Finite Elements, Plasticity Theory and Linear Programming for Dimensioning Reinforced Concrete Slabs and Walls

Author(s):  
Edoardo Anderheggen
2018 ◽  
Vol 8 (3) ◽  
pp. 4-7
Author(s):  
Anton O. GLAZACHEV ◽  
Liliya Y. GIMADETDINOVA ◽  
Alexey P. GONCHARUK ◽  
Igor V. NEDOSEKO

The article presents a comparative analysis of the results of the calculation of rigid pavement on the shear stability obtained by the classical engineering method and using numerical calculations. The conclusion is made about the possibility of using modern design tools to select the optimal design of rigid pavement.


2019 ◽  
Author(s):  
Hector Andres Tinoco

This study presents a numerical procedure for the analysis of reinforced concrete slabs (RCS) that obey Nielsen's yield criterion (slabs orthogonally reinforced). An upper bound formulation combined with finite elements was established to solve the kinematic theorem as a conic optimization problem with the aim to determine the maximum bearing capacity of RCS. Discrete Kirchhoff finite elements were implemented and adapted to establish a limit state problem for the yield design. By using Nielsen´s criterion, a kinematic criterion was established applying the flow rule of plasticity. The kinematic criterion was included in the upper bound formulation with the aim to constraint the curvatures of the slab. The upper bound formulation was organized in the standard form of a second order cone programming (SOCP) problem since the kinematic criterion was formulated in conic form. Numerical examples were proposed to test the accuracy of the method including the adaptive remeshing strategy.


Author(s):  
V. P. Agapov ◽  
K. R. Aydemirov

Objectives. The finite element method for cracked reinforced concrete slabs analysis after they were reinforced with composite fabrics in order to determine the residual safety factor is considered. Method. The method is based on the use of algorithms for calculating of structures with the account of the geometrical and physical nonlinearities, implemented in the PRINS program. These algorithms assume the use of the same calculation scheme in the process of the problem solving. However, the specifics of the assigned problem is that the design sсheme of the structure before the appearance of defects in it and after its amplification with the help of composite materials should change. Result. Taking into account this circumstance, the algorithms of nonlinear calculation of structures under the PRINS program were supplemented with an option that allows changing the parameters of the design scheme in the process of through calculation. To study the bearing capacity of reinforced concrete slabs, multilayer finite elements are used, for each of which a specific package of materials is specified. Modernization of the design scheme in this case comes down to replacing one package of materials with another. An example of calculation of a slab with a crack reinforced with composite fabric is given. Conclusion. It is shown that the use of a tunable design scheme can significantly improve the accuracy of calculations. In this case, the final result depends on what stage of the formation of defects in the slab its strengthening is realized. The special  multilayered finite elements of a quadrangular shape are used in calculations. The elements consist of four simple triangles, for which most of the matrix characteristics are calculated in a closed form. This is especially important when carrying out nonlinear calculations that require repeated computations of these characteristics. 


2017 ◽  
Vol 21 (2) ◽  
pp. 99-109
Author(s):  
I. N. Serpik ◽  
K. V. Muymarov ◽  
S. N. Shvachko

A computation scheme for the analysis of reinforced concrete slabs using the finite element method providing possibility to consider unilateral connections has been developed. The stress-strain state of a slab is modeled taking into account physically nonlinear behavior of concrete and reinforcement, reinforcement discreteness, formation of transverse cracks in concrete. Kirchhoff hypotheses are considered to be true for a slab as a whole. It is believed that reinforcement out of cracks has a perfect adhesion with concrete. Concrete is represented by a system of thin layers, each of which is in a two-dimensional stress state. Approximation of displacements in this multilayer scheme is performed using triangular plate finite elements. Deformation of the reinforcement is described by means of rods working only in tension or compression. Unilateral connections are the contact finite elements. Concrete strength is evaluated according to Karpenko criterion. Deformation of concrete between cracks is described in accordance with Murashev’s approach.On the basis of the principle of virtual displacements assembling of elements takes place. A secant method case providing the convergence of the iterative process for a complex nonlinear problem of this type is proposed. At the first stage, a step-by-step increase of external forces is provided until the actual level of loading is achieved. Only one iteration of the secant method is performed at each step. Then, the iterative solution of the problem with repeated change of secant modulus is applied. The efficiency of this algorithm is confirmed on the basis of theoretical analysis and experiment for a rectangular in terms of bending reinforced concrete slab with free bearing on three sides, and not fixed on the fourth side. Three slab samples were tested and formation of cracks was monitored, measurement of deformations and displacements were performed


Sensors ◽  
2021 ◽  
Vol 21 (13) ◽  
pp. 4622
Author(s):  
Kevin Paolo V. Robles ◽  
Jurng-Jae Yee ◽  
Seong-Hoon Kee

The main objectives of this study are to evaluate the effect of geometrical constraints of plain concrete and reinforced concrete slabs on the Wenner four-point concrete electrical resistivity (ER) test through numerical and experimental investigation and to propose measurement recommendations for laboratory and field specimens. First, a series of numerical simulations was performed using a 3D finite element model to investigate the effects of geometrical constraints (the dimension of concrete slabs, the electrode spacing and configuration, and the distance of the electrode to the edges of concrete slabs) on ER measurements of concrete. Next, a reinforced concrete slab specimen (1500 mm (width) by 1500 mm (length) by 300 mm (thickness)) was used for experimental investigation and validation of the numerical simulation results. Based on the analytical and experimental results, it is concluded that measured ER values of regularly shaped concrete elements are strongly dependent on the distance-to-spacing ratio of ER probes (i.e., distance of the electrode in ER probes to the edges and/or the bottom of the concrete slabs normalized by the electrode spacing). For the plain concrete, it is inferred that the thickness of the concrete member should be at least three times the electrode spacing. In addition, the distance should be more than twice the electrode spacing to make the edge effect almost negligible. It is observed that the findings from the plain concrete are also valid for the reinforced concrete. However, for the reinforced concrete, the ER values are also affected by the presence of reinforcing steel and saturation of concrete, which could cause disruptions in ER measurements


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