Evaluation of limit state of stress and strain of free-fixed columns with variable geometry according to criteria from the Brazilian code for concrete structures

Abstract

The ultimate limit state of stability by equilibrium bifurcation, the limit states for stress and strain resulting from this condition were evaluated for an extremely slender real structure of reinforced concrete, with geometry varying along its length. The aspects related to nonlinearities of the material were considered through the recommendations on NBR 6118:2014, from the Brazilian Association of Technical Standards (ABNT). In the analytical solution, developed for stability analysis, all elements of the structural dynamics present in the system were taken into account, including the column self-weight. The critical buckling load was then dynamically defined to different instants of time. Reductions of 70% for the modulus of elasticity and 59% for the critical buckling force were found in analyses performed from zero and five thousand days. It was also possible to obtain the induced stresses on the homogenized cross-sections and those transferred to reinforcement steel bars. KeywordsLimit states, critical buckling load, analytical solution, NBR 6118:2014. Graphical AbstractEvaluation of limit state of stress and strain of free-fixed columns with variable geometry according to criteria from the Brazilian code for concrete structures Alexandre de Macêdo Wahrhaftig et al.

Stress assessment in reinforcement for columns with concrete creep and shrinkage through Brazilian technical normative

“…Comparing the results obtained in the previous paper (Wahrhafig et al [2]), it was possible to note that the critical buckling load grew by 14.04% without the creep effect, (t = 0) and 26.52% when the creep effect is taken into account for the final time interval (t = 5000 days). The current adoption of the initial modulus of the concrete instead of the secant modulus contributed to that.…”

“…In this order, the stresses found were 108.20 MPa and 35.84 MPa The evolution of the relative stresses in each reinforcement bar for case (1) can be seen in Fig. 8 and for case (2) in Fig. 9.…”

“…When adopting the initial tangent modulus, an increase of 9% in relation to the secant one is found, with the structure becoming stiffer. • When the temporal variation of the homogenizing factors of inertias is not introduced in the calculation of the flexural stiffness; the creep effect is calculated for the weighting average of the geometry; and the modulus of elasticity considered in the calculation is the secant one; the maximum stress on the reinforcement corresponds to 7.49% of the design yield strength, as observed in previous investigations (Wahrhaftig et al [2]).…”

“…Due to the temporal nature of the moduli of elasticity of concrete, originated by the viscoelastic behavior, the homogenization factors become also time-dependent. The mathematical base used for calculating the homogenizing factors can be found in Wahrhaftig et al [2]. A programming routine, as shown in Fig.…”

“…In the first investigation (Wahrhaftig et al [1]), the analytical solution currently presented in the mathematical modeling was built and evaluated in comparison with the finite element method (FEM). In the second one (Wahrhaftig et al [2]), aspects related to the limit states of design were analyzed considering the concrete creep only and the secant modulus of elasticity of the concrete. In the present article, the temporal homogenization of inertias of cross sections subject to creep, as well as the shrinkage of the concrete, was added to the calculations together with the initial modulus of elasticity of the concrete.…”