Multi-storey Frame Research Articles

Seismic Response Analysis of a Vibrating Stirred Steel Fiber Concrete Frame Structure Based on Probability Density Evolution

In this paper, an experimental study of steel fiber concrete using vibration mixing technology and the probability density evolution theory is applied to establish a nonlinear stochastic seismic response model for multistory concrete frame structures considering the randomness of structural parameters. The random evolution characteristics of the structural response are studied and analyzed, and a reliability analysis method for concrete frame structures based on PDEM theory is proposed. The equations are solved by the finite difference method in the TVD format, and the probability distribution of the deformation index of the concrete frame structure is obtained by summation, where the reliability is given according to the limit value of the index. The results confirm that the PDEM theory can accurately assess the functional reliability of the structure, and it is also found that the randomness of the structural parameters has a significant effect on its nonlinear dynamic response law, and that consideration of the randomness of the structural parameters at the early stage of the design can be of great help to the seismic resistance of the structure. This study not only provides a scientific basis for the optimization of the performance of steel fiber concrete but also provides a new perspective and tool for the analysis of probability density evolution in the field of structural earthquake engineering.

Estimating response of structures to earthquake-induced tsunami: A simple approach per unidirectional analysis

The orientation of a structure with respect to the direction of propagation of tsunami wave may often be arbitrary. As such, it may be convenient to consider the tsunami wave as a combination of two orthogonal pair. The response of structures may then be computed to the simultaneous action of two components (bidirectional) covering multiple incidence angles. However, analysis of structures in three-dimension under two orthogonal components is a daunting exercise for routine design. Against this backdrop, beginning with the validation of the simulation of tsunami against real records, a detailed scrutiny of the response of simple building frames to tsunami is made over a range of orientations per both unidirectional and bidirectional analyses. This indicates the sensitivity of response over orientations and suggests that the maximum response to a bidirectional tsunami attack can be closely estimated by unidirectional analysis at appropriate orientations. This reveals the existence of the most intense orientations in which the response to unidirectional loading may approximately represent the maximum response to bidirectional loading over all orientations. Observing statistically significant positive correlation of tsunami potential (Pd) and peak destructive potential (Id) to the response to unidirectional tsunami attacks, these pure tsunami parameters are selected as suitable intensity measures (IM). Analytical (as well as graphical through standard Mohr’s circle) expressions are then derived for the orientations in which such IM can assume the maximum. It is shown that the unidirectional analysis conducted in these orientations can closely estimate the maximum response to bidirectional attacks out of all possible orientations for single story and multistorey building frames. Hence, the straightforward unidirectional analysis in the most intense orientations may be adopted for design of coastal structures.

Experimental evaluation of multi-story self-centering prestressed concrete frames with web friction devices under cyclic loading

The self-centering prestressed concrete (SCPC) frame with web friction devices is a novel resilient structural system capable of achieving minimal post-earthquake residual displacement. However, present research on its seismic performance under cyclic loading is primarily focused on single-story structures, with little consideration given to the influence of web friction device performance deterioration induced by variations in clamping force applied through bolts. Because of more complicated mechanical systems, multi-story structures' seismic performance may differ from that of single-story ones. Given this, this study performed a thorough investigation of the seismic performance of a multi-story SCPC frame through quasi-static tests. To further detect the variation in the performance of the web friction device during the test, clamping forces were monitored. The experimental results reveal that structural behavior may not scale linearly with structure size, while the multi-story frame exhibits notable displacement-dependent behavior. The lagging effect of the web friction device was observed, where the frame with lower clamping forces (or friction forces) demonstrates a higher energy-dissipating capacity under small drift levels. Simultaneously, higher energy-dissipating capacity is accompanied by greater residual displacement. Besides, higher post-tensioning (PT) forces provide better stability and more consistent clamping forces, whereas lower PT forces result in greater variability in bolt clamping. While limited cracking patterns were observed, the study notes concern about PT tendon anchorage abrasion. These findings offer crucial insights for optimizing SCPC frames across various structural sizes, underscoring the importance of a balanced design approach that considers energy dissipation, self-centering capabilities, and structural complexity.

