Maximum Structural Response Research Articles

A new processing method of ground acceleration data for fast and accurate evaluation of maximum seismic structural response

AbstractA new processing method of ground acceleration data is proposed for the fast and accurate evaluation of the maximum seismic structural responses. The proposed method consists of a trimming method and a down‐sampling method. The proposed trimming method is based on ground acceleration power and contains compensation procedures for the trimmed ground acceleration. The proposed down‐sampling method effectively uses FIR filter, whose weight coefficients are derived from the correspondence between the responses under a triangular wave and the equivalent impulse input. It is demonstrated through numerical examples for response spectrums and a full‐scale high‐rise building model that the proposed method enables fast and accurate evaluation of the maximum seismic structural responses.

Shaking table test and numerical simulation of rocking wall frame structure considering dynamic soil-structure interaction

This study investigates the seismic response of a rocking wall frame structure considering dynamic soil-structure interaction (DSSI) through shaking table tests. A comparison with conventional frame structures and structures with fixed-base foundations is made to examine the influence of DSSI effects on various aspects including structural damage distribution, dynamic characteristics, and floor responses. Test results indicate that the presence of a rocking wall reduces structural responses across different site conditions, although the reduction is less significant under soft soil conditions compared to fixed-base foundation conditions. Overall, DSSI diminishes the mitigating effect of the rocking wall on the maximum structural response. Furthermore, a three-dimensional finite element model of the shaking table test is established. The numerical model employs the equivalent linear method to simulate the soil's nonlinear behavior and incorporates the concept of the rocking wall. Comparative analysis between experimental and simulated results demonstrates that the model effectively predicts the dynamic response of the rocking wall frame structure in DSSI systems.

Frequency Identification using Resonance Curve-Based Drive-by Monitoring: Field Validation

Railway bridges have a long service life - in Germany, for example, the average is 122 years. During this time, vehicles are constantly evolving, leading to innovative axle configurations and higher speeds. This leads to loads for which the bridges were not originally designed, which can lead to resonant structural responses. A key parameter for calculating and evaluating the dynamic behaviour of bridge structures, is the resonance frequency. Due to the large number of bridges in the network, conventional methods using sensors on the structure would be very laborious. A cost-effective alternative would be drive-by monitoring, using sensors on a passing train. In railway bridge contexts, drive-by monitoring to identify frequencies faces challenges from short spans and high speeds, leading to brief contact periods. The brief periods cause a low resolution of the signals in the frequency domain. An approach to overcome this issue is the use of resonance curve-based drive-by monitoring. The term resonance curve describes the maximum structural responses as a function of speed. In conjunction with the known axle configuration of the train, the resonance frequency can be determined from the resonance curve. In this paper, data from two field tests are analysed, in which synchronised acceleration measurements were conducted on the main girders of the bridges and the axle boxes of the trains. An ICE 4 was used on a bridge with a 19.5-metre span, and an ICE TD on a bridge spanning 16.4 metres. The analyses show that frequency identification using indirect resonance curves is feasible under real operating conditions. Thus, this approach enables the determination of a key parameter essential for calibrating structural models. Furthermore, this method enables the avoidance of resonance crossings by speed adaptation, either by acceleration or deceleration. This strategy has the potential to significantly increase the service life of bridges.

Dynamic Response Study of Overhead Contact System Portal Structure Based on Vehicle–Track–Bridge Coupled Vibration

In light of the rapid development of electrified railways, the safety and stability of train operations, as well as the catenary’s interaction with current quality, have garnered widespread attention. Electrified train operation with additional track irregularities serves as a principal excitation source within the vehicle–bridge–catenary system, significantly influencing the vibration characteristics of the system. Addressing the aforementioned issues, we first established the vehicle–track dynamics model and the bridge–catenary finite element model based on the principles of coupled dynamics of the vehicle–track system. These models are interconnected using dynamic forces between the wheel and rail. Subsequently, within the vehicle–track coupled system, track random irregularities are introduced as input excitations for the coupled model, and the dynamic response of the system is simulated and solved. Then, the obtained wheel–rail forces are applied to the bridge–catenary coupled system finite element model in the form of time-varying moving load forces. Finally, the dynamic response characteristics of the catenary portal structure under different conditions are determined. Meanwhile, a study on the vibration characteristics of the truss-type pillar portal structure was conducted, and the results were compared with those of existing models. The results indicate that the vertical and lateral forces between the vehicle and track are positively correlated with the speed and irregularity amplitude. Response values such as the derailment coefficient and wheel load reduction rate are within the specified range of relevant standards. The low-order natural resonant frequency of the truss-type pillar structure has, on average, increased by 0.86 compared to the existing pillar structure, which signifies improved stability. Furthermore, under various conditions, the average reductions in maximum displacement and stress response of this pillar structure are 13.2% and 14.19%, respectively, in comparison to the existing pillar structure, rendering it more suitable for practical engineering applications.

