International Journal of Structural Stability and Dynamics

In this paper, by implanting the rigid body rule (RBR)-based strategy for static nonlinear problems into the implicit direct integration procedure, an efficient and robustness nonlinear dynamic analysis method for the response of framed structures with large deflections and rotations is proposed. The implicit integration method proposed by Newmark is improved by inserting an intermediate time into the time step and by adding the 3-point backward difference in the second substep so as to preserve the momentum conservation and to maintain the stability of the direct integration method. To solve the equivalent incremental equations of motion, the RBR is built in to deal with the rigid rotations and the resulting additional nodal forces of element. During the increment-iterative procedure, the use of RBR-qualified geometric stiffness in the predictor reduces the numbers of iterations, while the elastic stiffness alone in the corrector to update the element nodal forces makes the computation efficiency and convergence with no virtual forces caused by the ill geometric stiffness. The proposed algorithm is advanced in the applications of several framed structures with highly nonlinear behavior in the dynamic response by its simplicity, efficient and robustness.

Steel structures such as transmission towers may have cracks and other damages during the service period. When the structure vibrates, the cracks will open and close, which makes the structure have nonlinear characteristics of variant stiffness. In order to identify this type of nonlinear damage, a time-domain damage identification method based on the residual deviation distance (RDD) of the autoregressive conditional heteroskedasticity (ARCH) model is proposed. First, the basic theory of the ARCH model is introduced, and the methods of model order determination and parameter estimation are given. Then, the time-domain nonlinear damage characteristics are analyzed, and the second-order variance (SOV) index based on the ARCH model is introduced. Considering that both the ARCH model coefficient and the RDD contain nonlinear information, a conversion index is constructed using the Euclidean distance (ED) of the ARCH model coefficients before and after the damage. On this basis, an RDD conversion index is further proposed to improve the identification accuracy. Finally, a three-storey frame experiment and a complex transmission tower model experiment are used to verify the effectiveness of the proposed method. The experimental results show that the proposed RDD conversion index can better identify the location of structural damage, and the identification results of the RDD conversion index are obviously better than those of the SOV conversion index and the ED conversion index.

The application of reinforcement with headed bars is widely used in the construction industry. Moreover, when the net distance between headed bars is close, the concrete areas for distributing bearing under the headed bars will overlap with each other. The local bearing capacity of concrete will also be affected by the overlapping area. To evaluate the effect of the overlapping area on the local bearing capacity of concrete, the experimental study was conducted on 6 concrete pull-out specimens. Based on the pull-out test, the parameter that net distance between headed bars was researched. The failure modes of specimens can be divided into two types. The first failure mode was marked by the formation of the dovetail slot structure during the failure process, and the second failure mode was characterized by the formation of through cracks in the cross section of specimens. The pull-out test results show that the local bearing capacity of concrete decreases firstly with the increase of net distance and then increases with the increase of net distance. Therefore, the relationship between the ratio of net distance to the side length of headed bars and the percentage decrease value of the local bearing capacity were given for the two segments. In addition, the critical value of the two segments was also analyzed and the corresponding formulas were also proposed. In order to verify the accuracy of formulas for the two segments, the test data from the similar pull-out tests with two or three headed bars were collected. And the calculation was recalculated according to the method proposed in this paper. Based on the ratio of the test data to the calculated values, the average value, standard deviation, and coefficient of variation are 1.08, 0.12, and 0.11 for the descending segment, respectively. And the values are 1.21, 0.22, and 0.18 for the rising segment, respectively. It is proved that there is a high accuracy for the formulas and the calculation method for the local bearing capacity of concrete under the interaction of headed bars was established.

To rapidly repair the damaged buckling-restrained brace serving as energy absorption member during earthquake, the assembled method of wrapping the component with FRP cloth is proposed. In this research, a series of cyclic tests on six assembled buckling-restrained brace (ABRB) wrapped with three kinds of FRPs (carbon fiber, glass fiber and basalt fiber) were performed. The tested results show that all the specimens show excellent hysteretic performance and similar damage mode, namely core unit fracture, whilst short specimens show better ductility, but worse energy dissipation ability than the long specimen. A parametric analysis is performed based on a finite element model validated against the test result. The effects of the gap and friction force between core unit and infilled concrete and the thickness of FRP cloth are analyzed. The modes of multi-wave buckling of core units are exhibited, and the influence of multi-wave buckling on component performance is evaluated. Based on the test and simulation analysis, CFRP is suggested to be used in the wrapped buckling-restrained brace.