A machine learning framework for seismic risk assessment of industrial equipment

The paper aims to propose a novel machine learning framework for seismic risk assessment of industrial facilities. In this respect, a compound artificial neural network model is employed, which is based on two different artificial neural network models in series. The first artificial neural network is a regression model employed to generate samples of a vector-valued intensity measure. The second one is a classification model that is used to predict structural damage, starting from the outcomes of the first artificial neural network model. The datasets used for training and validation of the two artificial neural networks are based on hazard-consistent accelerograms and numerical analyses that are performed with an efficient finite element model of the structure. The methodology entails a preliminary feature selection phase for the identification of the aforementioned vector-valued of intensity measures that better classifies the damage/no-damage condition of the structure. This phase is implemented through the principal component analysis method. Subsequently, the Metropolis–Hastings algorithm is used to generate samples of a selected intensity measure, feeding the first ANN model. In turn, the chosen features are used as input parameters of the second ANN model to generate samples of damage/no-damage events. Using the two ANN in series, the mean annual frequency of exceeding a specific limit state is derived. The proposed framework is validated using a typical multi-storey steel frame, focusing on the seismic risk assessment of a vertical storage tank located at the first floor of the primary structure. The proposed method exhibits some clear advantages of combining numerical models with ANN techniques, mainly related to: a reduced computational time; the avoidance of any prior information on the probabilistic model of fragility curves; and the use of model-driven data.

Expeditious numerical capacity assessment in precast structures via inelastic performance-based spectra

The seismic design of precast structures hinges on unique characteristics intrinsic to precast technology. Emphasis is placed on lightweight structural elements for efficient on-site assembly and cost reduction. This leads to increased slenderness in beams and columns compared to traditional cast-in-situ constructions, accentuating the role of second-order effects. Dry pinned joints, favoured for connecting beams and columns, contribute to the overall efficiency in assemblage. Cast-in-situ concrete is typically reserved for connection to foundations and topping precast floor elements. Pinned joints transform the structure into an ideal isostatic system, with cantilevered columns anchored securely at the base, in designers' mind. However, this transformation reduces the energy dissipation capacity, preventing plastic hinge formation in beams and amplifying P-Delta effects in columns. The simplified approach proposed herein assesses dynamic instability in single and multi-storey precast hinged frames, providing a tool for expeditious numerical capacity assessment, useful at the initial design stage. The goal is to predict dynamic collapse and/or the attainment of specific seismic-oriented limit states based on fundamental structural parameters. Incremental nonlinear dynamic analysis, utilising far-field ground motion records, is employed to evaluate performance of a variety of precast structures modelled as equivalent single-degree-of-freedom systems. The outcomes yield inelastic spectra that provide insights into the structural capacity in terms of response modification factor and could help analysts/designers towards seismic performance-based design as well as the assessment problem. These spectra, which can themselves be taken as metrics for structural performance evaluation (in addition to as a reliable tool/means for design), are generated based on various structural parameters, including building height, column aspect ratios, and floor mass configurations, in relation to different limit states typically deemed crucial in the design of these structures for earthquake-induced actions. Regression analyses of median spectra show that polynomial expressions could fit them with good accuracy, as testified by a coefficient of determination in the 0.76–0.98 range for most of the cases.

Modal analysis and seismic optimization of multi-storey gymnasium frame

In order to improve the seismic resistance capacity of the multi-storey gymnasium frame, based on the finite element analysis method, the dynamic response characteristics were analyzed, and the natural frequencies and vibration modes were obtained. Based on the results of the modal analysis, different reinforcement methods were proposed for verification. Under the excitation conditions of Borego waves, the vibration responses of different nodes in initial model were obtained. Modal verification was carried out by using two methods of shear strengthening and support rod strengthening respectively. The analysis results show that the bearing capacity of the single-span frame is insufficient, the lateral stiffness is small, and it is prone to cause severe torsional vibration damage. It can also be known that the seismic resistance capacity of the support rods reinforcement is more balanced in different directions. It can not only effectively improve the lateral stiffness and bearing capacity of the structure, but also improve the seismic performance of the main structure through the energy dissipation of component yield, which is more suitable for multi-story buildings.

