Flexible Diaphragms Research Articles

Seismic response of irregular multi-storey buildings with flexible inelastic diaphragms

SUMMARY The effectiveness of rigid floor modelling in the seismic design of multi-storey building structures as well as the influence of some structural parameters are deeply investigated through an extensive parametric study. The nonlinear behaviour of 216 structures has been simulated. The basic structural model consists of a symmetrical two-storey system which is supported by seven lateral load-resisting vertical elements with degrading stiffness properties. Different stiffness and strength distributions in the lateral load resisting system and in the floors are considered. The elastic design analysis is carried out by modelling floors as rigid diaphragms or, alternatively, as flexible beams, while the seismic inelastic analyses take into account the real in-plane stiffness and strength of floors. Diagrams show the behaviour of the most important structural element in detail, while statistical techniques are used to identify the most important structural parameters. The results of this study show that the rigid floor hypothesis generally leads to a conservative design for multi-storey buildings, thus confirming the findings of some previous studies on single-storey building structures. Moreover floors need to be adequately designed for strength when they have re-entrances and the stiffness distributions of the lateral-force resisting system is markedly non-uniform. 1997 by John Wiley & Sons, Ltd.

Seismic response of irregular multi‐storey buildings with flexible inelastic diaphragms

The effectiveness of rigid floor modelling in the seismic design of multi-storey building structures as well as the influence of some structural parameters are deeply investigated through an extensive parametric study. The nonlinear behaviour of 216 structures has been simulated. The basic structural model consists of a symmetrical two-storey system which is supported by seven lateral load-resisting vertical elements with degrading stiffness properties. Different stiffness and strength distributions in the lateral load resisting system and in the floors are considered. The elastic design analysis is carried out by modelling floors as rigid diaphragms or, alternatively, as flexible beams, while the seismic inelastic analyses take into account the real in-plane stiffness and strength of floors. Diagrams show the behaviour of the most important structural element in detail, while statistical techniques are used to identify the most important structural parameters. The results of this study show that the rigid floor hypothesis generally leads to a conservative design for multi-storey buildings, thus confirming the findings of some previous studies on single-storey building structures. Moreover floors need to be adequately designed for strength when they have re-entrances and the stiffness distributions of the lateral-force resisting system is markedly non-uniform. © 1997 John Wiley & Sons, Ltd.

RESPONSE OF UNREINFORCED MASONRY BUILDINGS

A summary of dynamic measurements are presented that illustrate relations between linear seismic demand and true nonlinear response of unreinforced masonry buildings with flexible diaphragms and rocking piers subjected to a series of simulated earthquake motions.

Seismic Behavior of Structures with Flexible Diaphragms

The influence of floor flexibility on the seismic response of building structures is discussed through comparison of the computed seismic response for structures with flexible diaphragms and counterpart structures with rigid diaphragms. Case studies of three existing buildings with flexible diaphragms and analogous systems with rigid diaphragms are presented to illustrate these differences. Each building was subjected to the 1989 Loma Prieta Earthquake. The structures were: (1) A two-story firehouse in Gilroy with unreinforced masonry walls; (2) a two-story timber office building in Palo Alto with grouted and reinforced clay-unit masonry shear walls; and (3) an eight-story hotel in Oakland with unreinforced clay-unit masonry and reinforced-concrete shear walls. The analytical studies show that, in some cases, diaphragm and shear-wall accelerations can increase with the flexibility of the diaphragm. Torsional forces can reduce considerably as diaphragm flexibility increases. Further, approximate expression...

Simplified 3-D dynamic analysis of structures with flexible diaphragms

Simplified 3-D dynamic analysis of structures with flexible diaphragms

EBEF Method for Distortional Analysis of Steel Box Girder Bridges

A practical approach to the distortional analysis of steel box girders is presented herein. The EBEF (equivalent beam on elastic foundation) method is an enhancement of the BEF (beam on elastic foundation) method, which has been widely used in design practice. Using the EBEF method on closed (or quasi-closed) box girder analysis provides a simplified procedure to account for the deformation of the cross section for the effect of rigid or flexible interior diaphragms and continuity over the supports. The methodology, numerical examples, and stiffness matrix are also presented in this paper.

