Three-dimensional Nonlinear Analysis Research Articles

The performance of transmission pipelines on February 6th, 2023 Kahramanmaras earthquake: a series of case studies

AbstractThe Mw 7.8 earthquake that struck Kahramanmaras on February 6, 2023, caused significant damage to hydrocarbon and water transmission lines due to permanent ground deformations. Explosions occurred in the Kahramanmaras–Gaziantep Natural Gas transmission pipeline causing disruption of gas in the cities of Gaziantep and Hatay Fault Displacement Hazard. Water transmission pipelines were also damaged due to extreme fault offsets. This paper presents the findings from the earthquake affected zones. Particular attention was given to the performance of the 2600 mm diameter Duzbag–Gaziantep water transmission pipeline due to three reported challenges: (#1) The behavior of the pipe in the Duzbag tunnel, (#2) The pipe bend behavior at the fault crossing, and (#3) The pull-out of the pipe at valve room. Based on field observations, extreme damage forms at pipes were presented. A three-dimensional nonlinear numerical analysis was performed to simulate the observed damage of the reoriented water pipe at the fault crossing for Case #2. The nonlinear finite element model was able to capture the complex nature of the post-yield behavior of steel pipe as well as the damage locations along the pipe and their sequence of occurrences. As a mitigation measure for new pipes, the need for using flexible connections at critical crossings was highlighted. For existing pipes, the importance of developing secondary (by-pass) lines was emphasized.

Seismic and vibration control of segmented isolation layer in underground structure-diaphragm wall system

In this paper, a seismic and vibration reduction measure of subway station is developed by setting a segmented isolation layer between the sidewall of structure and the diaphragm wall. The segmented isolation layer consists of a rigid layer and a flexible layer. The rigid layer is installed at the joint section between the structural sidewall and slab, and the flexible layer is installed at the remaining sections. A diaphragm wall-segmented isolation layer-subway station structure system is constructed. Seismic and vibration control performance of the diaphragm wall-segmented isolation layer-subway station structure system is evaluated by the detailed numerical analysis. Firstly, a three-dimensional nonlinear time-history analysis is carried out to study the seismic response of the station structure by considering the effect of different earthquake motions and stiffness of segmented isolation layer. Subsequently, the vibration response of site under training loading is also studied by considering the influence of different train velocities and stiffness of the segmented isolation layer. Numerical results demonstrate that the diaphragm wall-segmented isolation layer-subway station structure system can not only effectively reduce the lateral deformation of station structure, but also reduce the tensile damage of the roof slab. On the other hand, the developed reduction measure can also significantly reduce the vertical peak displacements of site under training loading.

Three-dimensional nonlinear stress analysis of functionally graded shells subjected to displacement-dependent loads

The nonlinear geometrically exact (GeX) hybrid-mixed four-node solid-shell element under non-conservative loading, developed in the companion paper, is here extended to the stress analysis of functionally graded material (FGM) shells. The term GeX means that the middle surface is described by analytical functions, including spline functions, and, therefore, the coefficients of the first and second fundamental forms can be taken exactly at element nodes. The FGM solid-shell element formulation is based on the choice of N sampling surfaces (SaS) parallel to the middle surface and located at Chebyshev polynomial nodes within the shell as well as on the outer surfaces, to introduce the displacements of these surfaces as basic unknowns. The use of Lagrange polynomials of degree N–1 in the distributions of displacements, strains, stresses, and elastic coefficients through the thickness of the shell leads to an efficient 3N-parameter shell formulation. To develop the FGM four-node solid-shell element based on the hybrid-mixed method, in which strains and stresses are utilized as primary variables, the Hu-Washizu variational principle is applied. Due to the analytical integration used to evaluate the tangent stiffness matrix, the developed FGM solid-shell element subjected to displacement-dependent loads shows superior performance in the case of coarse meshes and allows the use of only one load step in most of the considered benchmark problems. It has been established that the difference between the second Piola-Kirchhoff and Cauchy stress tensors in non-conservative problems for FGM shells undergoing moderately large strains can be significant.