Vibration control of an eleven-story structure with MR and TMD dampers using MAC predictive control, considering nonlinear behavior and time delay in the control system

In the last two decades, model predictive control has made significant progress in research and industrial process control. This achievement is through the high ability of model predictive control to solve industrial process control problems in the time domain. It is applicable in many control systems, such as delayed systems, univariate and multivariable systems, non-minimum phase systems, and unstable systems. This strategy is essentially for controlling delayed systems. It is possible to create a time delay in transmitting structure movement data in the systems that use sensors and receivers of sensor-recorded data, which is a factor to reduce the efficiency of the control system and even the instability of the structure. In this study, to investigate and compensate the effect of time delay in the hybrid vibration control system, an 11-story structure with a tuned mass damper and an MR damper was used by model algorithmic control (MAC) and nonlinear behavior of the structure in the control process. The linear and nonlinear structural models are created in OpenSEES, the control system in MATLAB; and the TCP/IP connection method was used to connect two programs. The fuzzy decision system is based on accelerating and decelerating movement. The structure has been subjected to seven earthquakes with maximum accelerations of 0.1 g to 1.0 g with an incremental step of 0.1 g. According to the results of incremental dynamic analysis, the average percentage of the fuzzy control system performance reduction, considering the time delay, is 15.28% and 38.57% for the maximum displacement and base shear in the linear structure, and 8.04% and 5.97% for the nonlinear structure, respectively. The assumed time delays have been effectively overcome using the model algorithmic control system (MAC), determining the prediction horizon of the structural behavior, and optimizing the control force in the control horizon. The performance of the MAC control system has been better than the fuzzy control system and the passive control with TMD. The average improvement percentage of the results of the maximum linear and nonlinear structural displacement response is respectively equal to 10.2 and 11.8 with the MAC control system, compared to the fuzzy control system without time delay. For the maximum base shear, it is equal to 8.32 and 2.49, respectively.

Dynamic reliability analysis of Aerial Building Machine under extreme wind loads using improved QBDC-based active learning

Aerial building machine (ABM) is a new comprehensive construction equipment used for the construction of high-rise buildings, and the research of its wind-induced response is essential for structural safety. However, the traditional reliability estimation for complex structures is generally computationally expensive. This study proposes a novel and time-saving active learning (AL) approach to predict the structural time-variant response and calculate the reliability under extreme wind loads based on improved Query-by-Dropout-Committee (QBDC), Deep Learning (DL) and Probability Density Evolution Method (PDEM). To establish an effective training set, the load sample pool from the turbulent wind field is constructed by the number theory method (NTM). Then a DL surrogate model, aimed to simulate the excitation-response relationship of the structure, is well-trained from data calculated by the Finite Element Method (FEM) under the workflow of the improved QBDC-based AL approach. Lastly, the structural responses predicted by the surrogate model are used to solve the Generalized Density Evolution Equation (GDEE) to obtain the Probability Density Function (PDF) of the structural response. The dynamic reliability can be gained using absorbing boundary condition. To demonstrate the feasibility of the proposed approach, an ABM in China is taken as a case study. It is found that (1) The external trusses of the platform are weak positions under the horizontal wind loads. It is suggested to append the longitudinal (windward direction) trusses to reduce the local stress and deformation. (2) Under turbulent wind loads with the average speed of 40 m/s, the maximum structural response of the ABM will exceed the threshold value and the reliability is 0.932. (3) The reliability calculation error derived by the proposed approach and the traditional PDEM is within 0.5 % in this study, while the computational efficiency of the AL approach is 77.08 % higher than that of the traditional PDEM. The novelty lies in the proposed active learning approach that can easily obtain the stochastic response and dynamic reliability of the ABM, where the analysis workflow not only has a low computational cost but also maintains a high calculation accuracy.

