Offshore Platforms:Observed Behavior and Comparisons With Theory

The dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads is analysed. The non-dimensional form of the motion equation of a beam crossed by a moving harmonic load is solved through a perturbation technique based on a two-scale temporal expansion, which permits a straightforward interpretation of the analytical solution. The dynamic response is expressed through a harmonic function slowly modulated in time, and the maximum dynamic response is identified with the maximum of the slow-varying amplitude. In case of ideal Euler-Bernoulli beams with elastic rotational springs at the support points, starting from analytical expressions for eigenfunctions, closed form solutions for the time-history of the dynamic response and for its maximum value are provided. Two dynamic factors are discussed: the Dynamic Amplification Factor, function of the non-dimensional speed parameter and of the structural damping ratio, and the Transition Deamplification Factor, function of the sole ratio between the two non-dimensional parameters. The influence of the involved parameters on the dynamic amplification is discussed within a general framework. The proposed procedure appears effective also in assessing the maximum response of real bridges characterized by numerically-estimated mode shapes, without requiring burdensome step-by-step dynamic analyses.

Detailed laboratory datasets of the dam break-induced surge impact pressures measured by Lobovský et al. are analyzed, upon which the dynamic amplification factors (DAF) of the single degree of freedom structures with different natural periods are calculated to quantify the dynamic responses of the measured total pressure series, the decomposed impulsive and quasi-steady pressure series based on the Hilbert-Huang transform algorithm. The maximum DAFs of the measured total and decomposed impulsive pressure series increase with the decrease of structure natural periods, while those of the decomposed quasi-steady pressure series show no relation with structure natural periods. The impulsive pressure is more influential to structures with small natural periods, whereas the quasi-steady pressure plays a predominant role regarding structures with large natural periods. Due to the resonance effect, the oscillatory pressure can significantly increase the maximum DAFs and delay its occurrence time of the measured total pressure series for structures with small natural periods. Nevertheless, the damping effect can generally decrease the DAFs of structures and therefore the resonance effect. Considering the damping coefficient varies from 0 to 0.1 in reality, increase of the maximum DAF induced by resonance is non-negligible for structures with small damping and short natural period.

To investigate the dynamic behavior of offshore structures to irregular waves, we conducted model tests using frame and column models, and took field measurements of the vibrations of an offshore structure installed in 80 m of water. We also conducted theoretical analyses of the dynamic response of offshore structures to irregular waves, and compared calculated values with the results of model tests and actual field measurements. From these studies to evaluate the dynamic response characteristics of offshore structures to irregular waves, we obtained data necessary for the dynamic design of deep-water offshore structures. INTRODUCTION The design of large offshore structures to be installed in deep water must be based on dynamic analysis, but strict analysis of their dynamic behavior requires frequent use of large computers. To avoid this costly procedure, it is necessary to employ either hypotheses or the approximation method in analyzing phenomena ranging from sea-surface fluctuations to vibration responses. To be analyzed by the approximation method, vibration phenomena must be clearly defined, so we analyzed the dynamic behavior of offshore structures under the influence of irregular waves by conducting model tests. We also conducted field measurements of the vibrations of an offshore platform. Further, we determined the responses by linear analysis using relatively simple models and evaluated the dynamic behavior characteristics by comparing calculated and measured results. The model tests comprised free vibration tests in which column and frame models were tested both in the submerged state and in air and dynamic response tests in which the models were tested using two dimensional irregular waves. In the former tests, the natural periods, damping constants and vibration modes of the models were determined in the latter, the fluid force coefficients of irregular waves and the response displacements and stress range frequency distribution characteristics of offshore structures were obtained. In the field vibration measurements, the natural period and damping constant of the platform were determined from its response power spectra in the tremor state. Our field measurements also revealed wave response characteristics of offshore structures during the passage of a storm center and their vibration characteristics during drilling. In the theoretical analyses, a lumped-mass model was substituted for the structure using the natural periods and damping constants obtained in the model and field tests. Borgman's wave force spectrum1 was used for the wave force spectrum in determining the response values. Then these theoretical response values were compared with the measured values. OUTLINE OF THE MODEL TESTS The column and frame models shown in Fig. 1 were used in the model tests. They were made of Acrylite. In the free vibration tests, plates each weighing about 5 kg were used as a load on the deck of each model.