Study on Reinforcement Method and after-Reinforcement Performance of Beam-Column Joints in an in-Service Multi-Story Steel Frame

Study on Reinforcement Method and after-Reinforcement Performance of Beam-Column Joints in an in-Service Multi-Story Steel Frame

Nonparametric identification of multi-degree-of-freedom nonlinear systems from partially measured responses under uncertain dynamic excitations

With the rapid advent of new materials and novel structures, it becomes difficult, if not impossible, to accurately model and simulate the nonlinear response of complex systems under uncertain dynamic excitations based on close-formed nonlinear functions and parametric identification. In this study, a two-step structural nonlinearity localization and identification approach for multi-degree-of-freedom (MDOF) nonlinear systems under uncertain dynamic excitations is developed by integrating an extended Kalman filter with unknown inputs into the equivalent linearized systems. In the first step, unmeasured responses and excitations are estimated as well as unknown structural parameters and nonlinearity locations are identified by fusing acceleration with displacement time histories at the observed degrees of freedom (DOFs). In the second step, the nonlinear restoring force of the detected nonlinear structural members is identified nonparametrically using three polynomial models, including a power series polynomial model (PSPM), a double Chebyshev polynomial model (DCPM), and a Legendre polynomial model (LPM). Linear multi-story shear frames controlled by nonlinear magnetorheological (MR) dampers are modelled computationally to demonstrate the generality of the proposed methodology. The multi-source uncertainties considered in these representative examples include the location and the type of nonlinearities represented by a Bingham model and a modified Dahl model of the dampers, the location of response measurements, the location and intensity of dynamic excitations, the level of measurement noise, and the initial assignment of structural parameters. The acceleration, velocity, and displacement time histories of structures can be evaluated accurately with a maximum error of 2.62% even with the presence of 8% measurement noise, while the external excitations can be estimated within an error of 1.77%. The location of nonlinear elements can be detected correctly. The structural parameters, the NRFs provided by MR dampers and the corresponding energy dissipation can be identified with a maximum error of 2.08%, 1.19% and 0.39%, respectively, even 8% measurement noise and very rough initial assignment of structure parameters (−70%) are considered. Moreover, the numerical results change little (<0.20%) even the initial assignment of structural parameters varies from 50% to 30% of their original values, no matter which nonparametric model is employed. Results indicate that the presented algorithm can effectively identify unmeasured dynamic responses, structural parameters, unknown excitations, nonlinear locations, and NRF of nonlinear elements in a nonparametric way.

Development of a Computer-Aided Algorithm to Determine the Floor Wise Column Size for Multi-storey Base-Isolated RC Frame Buildings

Development of a Computer-Aided Algorithm to Determine the Floor Wise Column Size for Multi-storey Base-Isolated RC Frame Buildings

Seismic performance of frame with middle partially encased composite brace and steel-hollow core partially encased composite spliced frame beam

Steel-hollow core partially encased composite spliced frame beam (SHSFB) and middle partially encased composite brace (MPECB) demonstrate the potential to economize on steel consumption while exhibiting superior performance. To investigate the seismic performance of frames with SHSFBs and MPECBs, horizontal low-cyclic loading tests were conducted on four frame specimens, involving two two-story frames with no brace and two multi-story X-braced frames. Numerical simulations were performed using the “Open System for Earthquake Engineering Simulation” (OpenSees). The results indicate that the novel composite frames exhibit commendable seismic performance and energy dissipation capacity. The unbraced frame with SHSFBs has deformation capacity and mechanical properties comparable to bare steel frame. In contrast to the frame specimen equipped with bare steel braces featuring a 6 mm flange thickness, the specimen utilizing MPECBs with 4 mm flange thickness exhibits only a slight reduction of 3.60 % in maximum bearing capacity and 2.68 % in initial lateral stiffness. Significantly, each SHSFB and MPECB component reduces steel consumption by 16.71 % and 24.79 %, respectively, compared to bare steel components. Therefore, while ensuring adequate mechanical properties, frame structures equipped with SHSFBs and MPECBs will require less steel. Based on both experimental and simulation results, the formulas for predicting the ultimate bearing capacity and initial lateral stiffness of the novel composite frame were proposed, and the structural design for the multi-story X-braced frame was analyzed, offering valuable insights for practical engineering applications.

