearities considered is this study cover thestructure system geometrical nonlinearity (large displace-ment and P-�), material nonlinearity, and wave nonlinearinput. Effect of geometrical nonlinearity on structuralresponse is compared to that using linear formulation. How-ever the material nonlinearity is checked, the structure sys-tem displays elastic behavior. The wave load calculationsare based on the requirements presented in the AmericanPetroleum Institute 2000 reference [3]. It generates loads onthe structure resulting from waves, current flow, buoyancyand wind. Wave plus current kinematics (velocity and accel-eration fields) are generated using fifth-order Stokes wavetheory. The horizontal components of the wave velocity andacceleration fields are multiplied by a wave kinematics fac-tor that is intended to account for direction spreading and

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Table 1 Wave loading parameter values

Definitions Water depth (ft) LAT (ft) HAT (ft) Tide (ft) Hmax. (ft) Tp (sec)

1-year return period wave for operating conditions 110′ −6′ 6′ 3′ 17′ 6.5

100-year return period wave for storm conditions 5′ 26′ 8

1st sway-Y 2nd sway-X 1st torsion

Fig. 5 Vibration modes with predominance of the steel jacket system

Table 2 Natural period and vibration mode

Modes 1st mode 2nd mode 3rd mode 4th mode 5th mode 6th mode

Period (s) 0.622 0.616 0.472 0.253 0.252 0.251

Vibrationmode

1st sway-Y,global mode

1st sway-X,global mode

1st torsion,global mode

Horizontal bracinglocal mode

Vertical bracinglocal mode

2nd sway-Y, global modeand vertical bracinglocal mode

irregularity of the wave profile. The wave force acting on themember is calculated using Morison’s equation. The size of amember used to calculate the wave load force is based on thesection assignment, the specified marine growth. Responsesare linear with respect to excitation, if a change in the mag-nitude of excitation induces the same magnitude change forresponses. However, in high waves the linearity assumptionof wave loads with respect to wave height is not usually valid.If the responses are strongly nonlinear, the determination ofloads is usually carried out in time domain.

To provide a more accurate and effective design for fixedoffshore platform under structural and lateral wave loads, afinite element model is employed herein to determine thestresses and displacements in a jacket structure under differ-ent loading conditions. A parametric study of varying cer-tain parameters of the wave and current loads such as cur-rent and/or wave incidence angle is conducted to study theireffects on the internal forces distribution and platform dis-placement under various combinations of wave loading con-ditions, Table 3.

5.3 Displacement Response of the Structure

To have a better understanding of the behavior over the entireheight of the platform jacket, the analysis was conductedfor a 110 ft water depth for the maximum wind and waveforces. Although time series deflections of the platform wereestimated, only the maximum deflections to each wave andwind forces are extracted. The deflection responses U1, U2

and Uabshz (absolute horizontal displacement is calculatedas square root of the summation of square of U1 and U2)along the platform jacket height to the wave loading of 1- and100-year return period conditions are shown in Figs. 6 and 7,respectively. It should be noted that the responses consideredare the deflections U1 and U2 in global X - and Y -directions,respectively.

The jacket displacement U1 is dominated by the first swaymode of vibration in wave direction and increases nonlinearlyalong the height of the platform jacket, while the deforma-tion, U2, is dominated by second sway mode of vibration.For the 1-year return period wave for operation conditions,

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Table 3 Load combinations forwave and current incidenceangle effects

Load combination Description

Comb01 DL + LL “Reference case”

Comb02 DL + LL + (wave + wind)1-year + wave/wind/current incidence angle 00.0

Comb03 DL + LL + (wave + wind)1-year + current incidence angle 45.0

















the platform jacket displays maximum deflection demandsfor the coincidence of the wave; current and wind direc-tions “Comb02” in the wave direction of 0.116 and 0.063 ftat platform heli-deck level (+54 ft) and jacket–deck con-nection level (+10 ft). The displacement responses decreaseslightly as the current incidence angle deviate from the wavedirection and this reduction reaches at maximum 14.5 %for current incidence angle of 180◦ “Comb06”. While thewave incidence angle has significant effect on the displace-ment demands, this effect reaches 62 % reduction in the U1