Performance Assessment of Reinforced Concrete Bridges Under Coupled Horizontal and Vertical Ground Motions Using Fragility Surfaces

ABSTRACT The objective of this study is to explore the seismic fragility of reinforced concrete bridges, specifically in response to the vertical components of ground motions, utilizing fragility surfaces. The examination of bridge responses involves the application of optimally selected intensity measures through three-dimensional nonlinear time-history analyses, encompassing uncertainties in both superstructure materials and soil–structure interaction effects. In this investigation, an extended Probabilistic Seismic Demand Model (e-PSDM) is employed, leveraging fragility surfaces to concurrently consider vertical and horizontal excitations. The results obtained from this approach are compared with traditional fragility curves. This study emphasizes Pile-cap displacement and drift ratio as pivotal engineering damage parameters, acknowledging their sensitivity to the influences of both soil–structure interaction effects and vertical ground motion. The fragility surfaces derived from the study reveal a correlation between increased vertical spectral accelerations and elevated probabilities of surpassing both slight damage and collapse limit states. These observations underscore the critical significance and practical utility of fragility surfaces in the context of performance-based seismic assessment and design for reinforced concrete bridges. The findings from this research contribute valuable insights into the nuanced behaviour of reinforced concrete bridges under seismic conditions, emphasizing the relevance of incorporating vertical components in fragility assessments for a more comprehensive understanding of structural vulnerability.

Research on Dynamic Characteristics of Loess Homogeneous Dam under Seismic Waves

Based on the relevant provisions of the seismic design code, the three-dimensional nonlinear seismic response analysis of an actual loess homogeneous dam engineering is carried out. The seismic waves use the ground motion time history generated by the relevant design response spectrum of the set seismic site. The research results show that the homogeneous dam in the V-shaped valley has a significant amplification effect in the middle of the valley. The acceleration amplification area of the dam is above 4/5 of the dam height and within the range of 1/3 of the dam axis length. The regularity shows obvious "whiplash effect" and three-dimensional river valley effect.

Numerical Analysis of Double Riveted Lap Joints

In a previous work, the fatigue behaviour of different hot riveted joints under fatigue loadings were experimentally calculated. In particular, the experimental data showed a Wöhler curve slope close to five against the slope of three proposed by Eurocode 3. However, two series of shear splice riveted joints showed, at two million cycles, a stress range very close to the value suggested by Eurocode for shear splices that use non-preloaded high-strength bolts. In order to clarify the fatigue behaviour of riveted joints at high- and medium-fatigue regimes, this paper presents a preliminary three-dimensional non-linear FE analysis of a double-riveted lap joint previously analysed experimentally. Different friction coefficients and rivet clamping stress have been taken Into account, as well as the elastoplastic behaviours of the main plate subjected to tensile loadings. The numerical analysis shows that the friction force tends to reduce the range of stresses at the net section during fatigue loadings, and the force distribution or the stress concentration on the rivets is always critical for the external rivet, which is also the case regarding the non-linear behaviour of the material.

Three-dimensional nonlinear flutter analysis of long-span bridges by multimode and full-mode approaches

Based on amplitude-dependent flutter derivatives (FDs), the present study established three-dimensional (3D) nonlinear flutter analysis methods, including a multimode and a full-mode approach, for long-span bridges. Then, by adopting the proposed methods, the influences of 3D effects, self-excited drag force, and multimode aerodynamic coupling effects on nonlinear flutter response were investigated. Besides, critical structural modes that have a great impact on nonlinear flutter were identified, their contributions were quantified and roles were clarified. The results show that the 3D effects of structural modes can reduce the system stability mainly by increasing the negative uncoupled aerodynamic damping. Thus, if the 3D effects are ignored, the stable amplitude of nonlinear flutter will be underestimated. For long-span bridges whose foundational symmetric torsional mode couples a minor lateral-bending mode shape, the added aerodynamic damping from self-excited drag force, especially the term of FD P1∗∗1, can improve the stability of the system. Thus, it will overestimate the nonlinear flutter response if the self-excited drag force is ignored. Meanwhile, the aerodynamic coupling effect among different structural modes should be considered, otherwise the nonlinear flutter responses of long-span bridges may be misestimated significantly. For the nonlinear flutter dominated by the fundamental symmetric torsional modal branch, the symmetric vertical bending modes with a frequency lower than the fundamental symmetric torsional mode should be considered. Besides, the other higher-order structural mode coupled with relatively significant fundamental symmetric torsional mode shape is also worth being taken into account. The selection of structural modes is an important and experience-based work in the multimode method. Thus, the full-mode method, which can consider the potential higher-order structural modes that may have contributions to the 3D nonlinear flutter, is also needed, especially when the amplitude is large enough. Otherwise, the nonlinear flutter response may be underestimated by the multimode method.

