Dynamic Behaviour of Minimum Platforms Under Random Seas

Dynamic amplification factors of corrugated steel plate culverts

The measured static and dynamic response characteristics of four jacket-type platforms in water depths up to 373 feet are described. Fundamental periods and damping were determined both by free vibration tests and spectral analysis of random response data. For each platform, measured end-on and broadside natural periods were nearly equal with values ranging from 1.5 to 1.9 seconds; the theoretically predicted natural period for one of these platforms was close to the measured value. Damping estimates range from approximately 1.0 to 5.0 percent of critical depending on the methods of testing and data analysis. For one platform spectra of both deck motions and wave heights are presented; measured amplitudes of response are compared to theoretical predictions. Motions predicted using regular Airy wave theory overestimate the measured motions for the tested platforms and the low sea states considered. INTRODUCTION Importance of Dynamics. In the design of offshore platforms, the possibility of dynamic response must be considered in the member force analysis. For platforms installed in active earthquake regions dynamic response analysis is mandatory. For regions where extreme waves and high cycle fatigue control the design, the need to consider dynamic response is not as clear. Estimates of dynamic response should first be made with simple models to determine if costly detailed analyses are required. Simple models are also quite powerful for examining a range of dynamic response conditions thus fostering a better understanding of dynamic platform behavior and allowing a more appropriate and efficient use of detailed analysis. In addition, with reference to the subject of this paper, the simple models indicate which parameters are important enough to be considered for experimental investigation. As a first approximation wave forces are often assumed to vary sinusoidally and the familiar steady-state response spectrum for single degree freedom (SDF) systems is used to estimate the importance of considering dynamic response (Figure 1). For this model and idealized force, dynamic amplification factor, AF, is dependent only on the perio9 ratio, R, and the system damping, S. Clearly, AF is large and very sensitive to damping for values of R near one (resonance). Using these curves to estimate the dynamic effect of a 12 second force on a four second structure (R =3.0), AF is seen to be about 1.12, i.e., maximum dynamic response is 1.12 times the maximum static response. For this period ratio AF is nearly independent of damping. Thus dynamic response to extreme waves is predicted to be small and insensitive to damping on the basis of this model. On the other hand, for the fatigue life calculation the waves of interest are much smaller with periods ranging from three to six seconds. For the same example four second platform, corresponding R values range from 0.75 to 1.5. In this region of the response spectrum AF is large and strongly dependent on damping. In fact, when damping is small, the AF at resonance can be expressed approximately as(Equation available in full paper)

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.

Shaking table tests on a deep-water high-pier whole bridge under joint earthquake, wave and current action

Single Station Microtremor method, which is widely used nowadays, is an effective and easy applicable method. In this study, dynamic amplification factor distributions of the study area were obtained using scenario earthquake parameters with single station microtremor data gathered at 112 points. In addition, a surface wave active method, which is known as MASW (Multichannel Analysis of Surface Waves), was applied at 43 profiles to calculate the soil amplification values. Dynamic amplification factor (DAF), soil amplification, the predominant soil period (PSP), geology and topography data of the study area were analysed together. Dynamic amplification factor and soil amplification values were obtained 2 or higher at about sea level parts of the study area which are generally composed of alluvial units. Additionally, in high altitude regions that are composed of volcanic rocks, relatively lower dynamic amplification factor and soil amplification values were obtained. The minimum amplification value in the study area was 1.15, while the maximum amplification value was 3.05 according to the dynamic amplification results and the soil amplification values were between 1.16 and 3.85 in harmony. It is seen that the obtained DAF values and the soil amplification values calculated from the seismic velocities are very similar to each other numerically and regionally. Because of this, it is concluded that the values of the soil amplification obtained by the MASW method and the calculated DAF values in this study are in harmony with each other. Although the depths of research in these two calculation methods are different from each other, the similarity of the results allows us to arrive at the result of how effective the ground layer is on the amplification. It has a great importance to calculate the amplification values and other dynamic parameters by in situ measurements for a planned plot because geological units can vary even at very short distances in heterogeneously distributed areas.