Dedicated to Prof. Dr. Akimitsu Kurita on his 70th birthdayIn current bridge design codes or specifications, the dynamic effects of vehicles are considered by using a dynamic amplification factor (DAF) or dynamic load allowance (IM). However, a DAF is defined based on the ratio of the maximum dynamic load responses to the static load responses, and it is more appropriate for maximum value‐based strength design. For fatigue design, stress cycles other than the maximum stress ranges could contribute to fatigue damage accumulations. Meanwhile, on the capacity side, a reduction in fatigue strength due to structural deterioration, which is related to local environmental conditions, including temperature, humidity, etc., could introduce more uncertainties into structural safety and reliability evaluation. However, such multiple stress range effects and structural deterioration are not included in current bridge fatigue design. To evaluate the vehicular dynamic effects for the life cycle fatigue design of short‐span bridges, the present study proposes a new dynamic amplification factor for life cycle bridge fatigue design (DALC), which is defined as the ratio of the life cycle nominal live load stress range to the maximum static stress range. In contrast to other traditionally defined dynamic factors, the newly defined DALC includes information about both the structural loading and the structural capacity. Therefore, the multiple stress cycles from vehicle‐induced vibrations and the structural deteriorations from road surface conditions and corrosion of structural members are included. Parametric studies of DALC were carried out for multiple parameters and variables in the bridge's design life cycle, for instance, possible faulting days in each year, fatigue strength exponent, corrosion parameters and corrosion level. The stochastic properties and uncertainties from these variables are also considered in the DALC calculation.

This paper presents a procedure a coupling of the finite element method and normal mode technique for obtaining the elastic dynamic response of offshore platforms subjected to arbitrary time and space-dependent forces. The finite element method deals with the complexities of the actual problem by reducing it to an assembly of structural elements, with known elastic and inertial properties, connected together at a discrete number of points on their boundaries. The normal mode technique is then used to reduce the resulting matrix equation of order N to the solution of N single degree-of-freedom equations with certain constraints on the assumed form of damping. An example analysis, utilizing this procedure and an actual offshore platform under the action of two different types of dynamic forces, is presented. These forcing functions are: wave forces as determined through the use of a fifth-order gravity-wave theory and seismic forces as generated by the north-south component of the May 18, 1940, El Centro, California, accelerogram. The platform is assumed to respond according to the assumptions associated with the Bernoulli-Euler beam and bar theory. INTRODUCTION In the field of offshore platform analysis and design, as in many other fields, the tools of analysis are derived through an evolutionary process. As knowledge and ability increase for more accurate prediction of the environmental forces on platforms, the methods of analysis must improve to maintain consistent accuracy. The American Petroleum Institute(l) in its Recommended Practice for Planning, Designing, and Constructing Fixed Offshore Platforms recognizes this evolutionary process and encourages designers of offshore platforms to use "all research advances available to them" The advent of high-capacity, high-speed digital computers has revolutionized the field of structural dynamic analysis. In the past the approach was to reduce the structural model to the simplest form, usually an "equivalent"single-or dual-degree-of-freedom system or "equivalent" beam or bar model for which known closed-form solutions to the dynamic equations were available. While this approach gave valuable insights into the nature of the dynamic response problem, it did not give the detailed elastic response information that is possible today. This paper presents a method which the authors believe is the next step in the evolutionary process of offshore-platform dynamic analysis. It is a combination of the finite element method and the normal mode technique. The finite element method more accurately takes into account the geometry of the system than the so-called "equivalent" methods. Although the finite element method and the normal 'mode technique have been known for a number of years, it is only with advanced computer technology that these approaches have been economically feasible for the analysis of large complex structures. This economic feasibility, the increased accuracy of predictions of dynamic forces on platforms in the operating environment, and the desire of operators to construct offshore platforms in deeper water and use them under more hostile operating conditions, will force designers to use more advanced methods of dynamic analysis.

Equivalent static load method for hierarchical stiffened composite panel subjected to blast loading

The term “spatial variability of seismic ground motions” denotes the differences in the amplitude and phase content of seismic motions. The effect of such spatial variability on the structural response is still an open issue. In-situ experiments may be helpful in order to answer the questions regarding both the quantification of the spatial variability of the ground motion within the dimensions of a structure as well as the effect on its dynamic response. The goal of the present study is to quantify the variability of the seismic ground motion accelerations in the shallow sedimentary basin of Argostoli, Greece, and thereafter to identify its effect on the linear and non-linear elasto-plastic response of a single degree of freedom system in terms of spectral displacements. Around 400 earthquakes are used, recorded by the 21-element very dense seismological array deployed in Argostoli with inter-station spacing ranging from 5 to 160 meters. The seismic motion variability, evaluated in terms of spectral accelerations, is found to be significant and to increase with inter-station distance and frequency. Thereafter, the amplitude variability in terms of spectral displacements, which is indeed the linear response of a single degree of freedom (SDOF) system with various fundamental periods, is compared with the amplitude variability of a SDOF with non-linear elasto-plastic response. The variability of the maximum top displacement of the linear single degree of freedom system is estimated to be on average 12% with larger variabilities to be observed within two narrow frequency ranges (between 1.5 and 1.7 Hz and between 3 and 4 Hz). Such high variabilities are caused by locally edge-generated diffracted surface waves. The non-linear perfectly elasto-platic structural response of the SDOF system shows that although the variability has the same trends as in the case of linear response, it is almost constantly increased by 5%.

