Random seismic response analysis of truss structures with uncertain parameters

A new method for random vibration analysis of stochastic truss structures

Pre-tensioned cable net systems are being increasingly used in building façades. Due to the geometrical nonlinearities exhibited by the cables, people have to resort to the nonlinear response history analysis approach for analyzing the seismic responses of cable net structures. This article studies the effectiveness of linear response spectrum analysis method for nonlinear cable net systems. An energy-based parameter is used to describe the structural stiffness, based on which the equivalent single-degree-of-freedom systems for cable net structures with various irregularities could be established. By means of a pseudo-energy-equivalent approach, the nonlinear equivalent single-degree-of-freedom systems are transformed into linear ones, whose seismic responses are reasonable approximations of the accurate nonlinear results. It is revealed that the vibrating period of the equivalent linearized system is close to that of the nonlinear equivalent single-degree-of-freedom system, indicating that the nonlinear effects on seismic responses of cable net structures are not serious. Inspired by the theoretical analysis, large-scale numerical computations are carried out to check the accuracy of linear response spectrum analysis for nonlinear cable net structures. In the numerical computation, four cable net models are excited by 80 seismic records. Considering 19 different degrees of earthquake intensity, a total number of 6080 nonlinear response history analyses are executed, and the results are compared with those obtained from the linear response spectrum analysis. From the numerical results, the linear response spectrum analysis yields proper overestimations of seismic responses with errors within 35%, which may lead to slightly conservative yet acceptable designs in engineering practice. Given all the aforementioned discussions, it is concluded that the linear response spectrum analysis method is effective for seismic response analysis and aseismic design of nonlinear cable net structures.

At present, specific earthquake motion is often used for analyzing the influence of trains on high-speed railway structure; however, the uncertainty of earthquake motion is rarely taken into consideration. In this study, on the basis of considering the uncertainty of earthquake motion, and taking a simply-supported beam with CRTS II track system and CRH2 high-speed train in China as the research objects, a finite element analysis model of vehicle-bridge coupled model was established and verified by tests. The influencing mechanism of the trains on structural response under the action of uncertain earthquake was analyzed, and the range of the influence levels of trains on seismic response of structure was calculated. The research findings show that under the effect of earthquake, the presence of trains decreases the responses of piers and bearings, while increases the response of track structure. With increasing peak ground acceleration, the effect of trains on the track structure deformation increases, while that on the bending moment of piers, shearing force, and bearing deformation all decrease. The increase in train speed will not significantly affect the seismic response of structures. The ratio of seismic response between the operating conditions with and without vehicles was kept within a certain range, so that the demand range for seismic response under the operating condition with vehicles can be approximately simplified.

Seismic Response of Base-Isolated Structures with LRB and FPS under near Fault Ground Motions

Spatially incoherent seismic ground motions are represented in both frequency and time domains. The frequency domain representation is employed to obtain closed form solutions for axial and bending stresses that develop in line structures on rigid foundations due to ground motion incoherence. Axial and lateral response of long gravity dams is then investigated including dam-reservoir-foundation interaction. The results indicate that ground motion incoherence can produce significant additional stresses on long dams and other extensive structures. INTRODUCTION Seismic design of engineering structures is usually conducted with input ground motion specified in terms of a response spectrum, a power spectral density function or a single accelerogram. Such representations consider the ground motion variation with time but ignore its variation in space. This is sufficient for structures with small bases, e.g. slender towers and residential buildings, but may not be adequate for extensive structures such as large dams, long tunnels, bridges and pipelines. Extensive structures suffer not only from the ground motion variation with time but also from its variation in space. Spatial variabilities of seismic ground motion are clearly indicated in data recorded at large scale seismographic arrays [2 and others]. They result from random mechanical factors along the wave paths (spatial coherency effects) as well as time lags due to non-vertical travelling waves (wave passage effects). Previous studies have shown that the Transactions on the Built Environment vol 3, © 1993 WIT Press, www.witpress.com, ISSN 1743-3509 462 Soil Dynamics and Earthquake Engineering ground motion spatial variabilities (or incoherence) may significantly modify the seismic response of extensive structures [4,5,7 and others]. Spatial incoherence of the ground motions reduces the seismic response of rigid structures and simply-supported beams but may produce considerable stresses in multi-supported systems. This paper describes a comprehensive approach for the inclusion of ground motion incoherence in the seismic response of structures. First, spatially incoherent ground motion is mathematically described in both frequency and time domains. With soil-structure interaction neglected, variances of the axial and bending strains in line structures due to ground motion incoherence are then established in closed forms. This yields the upper limits for the strains. Finally, the effects of ground motion incoherence on the axial and lateral response of concrete gravity dams are investigated in detail, including dam-reservoir-foundation interaction. MODELLING INCOHERENT GROUND MOTIONS Frequency Domain Representation To fully describe the space-time random field of the ground motion, cross-spectra between every two points in the random field are needed. For statistically homogeneous random fields such as that of the ground motion, the cross-spectrum between any two points can be described as

