Floor Diaphragms Research Articles

Dynamics of a Class of Horizontal Setback Buildings

Dynamics of a class of horizontal setback buildings with flexible floor diaphragms has been studied by developing a “separable model.” A rectangular plan building, with flexible floor diaphragms, is a particular case of the horizontal setback building. The mass and stiffness matrices have been written in terms of direct products of matrices. The separable buildings have two types of natural modes of vibration: (a) those which involve in-plane floor deformation, and (b) those in which the floors do not undergo in-plane deformation. Further, spatially uniform ground motion does not excite the modes involving in-plane floor deformation. Therefore, the problems associated with diaphragm flexibility, e.g., stress concentration at the re-entrant corners, are avoided in separable buildings. General conditions for a building to be separable have been obtained. In simplistic terms, these conditions imply that (a) all wings of the building should have identical value of lateral stiffness per unit plan area divided ...

Preliminary Analysis of High-Rise Braced Frames with Facade Riggers

In this paper, a simple method of analysis for preliminary analysis of facade rigger stiffened braced frames in tall buildings subjected to horizontal loading is presented. The facade riggers in the structure are located in the exterior frames in the direction of the lateral loading. The interaction between the braced frames and facade riggers is through the floor diaphragms adjacent to the chords of the riggers. The method of analysis requires the calculation of five stiffness parameters: bending and racking shear stiffnesses of the braced frames and facade riggers in addition to a bending stiffness of the exterior frames in which the riggers are located. The method allows a graphical procedure for obtaining the optimum level of the facade riggers in addition to a rapid assessment of the influence of the facade riggers on the performance of the high-rise structure such as the reduction in lateral deflection at the top and the overturning moment at the base of the braced frame.

Experimental parametric study on the in-plane stiffness of wood diaphragms

This paper presents the results of in situ quasi-static tests on a full-scale wood floor diaphragm in a two-storey woodframe house. The main objective of the study was to investigate the in-plane flexibility/rigidity of the diaphragm. Fourteen different diaphragm and structural configurations were investigated. The main parameters considered in the study included the nail schedule, panel-edge blocking, sub-floor adhesive, perpendicular walls above and below the diaphragm, and wall finish materials. The results indicated that panel-edge blocking increased significantly the diaphragm shear stiffness, particularly for diaphragms without sub-floor adhesive. Also, the presence of perpendicular walls acting as additional chord members caused a significant increase in the flexural stiffness of the diaphragm. The design procedure included in the Uniform Building Code (UBC) to compute in-plane diaphragm deformations was assessed by comparing its predictions with the experimental results. The UBC predictions agreed well with the experimental results for some configurations, but the correlation was poor for others.Key words: diaphragms, floor, tests, wood, wooden structures.

Validation of seismic design parameters for wood-frame shearwall systems

A methodology for assessment of seismic design parameters for a wood-frame shearwall system is developed, consisting of a test program of shearwalls and the application of nonlinear time history analyses to a four-storey wood-frame building that was designed to resist the seismic requirements for Vancouver, British Columbia. Analyses employed 22 selected earthquake accelerograms that were scaled upwards until an ultimate peak ground acceleration (Au) was reached where the shearwall reached a "near-collapse" state. The 22 values of Au were found to be greater than the "design" peak ground acceleration, indicating the adequacy of the current design procedures for the particular shearwalls investigated. The influence of gypsum wallboard on the behaviour of the shearwalls was also evaluated, and a new force modification factor "R" for walls composed of a mixture of wood-based and gypsum panels was proposed. The effect of flexibility of floor diaphragms was considered separately for a symmetric building and was found to have 5-30% reduction on the Au values obtained for the rigid diaphragm case.Key words: seismic design, earthquake loads, timber structures, wood shearwalls.

CODE PROVISIONS AND ANALYTICAL MODELLING FOR THE IN-PLANE FLEXIBILITY OF FLOOR DIAPHRAGMS IN BUILDING STRUCTURES

In this paper a review of the provisions of some modern seismic codes for the analytical modelling of the floor diaphragm action is made and a methodology using simplified 2-D finite elements models for monolithic floors is suggested, taking into consideration the in-plane flexibility of them. The simplified models use the coarsest discretisation mesh possible, simply taking into account all the connection points of the vertical structural elements on the diaphragm of each storey. The efficiency of the proposed simplified F.E. models is tested with comparative response-spectrum dynamic analyses of various building structures with different plan shapes, according to EuroCode 8 [EC8, 1994]. The simplified models provided excellent results for the dynamic characteristics of the entire building and the stress state of the framing substructure and a fair estimation for the in-plane stresses of the floor diaphragms.

