Implication of Yield Lines Theory in Method Three of the ACI Code for Two-Way Reinforced Concrete Slabs

Abstract

Reinforced concrete slabs are one of the most important and complicated elements of a building. For supported edges slabs, if the ratio of long span to short span is equal or less than two then the slab is considered as two-way slab otherwise is consider as one-way slab. Two-way reinforced concrete slabs are common in use in reinforced concrete buildings due to geometrically arrangement of columns suggested by architects who prefer a symmetric distribution of columns in their plans. Elastic theory is usually used for analysis of concrete slabs. However, for several reasons design methods based on elastic principles are limited in their function. Correspondingly, limit state analysis offers a powerful technique for considering such matter. The Yield Lines Theory, which is one of limit state analysis based on expected failure criteria of slabs. The assumed failure criteria is termed by a pattern of yield lines, along that the reinforcement has yielded and the location of which counts loads and boundary conditions. This paper deals with comparison of Method 3 for two-way slabs that was provided by the ACI Code and exact derivation of this method by the Yield Lines Theory. Total of nine cases of slabs that have been described by method three are studied and evaluated by plastic analysis assumptions of the yield lines theory. The results are summarized in terms of proposed formulae that derived according to the Yield Lines Ttheory, which could be used as an alternative method for design of two-way reinforced concrete slabs in the ACI Code.

Analysis of Orthotropic RC Rectangular Slabs Supported on Two Adjacent Edges - A Simplistic Approach

“…It generally depends on boundary constraints and type of loading. For slabs supported on two adjacent simple supports, there are only two possible failure mechanisms suggested by Kennedy (2003) and Al-Ahmed (2020) [15,21]. The ultimate moment of resistance of the slab supported on two adjacent edges can be determined using Equation 10 for the failure mechanism as shown in Figure 2 and Equation 11 for the Failure mechanism as shown in Figure 5.…”

“…Therefore, for failure mechanism as shown in Figure 2, moment carrying capacity can be obtained from Equation 10 which comes out be 15.401 kNm/m. For the case of cantilever failure as shown in Figure 5, moment of resistance can be determined from Equation 11 proposed in Al-Ahmed (2020) [21] and comes out to be 6.94 kNm/m. The approach proposed in this paper precisely predict the moment-field of the slab only if moment carrying capacity obtained from failure mechanism shown in Figure 2 is greater than moment carrying capacity obtained from failure mechanism shown in Figure 5 which is fulfil in above stated example.…”

“…Al-Ahmed et al [21] carried out the limit analysis of orthotropic RC slabs supported on four sides carrying uniform distributed load using yield line theory and prepared the design coefficients for the same. Results obtained were compared with ACI code recommendations and it was observed that results from simple yield line theory gives less design bending moment than ACI recommendations which will reduce the cost of construction.…”

Yield Line Analysis of Two Way Reinforced Concrete Slab of Three-Sides Supported with Various Loading Conditions

“…For slabs and sideward restrained strips supported by four sideward unrestrained edges, the analytical model was validated. Using yield line theory, Al-Ahmed et al [10] performed a analysis on four sides supported RC slabs and supporting a UDL and created design coefficients for the analysis. When the acquired results were compared to the ACI code recommendations, it became clear that the uncomplicated yield line thesis results provided bending moment is smaller than the ACI guideline, which would save construction costs.…”