Rigid Floors Research Articles

Assessment of the in-plane deformability of RC floors with traditional and innovative lightening elements in RC framed and wall structures

In this paper, the in-plane deformability of floors in Reinforced Concrete (RC) structures has been investigated in order to establish the role of lightening elements made of both traditional ceiling bricks and Expanded Polystyrene (EPS) blocks. The study has been firstly developed via the implementation of three-dimensional finite element models simulating the real geometry of the floors. The numerical results have been, then, used to assess the thickness of equivalent slabs introduced in three-dimensional finite elements models of simple structures made of Reinforced Concrete frames or walls. These models have been used for verifying the effective in-plane floor deformability as a function of the vertical resistant elements typology (frames or walls), the building geometry (plane shape ratio, height, number of floor, dimensions of vertical elements), and the thickness of the equivalent slab. The numerical analyses have enabled to give interesting indications about the reliability of the hypothesis of rigid floors as the investigated parameters change.

A Method for Extracting Building Empirical Capacity Curves from Earthquake Response Data

A method is presented for extracting empirical capacity curves from building earthquake response data. The method can be applied to buildings with acceleration response records from each floor to develop story empirical capacity curves assuming the building has flexible columns and rigid floors. The method can also be applied to buildings with acceleration response records from the roof and ground to develop a fundamental mode empirical capacity curve. The method relies on extracting the restoring force and relative displacement of the system by removing damping force, considered as equivalent viscous damping, from the inertial response, using a proposed viscous damping identification procedure. The method is demonstrated using data from a small-scale, three-story experimental model subjected to strong base motion.

Passive/Active Autoparametric Cantilever Beam Absorber With Piezoelectric Actuator for a Two-Story Building-Like Structure

This work deals with the design and experimental evaluation of a passive/active cantilever beam autoparametric vibration absorber mounted on a two-story building-like structure (primary system), with two rigid floors connected by flexible columns. The autoparametric vibration absorber consists of a cantilever beam with a piezoelectric patch actuator, cemented to its base, mounted on the top of the structure and actively controlled through an acquisition system. The overall system is then a coupled nonlinear oscillator subjected to sinusoidal excitation in the neighborhood of its external and internal resonances. The addition of the piezoelectric patch actuator to the cantilever beam absorber makes active the passive vibration absorber, thus enabling the possibility to control its equivalent stiffness and damping and, as a consequence, the implementation of an active vibration control scheme able to preserve, as possible, the autoparametric interaction as well as to compensate varying excitation frequencies and parametric uncertainty.

Assessment of the structural stability of Blockhaus timber log-walls under in-plane compression via full-scale buckling experiments

Blockhaus structural systems are obtained by assembling multiple timber logs able to interact with each other by means of simple mechanisms (e.g. contacts, tongues and grooves, and carpentry joints, also referred to as ‘corner’ joints). Although these systems have ancient origins, the structural behaviour of Blockhaus systems under well-defined loading and boundary conditions is still complex to predict. The paper focuses on the assessment of the typical buckling behaviour and resistance of in-plane compressed timber log-walls. The effects of various mechanical and geometrical aspects such as in-plane rigid inter-storey floors, load eccentricities, different types of lateral restraints, openings (e.g. doors or windows) or additional metal stiffeners, are investigated by means of full-scale buckling experiments. Results are then critically discussed and preliminarily assessed via analytical formulations taken from classical theory of plate buckling and column buckling. Although further advanced studies are required for the development of a generalized buckling design method, it is shown that several mechanical and geometrical aspects should be properly taken into account to correctly predict the structural capacity of Blockhaus systems under in-plane compression.

Response control of irregular structures using structure-TLCD coupled system under seismic excitations

An energy-based semi-active control strategy is presented to reduce structural vibration. The equation of motion is derived from a structure-TLCD coupled system. Material and geometrical nonlinearities have been considered in the 3D irregular system. The rigid floors and plan irregularity in the system are assumed. An on-off control orifice is located in the middle of the U-shaped tube TLCD system. The El-Centro 1940 earthquake excitation record is employed to train the algorithm, and two other earthquake excitations are applied to evaluate the performance of the proposed method. The results show that the RMS values of displacement and acceleration responses of the structure reduced significantly under seismic excitations.

