Flexural Behaviour of Reinforced Concrete Slabs with Generalized Edge Conditions

Abstract

Slab is the most widely used structural element. It is used almost in every type of structural system to build and/or enclose the space along with some other structural elements such as walls, columns etc. However, unlike other structural elements, a slab is highly redundant in nature due to the coupling of the internal stress resultants and consequently offers multiple load paths to the applied loading. Because of coupling of internal force-resultants, the structural behavior of the slabs is highly sensitive to the type, layout of the supporting system and/or stiffness of the supporting structural member(s). Any change in the physical parameters of the supporting systems will cause a considerable change in the moment-field induced in the slab under given loading conditions. The moment coefficients recommended by the design code [IS 456 (2000) and BS EN 1992-1 (1994)] are applicable only for the rectangular slabs with various end-restraints and supported over the non-yielding edges on the outer four edges. But in routine design practice, number of case are encountered by the designers whereby the beam-drop and the beam-spans are restricted by architects to a level that are not sufficient to provide a non-yielding edge at the outer boundary of the slab and as such, these coefficients predict the moment-field highly on the unsafe side and produce a structurally deficient slab section. In the present thesis, an analytical model has been developed for a rectangular slab-system resting over the non-yielding edges at its outer boundary and cast monolithic along with equally spaced internal shallow beams using the principle of the limit analysis. It can also be used for predicting the collapse load of skew slabs, design of multi-panel slabs but it must be supported over the equally spaced shallow beams along one direction and non-shallow beams at regular intervals along the other direction of the slab. The slab is subjected to an out-of-plane uniform area load acting over its entire surface, thereby providing an alternative solution to the finite element based software for the analysis of the slab-system supported over the internal beams incapable of providing a non-yielding edge to the slab panels. It will supplement the design guidelines recommended by various codes which allow that any procedure can be used for designing a slab-system that satisfy the conditions of equilibrium, geometric compatibility and the requirements of strength, and serviceability stipulated by design codes. However, the proposed model can only be used to satisfy the strength criterion enshrined in various design codes and serviceability criterion has been kept in scope for future studies. This model will also provide an alternate method to finite element procedures which is a costly, time consuming process for proportioning regular slab-systems. The results from the proposed analytical model and the design equations are validated experimentally in the laboratory. These are also compared with the results from the well-established literature on the slab analysis and are found to be in good agreement. The actual crack pattern at the collapse load, for the two and three-panel slabs tested in the laboratory, was found to be in good agreement with the analytical results. A non-dimensional parameter called as moment-manipulator, λ (= moment of resistance of beam/moment of resistance of beam required for the simultaneous formation of a global and a local collapse mechanism) has been proposed to distinguish the nature of the shallow beams. Test slabs designed using the λ-value less than unity failed following a global-collapse mechanism with a load factor of more than 1.40. However, these slabs show more deflection at the design load than the permissible values but selecting a highest possible value of the beam depth satisfying both the serviceability criterion as well as the span/depth ratio of the shallow beam can reduce the actual deflection of the slab system under the design load. It is suggested that the actual slab-beam system with shallow beams should never be proportioned with λ-value more than unity as it leads to failure of the slab in a local-collapse mechanism with a reduced load factor. The test slabs designed for λ-value more than unity, and supported over the shallow beams failed following a local-collapse mechanism with a load factor ranging from 1.30 to 1.40, with the formation of negative yield lines near the beam-ends. At the design load, these slabs show a reduced deflection in comparison to the slabs designed for λ-value less than unity but this value of the deflection was more than permitted by the design codes. Therefore, it is suggested that the actual slab-beam system with shallow beams should never be proportioned with λ-value more than or equal to unity. Working procedure is illustrated with the help of design examples. It is shown that with the use of shallow beam in the slab-systems, the unit cost of the material-consumption comes out to be nearly same but the beam-drop of the supporting beams along the short span of the slab-beam system reduces by about 40-50% in comparison to the slabs supported over the non-shallow (rigid) beams.