Numerical Evaluation of Drag Force on Integral Abutment Piles

Piles transmit structural loads through skin friction, end-bearing, or both to deeper and stronger soil layers. Surcharge loads, site grading, or dewatering activities induce downward movement in the soil that is adjacent to piles installed in a compressible soil layer. This movement causes negative skin friction stresses that act downward at the pile–soil interface, which causes an additional force denoted the drag force (Qn) that is applied to the pile, which results in a larger axial load in the pile shaft. The end-bearing force and positive skin friction that develops in the pile part within stable (incompressible) soil resist the applied loads [e.g., dead load (Qd) and Qn]. This paper aimed to evaluate Qn that was mobilized on driven H-piles that were installed in soft clay with three-dimensional (3D) nonlinear finite-element analysis. Two numerical models were validated against the field data from two instrumented H-piles, which were part of a three-span bridge (E-21) on Highway 418, Ontario, Canada. The calculated settlements and Qn agreed well with measured field data. The validated numerical models were employed to conduct a parametric analysis to investigate the location of the neutral plane (NP) at which the skin friction changed from negative to positive. In addition, the performance of the piles that were installed in small and large groups was investigated, which considered Qn and group effects. It was found that the group effect was negligible for piles that were installed in one row but were significant for piles that were installed in large groups. Finally, a group factor was proposed to calculate the drag force for piles in a group (Q(n)pile in group).

Low velocity impact behaviour of curved nano composite Panel- A Numerical study

This paper presents a numerical interrogation of the impact behaviour of steel and nano polyurea composite panels of the different radii of curvature (Infinite, 305 ROC, 112 ROC) with 203 mm × 203 mm × 1.5 mm thick subjected to low-velocity impact. Three-dimensional non-linear FE analysis using the LS DYNA code was used to replicate the experimental impact testing. It has been found that the numerical results closely resemble the test results reported in the literature. Based on the validated finite element model, the effect of impact velocity (1.98 m/s, 2.43 m/s & 2.8 m/s), impactor shapes (flat, hemispherical, and conical) and different thickness combinations (0.5 mm nanopolyurea-1 mm steel, 1 mm nanopolyurea-0.5 mm steel, 0.8 mm nano polyurea- 0.7 mm steel, 0.4 mm steel-0.7 mm nano polyurea-0.4 mm steel) on the low-velocity impact were studied. The numerical results make it evident that all the above configurations have a significant impact on the low-velocity impact.

A CFD-FEA Method for Hydroelastic Analysis of Floating Structures

The so-called large multi-body floating offshore structure is a new type of offshore structure with a huge and extremely flat deck area, which has a promising prospect as a floating port and also in applications in the area of marine space exploitation. Due to its unique structural form, the hydrodynamic and structural response characteristics are very complex. Specifically, due to the instantaneous position variation in the body surface, the nonlinearity of the free surface, the interactions between floating bodies, and the elastic deformation of floating bodies, the nonlinear factors are significant and cannot be neglected. For these kinds of problems, methods based on CFD-FEA (computation fluid dynamics–finite element analysis) coupling simulation have significant advantages over traditional methods. In the present paper, the hydrodynamic and structural response characteristics of a large multi-body floating offshore structure are studied using a CFD-FEA method, and the results are compared with those obtained by the potential-flow-based commercial code SESAM/WADAM, and a three-dimensional nonlinear hydroelastic analysis commercial code COMPASS-WALCS-NE. The comparison and the analysis of the results show that the CFD-FEA method presented in this study can well simulate the behavior of the hydroelastic responses of flexible floating structures and has the potential to capture complex nonlinear behaviors.

Fragility and comfortability curves development and seismic risk assessment of a masonry building under earthquakes induced by geothermal power plants operation

This research is an attempt to estimate the seismic risk of geothermal power plants (GPPs) operation on the masonry buildings located in the vicinity of these infrastructures through a probabilistic framework. In this regard, a typical masonry building in Germany is considered. In the first part, the fragility and comfortability curves of this building are established. For this purpose, a set of 30 ground motions recorded due to GPPs activity are used for performing elaborated three-dimensional nonlinear incremental dynamic analysis to construct the fragility and comfortability curves. In the second part of the research work, by using the Monte-Carlo simulation technique and adopting the hazard model capable of simulating both seismological characteristics and ground motion intensities, the required number of probable hazard scenarios are generated for different ranges of GPPs injection flow rates. Afterward, the seismic risk imposed on the masonry building is evaluated by considering the developed fragility and comfortability curves. The outcomes highlight that the risk of facing structural damage is not significant; however, the disturbance of buildings’ residents is highly probable and can lead to considerable seismic risk. In addition, in the close vicinity of the earthquake epicenter (less than 5 km), the estimated risk increases tangibly in comparison with the larger distances (more than 15 km).