Numerical and analytical assessment of the buckling behaviour of Blockhaus log-walls under in-plane compression

Blockhaus structural systems are commonly obtained by assembling multiple timber logs, by stacking them horizontally on the top of one another. Although based on simple mechanisms of ancient origins, the structural behaviour of Blockhaus systems under well-defined loading and boundary conditions is complex to predict.The paper focuses on the assessment of the typical buckling behaviour and resistance of vertically compressed timber log-walls. The effects of various mechanical and geometrical variables such as possible load eccentricities and initial curvatures, openings (e.g. doors or windows), fully flexible or in-plane rigid inter-storey floors are investigated by means of detailed finite-element (FE) numerical models. These FE models were first validated on test results of past buckling experiments performed on scaled log-wall specimens, as well as on recent buckling experiments carried out on full-scale timber log-walls, demonstrating the capability to appropriately describe the effective interaction between timber logs and to correctly predict the expected buckling failure mechanisms and ultimate resistance for the log-walls that were investigated. Comparisons with analytical solutions partly derived from classical theory of plate buckling and column buckling are also presented and critically discussed, in order to assess the applicability of these existing formulations – although specific for fully monolithic and isotropic plates and columns – to Blockhaus structural systems. A closed-form solution is finally proposed as a simplified design buckling method for timber log-walls under in-plane compression.

PERFORMANCE EVALUATION OF A MULTI STOREY CAR PARKING STRUCTURE UNDER STRENGTH IRREGULARITIES BY PUSH OVER ANALYSIS

Buildings, which appeared to be strong enough, may crumble like houses of cards during earthquake and deficiencies may be exposed. In last decade, four devastating earthquakes of world have been occurred in India, and low to mild intensities earthquakes are shaking our land frequently. It has raised the questions about the adequacy of framed structures to resist strong motions, since many buildings suffered great damage or collapsed. A number of multi-storey car parking structures in urban India are constructed at airports, railway stations, etc. in regular and irregular shape for architectural, aesthetic or economic reasons to reduce the problem of parking. The materials being used for the structures may be having same properties and in some times it may vary in strength, mass etc. To evaluate the performance of framed buildings under future expected earthquakes, a non-linear static pushover analysis has been conducted on a typical multi-storey car parking structure. To achieve this objective, a 3D framed multi storey car parking structure (G+3) is modeled in SAP 2000 in which the structure is open in all stories with rigid floors. Such features are highly undesirable in buildings built in seismically active areas because of lesser mass of the structures, this has been verified in numerous experiences of strong shaking during the past earthquakes. We are investigating the effect of strength irregularities in the present multi-storey car parking structure of R/C frames on the seismic performance using nonlinear static push-over analysis based on computational models. From output non-linear analysis, we compare the Base shear and Displacement occurs in different strength irregularities for the different load combinations in seismic zone IV.

Response features and parametric identification of shear-deformation buildings with continuous–discrete modeling

This study presents fundamental response features of seismic shear motion in multi-story buildings with a continuous–discrete model and its degenerated ones, and shows their applications in inverse parametric identification. In particular, the building is modeled as a series of continuous shear-beams for inter-story columns/walls and discrete lumped-masses for rigid floors. Shear motion response at one location of the building is then obtainable to an impulsive motion at another location in the time and frequency domains, termed here as generalized impulse and frequency response functions (GIRF and GFRF). The GIRF and GFRF are not only fundamental in relating seismic responses at the two locations of a building structure subjected to ground seismic excitation that is not fully known due to the complicated soil–structure interaction. They also play a key role in characterizing structural responses, as well as in identifying dynamic parameters of the building.For illustration, this study examines response features of ten-story building of Millikan Library in Pasadena, California with the Yorba Linda earthquake of September 3, 2002. With the use of the continuous–discrete model as well as its degenerated ones, structural responses are interpreted from the perspective of wave propagation, and more importantly validated with the pertinent recordings and discrete-model-based results. Parametric identification of the building with a pair of seismic recordings is then presented. This study finally comes up a conclusion that the proposed approach with continuous–discrete modeling is efficient and robust in forward predicting analysis and inverse system identification.

A Transfer Matrix Method for Frame Shear Wall Structures

This paper established the theoretical equations of transfer matrix method for frame shear wall structures to solve natural vibration and elastic response under earthquakes. Columns at each storey are combined into an equivalent shear member and shear walls are combined into an equivalent bending member. The structure is simplified as a double member system with the two members being coordinated by the in-plane infinite rigid floors. Transfer matrix of the structure was derived according to the fluctuated equations of equivalent members and the equilibrium and displacement compatibility conditions. After considering the boundary conditions at the bottom and top of structure, it presented the equations and method to solve seismic response, natural frequencies and modes of vibration of the structure. In comparison with FEM, it is a more convenient and universal method and is recommended for preliminary design of frame shear wall structures.