Simplified 3‐D dynamic analysis of structures with flexible diaphragms

AbstractA simplified method of 3‐D dynamic analysis, named 3‐D quasi‐dynamic analysis, is presented. This method has been primarily used to evaluate stress states at identified times of peak dynamic responses of structures with flexible diaphragms. The quasi‐dynamic analysis consists of extracting the accelerations predicted by the time‐step integration analyses of two 2‐D discrete MDOF dynamic models of a given structure (each discrete model corresponding to one of the principal orthogonal directions of the structure) at given times of interest. These accelerations are imposed on a 3‐D representation of the structure (for example, a finite element mesh) as equivalent static forces. Accelerations at the diaphragms are assumed to act over the same tributary areas of the diaphragms considered in the 2‐D discrete dynamic models.The study of the firehouse of Gilroy (an unreinforced masonry structure with flexible diaphragms) during the Loma Prieta Earthquake is presented to illustrate the 3‐D quasi‐dynamic seismic analysis. This method was compared to the more traditional 3‐D modal time‐step integration and 3‐D response spectra analyses. The quasi‐dynamic analysis had a general good agreement with the more formal, complex and computationally extensive modal time‐step integration analysis. The 3‐D response spectra analysis was very conservative and had a poor correlation with both the quasi‐dynamic and the modal time‐step integration analyses. The case study of the firehouse of Gilroy suggested that if 3‐D effects have to be considered in the evaluation of a given structure, the quasi‐dynamic analysis constitutes a reliable and computationally cheaper alternative to the more traditional methods of 3‐D dynamic analysis.

Effect of horizontal diaphragm flexibility on the P-delta analysis

This paper investigates the importance of including the effects of the flexibility of the horizontal diaphragms when using the P-delta method of analysis, especially when considering the loads applied to intermediate frames on trusses that are not part of the lateral force resisting system. Analyses were conducted for structural systems with a variable number of stories, number of bays and diaphragm stiffnesses and supported by rigid jointed plane frames or vertical trusses.

Seismic Evaluation of Unreinforced Masonry Structures with Flexible Diaphragms

A discrete linear-elastic, multi-degree-of-freedom (MDOF) dynamic model developed for the dynamic analysis of unreinforced masonry (URM) structures with flexible diaphragms is presented. The discrete MDOF dynamic model represents the dynamic response of the structure in a given direction by a reduced number of discrete masses associated to translational degrees of freedom acting in that direction. The discrete model considers the flexibility of the diaphragms and the rotations of the walls, which are included into the global translational degrees of freedom through static condensation. Soil-structure interaction effects can be easily incorporated in the method. The applicability of the method in the study of the dynamic response of a URM structure with flexible diaphragms is presented. The structure, an old firehouse located at Gilroy, California, has been instrumented by California Strong Motion Instrumentation Program (CSMIP). Instrumented records of the dynamic response of the firehouse of Gilroy during the Loma Prieta Earthquake are available. The firehouse survived the earthquake with little damage. The discrete dynamic model presented in this work has been able to reproduce well the recorded dynamic response of the firehouse of Gilroy during the Loma Prieta Earthquake.

Torsion of Box Girders with Deformable Cross Sections

This paper studies thin‐walled trapezoidal cross‐section beams with lateral cantilevers subjected to a torsional load, considering the distortion of the cross section. Transverse and longitudinal displacements of the walls are governed by six shape functions, which describe bending in the horizontal plane, as well as torsion and distortion of the cross section; the shearing strain in the middle plane of the walls is considered; the shear center is not used. The theorem of minimum total potential energy is used to derive the governing equilibrium equations (and boundary conditions), whose solution is given in closed form. A wide set of constraints is studied (rigid or flexible transverse diaphragms, mixed kinematic and static boundary conditions), from a theoretical point of view and in numerical examples. The following results were obtained: (1) Torsion and distortion are a pair of coupled problems: distortion and warping stresses are always present; in particular, the longitudinal stress at the side cant...