Code Provisions and Analytical Modelling for the In-Plane Flexibility of Floor Diaphragms in Building Structures

In this paper a review of the provisions of some modern seismic codes for the analytical modelling of the floor diaphragm action is made and a methodology using simplified 2-D finite elements models for monolithic floors is suggested, taking into consideration the in-plane flexibility of them. The simplified models use the coarsest discretisation mesh possible, simply taking into account all the connection points of the vertical structural elements on the diaphragm of each storey. The efficiency of the proposed simplified F.E. models is tested with comparative response-spectrum dynamic analyses of various building structures with different plan shapes, according to EuroCode 8 [EC8, 1994]. The simplified models provided excellent results for the dynamic characteristics of the entire building and the stress state of the framing substructure and a fair estimation for the in-plane stresses of the floor diaphragms.

Nonlinear inelastic analysis of building frames with thin-walled cores

A second-order inelastic analysis by combining the theories of stability and plasticity is proposed for studying frames with thin-walled cores. In the proposed approach, steel frameworks surrounding the cores are modelled by using the plastic hinge beam-column approach, and core walls modelled by using the thin-walled beam-column approach. Transformation procedures are proposed to consider the kinematic relationship between beams, columns, core walls and floor diaphragm. Nonlinear solution procedures are incorporated for the incremental analysis. The proposed inelastic analysis is used to investigate the inelastic behaviour and ultimate strength of core-braced frames.

Design of Wood Diaphragms with Openings

The existence of openings in diaphragms causes concentration of shear forces around the openings and the generation of axial forces in the framing. In 1981, the Applied Technology Council developed the only guidelines for designing diaphragms with openings. The procedure for determining the shear around the opening, however, is complicated and has not been experimentally verified. Accordingly, simplified equations for determining the shear forces in diaphragms with openings are derived in this paper. The application of the membrane-to-brace replacement method to diaphragms is also discussed. Horizontal loading tests are conducted on three floor diaphragms designed to the same load. The ultimate loads are almost the same, regardless of the existence of the opening. The observed unit shear around the opening is close to the calculated value. The observed deflection is smaller than the value calculated on the basis of the nominal stiffness for the materials and the fasteners by 14–28%. It can be said from these results that all the methods perform well as a practical design tool.

Dynamics of Buildings with Y-Shaped Plan and Flexible Floor Diaphragms

A long, narrow multistory building with Y-shaped plan having a number of identical frames and floors placed uniformly is modeled including in-plane floor flexibility and analyzed using the equivalent vertically oriented anisotropic plate concept. It is observed that for unequal stiffness of a wing in the transverse and longitudinal directions, all natural modes of vibration involve in-plane floor deformations. However, if the two stiffnesses are equal, rigid floor as well as flexible floor modes exist, but the latter are not excited by spatially uniform ground motion. A Y-shaped building could therefore be configured so as to have some total lateral stiffness in the two directions for each wing. This will ensure that stress concentration at reentrant corners, caused by the floor-diaphragm flexibility, does not take place. The method is illustrated with a numerical example. In general, the in-plane floor flexibility does not substantially alter the natural periods, even though this may significantly affect...

Hormonal Treatment and Pelviscopic Myomectomy

In cases of benign lesions, pelviscopy is used in about 70% of all abdominal operations at our Department of Obstetrics and Gynecology. From 1990 to 1992, 851 patients with myomas were treated by surgery. In 57% pelviscopy, in 2% laparotomy, and in 1% hysteroscopic myomectomies were treated. In 11%, a CISH (Classical Intrafascial SEMM—serrated edged macro morcellator—Hysterectomy) without colpotomy was applied using the operative technique of pelviscopy or laparotomy. The application of this new surgical technique preserves the patient's pelvic floor (diaphragm pelvis and urogenitalis), its blood supply, and neural function. Details of the surgical techniques used in pelviscopic myomaenucleations are described. One hundred sixteen patients were treated with a gonadotropin releasing hormone analogue (GnRH-a) before the pelviscopic myomaenucleation took place. In this study, 64 (55%) patients received 3,75 mg leuprorelin, and 52 (45%), patients 3.75 mg triptorelin. The monthly injections took place over a period of 3 to 6 months. After 3 months, an identical reduction of the myomas of about 10% to 50% was observed in 103 patients (88%) in both therapy groups. The preservation of the uterus by this minimal invasive surgery technique was generally accepted. No serious complications occurred.