Damage detection of frame structure using a novel time-domain regression method

Shear structure model is the most frequently used to model for the damage detection of frame building structures. However, due to the existence of modelling error, using a shear structure model to perform damage detection of a complex frame structure often results in inaccurate detection results. In this paper, a novel reduced model for the frame is proposed, which converts a multi-story multi-bay plane frame into a beam-like model, having one translational and two rotational degrees-of-freedom for each floor. Based on the new model, a novel time-domain regression method (TDRM) was established using the spectral density function between the horizontal acceleration of the frame floor and the reference response to identify the equivalent layer stiffness and damping parameters. Finally, a five-story two-bay frame structure is used to demonstrate the efficacy of the proposed time-domain regression method of estimating structural parameters and identifying structural damage.The results show that this method can identify, locate, and quantify the structural stiffness changes accurately.

A novel LSTM-integrated non-intrusive ROM for reliability analysis of hysteretic systems with large stochastic dimension

Failure probability estimation of hysteretic systems subjected to random process excitation appears in many practical engineering applications, such as structures subjected to earthquake and vibration control. This task is computationally challenging due to the need for repeated solutions of a high-resolution model. This cost grows significantly with the stochastic dimension — characterized by the number of random variables, in this case, arising from the discretization of the random excitation. To address this issue, a novel non-intrusive reduced order model (ROM) is proposed in this paper. Accordingly, the complexity due to spatial discretization is first reduced using proper orthogonal decomposition. However, interpolation among response time histories in the resulting reduced solution space is computationally infeasible due to large stochastic dimensionality. An existing ROM developed by the authors is now improved by adopting a long short-term memory (LSTM) network for this interpolation. Furthermore, this adoption required two additional modifications in the mathematical structure of the ROM related to data compression and nonlinear coupling. The proposed methodology can be seamlessly integrated with black-box nonlinear solvers. Through detailed numerical studies on a beam on Winkler foundation and a multi-storied building frame subjected to stationary and non-stationary excitations, the proposed ROM is found to be accurate, efficient, and robust with respect to the frequency band of interest. The ROM has shown reduction of two orders of magnitude in the computational time. Furthermore, the proposed ROM is inherently parallelizable and holds promise to be scaled to other types of nonlinear systems with large stochastic dimensionality.

Quantitative Carbon Emission Prediction Model to Limit Embodied Carbon from Major Building Materials in Multi-Story Buildings

As the largest contributor of carbon emissions in China, the building sector currently relies mostly on enterprises’ own efforts to report carbon emissions, which usually results in challenges related to information transparency and workload for regulatory bodies, who play an otherwise vital role in controlling the building sector’s carbon footprint. In this study, we established a novel regulatory model known as QCEPM (Quantitative Carbon Emission Prediction Model) by conducting multiple linear regression analysis using the quantities of concrete, rebar, and masonry structures as independent variables and the embodied carbon emissions of a building as the dependent variable. We processed the data in the detailed quantity list of 20 multi-story frame structure buildings and fed them to the QCEPM for the solution. Comparison of the QCEPM-calculated results against the time-consuming and error-prone manual calculation results suggested a mean absolute percentage error (MAPE) of 2.36%. Using this simplified model, regulatory bodies can efficiently supervise the embodied carbon emissions in multi-story frame structures by setting up a carbon quota for a project in its approval stage, allowing the construction enterprise to carry out dynamic control over the three most important audited building materials throughout a project’s planning and implementation phase.

Collapse modes and mechanisms of planar multi-story large-span steel frames under fire

This paper investigates the collapse modes and mechanisms for planar multi-story large-span steel frames exposed to fire. Based on a systematic parametric analysis conducted with a wide range of parameters, including structural topological forms, fire scenarios, component sizes, load cases, fire protection levels, section temperature gradients, and wind loads. Eight potential collapse modes are identified: general inward collapse, rebalancing collapse, partial lateral collapse, heated large-span beam-induced inward collapse, restraint failure-induced collapse, overall downward collapse, unheated large-span beam-induced inward collapse, and overall lateral collapse. Simultaneously, by combining typical fire cases, corresponding structural collapse mechanisms are explored to reveal the differences in the failure sequence of locally heated components and the final structural collapse extent for different collapse modes. Furthermore, this study also analyzes the evolution laws of key horizontal and vertical displacements and velocities within the fire area for various modes, highlighting distinctions resulting from diverse collapse mechanisms. Finally, a detailed summary of various collapse modes is provided, involving reasons for inducing structural local collapse, the final extent of progressive collapse, possible areas of occurrence, and potential mode transitions as parameters change.