The gravity cooling water tank is a remarkable structural feature of third-generation pressurized water reactor nuclear power plant. To investigate the influence of fluid-structure interaction (FSI) on the seismic response of the structure, this study designed two 1 : 50 simplified models of the AP1000 shield building. A series of shaking table tests were conducted to study the seismic responses with and without FSI effect. The natural frequency, acceleration, strain, and hydrodynamic pressure of the two models were analyzed, and the seismic reduction effect of the water tank was evaluated. Moreover, the test data were compared with the results of numerical analysis using the ABAQUS software. The results show that the presence of water and the sloshing of water reduce the natural frequency and seismic response of the model structure. Thus, the gravity cooling water tank has a certain seismic reduction effect. The simplified model of water sloshing can be used to analyze the seismic response of the shield building.

Effect of nearby ground structures on the seismic response of underground structures in saturated sand

This paper presents a parametric study on the lateral-torsional coupling behaviours of soil-multistorey bidirectional eccentric structure interaction system from elastic stage to nonlinear inelastic stage. A simplified bidirectional eccentric multistorey dual lateral load-resisting model for the superstructure is proposed to conduct this parametric study. Incorporating the inter-storey restoring force model of the superstructure, the dynamic motion equations and the dynamic stiffness matrix of the soil-multistorey bidirectional eccentric structure interaction system in different loading stages are derived. Based on these, parametric analyses of frequencies and seismic responses for the soil-three storey structure interaction systems from elastic stage to nonlinear inelastic stage are evaluated. Effects of the uncoupled torsion to lateral frequency ratios (Ω) of the corresponding fixed base system, the stiffness eccentricities and different soil types on the frequencies and seismic responses are investigated. Results show that the soil can significantly reduce the lateral-torsional coupling effect and the structural seismic response of the soil-bidirectional eccentric structure interaction system; a smaller Ω value and larger values of the eccentricities lead to a larger reduction in the lateral-torsional coupling effect of the first order mode in nonlinear inelastic stage; the effects of different foundation conditions on the structural seismic responses are weakened by the development of structural inelastic; after considering the soil-structure interaction, the influences of Ω and eccentricities on the structural seismic responses are changed. A softer soil-structure interaction system has a more weaken lateral-torsional coupling effect, and its vibration modes in nonlinear inelastic stage are changed compared with the system situated on other soils.

Dynamic characteristic analysis of fuzzy-stochastic truss structures based on fuzzy factor method and random factor method

To investigate the isolation effect of the friction pendulum system (FPS) horizontal isolation bearing and the air spring‐FPS three‐dimensional (3D) isolation bearing in truss structure and the influences of long‐period ground motions on the isolated structure, the shaking table test of a truss structure is designed and conducted. The ordinary ground motions, near‐fault pulse‐like ground motions, and far‐field long‐period ground motions with different spectral characteristics are chosen to input into the structure, and the dynamic characteristics such as the acceleration, displacement, and stress of the truss are compared and analyzed. The horizontal frequency of the horizontal isolated structure is reduced after the horizontal isolation, while the vertical frequency is further reduced after 3D isolation. The isolation effect of nodal acceleration, nodal displacement, and member stress under 3D isolation is better than that of horizontal isolation, especially the vertical seismic response is significantly improved. When the ground motion intensity is small, the FPS horizontal isolation bearing slides little, and reducing the seismic response of the structure is limited. There is a better isolation effect of 3D isolated structure. The vertical frequency ratio Rf under ordinary ground motions is far away from 1 and close to 3, basically avoiding the main energy segment of the ground motions. The advantage of 3D isolated structure is relatively reduced under long‐period ground motions, which lies in the rich low‐frequency components of long‐period ground motions which are difficult to isolate effectively.

장경간의 대공간구조물은 지진하중에 의하여 일반구조물과는 다른 응답특성이 나타나고 있으므로 대공간구조물에 대한 내진설계를 위해서는 대공간구조물의 동적특성 및 지진응답특성에 대한 정확한 분석이 필요하다. 본 논문에서는 예제 구조물로 대공간구조물의 동적특성을 기본적으로 내재하고 있는 장견간의 아치구조물로 선정하여 다중지점 지진하중이 가진되는 대공간구조물의 진동응답 특성을 분석하였다. 다중지점 지진하중은 대공간구조물의 지점 지반조건이 다른 경우 그리고 시간지연을 갖는 지진하중이 가진되는 경우로 하여 수치해석을 수행하였다. 다중지점 지진하중 적용한 경우의 지진응답이 단일 지진하중 적용에 의한 지진응답과 비교하여 경우에 따라서 상이한 지진응답을 나타내고 있다. 따라서 대공간구조물의 경우에 정확한 지진응답 분석 및 적절한 내진설계를 위해서는 다중지점 지진하중을 적용하여 지진응답을 분석하는 것 바람직하다. Spatial structures have the different dynamic characteristics from general rahmen structures. Therefore, it is necessary to accurately analyze dynamic characteristics and seismic response for seismic design of spatial structure. Keel arch structure is used as an example structure because it has primary characteristics of spatial structures. In case of spatial structures with different ground condition and time lag, multiple support excitation may be subjected to supports of a keel arch structure. In this study, the response of the keel arch structure under multiple support excitation and with time lag are analyzed by means of the pseudo excitation method. Pseudo excitation method shows that the structural response is divided into two parts, ground displacement and structural dynamic response due to ground motion excitation. It is known that the seismic responses of spatial structure under multiple support excitation are different from those of spatial structure under simple excitation. And the seismic response of spatial structure with time lag are different from those of spatial structure without time lag. Therefore, it has to be necessary to analyze the seismic response of spatial structure under multiple support excitation and time lag because the spatial structure supports may be different and very long span. It is shown that the seismic response of spatial structure under multiple support seismic excitation are different from those of spatial structure under unique excitation.