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.

Three dimensional finite element models are developed to deal with the bridge-vehicle interaction problem of simply supported composite multi I-girders bridge. The bridge is modeled by using ANSYS 15.0 program with solid and shell elements to represent concrete and steel members, respectively. AASHTO HL-93 truck is idealized as 3D non-linear model consisting of five lumped masses connected by rigid beams and supported by spring-dampers. The separation between the tires and road surface and surface roughness condition are simulated by Gap and actuator elements, respectively. The road surface roughness profiles are generated from power spectral density (PSD) and cross spectral functions. The models used are capable to take all bridge and vehicle responses into consideration with no limitations on the complexity of the models. The dynamic responses of the multi I-girder bridge are investigated under conditions of various loading positions, roughness classes, vehicle speeds, and bump height. The dynamic behaviors are presented in terms of Dynamic Amplification Factors (DAF). The results show the girder that itself supporting the moving vehicle has lower value of DAF because of higher static responses. A 45 km/hr vehicle speed provides higher DAF value. The bump heights have significant effect on DAFs for bridge with short span.

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.

This paper presents the investigation of the effect of dynamic loads on the dynamic amplification factors (DAFs) of an existing continuous bridge. A three-dimensional analytical model to idealize the vehicle and a finite element model to analyze the bridge have been developed. Experimental testing of this existing bridge has been conducted by the Ministry of Transportation, Quebec. Two vehicle models, having seven and 11 degrees of freedom with and/or without trailers, are considered in the analysis of the interaction between the bridge and vehicles. Based on International Standards Organization specifications, the road-surface roughness of the approach roadways and bridge deck is generated from the power-spectral density function for very good, good, and average roads. The solutions obtained from the present models are compared with the experimental results for different vehicle speeds. The DAFs are computed from the present finite element model for three different types of measurements (displacements, strains, and reactions). The numerical results show that the DAFs computed with displacements are less than those estimated from strains and reactions. It is concluded that current design codes tend to underestimate dynamic amplification factors, especially for long-span continuous bridges.

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.

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.

Importance of ‘DAF’ in evaluating structural adequacy of gravity-load designed RC buildings

This research focuses on the application of the spatial system of finite element modeling for the vehicle-bridge interaction on reinforced concrete US Girder Bridge in order to obtain the effect of surface roughness. Single vehicle and multiple vehicles on reinforced concrete T beam bridge were studied with variable surface roughness profiles. The effects of six different surface roughness profiles (very good, good, measured, average, poor, and very poor) were investigated for vehicle-bridge interaction. The values of the Dynamic Amplification Factor (DAF) were obtained for single and multiple vehicles on T Beam Bridge for different surface roughness profiles, along with the distances between the axles of heavy vehicle. It was observed that when the bridge has very good, good, measured, and average surface roughness, the DAF values for the single vehicle over the bridge were observed to be within acceptable limits specified by AASHTO. However, for the bridge with multiple vehicles only very good and measured surface roughness profiles showed a DAF and vehicle axle distances within the acceptable limits. From the current studies, it was observed that the spatial system showed reliable responses for predicting the behavior of the bridge under variable road surface roughness conditions and was reliable in vehicle axle detection, and therefore, it has a potential to be use for realistic simulations.

In this paper, a finite element (FE) model for a cable-stayed bridge designed according to Australian standards is developed and analysed statically and dynamically with and without geometrical nonlinearities. The dynamic amplification factor ( DAF) and demand-to-capacity ratio ( DCR) in different structural components including cables, towers and the deck are calculated and it is shown that DCR usually remains below one (no material nonlinearity occurs) in the scenarios studied for the bridge under investigation, however, DAF can take values larger than two. Moreover, effects of location, duration and number of cable(s) loss as well as effect of damping level on the progressive collapse resistance of the bridge are studied and importance of each factor on the potential progressive collapse response of the bridgeis investigated.

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.