The buckling-restrained braces (BRBs) are widely applied in reinforced concrete frames (RCFs) to improve their performance under seismic loading. A procedure for designing such structures based on stiffness ratios was developed. The stiffness ratio was assumed to decrease gradually from the bottom story to the roof. The intermediate stiffness ratios were defined by linear interpolation. A step-by-step design procedure was presented. Three structures with 5, 10, and 15 stories were designed using the procedure and considering three seismic intensity levels. Linear time analysis showed that the stiffness ratio reduced along structural height had no significant effect on the inter-story drift ratio (IDR) of low-rise structures. The nonlinear time history analysis was performed to assess the structural seismic performance. On the basis of the analytical results in terms of the elastic and inelastic IDRs, reinforcements, hysteretic energy ratios of BRBs and structural damage, recommended range of stiffness ratios are proposed for various structures and design seismic intensities.

Due to its high load-bearing capacity, high-strength steel is progressively more used in present engineering applications. However, the current design codes methodology for the lateral-torsional buckling (LTB) ultimate capacity of laterally unrestrained steel beams is based on experiments limited to room temperature and mild steel. A numerical analysis of steel beams’ ultimate bearing capacity in bending was carried out to evaluate the lateral-torsional bending of different high-strength steels, namely, Q460, Q690, and Q960 steel at high temperatures. As a comparison, the lateral-torsional bending of Q235 steel beam was also studied. Finite element models (FEMs) were generated using Abaqus with taking into account initial geometrical imperfection and residual stress. The validation of the FEMs has been established by comparing the ultimate flexural resistances obtained from previous tests with those from FEM. A number of parametric studies were taken to investigate the effects of different factors such as various span lengths, residual stress, steel grades, temperatures, and cross-section size on the flexural-torsional buckling (FTB) behavior of laterally unrestrained steel beams. Furthermore, the overall bending capacity of laterally unrestrained steel beams has been shown to be deteriorating at high temperatures. In addition, based on findings from the FEMs, design curves were proposed for evaluating the FTB of high-strength steel beams at elevated temperatures. The results were compared with the design curves given by design codes of GB 51249-2017 and EN 1993-1-2.

The current cold-formed steel (CFS) wall is limited to the low-rise cold-formed thin-walled steel structure, which is inappropriate for multi-story constructions due to its low shear resistance and poor corrosion resistance of outer sheathing board. Therefore, a new composite wall of CFS frame sheathing with concrete and plasterboard was proposed, the cast-in situ concrete layer was used for the outer surface in response to the needs of corrosion resistance, and the plasterboard was utilized for the inner surface to reduce weight. This paper presented a quasi-static test on the seismic behavior of one CFS wall and three composite-walls’ sheathings with concrete and plasterboard to obtain different failure modes and investigate the influence of different sheathing and opening sizes. Combined with the finite element model, a large parametric study of composite walls was conducted to analyze the impact of load ratio, reinforcement ratio, sheathing board, and concrete and steel strength. Test and finite element analysis (FEA) results demonstrate that the seismic performance of composite walls with concrete and plasterboard is satisfactory considering their shear strength, ductility, and energy dissipation. Load ratio, opening size, and reinforcement ratio significantly affect the seismic performance of the composite wall, while the concrete and steel strength and sheathing board have minimal effects. The seismic design suggestions of composite walls are given based on this study.

As a generalized version of the base isolation, the inter-story isolation has increasing applications in tall buildings due to its better adaptivity. Compared with the seismic response of the base-isolated building, that of the inter-story isolated building is more complex because it is affected by dynamic characteristics of the lower structure (LS), isolation layer (IL) and upper structure (US), which deserves the in-depth study. This study presents a comprehensive investigation on the reduced model and the seismic response of the inter-story isolated building. The equations of motion are established using modal displacements of the linear lower and upper structures, as well as the displacement of the isolation layer with the nonlinear hysteretic restoring force character. In light of the contribution of the generalized stiffness, a method of selecting the adequate participating modes of lower and upper structures is proposed. The nonlinear time history analysis of example tall buildings to seismic excitations shows that the reduced building model can provide accurate estimation for important seismic responses. Based on the reduced building model, the influence of dimensionless parameters including frequency ratio, mass ratio, damping ratio, second stiffness ratio (i.e. ratio of the post-yield over pre-yield stiffness) and the ratio of yielding force to total weight of upper structure on structural responses are investigated systematically. Finally, the equivalent linearization method being suitable for the base-isolated structure is evaluated for the inter-story isolated structure, and the filter effect of the lower structure is emphasized.