Ring-shell projector

A ring-shell projector capable of simple disassembly and reassembly. The underwater transducer has a driving ring and a pair of flexible diaphragms on either side of the ring with their rims attached to the ring. The ring is formed of an array of electrostrictive elements and spacer elements, each spacer element having a pair of radial, outward extensions. A pair of coupling rings are provided each adapted to be positioned between the rim of one flexible diaphragm and a corresponding array of spacer element extensions to provide sealing engagement between the flexible diaphragms and the driving ring. Besides simplifying the repair of a projector, the improved design is more versatile, allowing a single driving ring to be used with different sets of shells, having different resonance frequencies and/or bandwidths. Moreover, an expensive step in the construction of a ring-shell projector is obviated, namely, the bolt holes in the metal staves and the subsequent custom matching of the shell holes.

Hydraulically damped resilient mounting

A hydraulically damped resilient mounting. Compared to undamped mountings, motor mounts having hydraulic damping transmit more noise because the damping device that is desirable for driving comfort favors the transmission of noise. The inventive damping device can be selectively activated or deactivated as needed by shifting the damping fluid, which is moved as a single incompressible body. For this purpose, the damping fluid is accommodated between two flexible diaphragms that are subjected to pressure differentials which are produced randomly or are controlled by a computer.

Analytical models for low‐rise buildings with flexible floor diaphragms

AbstractThe observed behaviour of buildings during earthquakes indicates clearly the importance of the flexibility of floor and roof diaphragms in the response of many structures. This paper presents a new analytical method for the dynamic analysis of some one‐ and two‐storey buildings whose floors may have significant in‐plane flexibility. The method begins by treating the floors as bending beams and the walls as shear beams. The equations of motion and the boundary conditions for the floors and the walls are then formulated in one coordinate system and solved exactly to obtain the characteristic equation for the system, which can be solved numerically to obtain the natural frequencies. These, in turn, can be used to determine the mode shapes of the system and the participation factors for earthquake response. Solutions are given for one‐ and two‐storey buildings that resist lateral loads in the transverse direction by two end walls. Perturbation techniques are also applied to simplify further the determination of the fundamental frequency of such single‐storey structures. To illustrate the method, a two‐storey structure, the Arvin (California) High School Administration Building, damaged in the Kern County earthquake of 1952, has been analysed in its transverse direction. It is seen that the first two modes, dominated by the floor and the roof vibrations, make the largest contributions to the total base shear in the structure.

Method of making a seismic apparatus

First Page

Parameters Influencing Behavior of Diaphragms

This paper presents a theoretical study of glue laminated lumber diaphragms. All glue lines are made up of elastomeric adhesives having stiffnesses of 90 psi‐900 psi. The use of such adhesives provides an incomplete partial composite. Three parameters which influence the behavior of diaphragms are studies. These include the stiffness of glue lines, the number of courses, and properties of the decking. Analytical results show that a large number of layers produces flexible diaphragms. It is also shown that gluing a few of the courses along the outer edges of the diaphragm may be sufficient to provide the proper strength and serviceability. In addition, the use of higher grade wood for the outer layers provides economical means of obtaining the strength required.

BEF Analogy for Analysis of Box Girders

An analysis for a box girder cell with deformable cross section and flexible interior diaphragms is developed using an analogy to the theory of beams on elastic foundations. The analogy gives a clear view of the effects of box girder and diaphragm proportions on the longitudinal warping and transverse flexural stresses induced by deformation of the cross section. Conventional flexural and torsional analyses do not reveal these effects; complex, refined analyses do not give insight into box girder behavior. The analysis is applicable to straight box girders and accounts for longitudinally or transversely stiffened plate elements, nonprismatic sections, continuity over intermediate supports, and arbitrary end support conditions. The analogy provides a basis for a direct and rational approach to box girder design.