Dynamic Response of Slender Vertical Structures Subjected to Thunderstorm Outflows

This study examines the maximum alongwind dynamic response of slender vertical structures subjected to thunderstorms, comparing the induced maximum response with the one induced via synoptic events. Two real structures are considered as case studies: a lighting pole and a telecommunications tower. The comparison between thunderstorm- and synoptic-induced dynamic responses is performed through a critical analysis of three ratios characterizing the difference between the two phenomena: the reference wind speed, the mean wind profile, and the gust response factor. The comparison shows that the definition of the reference wind speed and the height of the nose tip of the thunderstorm mean wind profile are crucial for the maximum response, as well as for the dependence of the turbulence intensity on the roughness length. The results show that thunderstorms provide the design loading condition in most cases.

Hull Girder Ultimate Strength Analysis of 17500 LTDW Oil Tanker under the Combined Global and Local Load using Explicit Finite Element Analysis

This study investigates the hull girder’s ultimate strength of 17500 LTDW Oil Tanker. The explicit finite element analysis is carried out to estimate the hull girder longitudinal strength of the Oil Tanker. The numerical analysis starts with the longitudinal strength analyses that examine the ship’s structural response behavior due to sagging and hogging bending moment load. The structural strength analyses were conducted to determine the maximum structural response behavior for withstanding the operational load. Afterward, the hull girder’s ultimate strength is undertaken to reflect the progressive collapse behavior of the oil tanker structure under the combined global bending moment and local hydrostatic pressure load. The explicit finite element analysis is performed to estimate the ultimate strength behavior, considering the effect of the hydrostatic pressure load and the material nonlinearities. The typical 17500 LTDW oil tanker represents Indonesia’s common oil vessel that supports national fuel oil distribution. Furthermore, this study can recognize the oil tanker’s ultimate hull girder strength characteristics.

Experimental study on impact response of seaborne rocket launch platform

This paper presents a novel test method for evaluating the impact response of a seaborne launch platform. By simulating and analyzing the platform's impact response to develop a test plan, designing an assistive test device to enhance data accuracy, and conducting a shipboard test, we analyzed the launch platform's impact response during cold launch. Results show that during the ejection stage, the platform experiences a sudden acceleration peak that quickly attenuates. During ignition, the vibration acceleration response oscillates and fluctuates. The maximum structural impact response occurs below the launcher, gradually attenuating to the bow, stern, and sides of the ship, and propagating slowly along the captain's direction. The vibration acceleration response varies along different directions, with the highest response in the vertical direction and the lowest in the longitudinal direction. FE numerical analysis confirms the experimental results. This study provides reference data for the structural anti-impact design of seaborne launch systems.

Thunderstorm gust response factor: General tendencies and sensitivity analysis

This paper aims to provide a sensitivity analysis of the thunderstorm gust response factor. The study is based on the extension of the gust response factor technique to the assessment of the maximum dynamic response of structures to thunderstorm outflows, starting from an evolutionary spectral model of the thunderstorm wind speed. The thunderstorm evolutionary spectral model depends on the modulating function of the slowly-varying mean speed, which is a function of two parameters, i.e. the background mean wind speed and the duration of the intense phase of the outflow. Starting from 129 full-scale thunderstorm records, the parameters of three different analytical models of the modulating function are extracted and a statistical analysis is carried out defining their range of variation. The dependence of the gust response factor on the analytical expression of the modulating function is studied as well as its sensitivity to the parameters of the function. Results show that the dependence of the gust response factor on the analytical expression of the modulating function is negligible, while it is very sensitive to the variation of the background wind and duration of the intense phase, especially for flexible and lowly-damped systems.

Field data observations for monitoring the impact of typhoon “In-fa” on dynamic performances of mono-pile offshore wind turbines: A novel systematic study

For offshore structures such as offshore wind turbines (OWT), typhoon is usually considered one of the most critical threats to structural safety performances and service life due to its heavy wind, wave, and even coexisted storm surge. Meanwhile, it is challenging to obtain the systematic data from the environmental conditions, structural dynamic vibrations and the SCADA record, when typhoon passes by the offshore wind farm. Taking into account these situations, a real-time multi-source monitoring system enabling the investigation of the typhoon impact on the performances of OWT, has been firstly established and implemented to a 4.0 MW mono-pile OWT in Rudong, Jiangsu, China. One of the major contributions in this work is to develop the monitoring system using a unique environment of real-world data that has been synchronously obtained from waves, winds, vibrational accelerations, inclinations of towers and SCADA data during the typhoon “In-fa” passing by the wind farm, and provide the scientific community with the underlying standards and technical recommendations. To investigate the influence caused by “In-fa”, comparison results of the measured data in the range of June to August have been analysed. It is worth noting that two conclusions have been obtained: (1) the region near the nacelle is not always the most critical vibrational area. Actually, the change of the maximum structural response in the position under different external loads should be applied to effectively evaluate the structural safety; (2) the measured accelerations exhibit an obvious decay process in the presence of the turbine rotor-stop, but not the yaw rigid-body motion. This observation promotes the accurate identification of modal parameters for the long-term monitoring. Consequently, these valuable findings to facilitate the assessment of structural operational conditions have been developed into two guide-lines. All the data and analyses presented in this paper provide a valuable insight into the design, energy efficiency, safety monitoring and damage diagnosis of OWT structures.

