The first step in the design of a structure is the definition of the geometry. This process includes the definition of the depth of slabs and beams. The depth of a flexural member is often determined by control of deflections, which can only be checked in detail at an advanced stage of the project. In order to optimize the design process, it is therefore very important to choose well the span-to-depth ratio at the beginning. In order to achieve this task in an easy manner, a lower limit to the slenderness of the beams in terms of span divided by the effective depth is proposed in most major codes. However, current proposals are rather coarse and are not necessarily on the safe side. In this paper, a new formulation for the slenderness limits, based on the physics of the problem, is presented. This formulation includes the effect of the composition of the load (live load to total load ratio) as well as the possibility of using different limits to maximum deflection and considering different, more general, support conditions. It is therefore more complete and has a larger application field than current proposals.
K E Y W O R D Sdeflection control, flexural members, serviceability, slenderness limits
| INTRODUCTIONThe first step in the design of a structure is the definition of the geometry. This process includes the definition of the depths of slabs and beams. The depth of a flexural member is often determined by control of deflections, which can only be checked in detail at an advanced stage of the project. In order to optimize the design process, it is therefore very important to choose the span-to-depth ratio well at the beginning. This is usually performed on the basis of experience with similar structures. However, these criteria are coarse, because the allowable depth actually depends on many parameters such as steel ratios, live load to total load ratio, loading history, rheological parameters, and so on. In order to maximize available space on one hand and promote sustainability by reducing concrete consumption, design should be aimed at maximizing the slenderness of flexural members while ensuring deflections, which do not impair the function of the structure.However, calculation of deflections in reinforced concrete beams is not an easy task due to the complex material behavior (cracking, tension stiffening, time-dependent effects, etc.) and the dependence of the results on the construction sequence and time of application of loads. Many complex models have been developed to this end, as for instance those of Marí et al, 1 Ghali et al, 2 or more recently Ulm et al. 3 The effect of shear deformations on deflections has been studied by Debernardi et al,4 leading to the conclusion that this effect is only important for very stocky elements and therefore negligible for common flexural members and will not be considered here.Owing to the complexity of these calculations, there has been a search for simplified methods. One of the better known methods was developed by Branson 5 and incorporated into the ACI-318...