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Simplified and Advanced Analysis of Membrane Action of Concrete Slabs

ACI Structural Journal, Jan/Feb 2008 by Bailey, Colin G, Toh, Wee S, Chan, Bok M

This paper presents a comparison between a simple analytical approach based on rigid-plastic behavior with a change of geometry, an advanced finite element model (FEM), and 14 tests on horizontally-unrestrained concrete slabs that reached vertical displacements up to 10 times the effective depth of the slab. Both analytical approaches predicted the membrane behavior of the slabs, comprising compressive membrane action around the slab's perimeter and tensile membrane action in the central span region of the slab. The simple approach produced good predictions of the load-displacement response toward the end of the test, whereas the FEM produced reasonable predictions over the full history of the test. By considering the magnitude and pattern of the stresses within the FEM, the assumptions adopted within the simple approach were investigated and are discussed. Overall, the comparison of the simple approach against the FEM and test results shows that it can safely be used for predicting the load-carrying capacity, due to membrane action, of concrete slabs under large displacements.

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Keywords: large displacements; membrane action; slabs.

(ProQuest: ... denotes formulae omitted.)

INTRODUCTION

The development of membrane in-plane forces within slabs under an applied load can, depending on the boundary conditions, significantly enhance the slab's load-carrying capacity above the commonly adopted design value based solely on flexural behavior. Previous experimental and theoretical research into membrane action can be traced back to the early 1920s where Westergaard and Slater1 observed membrane behavior in a number of full-scale floor panels that were tested to destruction. Undoubtedly, the significant contribution to the fundamental understanding of membrane action came in the 1960s, where a significant amount of research2-11 was carried out following Ockleston's landmark paper12 on the observed membrane action in the tests of the destruction of the Johannesburg Hospital.

The type, magnitude, and final failure mode of membrane action will depend on the horizontal restraint around the slab's perimeter. Most research work3 has concentrated on the behavior of slabs that have full horizontal restraint with compressive membrane action occurring at low vertical displacements, typically of the magnitude of 0.4 to 0.5 times the slab's depth. If the slab exceeds this deflection, instability occurs with the load-carrying capacity being drastically reduced. Provided this instability is not too violent, the slab goes into tensile membrane action with the reinforcement carrying the vertical load by acting as a kind of tensile net. With tensile membrane action, an increase in vertical deflection is beneficial with the load-carrying capacity increasing with an increase in deflection. The mode of failure for a horizontally-restrained slab is fracture of the reinforcement at the midspan of the boundaries of the slab. With the loss of horizontal restraint, overall collapse can be avoided, albeit with a decrease in the slab's load-carrying capacity, provided the slab's boundaries remain vertically supported. The use of membrane action at small displacements has been successfully used in practical design,13 notably in the assessment of bridge decks that have been subjected to reinforcement corrosion. Research into compressive membrane action at small displacements has continued throughout the years due to its practical application, whereas the research into membrane action at large displacements was curtailed following the work2-11 in the 1960s due to the perceived limited practical applications. Interest into large displacement behavior, however, has been revitalized recently due to the need to design structures subjected to accidental loads. In particular, the application of membrane action at large displacements has successfully been used in the practical design14 of structures subjected to fire.

Compared with horizontally-restrained slabs, only a limited amount of research work has been carried out on unrestrained slabs. Previous experimental and theoretical work on unrestrained slabs was presented by Sawczuk and Winnicki,4 Wood,8 Hayes,9 Taylor,10 and Kemp.11 Although limited in number, the experimental results previously presented by these authors showed that membrane action will occur provided the slab boundaries have, and maintain, vertical support. It was found that the slab supports the load by tensile membrane action occurring in the central region of the slab and compressive membrane action forming a supporting ring around the slab's perimeter (Fig. 1). A horizontally unrestrained concrete slab will support less vertical load compared with an equivalent reinforced restrained slab because less tensile membrane action is mobilized. The theoretical derivation previously presented by Hayes9 was modified recently by Bailey15,16 to correspond to the mode of failure observed in tests, comprising fracture of reinforcement at the center of the slab across its shorter span. The derivation by Bailey was used by Foster et al.17 to compare against a number of small-scale slab tests and was shown to provide excellent predictions.

Simplified and Advanced Analysis of Membrane Action of Concrete Slabs

ACI Structural Journal, Jan/Feb 2008 by Bailey, Colin G, Toh, Wee S, Chan, Bok M

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