Rapid evaluation of structural soundness of steel frames using a coupling coefficient (CC)‐based method

AbstractA method is proposed for evaluating the post‐earthquake condition of steel frame structures based on the coupling coefficient (CC). The CC is an index that reflects the internal force distribution of each storey and damage mechanism in frames. It is computed using the drift distribution of the maximum structural response estimated from limited monitoring data and the design drawings of the target structure. Preliminary finite element analyses showed that the CC contains some important information that is not obvious in displacement responses, such as the global and local working modes of the structure. Useful information of this type includes whether the damage to each storey is mainly distributed on the beams or columns. An incremental dynamic analysis with an 18‐storey steel frame tested at the E‐Defense shaking table facility confirmed that the structural condition identified by the CC‐based method corresponds to the damage information reported by visual inspection. The analysis results verify the theory of the CC‐based method and provide limit values for the damage grades of steel frames.

Dynamic response estimation of an equivalent single degree of freedom system using artificial neural network and nonlinear static procedure

This paper introduces an innovative methodology for predicting the maximum dynamic response of structures using capacity curves and artificial neural networks (ANNs). This novel approach offers a quick and accurate procedure for estimating target displacements, obviating the need for intricate supplementary computations. The method generates a comprehensive dataset encompassing the bilinear representation of a single-degree-of-freedom (SDOF) characteristic, with ground motion parameters as inputs and maximum inelastic displacement as the corresponding output. This dataset is used to train an ANN model, with meticulous calibration of hyperparameters to ensure optimal model performance and predictive precision. The findings of this study demonstrate that the ANN model showed operational efficacy in approximating dynamic displacements. It is notably revealed that the size of the dataset significantly influences the ANN's performance and predictive accuracy. Through comparative analysis with established methodologies such as the displacement coefficient method and the modified coefficient method adopted by the Federal Emergency Management Agency (FEMA), the ANN model emerges as a fast tool for precisely predicting the dynamic response of single-degree-of-freedom systems, particularly those characterized by vibration periods exceeding 0.5 seconds. Consequently, this research culminates in the assertion that the ANN, owing to its inherent simplicity and impressive precision, is an alternative tool for estimating target displacements.

非線形オイルダンパーを有する平面骨組モデルのダンパー減衰性能のばらつきに対する地震時応答上限値の簡易評価法

A new uncertainty analysis method is developed for planar frame structure models equipped with oil dampers of linear and nonlinear force-velocity relationships. The structural analysis software SNAP® is collaborated with previously proposed uncertainty analysis method called NURP to obtain the maximum structural response when the damper characteristics are varied. In order to consider the uncertainties in the input, the critical double impulse is employed in addition to standard design ground motions, and we proposed the practical solution to use it in the structural analysis software. The validity of the proposed uncertainty method for frame structure models is investigated by comparing the result with maximum response derived by genetic algorithms. As a simplified method to evaluate the maximum value of the frame structure response, a method that uses a shear model equivalent to the frame structure model is also proposed.

Finite element modeling of reinforced concrete short columns subjected to shear in two perpendicular directions

