SP-161 All the papers presented in this publication were reviewed by recognized experts in accordance with the ACI review procedures. It is hoped that designers, constructors, and codifying bodies will be able to draw on the material presented in this volume in conjunction with the ACI 435 Committee Report "Control of Deflection in Concrete Structures", in improving the long-term deflection behavior and performance of concrete constructed facilities.

Load-deflection responses of simply-supported (SS) and simply-supported all-round (SSAR) steel fiber reinforced (SFR) concrete square slabs subjected to a central point load have been obtained. The slabs measured 810 mm x 810 mm x 50 mm. The elastic response alone is of particular interest and presented here because this has a major influence on the durability of SFR concrete. Results for each SFR concrete slab are compared with theoretical elastic solutions for both boundary conditions and also with the behavior of identical plain concrete and weldmesh reinforced slabs in each case. A modified depth instead of the full slab thickness is proposed for estimating the elastic response of SFR slabs for the two boundary conditions; the depth effectively reduces the elastic stiffness of the cross section. The limiting load level at which the initial response may be considered as linear is established, but the limiting load is dependent on the behavior of the slab. This limiting load level is compared with results calculated from a modified empirical expression for predicting the load at which first crack is perceived to occur. In the empirical expression, a triangular linear stress block with the modified depth is used. On average, the modified depth is about 0.7 times the overall SFR concrete slab thickness for both the SS and SSAR boundary cases. The influence of fiber type, fiber concentration, and boundary condition on the modified depth is not significant.

The usual design practice for analysis of reinforced concrete slabs with openings is to neglect holes if their area is less than 10- 12% of the total slab area. This practice is based in part on studies conducted in early sixties regarding the effects of holes on the elastic behavior of plates. A literature survey revealed no specific studies regarding the effects of holes on deflection and strength of reinforced concrete slabs with openings. This paper presents a numerical study of the effects of openings of different sizes on the behavior of reinforced concrete slabs. A nonlinear finite element model for reinforced concrete slabs is developed using three dimensional brick elements taking into account cracking and crushing of concrete, and plasticity of both reinforcement and concrete. Distributed and concentrated loads are applied to slabs until collapse. Results show that when slabs are subjected to uniformly distributed loads, the openings do not have much effect on their strength and serviceability. The openings should be considered, however, when designing slabs subjected to concentrated loading where the opening ratios are larger than 2.5% .

North American design codes offer two methods to insure deflection serviceability. The design engineer can calculate the live load and sustained load deflections and check that they are less than code specified limits. Alternatively, the codes give maximum span/depth ratios for which serviceability can be assumed to be satisfied and deflections do not need to be calculated. However, the span/depth provisions of ACI 318-89 and CSA A23.3- M84 do not consider many of the factors which influence the deflection behavior of reinforced concrete beams and may not be consistent with the code specified deflection limits. The immediate and long term deflections of reinforced concrete beams were calculated using a layered, nonlinear finite element model. The long term deflections were calculated by a hybrid technique using an effective reduced modulus for concrete creep and a conventional finite element, time-dependent load vector for shrinkage and tensile cracking. The modelling technique was verified using the extensive experimental data of Christiansen. Span/depth ratios are proposed, which include the effects of concrete strength, tension steel ratio, and compression steel ratio, for incremental deflection criteria of span/500 and span/250. Long term deflection multipliers are given for sustained moments of 30, 50, and 70 percent of the design ultimate moment.

Presents available algorithms for deflection calculations of reinforced concrete (RC) beams, plates, and shells, using nonlinear finite element analysis. Detailed finite element formulations based on the layered approach and nonlinear constitutive laws are discussed and evaluated. The layered approach, through the rigorous treatment of the states of strain and stress can model complex behavior of both thin and thick plates. Further refinements can be incorporated using full three-dimensional modelling; this approach is briefly discussed in the paper. Alternative, simpler approaches based on the effective stiffness formulation are presented in the paper. The results of the finite element effective stiffness analyses are compared to both experimental results and the results of the layered analyses. Time-dependent effects of creep and shrinkage have a significant effect on deflections of reinforced concrete structures. The methods of incorporating these effects into layered and effective stiffness analyses are discussed in the paper. To demonstrate the usefulness of the finite element analysis, several examples of numerical results are presented and compared to experimental data. The examples include slabs with different loading, boundary, and reinforcement conditions.