This paper evaluates the earthquake-resistant design provisions of the 1990 edition of the National Building Code of Canada (NBCC 1990) for asymmetric building structures subjected to combined lateral shear and torsional dynamic loadings arising from earthquake base excitation. A detailed parametric study is presented, evaluating the dynamic edge displacement response in the elastic range, for the side of the building which is adversely affected by lateral–torsional coupling. A series of buildings is studied, with realistic ranges of the fundamental natural period, structural eccentricity, and uncoupled frequency ratio. These buildings are evaluated under base loadings arising from a total of 45 strong motion records taken from earthquakes in North America, Mexico, Europe, the Middle East, and Southern Pacific, categorized according to site soil conditions and the ratio a/v of peak ground acceleration to velocity. The latter parameter together with the uncoupled lateral period are found to influence strongly the combined dynamic edge response, with the greatest forces on edge members arising from earthquakes with high a/v ratio in structures with natural periods below 0.8 s. In this case the NBCC 1990 loading provisions significantly underestimate the elastic dynamic response. For buildings with periods longer than 0.8 s, the conservatism of the base shear provisions leads to overestimation of combined dynamic edge response in asymmetric systems, and this is also true in the short-period range for buildings subjected to ground motions with low a/v ratio. The NBCC 1990 provisions are reasonably conservative for short-period systems subjected to ground motions with intermediate a/v ratio. Key words: earthquakes, seismic, design, response, spectra, base, shear, torsional, provisions.

API RP2A WSD is a design code in practice for design of jacket platforms in the Persian Gulf but is based on the Gulf of Mexico environmental condition. So for the sake of using this code for the Persian Gulf, it is better to perform a calibration based on this specific region. Analysis and design of jacket platforms based on API code are performed in a static manner and dynamic analysis is not recommended for such structures. Regarding the fact that the real behavior of the offshore jacket platforms is a dynamic behavior, so in this research, dynamic analysis for an offshore jacket platform in the Persian Gulf under extreme environmental condition is performed using random time domain method. Therefore, a new constructed offshore jacket platform in the Persian Gulf is selected and analyzed. Fifteen, 1-h storm, simulations for the water surface elevation is produced to capture the statistical properties of extreme sea condition. Time series of base shear and overturning moment are derived from both dynamic and static responses. By calculating the maximum dynamic amplification factor (DAF) from each simulation and fitting the collected data to Weibull distribution, the most probable maximum extreme (MPME) value for the DAF is achieved. Results show that a realistic value for DAF for this specific platform is 1.06, which is a notable value and is recommended to take into practice in design of fixed jacket platform in the Persian Gulf.

Walk-to-work (W2W) concepts are widely used in the offshore wind farms as means of access to offshore wind turbine platforms. This is typically achieved using a Service Operation Vessel (SOV) equipped with a suitable W2W gangway. This system has also been explored in the Oil and Gas industry for temporary access to offshore platforms. However, the use of this system as a primary means of access to operating offshore oil and gas platforms remains limited. When it comes to selecting height of a W2W landing, from basic Naval Architectural hydrodynamic principles one can expect height of a W2W landing from sea level to have an inverse relationship with operability of the SOV gangway [1]. As such, the lower the W2W landing, the higher the SOV gangway operability. However, lowering the W2W landing, potentially exposes the W2W landing structure to extreme design wave loads (e.g. 10,000-year return period design waves). Loss of W2W landing to an extreme wave event could jeopardize further accessibility of the W2W landing and expose any subsea infrastructure to risk of dropped objects. This paper is intended to summarise results of an assessment where height of the “Munin” fixed offshore platform W2W landings with regards to SOV gangway operability is optimised. In this study effect of W2W landing elevation from mean sea level in relation to SOV gangway operability is quantified for the Munin Platform site specific conditions. Further, a qualitative evaluation is presented to show how benefits of raising W2W landings outside of the extreme wave load envelop outweighs the marginal SOV operability improvement due to lowering W2W landings elevation.