Lateral load effects on tall shear wall structures of different height

A three-dimensional formulation is proposed to analyze the lateral loading distribution of external actions in high-rise buildings. The method is extended to encompass any combination of bracings, including bracings with open thin-walled cross-sections, which are analyzed in the framework of Timoshenko-Vlasov's theory of sectorial areas. More in detail, the proposed unified approach is a tool for the preliminary stages of structural design. It considers infinitely rigid floors in their own planes, and allows to better understand stress and strain distributions in the different bearing elements if compared to a finite element analysis. Numerical examples, describing the structural response of tall buildings characterized by bracings with different cross-section and height, show the effectiveness and flexibility of the proposed method. The accuracy of the results is investigated by a comparison with finite element solutions, in which the bracings are modelled as three-dimensional structures by means of shell elements.

Shear building representations of seismically isolated buildings

Seismic isolation, with its capability of reducing floor accelerations and interstory drifts simultaneously, is recognized as an earthquake resistant design method that protects contents of a building along with the building itself. In research studies, superstructures of seismically isolated buildings are commonly modeled as idealized shear buildings. Shear building representation corresponds to an idealized structure where the beams are infinitely stiff in flexure and axially inextensible; columns are axially inextensible; and rigid floors are supported on these columns. Although it is more convenient to model and analyze a shear building, such an idealization may influence the seismic responses of seismically isolated buildings. This study presents a comparison of the seismic performances of seismically isolated buildings with superstructures modeled as shear buildings to those with full three dimensional superstructures. Both linear and nonlinear base isolation systems with different isolation periods and superstructures with different number of stories are considered.

Low stiffness floors can attenuate fall-related femoral impact forces by up to 50% without substantially impairing balance in older women

Low stiffness floors such as carpet appear to decrease hip fracture risk by providing a modest degree of force attenuation during falls without impairing balance. It is unknown whether other compliant floors can more effectively reduce impact loads without coincident increases in fall risk. We used a hip impact simulator to assess femoral neck force for four energy-absorbing floors (SmartCell, SofTile, Firm Foam, Soft Foam) compared to a rigid floor. We also assessed the influence of these floors on balance/mobility in 15 elderly women. We observed differences in the mean attenuation in peak femoral neck force provided by the SmartCell (24.5%), SofTile (47.2%), Firm Foam (76.6%), and Soft Foam (52.4%) floors. As impact velocity increased from 2 to 4 m/s, force attenuation increased for SmartCell (from 17.3% to 33.7%) and SofTile (from 44.9% to 51.2%), but decreased for the Firm Foam (from 87.0% to 64.5%) and Soft Foam (from 66.1% to 37.9%) conditions. Regarding balance, there were no significant differences between the rigid, SmartCell, and SofTile floors in proportion of successful trials, Get Up and Go time, balance confidence or utility ratings. SofTile, Firm Foam, and Soft Foam caused significant increases (when compared to the rigid floor) in postural sway in the anterior-posterior and medial-lateral directions during standing. However, SmartCell increased sway only in the anterior-posterior direction. This study demonstrates that two commercially available compliant floors can attenuate femoral impact force by up to 50% while having only limited influence on balance in older women, and supports development of clinical trials to test their effectiveness in high-risk settings.

Impact of explosive eruption scenarios at Vesuvius

Impact of explosive eruption scenarios at Vesuvius

Hybrid control of irregular steel highrise building structures under seismic excitations

Control of irregular highrise building structures under various seismic excitations is investigated using a hybrid control system consisting of a passive supplementary damping system and a semi-active tuned liquid column damper (TLCD) system. Equations of motion for the combined building and the TLCD system are derived for multistorey building structures with rigid floors and plan and elevation irregularities. Major steps involved in optimal control of three-dimensional irregular buildings equipped with a hybrid damper-TLCD system are delineated. A wavelet-based optimal control algorithm is applied to find the optimum control forces. Simulation results for control of two multistorey moment-resisting space steel structures with vertical and plan irregularities show clearly that the hybrid damper-TLCD control system significantly reduces responses of irregular buildings subjected to various earthquake ground motions as well as increases reliability and maximum operability during power failure.