Determination of dynamic collapse limit states using the energy-based method for multi-story RC frames subjected to column removal scenarios

The Alternative Load Path method is widely adopted to perform progressive collapse analyses for reinforced concrete (RC) frame structures subjected to column removal scenarios. Considering that the progressive collapses are usually dynamic phenomena, nonlinear dynamic analyses can yield the most accurate results. However, the associated computational cost is high. Alternatively, the energy-based method (EBM) can be employed to efficiently calculate the maximum dynamic responses. Unfortunately, collapse or dynamic limit states (DLS) cannot be directly determined when the EBM is adopted for the progressive collapse analyses, because it is essentially a quasi-static approach. To tackle this issue, in this paper an EBM-Intersection Point-based (EBM-IP-based) method is proposed to effectively determine the DLS. The method is considering that the dynamic instability will occur once the dynamic capacity curve exceeds the corresponding static capacity curve. Hence, it is possible to determine the DLS by making a correction on the intersection point of the aforementioned two curves without performing nonlinear dynamic time-history analyses. Compared with the other energy components, the kinetic energy at the moment of the peak displacement response is relatively small and the effectiveness of the EBM is verified. Through both static pushdown analyses and incremental dynamic analyses for 48 column removal scenarios of six different multi-story RC frames, the effectiveness of the proposed EBM-IP-based method is verified and the associated coefficients are calibrated. Statistical information and (joint) probabilistic density functions (PDF) of the coefficients are identified. Further, stochastic analyses are carried out in order to quantify the model uncertainties when adopting the EBM-IP-based method. On the basis of all the calculation results, a Gumbel distribution is adopted to capture the PDF of the model uncertainty in relation to displacements, while a lognormal distribution is adopted to fit the PDF of the model uncertainty in terms of resistances. Moreover, a multi-variate Gaussian distribution model with two components is employed to fit the joint PDF.

Performance evaluation and FRP strengthening of concrete-filled steel tubular columns subjected to vehicle impact

Concrete-filled steel tubular (CFST) columns have been widely used in multi-story and high-rise frame structures. During the service period, they may suffer vehicle impact due to traffic accidents or terrorist attacks. This paper numerically evaluates the performance of CFST columns under vehicle impact and investigates the effects of carbon FRP (CFRP) wrapping arrangements on performance improvement of the columns. Before that, a numerical model was developed to simulate the responses of CFST columns without and with FRP wrapping under vehicle impact and post-impact axial compression, and then calibrated by reported tests. Evaluation results show that the performance of CSFT columns under vehicle impact is divided into five levels, i.e., no repair required, rapid repair required, minor repair needed, major repair needed, and replacement needed. The performance level decreases with the increase in the vehicle weight or speed and increases with the increase in the column diameter or steel tube thickness. The column height has little effects on the performance level. A higher axial load ratio, e.g., 0.5, might reduce the performance level. Besides, a CFST column tends to fail in flexure mode when hit by F800 medium truck, while it may fail in flexure &amp; shear mode when hit by C2500 pickup truck. Investigation results indicate that FRP wrapping with each layer orientation of 90° (i.e., in the longitudinal direction) and 0° (i.e., in the hoop direction) present the best performance improvement for a CFST column possibly undergoing flexure &amp; shear and flexure failure, respectively. The increase of the number of FRP layers effectively improves the performance levels of CFST columns but the excessive demand may be not economical. It is not necessary to employ an FRP wrapping range of 100% for improving the vehicular impact performance level of a CFST column to the expected one.

Energy-Based Design of Buckling-Restrained Steel Braced Frames for Concurrent Occurrences of Earthquake and Wind

This paper describes the development of a dual hazard spectrum for use in the dynamic analysis of steel frames subject to the combined effects of earthquakes and wind. The proposed spectrum is obtained by combining the power spectra of earthquakes and wind using the square root of the sum of squares (SRSS) combination method. An equivalent time excitation function is then computed using an inverse fast Fourier transform (IFFT) and serves as input for the dynamic analysis. Using time-history analysis on the OpenSees platform, the dynamic responses expressed in terms of peak and residual inter-story and roof drifts for two multistory steel frames located in two US cities (Los Angeles and Charleston) are obtained to demonstrate that designing these buildings based on just one hazard may not be adequate. For frames that are considered under-designed, an energy-based design procedure that uses buckling-restrained braces (BRBs) to dissipate the excess energy imparted to these frames is proposed so they will satisfy the FEMA 356 recommended drift limits for the performance levels of immediate occupancy and life safety.