PurposeShort columns can cause serious damage when subjected to an earthquake due to their high stiffness with low ductility. These columns can be exposed to multidirectional shear forces, which encouraged this study to investigate the behavior of structural short columns under bi-directional shear.Design/methodology/approachFinite element analysis (FEA) using ABAQUS is conducted and calibrated based on experimental data tested by previous researchers who studied the uni-directional behavior of short columns subjected to cyclic shear displacements. Then, the calibrated column models are further investigated to study the influence of bidirectional cyclic shear. Two scenarios are investigated, namely “simultaneous” and “sequential,” to compare the performance in terms of shear strength reduction.FindingsThe results show that the shear strength reduction significantly appears when 1:1 simultaneous bi-directional cyclic shear is applied. However, the shear reduction is more significant when the sequential scenario is applied. The seismic forces or deformations applied in orthogonal directions should be combined to achieve the maximum seismic response of structures as specified in Federal Emergency Management Agency (FEMA) 356 Standard. Finally, the combinations presented in literature to consider bi-directional shear are investigated. Based on FE results, the effect of applied 1:0.30 bi-directional cyclic shear simultaneously does not result in significant effect on the considered columns properly design for seismic forces.Originality/valueTo investigate the effect of multidirectional shear forces on the shear strength capacity of short columns, the presented effect of multidirectional shear forces in literature to consider bi-directional shear are investigated.

Dynamic Response of a Heavy-Haul Railway Tunnel’s Bottom Structures in Hard Rock

A train–tunnel–surrounding rock numerical model was established by using ABAQUS to analyze the dynamic response of a heavy-haul railway tunnel in hard rock, quantify the influence of the train axle load on the tunnel dynamic response and determine its potential vulnerable position. The results suggested that: Under the 30 t train load and surrounding rock pressure coupling, the maximum principal stress caused by rock pressure was 1.27 MPa, located at the bottom of the structure below the side drain; the maximum dynamic response of the tunnel structure and base rock was located directly below the rail. The lower part of the side drain and rail was the vulnerable position in the tunnel bottom structure, and the probability of base disease under the rail may be higher than that in soft-rock tunnels, for it has a greater dynamic response and thinner structure compared to a soft-rock tunnel. The maximum principal stress amplitude of the tunnel structure and base rock were 129.3 kPa and 43.0 kPa, respectively. When the axle load increased by 1 t, the dynamic amplitude of the structure’s maximum principal stress increased by about 4.14 kPa, and the base rock’s maximum principal stress increased by about 1.33 kPa. The rock pressure was not negligible in the dynamic analysis of the railway tunnel, and the dynamic response of the tunnel bottom structure and base rock will decrease, obviously, when the rock pressure is ignored.

Real‐time hybrid simulation with multi‐fidelity Co‐Kriging for global response prediction under structural uncertainties

AbstractReal‐time hybrid simulation (RTHS) provides an effective and efficient experimental technique to enable large‐ or full‐scale experiments to account for rate‐dependent behavior in size limited laboratories. Traditional practice of RTHS assumes deterministic substructure properties therefore could not account for structural uncertainties in global response prediction. This study explores the use of Co‐Kriging metamodeling for global response prediction under the presence of structural uncertainties. RTHS in laboratory is used as high‐fidelity (HF) modeling while computational simulation of the prototype structure under investigation is used as low‐fidelity (LF) modeling. Multifidelity modeling is integrated through Co‐Kriging to render accurate response prediction over the entire sample space of structural uncertainties. An entropy‐based adaptive strategy is used to sequentially determine the sampling points for HF RTHS and LF simulation. The proposed multifidelity Co‐Kriging approach is experimentally evaluated through RTHS of a single‐degree‐of‐freedom structure with a self‐centering viscous damper. The Co‐Kriging predicted maximum structural responses are further compared with validation tests. It is demonstrated that the Co‐Kriging can effectively reduce the number of RTHS tests in laboratory and significantly improve the metamodel accuracy for global prediction of structural response under uncertainties. The presented study presents an innovative way to further expand the capacity of RTHS for uncertainty quantification toward seismic hazard mitigation.

Improving the torsional response of asymmetric buildings with self-centering controlled rocking steel braced frame system

Self-centering controlled rocking steel braced-frame (SC-CR-SBF) is proposed as an earthquake-resistant system with low damage. Pre-stressed vertical strands provide a self-centering mechanism in the system and energy absorbing fuses restrict maximum displacement. Presence of asymmetry in structures can highlight the advantages of employing this structural system. Moreover, these days designing and constructing asymmetric and irregular structures is inevitable and as a result of architectural attractiveness and requirements of different functions of buildings, they are of great importance. Consequently, in these types of structures in order to minimize seismic responses, particular measures should be taken into consideration. Proper distribution of strength and stiffness throughout the plan of structures with self-centering systems can play a considerable role in resolving problems associated with asymmetry in these structures. In this study, the asymmetric buildings with 10% and 20% mass eccentricities and having different arrangements of centers were simulated. The models were analyzed under a set of 22 bidirectional far-field ground-motion records and corresponding responses of maximum roof drift, acceleration and rotation of the roof diaphragms of the structures with different arrangements of the center of mass, stiffness and strength were computed and studied. Results show that proper distribution of stiffness and strength throughout the plan of the structures with SC-CR-SBF system reduces the maximum roof drift as well as the rotation of the roof diaphragm. With appropriate arrangement of the centers, maximum drift response of the asymmetric structure decreases as much as roughly 20% and the ratio of the maximum drift response of the asymmetric structure to the response of the similar symmetric structure with the same overall stiffness and strength was 1.1. In other words, maximum drift response of the asymmetric structure with SC-CR-SBF system is acceptably close to the one for the symmetric building.

