ON THE NONLINEARITY OF DEFORMATION OF REINFORCED CONCRETE FLEXURAL ELEMENTS

Abstract

It is shown that in most calculations of reinforced concrete elements, the descending branch of the concrete deformation diagram should not be taken into account. This is due to the fact that in the calculation it is impossible to exceed the value of the stress in concrete, the value of the design resistance. It is shown that the "moment-curvature" dependence has a linear character both before the formation of cracks and after the formation of cracks. At the same time, calculations using software systems are greatly simplified with almost no loss of accuracy.

The use of nonlinear methods for determining the stress-strain state in design leads to significant difficulties. In addition, these methods do not add accuracy to the calculation, but lead to ill-conditioned design schemes.

The ascending branch of the concrete diagram can be approximated by a straight line, which greatly simplifies the calculations without a noticeable decrease in accuracy. The use of a non-linear form of the concrete diagram complicates the calculations, especially when used in software systems. This is because the roots of any equation greater than the first degree have two or more values for the same value of moment or stress. Therefore, it is difficult to choose the desired root in the software package. The use of a linear function always has a unique solution, while the accuracy decreases quite slightly.

The statement about the linear relationship "moment-curvature" is also proved by the approach that is adopted in the US standards. If we pass from the formula for determining the moment of inertia of an element with cracks to the “moment-curvature” dependence, then we can see that this dependence is linear.

The article shows how to use linear dependencies in the calculations of beam elements and slabs. The proposed approach to the design of reinforced concrete slabs using the finite element method involves changing the rigidity of the finite element depending on the presence or absence of cracks. In this case, the stiffness can have only two values, which are approximated by linear dependencies.