The wind-induced fatigue damage is an important reason for the structural deterioration of transmission tower-line systems. The study of the fatigue damage of transmission towers is a basic requirement to ensure their normal service. To simulate the fatigue damage evolution occurring in the joints of the tower, a verified hybrid multiscale finite element (FE) model is first developed by concurrent modeling and substructuring techniques. Second, a fatigue damage model based on continuum damage mechanics is calibrated by conducting a fatigue crack initiation experiment and integrated into the FE material model by subroutines technique. Third, an improved Bayesian updated probability density evolution method (BUPDEM) with higher efficiency is proposed based on the Kriging method. Finally, based on the multiscale FE model and the damaged material model, the strategies for stochastic analysis of fatigue damage of transmission tower-line systems are proposed together with a numerical example for illustration. The results of the example show a good accuracy of the proposed BUPDEM.

The vortex shedding phenomenon caused by flow separation at windward corners of a high-rise building would lead to significant vortex-induced vibrations (VIVs). This paper proposes a novel and efficient two-way coupled fluid-structure interaction (FSI) method named as equivalent lumped mass system (ELMS) method to study the wind-induced responses of the Common Advisory Aeronautical Council (CAARC) building. The numerical results of ELMS are validated based on available data of aeroelastic tests. To verify the computational efficiency of ELMS method, this study also employs the other two two-way coupled FSI methods (free-form deformation (FFD) method and mapping interpolation algorithms in system coupling (MIASC) method) to simulate the response of the same high-rise building. Furthermore, the VIV mechanisms of the high-rise building are explicitly discussed based on the numerical results of the ELMS method combined with large eddy simulation (LES). The outcomes show that the ELMS method could well capture the significant amplification of cross-wind response and “lock-in” phenomenon at the range of the critical wind speed. Moreover, the computational efficiency of the ELMS method is much improved compared with the other two FSI methods. The spatial correlation and spectral coherence of the local loads at different heights of the building are increased significantly at the “lock-in” stage. The findings in this study would facility the comprehensive understanding of the VIV phenomena of the high-rise building and provide an efficient two-way coupled FSI method for engineers and researchers involved in the wind-resistant design of slender tall buildings.

Reinforced concrete (RC) split-foundation frame structures are widely used in mountainous areas. There are two grounding terminals with different heights in the split-foundation frame structures. Under the earthquake, the local damage phenomenon of the structures is severe due to the uneven stiffness distribution. It is one way to improve the seismic performance of the split-foundation frame structures to install steel braces in the upper embedding floor. According to the deformation characteristics of the upper embedding floor, three types of steel braces arrangement for the split-foundation frame structures were proposed: horizontal braces, V-type braces, and V-$\mathrm{\text{type}}+\mathrm{\text{horizontal}}$ braces. Then based on the ratio of lateral stiffness of steel braces and concrete frame columns, the section of steel brace was designed. A quasi-static test was carried out to analyze the influence of steel braces on the failure mode of the RC split-foundation frame. The reasonable seismic waves were selected to carry out the nonlinear dynamic time history analysis. Then the seismic response and failure mode of the split-foundation frame structures with different braces arrangements were compared. On this basis, fragility analysis was carried out, and the earthquake-induced collapse resistance capacity of split-foundation frame structures with steel braces was preliminarily evaluated. The results show that the horizontal steel brace can improve the phenomenon of damage concentration of the split-foundation frame structures. Furthermore, setting V-shaped braces can significantly reduce the damage degree of the upper embedding end columns and change the phenomenon of locally severe damage of the split-foundation frame structures. Moreover, according to the design method proposed in this paper, setting steel braces can improve the seismic collapse resistance capacity of the split-foundation frame structures.

This paper presents a method for modeling the initiation and propagation of the damage in steel structures under combined fatigue loading. An existing model in the literature is used as the main key to the development of the new formulation herein proposed, where a significant computational improvement for the cracking incubation phase under high cycle fatigue (HCF) is achieved. The results show a satisfactory comparison with experimental data available in the literature and the carried parametric simulations demonstrate the effectiveness of the model once strength reduction could be estimated after 0, 20, 40, and 60 years of HCF. The reduction of the structural capacity was evaluated by the consideration of the final damage due to a high-intensity dynamic loading at the end of the HCF phase.