Efficient seismic risk assessment of irregular steel‐framed buildings through endurance time analysis of consistent fish‐bone model

SummaryThe seismic risk framework of building structures has been presented to reduce earthquake‐induced adverse consequences. In this context, probabilistic analysis of engineering demand parameters (EDPs) is always associated with many uncertainties and high computational demand for use in practical applications. This study has been presented to efficiently estimate the distribution of EDPs in probabilistic seismic risk assessment of irregular steel moment‐resisting frames (SMRFs). For this purpose, the incorporation of the consistent fish‐bone (CFB) model and the endurance time (ET) analysis method has been used. The proposed method (i.e., CFB‐ET) has a substantial impact on reducing the complexities of the new generation of performance‐based earthquake engineering (PBEE) by significantly reducing the degrees of freedom (DOFs) of the original building and the number of required nonlinear time history analyses (NLTHAs). The efficiency of the proposed method has been evaluated using three 3‐, 9‐, and 20‐story SMRFs irregular in bay lengths and three other SMRFs with the same number of stories but irregular in height. In this evaluation, the maximum structural response at all seismic intensity levels up to the collapse stage and also the structural response profile along the building height at service‐level earthquake (SLE), design‐based earthquake (DBE), and maximum credible earthquake (MCE) seismic intensity levels have been investigated. Next, the efficiency of the proposed method in seismic risk assessment is investigated by using seismic fragility and vulnerability curves. The results of these evaluations have been compared with the full incremental dynamic analysis (IDA) of the full DOF model of the building (i.e., SMRF‐IDA) under 44 far‐field ground motions of FEMA P‐695 in terms of computational accuracy and effort. Furthermore, a new approach to estimating the dispersion of the structural response in the ET method has been proposed, whose efficiency has been investigated in the above‐mentioned evaluations. The results show that the proposed method allows for using the new generation of PBEE in engineering applications by significantly reducing computational demand and having sufficient accuracy in the seismic assessment process.

Numerical study on wave-induced hydro-elastic responses of a floating raft for aquaculture

The paper presents the study on hydro-elastic responses of a floating raft with a mooring system in both regular and irregular waves. The floating raft consists of a number of buoys, plates and a mooring system, which are modeled by Morison type elements with proper coefficients, segmented line elements with stiffness and several mooring cables, respectively. The added mass coefficients of the buoys are computed by using the panel code WAMIT. Damping coefficients are obtained by CFD simulations of the forced surge/sway motions of a buoy with a free surface. Due to the nonlinear performance of the mooring system, the periods of maximum responses of the structure decrease as the wave height increases. For regular waves, the most of dangerous wave conditions are found in the wave periods 6∼10 s with the incident wave angles 0∘∼20∘ or 70∘∼90∘, while the floating raft is relatively safe for the incident wave angle being around 45°. For irregular waves, the impacts of randomness are analyzed by using different wave seeds. Most of the results are not sensitive to the randomness of the phase angles, except for the maximum mooring tensions which show noticeable fluctuations (∼15%). By comparing the results of the long-crested wave and short-crested wave, it is found that the predictions of the mooring tension and the responses of the floating raft are more conservative in long-crested wave than those in short-crested wave. Besides, the impacts of different frequency ranges on the time histories of the responses are discussed. The maximum structural responses are compared with the most probable maximum (MPM) values obtained by assuming Rayleigh distribution for the responses. The most vulnerable locations of the structure are analyzed based on the maximum dynamic loads on the plates of the floating raft. When the zero-crossing period exceeds 5 s, the relatively large tensions on the plates occur in the north and south sides of the floating raft. The relatively large shear force, bending moment, normal stress, torque and shear stresses on the plates always occur in the four corners of the floating raft.