Experimental study on the effective width of flat slab structures under dynamic seismic loading
Introduction
Flat slabs are extensively used to resist wind and seismic forces in low-to-moderate seismicity regions such as the Mediterranean area. The behavior of this type of structural system under gravitational loads is well established. In contrast, its behavior under lateral loads is not well understood, particularly under dynamic seismic loadings. In common practice, flat slab structures with a regular distribution of columns are analyzed as two-dimensional frames in the elastic domain, applying two approaches: torsional member methods and effective slab methods. The most common procedure pertaining to the first approach is the so-called Equivalent Column Method [1]. It defines a transverse torsional spring to model the torsional stiffness of the slab adjacent to the slab–column connection. This torsional stiffness is combined with column stiffness to define the properties of an equivalent column. In the effective slab width method [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], the slab is modeled as a beam and its equivalent width is adjusted to simulate the actual behavior of the three-dimensional system, while depth remains the actual depth of the slab. The calculated effective width takes into account that the slab is not fully effective across its transverse width.
The study presented in this paper focuses on the effective slab width method, which, in contrast to the torsional member method, can be easily used with conventional frame analysis software. The effective width of the slab is calculated using normalized or conventional approximations, generally based on Finite Element Method calculations [10], and static or quasi-static experiments [11], [12].
Hence, there is a need for documented experiments surrounding the equivalent width of flat slabs in the presence of realistic dynamic seismic loads. The behavior of structures under dynamic loads is not the same as under static loads, because of the influence of strain rate effects. The resistance of reinforced concrete (RC) members can increase anywhere from 7% to 20% with dynamic excitations [13].
Despite extensive work conducted in the past by numerous authors, the dynamic behavior of flat slab structures under lateral displacements is not well understood, meaning there is room for improving lateral design methods. Also scarce is research on the seismic behavior of corner slab–column connections that rely on structural steel I- or channel-shaped sections (shearheads) as shear reinforcement. Indeed, shearheads in corner connections are not specifically contemplated under the usual norms, for instance ACI Building Code [14], [15], [16], [17], [18] or Eurocode 2 [19]. Moreover, the contribution of this type of punching shear reinforcement (i.e. shearheads) cannot be completely included in well-known formulas for predicting effective width, such the one proposed by Grossman [9] or Luo and Durrani [7], [8]. Grossman´s equation [9] cannot account for the effect of shearheads, while the equations proposed by Luo and Durrani [7], [8] only partially include the effect of shearheads by means of the critical shear area considered in the stiffness reduction factor.
One formula proposed by Luo and Durrani is based on previous research conducted by Pecknold [2], who in 1975 developed a model of equivalent slab width in which the effective width coefficient (ratio between effective and original width) was deduced via elastic plate theory and a Levy type solution. Later, in 1977, Allen and Darvall [3] employed a Fourier series technique and published results that are concordant with Pecknold’s. Despite posterior debate, Pecknold’s equation was never widely accepted by engineers because it proved hardly practical.
In this context, this paper describes experimental investigation to study the effective width of RC corner flat slab–column connections with shearheads as punching reinforcement, subjected to dynamic shaking table tests. The paper discusses the predictions provided by different formulae proposed in the literature. It is observed that the effective width tends to increase with increasing values of the peak acceleration applied to the structure, and that this increase is limited by the loss of adherence between the reinforcing steel and the surrounding concrete. Also, a simple procedure is suggested for estimating the effective width on the basis of the experimental results.
Section snippets
Experiments
A prototype one-bay and one-story structure was designed, from which a test model was constructed and tested using the shaking table of the Laboratory of Structural Dynamics at the University of Granada, as explained below.
Overall response
The columns started to plastify at the top and at the bottom ends in the seismic simulation corresponding to 0.47g, which limited the maximum bending moment transferred from the column to the slab. The reinforcing steel of the slab did not reach its nominal yield stress in any of the seismic simulations, though it did get very close (up to approximately 90% of the yield stress). Fig. 5 shows the cracks on the concrete slab at the column locations. The cracks followed an approximately concentric
Conclusions
This paper describes experimental investigation of the effective width of RC corner flat slab–column connections with shearheads (steel C-shapes) as punching reinforcement, subjected to realistic seismic loadings through dynamic shaking table tests. It is found that the prediction of the effective width has to take into account the differences of rigidity inside the slab due to the presence of steel profiles that constitute the punching shear reinforcement. Owing to this fact, important
Acknowledgements
This research was funded by the local government of Spain, Consejería de Innovación, Ciencia y Tecnología (Project P07-TEP-02610) and by the European Union (Fonds Européen de Dévelopment Régional). We also express special thanks to the Spanish Ministry of Education for Grant Number FPU-AP2009-3475.
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