and Uabshz displacement responses “Comb10”. For the 100-year return period wave for storm/extreme conditions, theplatform jacket displays maximum deflection demands forthe coincidence of the wave; current and wind directions“Comb11” in the wave direction of 0.165 and 0.109 ft atplatform heli-deck level (+54 ft) and jacket–deck connectionlevel (+10 ft). The displacement responses decrease slightlyas the current incidence angle deviates from the wave direc-tion and this reduction reaches at maximum 32 % for cur-rent incidence angle of 180◦ “Comb15”. While the waveincidence angle has significant effect on the displacementdemands, this effect reaches 57 % reduction in the U1 andUabshz displacement responses “Comb19”.

For the current incidence angle 90◦ “Comb04 andComb13”, the displacement responseU2 is significantly amp-lified; however, its effect on the absolute horizontal displace-ment is negligible due to its small value, while for the waveincidence angle 90◦ “Comb08 and Comb17”, the displace-ment response U2 is significantly amplified and its contribu-

tion to the absolute horizontal displacement reaches 50 %.Large inter-story drift of the jacket leg is not allowed forthe jacket platform to satisfy the drilling and productionrequirements. Both the maximum deck acceleration and themaximum deck to top of jacket displacement were importantresponse parameters affecting the performance of equipment,vessels, and pipelines. On one hand, low maximum deckacceleration was desirable for the vessels and equipment,but on the other hand, a small deck-to-top of shaft displace-ment was desirable for the risers and caissons. The 1997 UBCrequires that story drift be limited to 0.025 for short periodstructures and 0.020 for long period structures [44]. ASCE 7-02 requires that story drift be limited based on the type and useof the structure [45]. Acceleration limit values (m/s2) rangesfrom 0.315 to 1.0. The value 1.0 is the acceptable accelerationvalues for human comfort in accordance with [46,47].

From analysis results, the displacement response is inves-tigated for the critical nodes: node A1 of jacket–deck con-nection level (+10 ft), node E of center of horizontal bracingat level (+10 ft) and node A0 of jacket top (heli-deck level+54 ft). A comparison of the maximum displacement at allnodal points for various load combinations could indicate thecurrent incidence angle, wave incidence angle and load con-ditions. Figures 8 and 9 show the horizontal displacements atjacket–deck connection level and at jacket level (+10 ft) fordifferent loads combinations. While the structural dead andlive vertical loads are kept constant for all combinations, theupward force of buoyancy for 100-year return period waveis greater than that of 1-year return period wave, so the dis-

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Fig. 6 Displacement with respect to jacket levels for 1-year operating conditions

placement (U3 direction) of node E2 (center intersection jointof horizontal bracing) is much less for the 100-year loadcombinations than for the 1-year load combinations due toreduction of vertical force effect as a resultant of buoyancyand structural forces. The results indicate that the currentincidence direction has a slight effect on the horizontal dis-placement response, while the wave incidence direction playssignificant effects on the displacement response value anddirections. The 100-year return period wave display 42 and

73 % higher displacement demands compared to that of 100-year return period wave at node A0 of jacket top (heli-decklevel +54 ft) and node A1 of jacket–deck connection level(+10 ft), respectively.

5.4 Deformation Shape of the Jacket at Level +10 ft

The critical plan of jacket is located at level +10 ft of thejacket and from analysis we notice the deformation shape

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Fig. 7 Displacement with respect to jacket levels for 100-year safety conditions

of jacket with load combination of wave extreme conditionswith different wave incidence angles, for 100-year wave loadcondition. Deformation shapes are plotted and are shown inFig. 10.