The objective of this study is to model the interaction between a concrete wall and a soil under seismic loading using the finite element method. The stiffness matrix of the soil is integrated to that of the structure to formulate the stiffness matrix of the entire system. To simulate the dynamic of soil–structure interaction, a numerical program was developed for this concern. So to resolve governed dynamic equations, the central difference method is used to compute displacement, velocity, and acceleration fields of soil, interface medium, and concrete wall nodes. The significance of soil foundation–structure interaction over fixed-base structure analysis showed that the integration of soil and foundation produces considerable changes in the seismic response. Obtained results using the soil–structure model and impedance functions are compared to those of fixed-base structure. The purpose is to calibrate the effects of soil properties and the soil–structure interaction on the seismic response of the structure and on the interaction medium.

Assessing seismic response equivalency for fixed pile-founded offshore platforms utilizing PSDA and IDA

To explore the seismic response, influence mechanism, and failure of long-span spatial structures with three-dimensional seismic excitations in a strong earthquake, 1/6-scale shaking-table tests of single-layer cylindrical reticulated shell structures with fixed hinged bearings, horizontal isolation bearings, and three-dimensional isolation bearings were conducted with three-dimensional seismic excitations. The accuracy of the numerical simulation method was verified by a numerical reconstruction analysis of the experiments. Dynamic time-history response analysis and incremental dynamic analysis of a full-scale single-layer cylindrical reticulated shell were conducted. The seismic response and failure states of the three-dimensional isolation structure were compared at different positions, different rise-span ratios, and different lower supporting structure heights. Studies have shown that horizontal isolation bearings cannot reduce the vertical vibration frequency and vertical seismic response of a structure; three-dimensional isolation bearings can effectively reduce the vertical vibration frequency and the vertical seismic response of the structure. The degree of plastic development is reduced by 82% in strong earthquakes; the initial plastic development position of the structure changes from the midspan to the four edges, and the ultimate bearing capacity of the structure increases by 40%. For a three-dimensional isolation structure, the natural frequency of the base-isolation structure is smaller, the ultimate bearing capacity is greater, and the isolation effect is better than with story isolation. With an increase in the rise-span ratio, the ultimate bearing capacity of the structure decreases. When the rise-span ratio is 1/2, the bearing capacity is 0.9g, and the structure tends toward dynamic instability. A greater height for the lower support produces a greater ultimate bearing capacity and better isolation.

Guidelines for seismic performance evaluation of existing structures have been published by FEMA and the European Commission. Additionally, these organizations have presented frameworks for strengthening the resilience of society and industry. These frameworks require countermeasures for early recovery after natural disasters. For rapid post-earthquake recovery, it is necessary to assess the structural integrity and implement repairs. To achieve this, the utilization of structural health monitoring is essential. In structural damage assessment, loads and response displacements are important physical quantities, but these are difficult to obtain directly from structures. Therefore, in structural health monitoring, structural integrity is evaluated using measured accelerations. However, the superposition of uncertainties related to seismic motion and structures can sometimes complicate the setting of thresholds for structural integrity evaluation. To detect structural anomalies caused by earthquakes rapidly and with high accuracy, structural health monitoring methods incorporating deep learning have begun to be researched. Additionally, by extracting features from measured data using deep learning, prior setting of evaluation thresholds becomes unnecessary. Generally, training deep learning models requires large amounts of training data. However, since it is difficult to acquire anomaly data from existing structures, seismic response analysis is utilized. Typically, to represent real phenomena, analytical models require many degrees of freedom. In frequency domain response analysis, the frequency response function is defined as the ratio of the Fourier spectra of the structural seismic response to the seismic motion. By modeling the frequency response function, the seismic response of structures can be calculated. In this paper, we develop a method to calculate structural seismic responses by modeling the frequency response function with an AR model. This eliminates the need to set parameters such as degrees of freedom, mass, and stiffness of the analytical model. Furthermore, we propose a structural health monitoring method that uses this approach for training deep learning models. Verification of this method using experimental data from a full-scale steel building demonstrated that anomaly detection was possible from limited observational data only.