RELIABILITY ASSESSMENT OF THE DEFLECTION SERVICEABILITY LIMIT STATE OF REINFORCED CONCRETE SLABS USING FOURIER SERIES ANALYSIS

Abstract

Reliability has been defined as the ability of a system or component to perform its required functions under stated conditions for a specified period of time. Structural reliability is an engineering branch that uses mathematical and statistical methods to determine the reliability of structures. Civil engineers need to have efficient tools that help them to design reliable and safe structures, as well as to assign priorities in maintenance policies. Therefore, the need for reliability-based structural management is evident. In this project, a limit state was generated for rectangular slabs with different support conditions using Fourier series analysis. Reliability analysis was conducted on this and a design example of reinforced concrete slab using different bearing ratio (depending on the support condition). The design is mainly to meet a deflection criterion of span/250, with span 4m for varying aspect ratio and slab thicknesses (150 mm, 175 mm and 200 mm respectively). The reliability estimate for various support conditions shows that reliability index β increases with slab thickness, and decreases with load ratio λ. The safety level for slab with aspect ratio 𝑏𝑎=2 is higher than the others. This indicates that safety level for one-way simply supported slab is higher than that of two-way simply supported slab, when Fourier Series Analysis is used to predict the deflection of the slab. The parametric study shows that the reliability index β decreases with the aspect ratio and the values are slightly higher for aspect ratio b/a = 2 in case I (Simply supported slab) compared to other cases. Case III (Three Edges Simply Supported and one Edge Fixed) on the other hand shows a lesser values for b/a = 2. In comparing the reliability indices between the FSA and BS 8110 (1997), it was observed that the reliability levels estimated with the use of FSA provide more realistic assessment of reinforced concrete slab compared with the ones obtained with use of BS 8110 (1997). For instance, when h = 150 mm, safety level for all slab types using FSA are much higher than when the BS 8110 (1997) requirement was used except for slab type III. It is quite interesting, that BS 8110 (1997) requirement for slab type III is rarely conservative. However this pattern changed as the thickness of the slab increased. The results show that the use of Fourier series analysis in estimating slab deflection is highly conservative. The static deflection using FSA shows a general trend of increasing deflection with load ratio, this trend was not very pronounced at b/a = 2.0. This implies that the prediction of FSA for one way slabs is highly insensitive to loading.