Seismic effects of bracing irregularity of light timber-framed buildings

Most residential buildings in New Zealand are low-rise light timber-framed (LTF) buildings, constructed according to a prescriptive standard – NZS 3604:2011 Timber-framed buildings. NZS 3604:2011 tabulates the seismic demand and also specifies the test procedure for evaluating the seismic resistance of proprietary LTF walls, which are often plasterboard walls. Designers need to ensure the provided total seismic bracing capacity is at least equal to the total seismic bracing demand, provided that bracing arrangements satisfy the specified irregularity limits. The irregularity limits of bracing arrangements in NZS3604:2011 were established based on engineering rules of thumb rather than rigorous scientific evidence. Earthquake damage observed in the 2010/11 Canterbury earthquake sequence demonstrated that simple regular LTF houses performed well while irregular houses often had significant damage that was uneconomical to repair. This suggested that the irregularity of LTF buildings was an important factor responsible for the exacerbated earthquake damage. To quantify seismic effects of permissible irregularities in NZS 3604:2011 and provide scientific evidence for elaborating irregularity limits in NZS 3604:2011, three single storey LTF buildings with varying degrees of permissible plan irregularities were designed and their seismic performance was studied by conducting three-dimensional non-linear push-over analyses. For the non-linear push-over analyses, the in-plane behaviour of LTF walls and ceiling diaphragms were modelled using the models, developed based on NZ practice, as reported in previous research. The study revealed that permissible irregular bracing arrangements in NZS 3604:2011 could amplify lateral deflections significantly, in comparison with the regular counterparts. As a result, irregular LTF buildings within the scope of NZS 3604:2011 could be susceptible to damage due to excessive deformations in earthquakes and this suggests that the irregularity limits in current NZS 3604:2011 be reviewed and tightened.

Three-dimensional nonlinear thermoacoustic instability analysis based on Green's function approach

In this work, nonlinear thermoacoustic instability analysis is made in a hard-walled box to investigate the limit cycle of thermoacoustic oscillation and the interplay of two modes. We model the flame as an acoustically compact source described by a generic Flame Describing Function, i.e. an amplitude-dependent Flame Transfer Function. The acoustic field in the hard-wall box could be described by an integral equation using a Green's function tailored to a three-dimensional (3-D) rectangular box with hard-wall boundary conditions. The integral equation is solved by two methods. Firstly, an iteration method, stepping forward in time, is used to give the time history of the acoustic velocity. The other method is done in the frequency domain to determine the thermoacoustic eigenfrequency and growth rate of thermoacoustic modes. We could observe the phenomenon of modes "jump" after two different time windows of the time history operated with the Fourier transformation. This result reveals that there are two modes in the system, the interference between modes will occur. In the early stage, the two modes work together. After reaching the limit cycle oscillation, the role of one mode is dominant and the other mode basically disappears.

Periodic motion of microscale cantilevered fluid-conveying pipes with symmetric breaking on the cross-section

A new theoretical model is developed for the three-dimensional (3D) nonlinear vibration analysis of cantilevered fluid-conveying micropipes with asymmetric cross-section. Fluid-conveying microscale pipes with ring-shaped cross-sections of O(2) symmetry are widely used in engineering. However, their cross-sections usually have a small symmetric breaking owing to manufacturing errors, which can be described by a small parameter. Hence, the dynamic behaviors of such geometrically imperfect micropipes are extremely required to be explored. This study mainly investigates the effects of the symmetric breaking parameter, flow velocity and dimensionless material length scale parameter on the dynamic behaviors of microscale cantilevered fluid-conveying micropipes. Based on the modified couple stress theory (MCST) and Hamilton's principle, the governing equation is derived, where the effects of the asymmetry of cross-section on the equation are reflected. Using the center manifold theory and normal form method, the original governing equation is rigorously reduced to a two-degree-of-freedom (2DOF) dynamical system, and the averaging equation of the reduced system is obtained by combining the averaging method. The existence and stability of the equilibrium point of the averaging equation are studied to obtain the results of the existence and stability of periodic motions of the original system. The results demonstrate that the types of periodic motions and stability when the pipe loses stability from different places on the curve of the critical flow velocity versus mass ratio (critical flow velocity curve) may differ. Meanwhile, the effects of various parameters on these periodic motions are presented. The increase in the dimensionless material length scale parameter increases the section corresponding to stable plane periodic motion and reduces the section corresponding to stable spatial periodic motion on the critical flow velocity curve. When dimensionless material length scale parameter is given, the existence and stability of various periodic motions of the system depend on the ratio of the increment of flow velocity around the critical value to the symmetric breaking parameter. In addition, some new phenomena are found in this paper. Stable 0 planar periodic motion of the macropipe can occur when pipe loses its stability from the hysteresis part of the critical flow velocity curve. Stable 0 planar periodic motion of microscale pipes can occur when pipe loses its stability from the non-hysteresis part of the critical flow velocity curve, and then stable 0 planar periodic motion and stable π planar periodic motion can coexist. Furthermore, stable planar and stable spatial periodic motions of pipes with symmetric breaking can coexist, and stable torus motion has also been observed; this is different from the dynamics of pipes with O(2) symmetry.

