A significant part of the territory of Russian Federation refers to seismically dangerous areas. In the current code in design of reinforced concrete buildings for seismic loads the development of plastic strains is supposed. They are taken into account while determining loads by introduction of reducing factor K1, but their influence on the strength of elements is neglected. Plastic strains of reinforcement lead to appearance of residual cracks in compressed zone of concrete and due to this the reduction of bearing capacity of bending elements takes place on following loading cycles. The approximate method of determination of the depth of open cracks and of the residual height of sections when changing the sign of internal forces after reaching the maximum deflection has been proposed. The depth of residual crack is determined from the condition of equilibrium of longitudinal forces with regard to stress-strain state of a section at three stages of loading: at a moment of achievement of maximum plastic strains, at the unloading stage and at a moment of the beginning of crack formation after changing the sign of internal forces. The comparison of results obtained by the approximate method and results of calculation of finite elements model of a beam has been carried out.
Now the design of reinforced concrete constructions for static and dynamic loads with regard to the elastoplastic resistance diagrams of materials is widely used. The model of a reinforced concrete beam is proposed, which consists of trapezoidal elements formed by the field of cracks directions. The theoretical angle of inclination of a crack at any point of a beam has been determined on the basis of minimum of external load, necessary for its formation, which has been obtained from the equation of energy balance. The deflections of each point of a beam have been obtained by solving a differential equation of motion at each step the account. The strains in any fiber of normal and inclined sections have been determined according to the hypothesis of bilinear sections. The stresses in concrete and reinforcement have been obtained with the help of the variable elastoplastic stress-strain curves «σ-ε». The failure mechanism of a beam has been determined on a basis of the transverse to longitudinal force ratio in compressed area of concrete. The internal forces have been determined with the help of numerical section height integration of stresses and from the equation of balance of elements above the crack.
Plastic deformations develop in bending reinforced elements under seismic loads. In calculation of reinforced concrete constructions by spectral method they are taken into account only at the stage of seismic loads determination by introduction of reducing coefficients. But the development of plastic strains in bending elements leads to appearance of cracks, which don’t close after changing the internal forces sign. Due to it the work height of a section decreases, and the strength of elements reduces during subsequent loading cycles. The experimental evaluation of the influence of plastic strains on the stress-strain state of beams under low-cycle alternating effects of high intensity has been carried out. The first group of beams, considered as reference, was loaded with a monotonously increasing load until complete destruction. The other groups of beams were loaded by the monotonically increasing load up to the specified value of plastic deformations was reached. Then they were unloaded and loaded by the force of the opposite sign up to destruction. The stress-strain state of normal sections at all stages of loading was studied. It has been discovered that when changing the sign of load the through cracks are formed which close later if the plastic deformations of reinforcement are not large. The limit value of plasticity coefficient in the first semi cycle of loading preventing the formation of non-closing through cracks when changing the sign of internal forces has been determined.
A large number of reinforced concrete frame buildings are located in seismically dangerous regions. In case of seismic impacts plastic strains and local destructions occur in elements of such buildings, which influence sufficiently on their bearing capacity and stress-strain state when changing the sign of internal forces. This fact is not taken into account in current Russian norms on earthquake-resistant construction. The numerical research of reinforced concrete beams behavior under action of alternating load with regard to elastic-plastic properties of concrete and reinforcement has been conducted. The evaluation of influence of plastic strain maximum value in tensed reinforcement on the relative bearing capacity of the beam when changing the force sign and on the limit value of coefficient of plasticity corresponding to the destruction of compressed zone of concrete has been made. The comparison of results of numerical simulation with the results of experimental tests of beams with the same parameters has been made, which has demonstrated good convergence of numerical calculations with experimental data both in terms of bearing capacity and deformations for plasticity coefficients less than 2.5. During the experiment it has been found that when changing the sign of internal forces the through cracks form in bending reinforced concrete elements throughout the entire section height, which close afterwards if the coefficient of plasticity for reinforcement deformations does not exceed 2.5. For greater values of coefficient of plasticity the through cracks closing doesn’t take place until the destruction of the specimens due to the rupture of reinforcement bars. According to the results of the study it was concluded, that the decrease by 40% of relative bearing capacity of beams compared with reference samples as the increase of coefficient of plasticity in the first semi cycle of loading takes place. Also with the increase of the coefficient of plasticity the three times decrease of the limit values of coefficients of plasticity, corresponding to destruction of compressed concrete, when changing the sign of forces is observed. The numerical calculations of beams models for 10 and 50 alternating load cycles have been conducted with cycle asymmetry coefficient equal to -1. The conclusion has been made that under the action of alternating load with the number of loading cycles not exceeding 50 and for maximum values of coefficient of plasticity not exceeding 1.62 the insignificant decrease of relative bearing capacity of beams, not exceeding 10%, takes place.
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