Dimensioning of strain or deformation-controlled reinforced concrete beams: Dissertation

The dimensioning of concrete structures for restraint effects caused by deformation controlled loads has in practice been shown to be difficult.These loads have therefore often been ignored, even in service state dimensioning, although their values are greatest just in the service state.This neglect, sometimes even deliberate, has often led to premature and unexpected cracking of structures and to other defects arising from cracking.In accordance with quality concepts in modern construction, the cracking of a reinforced concrete structure is a quality defect which should be avoided as far as possible or is to be limited at least to an acceptable level For the purpose of crack limitation a behaviour model for the structural elementary unit of a one dimensional structure was formed as follows.The length of the crack spacing was chosen as the length of the elementary unit, which thus decreases when the steel stress rises.The initiation density of new cracks is determined by the density function of the limited normal distribution, which also defines the crack spacing corresponding to the degree of steel stress.The internal stresses of the structural elementary unit and the relative deformations, as well as the slips, are determined by starting from the basic equations of the interaction between the concrete and reinforcement, which pertain to the so called sliding bond mechanism.The effect of the so-called non sliding bond mechanism is combined with the behaviour model by assigning that the bond does not act over a certain distance on both sides of the crack.This distance was determined experimentally.The rigidity of the structural elementary unit under different stress conditions and an approximate appraisal method for rigidity suitable for manual calculation are also determined by the average strains to be calculated.The relaxation of restraint effects due to cracking can also be determined by the proposed method applicable to calculation by a computer. Using this method the weighted rotations of structural elementary units are converted into the support rotations, and the corresponding moments are corrected by the amount which corresponds to the rotation.In order to limit the cracks caused by restraint effects a closed solution, which is valid in a limited region and based on the differential equation of sliding bond, is presented together with a corresponding numerical solution also including portions of non sliding bond, and which can be used for limiting cracking due to the restraint effect or brought about by combined load and restraint effects.For the purpose of dimensioning, diagrams are presented for different stress types and different concrete strengths, for all bar sizes in use and the bars having different bond properties and for different reinforcement levels as well as different variation coefficients of the tensile strength of concrete.In the experimental section, short term load tests were performed with two types of statically indeterminate structures which were subjected to indirect action or direct action or both In the long term tests the statically indeterminate beams were subjected to the stress of a thermal gradient or a certain settlement at one support which was forced to take place suddenly and slowly.The results were compared with the calculated results using a developed model based on the randomness of crack spacing and on the physical interaction between the concrete and the reinforcement as established empirically.No theoretical model for examination of a time effect is presented.The test results, however, give a suggestive idea of the relaxation of restraint effects due to temperature and time.