An enclosed pneumatic half-track

A novel design of pneumatic rubber half-track is presented. All moving parts are enclosed within the track and sealed from dirt by flexible rubber diaphragms integral with the outer track casing. The performance of the half-tracks is compared with that of wheels fitted with similar pneumatic tyres using a model vehicle operating under identical conditions.

Modern Solutions to Coupling and Transmission Problems of Aircraft Engines

SummaryAfter a brief review of the classification of the couplings from the kinematic and mechanical points of view, the problem of aircraft engine Interconnection is introduced, together with some solutions which have made it possible to overcome the difficulty presented by the joint, at the expense, however, of some other mechanical requirements. The troubles experienced with couplings are to be blamed on the following three aspects of the conventional coupling designs: the use of gear-tooth couplings, sliding splined shaft arrangements, and the use of couplings of excessive weight. Possible improvements in the conventional designs using splined shafts are described, also the correct means of ensuring lubrication and the possibility of avoiding the need of lubrication by use of elastic distortion. Some Information is given about the effect of materials to be used for joint faces. The author then deals with coupling systems which are essentially based on the elastic property of materials. Three systems are investigated: flexible shafts, diaphragms and flexible couplings. Although flexible shafts are excellent for small misalignments, they do not permit axial movements of which diaphragms and flexible couplings are capable. The author then deals with sliding motions by recirculation of rollers which considerably extend the possibilities of axial movement. While couplings are devices normally intended to (ink up adjacent units, they become transmissions when units are some distance apart, and the typical feature of transmissions is that they require to be supported on one or more bearings. Straight and curved transmissions are presented, together with a brief survey of the following problems:Torsional and bending strength, critical speeds, bearings, damping, loads on attachment points, effect of high and low temperatures, selection of materials, end couplings.Typical test results are given, including those for the Breguet 941 curved transmission which has been run for 17 000 hours, that is 3.6 X 1010 revolutions, with only one relubrication at 10 000 hours. A short length instructional film showed the operation of a flexible bearing under critical speed conditions (this bearing is a part of the Breguet 941 curved transmission), and also demonstrated the endurance of the joints using sliding-type flexible couplings.

Response Characteristics of Polarized Cathode Solion Linear Acoustic Transducers

A polarized cathode solion (SOLution-ION) linear acoustic transducer contains two matched sets of electrodes, normally biased between 0.2 and 0.8 V. The current passed by each cathode is substantially independent of bias voltage and is a nonlinear function of the velocity of electrolyte flow across it. The transducer output is the algebraic difference of the currents from the two individual flow sensors, which are mounted back to back between flexible diaphragms of compliance C, and which offer flow resistance R. Several transducers having different known values of the pertinent physical characteristics have been built and tested in the frequency range from 0.001 to 100 cps and the pressure range from 0.01 to 10 000 μbar. In accordance with a previously presented theoretical analysis, the pressure and frequency-response pattern can be specified in terms of the RC-controlled lower cutoff frequency fl, the diffusion-controlled upper small-signal cutoff frequency fh, the small-signal sensitivity S0, the equivalent background pressure P0, at which output equals the quiescent current from each cathode, and the steady-flow cathode saturation pressure Pm. Typical values for these response parameters are fl = 0.002 cps, fh = 0.2 cps, S0 = 10 μA/μbar, P0 = 50 μbar, and Pm = 1500 μbar. [Work sponsored by the U. S. Office of Naval Research.]

Electrokinetic Low Pressure Detectors

For the detection of sinusoidal pressures of low amplitude and low frequency, electrokinetic detectors have been constructed and tested. The detector consists of a Lucite cylindrical body, the ends of which are sealed with flexible polystyrene diaphragms, a capillary unit separating the body into two chambers, two platinum electrodes, and two vacuum filling plugs. The detectors are vacuum-filled with distilled water and tested over the frequency range of 20 to 350 cps. Amplitude and frequency response curves are given. The capillary elements consist of beeswax, sealing wax, sulfur, and paraffin. These detectors with capillary elements behave as low pass filters with a low Q.