Keywords: reinforced concrete, nonlinear analysis, cantilever beams, tension slab, gravity loads, finite elements.

Under gravity loads, a beam in a typical building will be subjected to positive (sagging) bending moments at mid-spans and to negative (hogging) bending moments at the supports. Sections subjected to positive moments are typically designed as T-sections with the slab being in compression. This design procedure is covered by design codes. However for a section subjected to negative moments, the section is typically designed as a rectangular section with the presence the slab being totally ignored. Although ignoring the presence of the slab reinforcement seems conservative, it can actually have other unfavourable effects on the overall behaviour and mode of failure of such beams. For example, it can cause an over- reinforcing effect when it acts as tension reinforcement together with the top beam reinforcement. It can thus shift the mode of failure from a ductile tension failure mode to either a shear failure mode or failure of the concrete compression block. The latter two modes are characterised by being brittle and of an explosive nature and should be avoided.

In this paper, an analytical investigation of the behaviour of T-shaped beams under gravity loads is presented. The study involved performing rigorous nonlinear finite element analyses of the beams. Several parameters are considered in the investigation. These parameters include the single and/or combined effects of the flange width, slab reinforcement, shear reinforcement ratio, beam tension reinforcement ratio, boundary conditions and loading pattern. The nonlinear finite element analysis program used in this study is that developed by the author [1] and is used for analyzing reinforced concrete structures in three dimensional space. Figure 114.1 shows the mesh discretization along the length of the beam.

The study concluded the following:

1. The reinforcement in the tension slab can significantly increase the beam's strength due to the joint action between them under gravity loads. In cases as those studied in this paper, the beam's capacity can be increased by as much as 50% of the capacity if the slab reinforcement were to be neglected.

2. Due to the observed over-strength, the mode of failure of the beam can shift from a ductile mode initiated by yielding of the tension reinforcement to a brittle mode initiated by either failure of the concrete compression block or by shear failure. This effect should be definitely taken into account in case beam over-strength is to be considered in design.

3. Slab continuity in the longitudinal direction did not affect the ultimate capacity of the cantilever however, can significantly influence the deflections possibly, under other loading conditions.

1

Emara, M.B. and Hosny, H.M. (1994), Program & User Manual, 'Asmbly3d', A 3-Dimensional Simplified Module of: "Assembly (Emara 1991-1994): A Nonlinear 3-D FE Analysis Program for RC Structures", ©M.B. Emara, Dept. of Civil Engineering, Helwan University, Cairo, Egypt.

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