System effects in T‐shaped timber shear walls: Effects of transverse walls, diaphragms, and axial loading

AbstractThis paper investigates the effects of transverse shear walls (TSWs), out‐of‐plane bending stiffness of diaphragms (FDIA), and axial loading (AXL) on the lateral response of strong wood‐frame shear walls (SWs) used for multistory light frame timber buildings (LFTBs) located in highly active seismic zones. Experimental tests were conducted to understand the requirements for SW‐to‐TSW connections to achieve desirable TSW effects in non‐planar SWs and to characterize the lateral cyclic response of T‐shaped SW assemblies with and without diaphragms and axial load. Both slotted and screwed connections were evaluated as SW‐to‐TSW connections, and both showed sufficient stiffness and strength to achieve TSW effects. However, the slotted connection is preferred because it has a more ductile failure mode. Tests on T‐shaped SW assemblies with and without diaphragms and axial load revealed that TSWs significantly enhance the lateral stiffness and strength but reduce the deformation capacity with respect to that of planar SWs. FDIA and AXL effects further influence the stiffness and strength, overcoming the limitation of smaller deformation capacity in T‐shaped SWs without diaphragms. Diaphragms also make the T‐shaped SW response more symmetrical and improve the evolution of the secant stiffness, the cumulative dissipated energy, and the equivalent viscous damping over increasing levels of lateral drift. Numerical analyses of a theoretical building model with T‐shaped SWs show significant reductions in lateral drift (up to 46%) and uplift (up to 100%) compared to the case with planar SWs only, emphasizing the importance of considering system effects in the seismic design of LFTBs.

Analytical identification of dynamic structural models: Mass matrix of an isospectral lumped mass model

AbstractCombining the accurate physical description of high‐fidelity mechanical formulations with the practical versatility of low‐order discrete models is a fundamental and open‐ended topic in structural dynamics. Finding a well‐balanced compromise between the opposite requirements of representativeness and synthesis is a delicate and challenging task. The paper systematizes a consistent methodological strategy to identify a physics‐based reduced‐order model (ROM) preserving the physical accuracy of large‐sized models with distributed parameters (REM), without resorting to classical techniques of dimensionality reduction. The leading idea is, first, to select a limited configurational set of representative degrees of freedom contributing significantly to the dynamic response (model reduction) and, second, to address an inverse indeterminate eigenproblem to identify the matrices governing the linear equations of undamped motion (structural identification). The physical representativeness of the identified model is guaranteed by imposing the exact coincidence of a selectable subset of natural frequencies and modes (partial isospectrality). The inverse eigenproblem is solved analytically and parametrically, since its indeterminacy can be circumvented by selecting the lumped mass matrix as the primary unknown and the stiffness matrix as a parameter (or vice versa). Therefore, explicit formulas are provided for the mass matrix of the ROM having the desired low dimension and possessing the selected partial isospectrality with the REM. Minor adjustments are also outlined to remove a posteriori unphysical effects, such as defects in the matrix symmetry, which are intrinsic consequences of the algebraic identification procedure. The direct and inverse eigenproblem solutions are explored through parametric analyses concerning a multistory frame, by adopting a high‐fidelity Finite Element model as REM and an Equivalent Frame model as ROM. Before mass matrix identification, modal analysis results indicate a general tendency of ROM to underestimate natural frequencies, with the underestimation strongly depending on the actual mass distribution of the structure. After the identification of the mass matrix and the elimination of unphysical defects, isospectrality is successfully achieved. Finally, extensions to prototypical highly massive masonry buildings are presented. The qualitative and quantitative discussion of the results under variation of the significant mechanical parameters provides useful insights to recognize the validity limits of the approximations affecting low‐order models with lumped parameters.

A convolution neural network-based technique for health monitoring of connections of a multi-story 3D steel frame structure

A convolution neural network-based technique for health monitoring of connections of a multi-story 3D steel frame structure