Shear failure is a common mode for bridge column collapse during a vehicle‐column collision. In current design codes, an equivalent static load value is usually employed to specify the shear capacity of bridge columns subject to vehicle collisions. But how to consider the dynamic effect on bridge columns induced by impact load needs further research. The dynamic amplification factor (DAF) is generally used in the analysis and design to include the dynamic effect, which is usually determined using the equivalent single degree of freedom (SDOF) method. However, SDOF method neglects the effect of the higher‐order modes, leading to big difference between the calculated results and the real induced forces. Therefore, a novel method to obtain dynamic response under concentrated impact load including the effect of higher‐order modes is proposed in the paper, which is based on the modified Timoshenko beam theory (MTB) and the classical Timoshenko beam theory (CTB). Finite element models are conducted to validate the proposed method. The result comparisons show that the results from the proposed method have more accuracy compared with the results from the CTB theory. Additionally, the proposed method is employed to calculate the maximum DAF of shear forces for bridge columns under impact load. Parametric studies are conducted to investigate the effect on the DAF of shear forces including slenderness ratio, boundary condition, and shape and position of impact load. Finally, a simplified formula for calculating the maximum DAF of shear force is proposed for bridge column design.

The dynamic behavior of bridges under the effect of moving loads simulating the vehicle moving along the bridge structure idealized by an Euler beam is analyzed. We will present the dynamic behavior of beams under the stress of moving loads (or masses) by the analytical and semi-analytical approaches. When the mass of the bridge structure is comparable to that of the vehicle, the mobile source requesting the bridge is simulated by a mass. In most practical cases, the mobile force used is due to the effects of the gravitational moving masses: . When the moving mass is small compared to the beam mass, the obtained solution under the effect of moving force is approximately correct for the solution obtained with the moving mass. Otherwise, the problem of the moving mass is imperative. To do this, we wrote a program in Matlab language which reflects the dynamic behavior of beams under the effect of moving charges, which gives the following results "The frequencies and modes of vibration, the dynamics deflection of the beam requested by moving force, the dynamic response (DAF: dynamic amplification factor) of the beam requested by a moving force, over the whole length of the beam, for all times and for different speeds. The numerical example that we look to see for study the dynamic behavior of this type of bridge under moving loads is that of a thin beam unamortised on simple support and length of 50m, under the solicitation of moving force and mass at a constant speed and varies from 0 to 100 m / s (M. A. Foda, 1997), depending on the relationship between the vehicle mass and the mass of the bridge that will allow us to see the contribution of the choice of modelling type on the total response and then the vibration of bridge, also we will study the effect of type of simulation of the load by moving force or mass on the dynamic amplification factor and comparing our results with those from the literature.

This paper describes the dynamic response of minimum facilities with different structural configurations which are subjected to random seas. The finite element models are kept simple with the aim of focusing on the physics of the phenomena involved. The response is studied in terms of the dynamic amplification factor (DAF), representing the ratio between the dynamic and the static response. Two different formulations of the DAF under random seas are compared. The first is defined in terms of standard deviation (DAF1), the second in terms of the most probable maximum value (DAF2). Ringing is observed to be a relevant feature of the dynamic response and to affect primarily the braced monopod configurations. Ringing is detected using DAF2. The paper also addresses the importance of the kinematic representation above the still water level. Different methods of stretching the velocity field in the wave zone (delta, Wheeler and exponential stretching) are shown to have a significant impact on the dynamic response of the platforms.

Investigated herein are the dynamic responses of three different single degree of freedom (SDOF) bilinear dynamical models of a cracked concrete beam subjected to the El Centro earthquake. The first model is an equivalent unilinear model while the other two models have different stiffness values but differ from each other in the dependence of their damping coefficients on the sense of amplitude. All three models have the same natural period. The three models have been found to predict different response spectra for the same bilinear dynamical system. The effect of constant loading on the dynamical response of the concrete structures subjected to sinusoidal and random loading has been found to be significant for more flexible structures. Implications of these theoretical predictions for seismic design of concrete structures are discussed.

The vibration active control problem of offshore jacket platforms with tuned mass damper (TMD) is studied. A single degree of freedom (SDOF) nonlinear dynamical model of offshore platforms affected by the wave loading disturbances is established. Based on sensitivity approach (SA), an approximate optimal vibration controller is developed for the offshore structures under wave loading for the first time. Numerical simulations illustrate the effectiveness of the proposed controller.