Seismic response of building structures with flexible inelastic diaphragm

AbstractThe inelastic response of one‐storey buildings subjected to lateral loads is analysed, making allowance for the real in‐plane rigidity and strength of the floors. The structural model consists of a floor diaphragm supported by seven vertical resisting elements with degrading stiffness properties. The elastic design analysis is carried out by modelling the floor diaphragm as a rigid or, alternatively, as a flexible beam. The actual nonlinear response of 240 structures is studied via numerical simulations. Different stiffness and strength distributions in the lateral resisting systems and in the diaphragm are considered. The results of the investigation emphasize the need for an adequate design of the floor diaphragm as a structural element. Also, the results show that the deformability of the diaphragms plays an important role only if the lateral‐force resisting system has a markedly non‐uniform stiffness distribution; even in such cases, however, adopting the rigid diaphragm hypothesis leads to a more conservative design.

Steel‐Deck‐Reinforced Concrete Diaphragms. II

This is the second of two companion papers that focus on the behavior and analysis of steel‐deck‐reinforced concrete floor diaphragms. (The companion paper presents experimental results and behavioral aspects, including the limit states observed in the test program, observed failure loads and initial stiffness values.) The research program included analytical studies in the form of finite‐element analyses and the development of expressions to determine strength and stiffness. The nonlinear behavior of arc‐spot welds, headed shear studs and deck‐concrete interface was incorporated in the finite‐element models. Comparisons between the finite‐element studies and experimental results are presented in this paper. The analytical procedure, based partly on the finite‐element results, provides expressions for calculating the strength and stiffness of composite diaphragms in a cantilever configuration. The strength calculations are based on the three limit states that are of practical significance; diagonal tension failure of the concrete slab, edge connector failure, or shear‐transfer mechanism failure. The second two limit states are dependent on force distributions at the perimeter framing members, which are determined from the finite‐element analyses.

Effects of inplane floor slab flexibility on the seismic behaviour of building structures

The rigid floor diaphragm assumption is widely used for the analysis of multistorey building structures because of the simplicity in the analysis procedure. But the application of this assumption to the seismic analysis of building structures may be not valid in many cases. There have been lively discussions about the validity of this assumption. In this study, an efficient analytical model for multistorey building structures including inplane floor slab flexibility without reducing the accuracy of the analysis results is proposed. In addition, a floor flexibility index is proposed for simplified estimation of the inplane floor slab flexibility. The effects of inplane floor slab flexibility are investigated through parametric studies in terms of floor displacements at the roof, seismic base shear, and the distribution of seismic base shear. The effects of the inplane floor slab flexibility on the seismic response are more significant when the aspect ratio of a floor slab system is high or the number of storeys is not great. The inplane floor slab flexibility may bring about a longer vibration period that results in the reduced seismic base shear. However, part of the structure may be subjected to increased stress due to shear force redistribution caused by the large inplane deformation of floor slabs. Therefore, it is desirable to include the inplane deformation of floor slabs in the seismic analysis of building structures for economical and safe design when the inplane deformation of floor slabs is expected to be large.

Seismic Response of RC Buildings with Inelastic Floor Diaphragms

The in-plane flexibility of floor-slab systems has been observed to influence the seismic response of many types of reinforced concrete buildings. The assumption of rigid floor diaphragms is often used to simplify engineering analyses without significant loss in the accuracy of seismic response prediction for most buildings. However, for certain classes of structures, such as long and narrow buildings (especially with dual-braced lateral load-resisting systems), and buildings with horizontal (T- or L-shaped) or vertical (setbacks or cross-walls) offsets, the effect of diaphragm flexibility cannot be disregarded. Moreover, if the floor slab panels experience cracking or yielding due to pronounced in-plane distortions, the seismic response of the entire building system may be significantly altered. This paper presents a simplified macromodeling scheme to incorporate the effect of inelastic floor flexibility in the seismic response analysis of RC buildings. The slab model includes effects of both in-plane flexure and shear. The inelastic behavior of diaphragms is emphasized through a study of narrow rectangular buildings with end walls. The study shows that the in-plane deflections of floor slabs impose a larger demand on strength and ductility of flexible frames than predicted values using the assumption of rigid or elastic slabs. These demands may in turn lead to a failure of the gravity-load supporting system. A quantitative estimate of this effect is presented in terms of the floor aspect ratios.

