Effective Slab Width Model for Seismic Analysis of Flat Slab Frames

An effective slab width model is developed to describe the lateral behavior of a reinforced concrete flat slab frame within a two-dimensional nonlinear frame analysis. The parameters of the model are based on experimental data from a two-story, two-bay flat slab frame tested under cyclic lateral loads. The model is useful for estimating the strength and stiffness of a flat slab frame either for the design of new structures or for economic seismic retrofit of older flat slab structures. The simplicity and usefulness of the model is demonstrated by a pushover analysis, which post-predicted observed earthquake damage to a slab-column frame. For a four story building with a stiff perimeter beam-column frame, the pushover analysis indicated that the interior slab-column frame carried a significant amount of the total base shear.

Keywords: effective width; flat slab; frame.

(ProQuest Information and Learning: ... denotes formulae omitted.)

INTRODUCTION

Flat slab structures are used extensively due to the economy of the structural system and the architectural versatility. The behavior and design of flat slab structures for gravity loads are well established. Their behavior under lateral displacements, however, is not well understood and lateral design methods are not well established. Transfer of lateral displacement-induced moments at slab-column connections is a complex three-dimensional behavior, consisting of flexure, torsion, and shear stresses in the slab around the periphery of column faces. Slab shear stresses caused by moment transfer are added to the gravity shear stresses at the connection. When the combined shear stresses become too large, a brittle punching failure will occur. If the connections are not properly detailed, punching failure may lead to progressive collapse.

Currently, codes allow the use of flat slab structural systems to resist wind and seismic forces in low and moderate seismic zones. Due to its flexibility, the flat slab must be combined with a stiffer lateral force resisting system in high seismic regions. The flat slab system must be able to drift with the lateral moment resisting system, however, and thus still requires special attention for lateral loadings. For typical frame structures, the flat slab frame has significant lateral stiffness, and thus attracts some load due to lateral displacements. If the connections do not have enough strength to transfer these lateral loads, local failures could result. Thus, estimating the lateral stiffness and strength of the flat slab frame is important for the design of new structures and for economic seismic retrofit of older flat slab structures. Finite element analysis could be used for this estimation, but requires excessive computational time and computer resources even for relatively small problems. Also, the output from finite element analysis is not as compatible with reinforced concrete design as the output from frame analysis. Thus, attempts have been made to model the properties of slab-column behavior as a two dimensional frame. Two approaches have been used: torsional member methods and effective slab width methods.

The most common torsional member method is the Equivalent Column Method, developed originally for gravity loads1 and adapted for lateral loads.2 It defines a transverse torsional spring to model the torsional stiffness of the slab adjacent to the slab-column connection. This stiffness is combined with column stiffness to give properties of an equivalent column. This model is inconvenient to implement in typical two-dimensional elastic frame programs, and is generally only applied to single story, twodimensional slab strips. This method has been adopted into the ACI Building Code (ACI 318-02).3

The effective slab width method models the slab as a beam, so it is easily used with frame analysis software. The equivalent width of the slab-beam element is adjusted to simulate the actual behavior of the three-dimensional system, while the depth remains the actual depth of the slab. The effective width accounts for the behavior of the slab that is not fully effective across its transverse width.

Effective slab widths were initially defined analytically by matching the model response to elastic plate theory and finite element analysis of a slab-column connection. More recent proposals for effective slab widths are calibrated to match experimental behavior of laterally-loaded slab-column systems. Many of the experimental results have been from isolated connections, which do not have the redundancy and moment redistribution capabilities of a full frame. The proposed models have obtained good correlations, but they are cumbersome and not readily adopted for use in a design office.

Research has identified parameters that affect the effective slab width in determining strength and stiffness of the model: the aspect ratio of the columns and panels,4 the type of connection (that is, interior, exterior, corner, edge)5-7, the level of gravity load,6,7 differing negative moment and positive moment response,8 the amount of initial cracking,5 and the presence of a drop panel.9 For all of these proposed models, it is difficult to account for the degradation of member and connection stiffness due to increased lateral drift while using an elastic analysis. Grossman5 and Robertson8 targeted their effective slab width models to match the experimental data at several discrete drifts. Whereas, Luo and Durrani6,7 proposed using an equivalent moment of inertia I^sub e^ based on M^sub a^/M^sub cr^ at each loading level.