International Concrete Abstracts Portal

The effects of creep and shrinkage on the time-dependent behavior of reinforced concrete flexural members are discussed and a procedure for the prediction of the long-term deflection of reinforced concrete beams and slabs is presented. The time-dependent deformations caused by creep and shrinkage are modeled using tractable formulations developed using the age-adjusted effective modulus method of analysis. The procedure includes the time varying nature of tension stiffening and the effects of time-dependent shrinkage-induce cracking. Sample calculations are provided. The method is validated against a wide range of test data and is shown to provide reliable estimates of in-service deformations.

A generalized design approach is presented using an effective moment of inertia to compute deflection of steel and fiber reinforced polymer (FRP) reinforced concrete. Realistic estimates of short term deflection are obtained by taking proper account of tension stiffening after cracking, shrinkage restraint, preloading from construction loads, and the variation in member stiffness along the member span. A simple slab example is used to demonstrate how account of the preceding effects can give a more flexible response and increase computed values of deflection four-fold. Long-term effects related to shrinkage and creep are also considered separately for computation of time-dependent deflection. Shrinkage is shown to affect both the short and long-term response of flexure members, and a slab example is used to demonstrate how the effects of shrinkage and creep can be considered separately in a rational manner to compute deflection.

The ACI 318-08 design code provides a direct computation method for deflection control of slender reinforced concrete beams. This method is based on the Navier-Bernoulli theory where shear deformations are presumed to be minimal. Using a database of twenty slender reinforced concrete beams with shear reinforcement, this paper reports on an analytical study which compared the service deflection predictions from the ACI 318-08 model, with predictions from a proposed MCFT-based sectional analytical deflection model and two MCFT-based numerical models, namely Response-2000 and VecTor2. The MCFT-based models all consider the deflection resulting from shear deformations in addition to the Navier-Bernoulli deflections. Emphasis in the study was placed on deflection predictions at the equivalent serviceability limit state for slender concrete beams longitudinally reinforced with either conventional or high strength steel and transversely reinforced with conventional stirrups. The results indicate that the ACI 318-08 deflection model can underestimate the service deflections by a large margin, especially for members with high transverse reinforcement ratios. The MCFT-based models gave results in better agreements with the test values for the full range of parameters studied. The average test-to-model deflection ratios were 1.77, 1.44, 1.50 and 1.09, and coefficients of variation were 23% 17%, 14% and 18%, for the ACI 318-08, Response-2000, VecTor2 and proposed MCFT-based sectional deflection models respectively.

The thickness of reinforced concrete slabs is usually governed by the need to limit deflections in service to avoid damage to finishes and partition walls. Deflection control has become more important over recent years due to requirements for longer spans and more economic use of materials as well as design method developments. It is well established that long-term slab deflections can be increased by early age construction loading and cracking induced by restrained shrinkage. The author has previously shown that long-term slab deflections in the European Concrete Building at Cardington were governed by construction loading. This paper examines the influence of short term peaks in loading on long term curvatures in slabs subject to sustained loading. A simplified method is proposed for taking account of the effects of construction loading in deflection calculations with Eurocode 2. The method is validated using laboratory data from tests on simply supported slabs carried out at Imperial College London.

Today’s slab designers face a quandary – economic efficiency demands the use of very thin slabs; however the deflection performance of these slabs is difficult to predict. Exacerbating the situation is that the construction methods and sequences to be utilized are unknown at the time of design. This paper looks at the predictions of several deflection calculation methods and then compares them to actual measured deflections in both the laboratory and field. The variability of deflections and the reasonable range of predictions are also discussed concluding with recommendations for design practice utilizing off-the-shelf software.