International Concrete Abstracts Portal

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.

Use of prestressed prisms as main reinforcement has been demonstrated to be effective in limiting cracks and reducing deflections in high-strength, high performance concrete beams. To further understand the load-deformation history of such type of structural members, computer-simulated analysis has been conducted. A nonlinear analytical model based on strain compatibility was established. Theoretical predictions are compared with the experimental data obtained by the authors. Comprehensive computer-simulated flexural tests were also performed on a theoretical member section to further identify the variables which may affect the structural behavior. Parametric study suggests that the section ductility is mainly controlled by the reinforcing index. The influences of the effective prestress and concrete strength on ductility is found to be insignificant. Fiber optic Bragg-grating sensor technology was developed and used to internally and externally measure the deformations and cracking in the specimens.

An optical technique has been developed whereby two angles and linear displacement can be simultaneously measured in a noncontact manner. The method depends upon the usage of a diffraction grating with linear variation of period along its length. The grating is attached to a structure at a point of interest, while all other system components are placed at a remote location. Evaluation of this measurement technique has been demonstrated on a laboratory- based structure, which simulated conditions found at deep trench (or tunnel) walls or bracing systems. In a construction site configuration, this sensor allows the user to determine if the walls are undergoing structural deformation. In addition, the magnitude of deformation may be measured and alarm conditions may be monitored. Experimental results obtained using this technique are presented and compared with theory.

Although structures with elastic response are fairly well understood, structures with inelastic response are more difficult to analyze. Furthermore, in studies of inelastic response, attention has generally been paid to the response of reinforced concrete structures with relatively little attention being given to pounding of reinforced concrete buildings. Generally, the mutual collisions, or pounding, result from excessive deflections of adjacent buildings. In this paper, an algorithm is described for computing the pounding response of reinforced concrete buildings. In this situation, the buildings are idealized as two-dimensional multi-degree-of-freedom systems with nonlinear force-deformation characteristics. Collision between adjacent masses can occur at any level and are simulated by means of impact elements. Using real earthquake motions, the effect of deflection is investigated. In this study, the following conclusions are found. 1. Pounding can cause high overstresses, mainly when the colliding buildings have excessive deflections. 2. The code-specified separation distance is adequate to prevent pounding. 3. Pounding problems of adjacent buildings with large difference in mass are common.

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.