5.5 Bending Moment and Axial Force Responses

Figures 11 and 12 show a comparison of the maximum bend-ing moments at critical levels along jacket leg. As the bending

moment is generally concentrated at the connection pointsbetween the different structural systems, the biggest valuecan be expected to occur at the fixed base of the structure;however, the bending moment response at level (10 ft) dis-plays comparable values and reach 235×103 lb.ft and 262×103 lb.ft for 1- and 100-year return period wave conditions,respectively. The results indicate thatthe current/wave incidence direction has a slight effect onthe bending moment demands for 1-year return period wave

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Fig. 8 The variation of displacements of jacket node A1 and A0 at “jacket–deck” connection

Fig. 9 Displacement variation of jacket center node E2 at level (+10 ft)

(Comb02–Comb11), while the current incidence directionplays significant effects on the bending moment demandsvalue and directions, reach 68 % for incidence angle of 180◦(Comb11–Comb15). The 100-year return period wave dis-plays 93 and 22 % higher bending moment demands com-pared to that of 100-year return period wave at fixed base ofthe jacket (level −122 ft) and of jacket–deck connection level(+10 ft), respectively. The effects of wave/current on forcesdemands decrease for the measured response at higher levelsalong jacket.

Figure 13 shows a comparison of the maximum axial forceat critical levels along jacket height. It is important in thedesign of platform leg to determine the location of maximumaxial force because the jacket diameter wall thickness can bereduced below locations of maximum stresses.

6 Conclusions

Safe and cost-effective design of offshore platforms dependto a large extent on the correct assessment of response de-mands which is expected to be encountered by the structureduring its life span; the extreme design conditions are site spe-cific. It is crucial to reduce the overall response of a jacketplatform subjected to environmental loads. In general, thereduction of dynamic stress amplitude of an offshore struc-ture by 15 % can extend the service life over two times [48]and can result in decreasing the expenditure on the mainte-nance and inspection of the structure.

The periodic inspection and monitoring of offshore plat-forms for certification need the study of the responses ofstructures owing to wave and wind forces. A finite elementformulation has been developed for the nonlinear response

- Comb 11 - Comb 16 - Comb17

Fig. 10 Deformation shapes of jacket level (+10 ft) for extreme load combinations

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Fig. 11 Bending moment response with load combinations

Fig. 12 Bending moment response with load combinations for different levels

of a fixed offshore platform jacket. The time-dependent waveforce has been considered as a drag component of the waveforce, which is a function of second-order water particlevelocity; hence, the nonlinearity due to the wave force hasbeen included.

The offshore structural analysis is used to obtain plat-form displacement response under varying external loadings.The deflection of the platform is studied for individual andcombined wind and wave forces. Offshore platform jacketdisplacement, axial forces, bending moments, and naturalmodes and frequencies of free vibration are evaluated. A

comparison of the maximum displacement at all nodal pointsfor various wave and current incidence angles is introduced.The results indicate that the current incidence direction has aslight effect on the horizontal displacement response, whilethe wave incidence direction plays significant effects on thedisplacement response value and directions. The displace-ment response, U1, increases nonlinearly with the height ofthe platform jacket, but there is a significant curvature tothe displacement response, U2, along the platform height.The results indicate that the current/wave incidence direc-tion has a slight effect on the bending moment demands for

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Fig. 13 Normal force response “N.F.” with load combinations for dif-ferent nodes

1-year return period wave, while the current incidence direc-tion plays significant effects on the bending moment demandsvalue and directions. The 100-year return period wave dis-plays 93 and 22 % higher bending moment demands com-pared to that of 100-year return period wave at fixed baseof the jacket (level −122 ft) and of jacket–deck connectionlevel (+10 ft), respectively. The effects of wave/current onforces demands decrease the measured response at higherlevels. Large inter-story drift of the jacket leg is not allowedfor the jacket platform to satisfy the drilling and productionrequirements. Both the maximum deck acceleration and themaximum deck to top of jacket displacement were importantresponse parameters affecting the performance of equipment,vessels, and pipelines. On one hand, low maximum deckacceleration was desirable for the vessels and equipment, buton the other hand, a small deck to top of shaft displacementwas desirable for the risers and caissons. Nonlinear analy-sis is required for a realistic determination of the behaviorof structures and to obtain an economical and rational struc-tural design. Results provide promising insights into designand fabrication of fixed platforms. The results of these inves-tigations highlight the importance of accurately simulatingnonlinear effects in fixed offshore structures from the pointof view of safe design and operation of such systems.

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Study on Nonlinear Response of Steel Fixed Offshore Platform Under Environmental Loads

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