FOR THE CALCULATION OF REINFORCED CONCRETE SLABS BY THE FINITE ELEMENT METHOD
DOI:
https://doi.org/10.31713/budres.v0i43.10Abstract
When modeling the work of reinforced concrete slabs with flat finite elements, one must be careful in schemes with uneven loads, as well as in schemes with holes. Torques in plates with flat finite elements can differ significantly from real torques. This, in turn, leads to errors in determining the main moments, as well as errors in determining the moment of crack formation. Errors in determining the moment of crack formation lead to errors in determining the deflections of reinforced concrete slabs. The difference between real and calculated deflections using flat finite elements can be different. This difference depends on the load scheme, the support scheme, as well as on the ratio of the dimensions of the slab. With pure torsion, the difference is two times. This is due to the fact that shear stresses, that act in the vertical direction, are not taken into account.
As an example, a diagram of a plate is considered, which is hinged at the ends and a distributed load acts on the right edge. A scheme is considered in which a monolithic slab rests on columns in the corners. The load schemes on one face and in the form of a load on half the area of the slab are considered.
It is shown that the greater the ratio of the plate width to its length, the greater the error between the real moment and the moment, which is determined by flat finite element modeling. With a small a/l ratio, the torque ratio approaches two, that is, it approaches the difference in pure torsion. As the a/l ratio increases, the torque ratio also increases. An explanation of this factor is shown as a result of the analysis of shear stresses in the finite element. To do this, shear stresses from bending should be added to the stress from pure torsion.
It is concluded that the error in determining torques when modeling with flat finite elements must be taken into account when designing. To prevent errors, it is recommended to use a rod approximation or volumetric finite elements