Semi-active control of 3D coupled response of building structures

The semi-active tuned liquid column damper (TLCD) system is investigated for control of coupled responses of 3D irregular buildings under seismic excitations. The TLCD system is a special type of tuned mass damper (TMD) system providing a performance similar to a TMD system but offers a number of practical advantages over the traditional TMD system. The equations of motion for the combined building and TLCD system are derived for multistory building structures with rigid floors and plan and elevation irregularities. Simulation results for control of two multistory moment-resisting space structures with vertical and plan irregularities show clearly that the semi-active TLCD control system reduces the responses of 3D irregular buildings subjected to earthquake ground motions efficiently.

Free vibration of flexural-shear plates

In this paper, multi-storey buildings with narrow rectangular plane configuration (narrow buildings) are treated as one-step or multi-step cantilever flexural-shear plates in analysis of free vibration. The governing differential equations for free vibration of flexural-shear plates with variably distributed mass and stiffness are established and reduced to Bessel’s equations by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. The general solutions of one-step flexure-shear plates are derived and used to obtain the frequency equation of multi-step cantilever flexural-shear plates. A new exact approach is presented which combines the transfer matrix method and closed form solutions of one step flexural-shear plates. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of the narrow buildings are in good agreement with the corresponding experimental data. It is shown that it is possible to regard a building with rigid floors as a cantilever flexural bar that is a special case of a cantilever flexural-shear plate. Thus, the proposed methods in this paper are suitable for the calculation of free vibrations of narrow buildings and common shear-wall buildings.

Closure to “Comparisons of Building Analyses Assuming Rigid or Flexible Floors” by S. H. Ju

Closure to “Comparisons of Building Analyses Assuming Rigid or Flexible Floors” by S. H. Ju

Vibration analysis of flexural-shear plates with varying cross-section

In this paper, multi-storey buildings with narrow rectangular plane configuration (narrow buildings) are treated as cantilever flexural-shear plates in analysis of free vibration. The governing differential equations for free vibration of flexural-shear plates with variably distributed mass and stiffness are established and reduced to Bessel’s equations or Euler’s equation by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. The general solutions of flexural-shear plates are derived. Numerical examples demonstrate that the calculated natural frequencies and mode shapes of narrow buildings are in good agreement with the experimentally measured data. It is also shown that it is possible to regard a building with rigid floors as a cantilever flexural bar that is a special case of a cantilever flexural-shear plate. Thus, the methods proposed in this paper are suitable for the calculation of free vibration of narrow buildings and common shear-wall buildings.

Object‐oriented animation system for seismic response of multistory structures

AbstractVisualizing the dynamic behavior of structures under earthquake loading is a challenge for students taking structural dynamics and earthquake engineering courses. A prototype animation system was developed for visualizing the dynamic response of multistory structures subjected to earthquake excitations, using the object‐oriented programming paradigm and implemented in Microsoft Windows and Borland C++ on a 33 MHz 80486‐based personal computer. At present, the animation system is limited to two‐dimensional multistory frames with rigid floors. The input can be any accelerogram (ground acceleration record) due to any real or artificial earthquake. The user of the system can change the input parameters of the structure or select the ground acceleration record and view their effect on the dynamic behavior of the structure. This object‐oriented animation model is an effective courseware or interactive computer tool that may be used in teaching structural dynamics and earthquake engineering courses.

A generalized coordinate method for the analysis of 3D tall buildings

A generalized coordinate method (GCM) is proposed for the reduction of unknowns in the 3D analysis of tall buildings when the displacement method is employed. The number of variables is reduced by the assumption of in-plane rigid floors and by use of a 2D polynomial approximation for the out-of-plane displacements of floors, and a 1D polynomial approximation of the displacements with the height of building. The overall stiffness equation is obtained in generalized coordinates. The transformations are performed at the member level so that calculations involving large matrices are avoided. The GCM might be considered as a reduction technique based on a combination of the FEM at member level and the Rayleigh-Ritz method at the structure level. The GCM has the advantages that (1) the number of unknowns is significantly reduced and is independent of the number of storeys: (2) the accuracy can be adjusted by selecting the number of terms of the displacement function. The storage needed, the required number of operations and the possibility of choosing hierarchical displacement functions to make the calculation adaptive are discussed. The method presented can easily be extended to nonlinear and dynamic analysis. However, the derivation in this paper is confined only to the linear elastic analysis of frame and frame-shear wall structures. Numerical examples are given to show the efficiency of the proposed method.