Three-dimensional nonlinear stability analysis of axial-thermal-electrical loaded FG piezoelectric microshells via MKM strain gradient formulations

The present study focuses on the moving Kriging meshfree (MKM) technique combined with the three-dimensional strain gradient continuum mechanics to analyze three-dimensional nonlinear stability response of thermo-electro-mechanical loaded functionally graded (FG) piezoelectric cylindrical microshells. The derived three-dimensional MKM model has the capability to present the transition of buckling mode containing different microsize-dependent gradient tensors. The microshells are made of a mixture containing PZT-4 and PZT-5H piezoelectric phases, the material properties of which vary continuously along the shell thickness and captured based on the power law composition scheme. With the aid of MKM strain gradient-based shell model, it is possible to satisfy the function property associated with Kronecker delta by putting the required boundary conditions directly at the associated nodes without any predefined mesh. The microsize-dependent nonlinear stability plots are obtained in the presence of modal transition relevant to various environment temperatures, external electric voltages, microstructural size dependency tensors, and power-law indexes. It is found that the stiffening character related to all three microstructural strain gradient tensors is more significant for the second nonlinear stability mechanical/electrical load in comparison with the first one. However, for the three-dimensional mechanical/electrical bifurcation load, the stiffening character of these gradient tensors becomes even lower than the first postbuckling load. Moreover, by applying an actuation via a positive voltage, the first three-dimensional critical buckling load and the associated end shortening reduce, while an actuation via a negative voltage results in to increase them. It is observed that by shifting to the postbuckling territory, the role of the electric actuation gets negligible.

A comprehensive approach for bridge performance evaluation under rockfall impact integrated with geological hazard analysis

Rockfall is one kind of major hazard that seriously threatens the safety of bridge structures passing through mountainous areas. The complexity of geological conditions in mountainous areas makes it difficult to determine the initial impact parameters of falling rock in the bridge performance analysis. At present, the subjective and deterministic methods are adopted to get the initial motion parameters of the falling rock for evaluating the structural responses. In this paper, the probability distributions of falling rocks collision parameters are obtained by the rockfall Monte Carlo simulations. Then the characteristic values from the probability distribution of rock motion parameters are taken as the input parameters in the dynamic simulation of bridge structure. Finally, three-dimensional nonlinear dynamic analysis is employed to evaluate the safety of the bridge structure under rockfall hazards. The residual resistance index (RRI) is presented for quantifying the post-impact performance of bridge pier and girder under rock collision. The structural safety is mainly dominated by the impact mass and translational velocity of the falling rock rather than the rotational velocity and impact angle. The rock shape also has non-negligible influence on the structural dynamic responses and performance, and the cube-like rock induces more severe structural damage than other shapes. According to the RRI and probability distribution of rock mass, the non-exceedance probability of RRI is obtained which can be used for the risk analysis of rockfall impacting on bridges. The proposed comprehensive approach for bridge performance evaluation considers the uncertainty of rockfall characteristics, and it provides more reasonable solution to investigate the impact performance of bridge structure under rockfall disasters.