Multidirectional Membrane Reinforcement

A method for analyzing local strength of reinforced concrete membranes reinforced with a multidirectional mesh and subjected to known in-plane internal forces is presented. Such structures occur often in practice, and include shear walls, floor diaphragms, folded plates, and shells. The effect of concrete cracking on the response of the shell under proportionately increasing loads is examined. The governing system of equations is derived, and a numerical, iterative procedure is developed to calculate local response at any load stage through ultimate. Gupta's conclusion that up to first yield crack direction remains constant and then rotates is confirmed. It is shown that at yield all bars are in tension, an ultimate ductile strength can be calculated from a simple relation; to obtain a time-history response, the method presented here has to be used. The procedure is illustrated with two numerical examples.

The Whittier Narrows, California Earthquake of October 1, 1987—Ticor Title Insurance Building Damage

The Ticor Title Insurance Building was a recently designed building that was significantly damaged by the recent October 1, 1987 Whittier Narrows Earthquake. The building experienced shear wall failures, floor and roof diaphragm failures, as well as failures of spandrel panel anchorages. The damage is chronicled by photographs in this article. This building, which is constructed chiefly of precast elements, shows the importance of tying together adequately different parts of a building. Special attention to building configuration, building deflection, connection and anchorage details is recommended.

Dynamic Analysis of Low‐Rise Buildings on Microcomputers

An analytical model for dynamic response analysis of low‐rise steel frame buildings on microcomputers is described. The model consists of an assemblage of planar frames with either braced or moment resisting connections. All but the frame lateral degrees of freedom are removed using static condensation prior to assemblage of the overall model. Floor diaphragms are modeled as either flexible or completely rigid in their own planes. Linear elastic behavior is assumed in the model and time‐history dynamic analysis is performed using the mode‐acceleration method. A FORTRAN computer program was written to implement the model on a microcomputer and a sample analysis of an actual building is presented to illustrate its use. The program was envisioned as a simplified analysis and design tool which could aid a designer in investigating a proposed structure or in rehabilitating an existing one for lateral forces.

Costs and Benefits of Seismic Upgrading of Some Buildings in the Boston Area

We examine here the costs and benefits of reinforcing some existing buildings in Boston at the time of remodelling with significant change of use. The buildings of interest are the unreinforced masonry warehouses and the reinforced concrete manufacturing buildings that are remodelled into apartment or office buildings. Given some estimates of the Boston seismicity and of the performance of these buildings in earthquakes with and without additional reinforcement, we evaluate three possible levels of reinforcement that the Masssachusetts Seismic Advisory Committee could recommend as part of the building codes. For the unreinforced masonry buildings, the first upgrading level is the addition of floor and roof diaphragms, and the two subsequent levels involve addition of internal walls and reinforcement of the existing ones. For the reinforced concrete buildings, the first level involves increase of the shear walls' size, and higher upgrading levels involve addition of shear walls and increase of the columns' size. We introduce in our study the market effects of the additional costs. We conclude that only the first levels of reinforcement that we considered could be adopted as regulations, and that higher standards should be left to the choice of the buildings' occupants.

Continuous Timber Diaphragms

Current design assumptions for diaphragms assume support conditions which are either simple span or fully continuous. The building codes require a design based on the highest values for moment and shear obtained under either of these two support conditions. More practical criteria for assessing continuity conditions at supports for wood diaphragms are needed. This investigation is to determine experimentally the effects of continuity conditions on timber floor diaphragms with plywood sheathing subject to inplane loads. Previous testing programs have evaluated simply‐supported diaphragms subject to uniform loading; this study evaluates the effects of other support conditions and non‐uniform loads. Static loading conditions were used to evaluate the response of the diaphragm for both deflection and ultimate strength. Six 8 ft×16 ft (2.44 m×4.88 m) floor diaphragms typical of certain residential construction techniques with three different sets of boundary and loading conditions were tested in accordance wit...

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.