The steel slit shear panel (SP), made by cutting slits in a monolithic steel plate, dissipates seismic energy through the flexural behavior of individual plate links separated by slits. To investigate the influence of different link designs and steel properties, three scaled SP specimens are designed and tested under quasi-static cyclic loading. Test results show that plate links with a larger width-thickness ratio buckle earlier and larger, and associated pinching in hysteresis is more serious. Significant strain hardening of low yield steel promotes plump shear hysteresis even with obvious out-of-plane buckling deformation. To investigate the effect of different SPs on the overall structural performance, moment resisting steel frame (MRSF) structures installed with SPs are built. Time-history analysis results show that the installation of SPs reduces the story displacement responses but increases the floor accelerations. The low yield SP works best in reducing both the maximum and residual inter-story drift.

This paper proposes a new method to identify local damages in frame structures based on approximate Metropolis–Hastings (AMH) algorithm and statistical moment. By analyzing the sensitivity of different statistical moment-based damage indices, the fusion index of fourth-order displacement moment and eighth-order acceleration moment is selected. Then the local damages in frame structures are primarily evaluated by AMH algorithm, where Gibbs sampling is adopted. Finally, the uncertainty of identified local damages is analyzed by using probability density evolution method (PDEM). Numerical simulations have been conducted to compare the proposed method with other similar damage detection methods, showing that the proposed method is more time-saving due to the involvement of Gibbs sampling and more accurate in assessing the damage severity. Experimental study of a 12-story benchmark frame testing has also been carried out, further validating the effectiveness of the proposed method.

Interference influence of the spacing and height ratio on the modal generalized force and wind-induced response of the low-rise building roof due to one adjacent high-rise building is investigated at three typical wind directions of 0^∘, 90^∘ and 180^∘, where the low-rise building was, respectively, located at the upstream, side-by-side and downstream of the high-rise building. The mean and standard deviation of the modal generalized force of the first vibration mode mainly exhibits reduction effects and amplification effects, respectively, at the wind direction of 0^∘ and 90^∘ at small building spacing, and first experiences shielding effects and then becomes amplification effects when the height ratio increases at the wind direction of 180^∘. The maximum displacement mainly presents reduction effects at the wind direction of 0^∘, the interference factor decreases with the increase of the reduced frequency in engineering range, and the minimum interference factor is close to 0.2. At the wind direction of 90^∘, the maximum displacement mainly presents amplification effects, these effects are obvious when the spacing ratio is small and the height ratio is large, and the maximum interference factor is close to 2.2 when the reduced frequency is larger than 0.3. At the wind direction of 180^∘, the maximum displacement shows significant amplification effects when the building spacing is small and the height ratio is large, the amplification effects gradually weaken and change into shielding effects as the building spacing increases or the height ratio decreases, and the minimum interference factor is close to 0.3. The minimum displacement experiences amplification effects at all three typical wind directions.

In order to reduce the estimation uncertainty for the wind energy output, the accurate assessment of the wind speed distribution plays an important role. Due to the influence of the complex terrain, the wind speed data in mountainous area may show the heavy tail. The tail has an important effect on the annual energy production of the wind turbine because of the power output being the cubic of the wind speed. Hence the heavy tail should be highlighted before choosing the proper distributions. To characterize the heavy tail, the box plot, QQ plot and conditional mean exceedance are used. In addition, the wind climate in the mountainous area is very complicated and typically mixed by local storms and large-scale wind flows. The distribution of the wind speed is prone to exhibit bimodal or even multi-modal nature. The conventional unimodal distributions such as Weibull may not well portray these distributions. The mixture distribution has more flexibilities to handle this challenge. Both generalized extreme value distribution and generalized Pareto distribution are considered to formulate the mixture distribution in modeling the tail. The maximum likelihood method and the constrained maximum likelihood method are used to estimate distribution parameters. The comprehensive evaluation criteria are adopted to determine the most appropriate distribution of four sets of wind speed in the mountainous area of Yunnan, China. Graphical tools, such as histogram density curve and QQ plot, are also used for evaluation. Results show that heavy tail distribution should be considered for the wind data in mountainous areas and the proposed mixture model with the constrained maximum likelihood method for the parameter estimation will be superior for the wind energy potential estimation.

There are no specific regulations regarding the interference effects that an adjacent building can place on the wind load distribution of a dome roof structure. Furthermore, the influence between an adjacent rectangular-section building and the dome roof structure on the wind-induced interference is not well understood yet. Thus, in this paper, computational fluid dynamics (CFD) is used to simulate the mean wind pressure of the dome roof structure after interference by a rectangular-section building facing the dome. The accuracy of numerical results is verified through a wind tunnel test. The effects of different building heights or widths as well as distances between the interference building and the dome on the interference are analyzed. Different wind directions in intervals of 15^∘ are examined in the analysis to identify the worst wind direction. The results reveal that the passage effect caused by the interference is the main reason for the increase of suction on the roof, and the height ratio has the greatest influence on the passage effect. The region of the roof nearest to the interference building experiences the greatest suction considering all wind directions, and the side regions of the roof are relatively safe in most cases. The results of this paper can provide a reference for engineers tasked with wind-resistant design of long-span dome structures.