Study on Working Behaviors and Improvement Strategies of Concrete Cutoff Wall with Slurry Cake in Thick Soil Foundation

Concrete cutoff walls are becoming more widely used to control foundation seepage for earth–rock dams built on a thick soil foundation because of the urgent demand for hydroelectric energy. As the lifeline impermeable structure, the safety of the concrete cutoff wall is of great importance and deserves increased attention. However, such walls have often been analyzed through linear-elastic modeling and simulated as a continuous structure. The working behavior of the discontinued concrete cutoff wall with slurry cake is still unclear. This paper presents a three-dimensional (3D) nonlinear finite-element numerical analysis of the concrete cutoff wall in a thick soil earth–rock dam foundation considering the effect of slurry cake. The results indicate that the damage degree and range in the concrete cutoff wall are significantly affected by wall discontinuity and slurry cake thickness. Moreover, the panel joints may open at the downstream side of the wall under the action of lateral water pressure, which will reduce the effective thickness. The joint opening and tensile damage degree decrease with a reduction in panel width, while the compression damage at the lower part of the wall becomes more serious. The thickness of slurry cake should be controlled reasonably because of its obvious effect on damage behavior of the wall. The working behavior of the concrete cutoff wall can be improved by arranging the width distribution of the panel reasonably and dealing with the problem of the slurry cake. This study can provide useful basis and suggestions for the design of a concrete cutoff wall with slurry cake between panels in thick soil foundations.

Three-Dimensional Nonlinear Dynamic Analysis of Base Isolated Cylindrical Steel Tank

Failure of a tank during an earthquake can result in significant financial, human, and environmental losses. Thus, their lack of resiliency against strong earthquakes may result in refinery disruption. This has the potential to have a considerable impact on any economic system. As a result, more research into the seismic performance of tank structures is required to attain the highest possible level of resistance against strong earthquakes. In this paper, we aim to look into the installation of seismic isolation systems in cylindrical steel storage tanks. A nonlinear 3D finite element model is developed with ANSYS software. Moreover, tank wall material nonlinearity, fluid-structure-interaction, and sloshing components are considered. The bilinear hysteretic LRB is used for modal and time-history analysis. In this work, three tanks with varying aspect ratios are studied: "Model A", "Model B", and "Model C". Furthermore, the fixed tank's fundamental frequencies were compared to the analytical results of the American API 650 Standard. Subsequently, the dynamic behavior response of the researched tanks to the horizontal component of the El-Centro 1940 earthquake with PGAs of 0.34g and 0.5g is investigated. As a result, the dominating frequency of the seismic isolation system is within the effective frequency range of seismically isolated systems. The results illustrate that the base isolation limits the tank wall movement with a large displacement in the isolators; the mode shape is a cantilever beam in all isolated circumstances. The total seismic response reduction in the slender tanks is greater as compared to the broad case in the base-isolated tanks. The sloshing displacement increases with an increase in the tank aspect ratio. Additionally, the isolation device eliminates tank buckling at the base and top of the tank shell during seismic excitation (elephant foot and diamond buckling). It can be concluded that the seismic isolation technique has a more significant impact on reducing the dynamic response of ground-supported tanks, particularly in taller tanks as compared to broad tanks. Doi: 10.28991/CEJ-2022-08-06-013 Full Text: PDF

Three-dimensional nonlinear aerostatic stability analysis of long-span suspension bridges under skew wind

Based on the aerostatic force model under skew wind, considering the nonlinear and three-dimensional effects of aerostatic forces and also structural geometric nonlinearity, a method of three-dimensional nonlinear aerostatic stability analysis under skew wind is presented, and the corresponding computational procedure (SNAA-SW) is developed. By taking a suspension bridge- the Runyang suspension bridge over the Yangtze River as example, 3D nonlinear aerostatic stability analysis of the bridge under skew wind is conducted, and the skew wind effect on the aerostatic stability of long-span suspension bridges is ascertained. The results show that the skew wind effect does not change the aerostatic instability mode of suspension bridges, which shows a spatial bending-torsion coupled instability mode as the same as normal wind case. The skew wind has positive and negative effects on the aerostatic stability of suspension bridge under different wind attack angles, and the evolutions of critical wind speed of aerostatic instability with wind yaw angle are completely different from the cosine rule as proposed by the skew wind decomposition method, for most cases, the lowest critical wind speed of aerostatic instability occurs under skew wind. With the increase of wind yaw angle, the skew wind effect on the critical wind speed of aerostatic instability becomes more prominent, and the influence is between −10.7% and 8.1%. Therefore, the skew wind effect needs to be accurately considered in the aerostatic stability analysis of long-span suspension bridges in particular at large wind yaw angles.

Three-Dimensional Seismic Nonlinear Analysis of Topography–Structure–Soil–Structure Interaction for Buildings near Slopes

Three-Dimensional Seismic Nonlinear Analysis of Topography–Structure–Soil–Structure Interaction for Buildings near Slopes