Steel moment frames supported on two different ground levels have been widely constructed in the mountainous high-seismicity regions of China. To investigate the seismic collapse behavior of such frames, 3D numerical analysis models were established in Perform-3D and verified to simulate the collapse process. Different structural configurations were considered, including the number of stories below upper ground and the number of spans supported on two different ground levels. Two limit states were defined according to the different structural parts that reach their limitations. Incremental dynamic analyses were performed in both the lateral and longitudinal directions. Seismic collapse fragility curves, collapse margin ratios, and collapse patterns corresponding to eight cases were exhibited. Seismic fragility curves corresponding to four performance levels were used to assess structural vulnerability. Analytical results indicated that two different collapse patterns would exist in the lateral and longitudinal directions. Therefore, two limit states should be considered in the analyses of such steel moment frames.

Wind effects on solar panels mounted on façade of high-rise residential building are studied through wind tunnel test. The model with scale ratio of 1:80 is adopted. Results show that the top floor panel is dominated by the upward negative wind load, and the panel at the mid height floor suffers the downward positive wind load, when the panels are mounted on the windward face. The influence of different inclination angles on force coefficient of the panel is also studied. It is found that positive peak force coefficient increases with the increase of panel’s inclination angle, most unfavorable extreme wind suction decreases with increase of panel’s inclination angle. Results show that the location of panels has significant effect on the design wind load. The peak force coefficient values of $-3.50$ and $+1.50$ can be used as the recommended values for design wind coefficients of the top floor panels. Peak force coefficient values of $-3.0$ and $+2.5$ can be used as the recommended values for design wind coefficients of the mid floor panels. The correlations between wind loads on different panels are also examined to check the flow mechanism around the panel. Different trends can be clearly checked from the results for different incident wind directions, suggesting the complex flow condition near panels. The greater the panel inclination is, the higher the correlation of net force coefficient between two adjacent panels is.

Model updating is a widely adopted method to minimize the error between test results from the real structure and outcomes from the finite element (FE) model for obtaining an accurate and reliable FE model of the target structure. However, uncertainties from the environment, excitation and measurement variability can reduce the accuracy of predictions of the updated FE model. The Bayesian model updating method using multiple Markov chains based on differential evolution adaptive metropolis (DREAM) algorithm is explored, which runs multiple chains simultaneously for a global exploration, and it automatically tunes the scale and orientation of the proposal distribution during the evolution of the posterior distribution. The performance of the proposed method is illustrated numerically with a beam model and a three-span rigid frame bridge. Results show that the DREAM algorithm is capable for updating the FE model in civil engineering. It extends the Bayesian model updating method to multiple Markov chains scenario, which provides higher accuracy than single chain algorithm such as the delayed rejection adaptive metropolis-hastings (DRAM) method. Moreover, results from both examples indicate that the proposed method is insensitive to values of initial parameters, which avoid errors resulting from inappropriate prior knowledge of parameters in the FE model updating.

The body of the new typical dry gasholder is a large stiffened cylindrical shell. Under the constraints of experimental and economic conditions, buckling characteristics of the body of gasholder are generally studied by scaled model experiments. Taking discrete orthogonally $T$-shaped stiffened cylindrical shells as the research object, generalized similitude requirements and scaling laws of the structure under external pressure are presented based on discrete stiffened theory and energy method. For partial scaled models with dimple/eigen-mode imperfection and material properties, partial similitude for nonlinear buckling of discrete stiffened cylindrical shells under external pressure is mainly investigated. The results show that using scaling laws for nonlinear buckling of stiffened cylindrical shells under external pressure, scaled models can accurately predict nonlinear buckling characteristic of prototypes. As the deviation of Poisson’s ratio between materials of the model and the prototype increases, the deviation of nonlinear buckling characteristic between the predicted prototype and its prototype increases gradually. At the same time, scaled generalized similitude requirements and scaling laws can provide useful reference for the model design and experimental verification of nonlinear buckling of discrete orthogonally stiffened cylindrical shells with initial geometrical imperfection under external pressure.