Uncertainty of concrete strength in shear and flexural behavior of beams using lattice modeling

This paper numerically studied the effect of uncertainty and random distribution of concrete strength in beams failing in shear and flexure using lattice modeling, which is suitable for statistical analysis. The independent variables of this study included the level of strength reduction and the number of members with reduced strength. Three levels of material deficiency (i.e., 10%, 20%, 30%) were randomly introduced to 5%, 10%, 15%, and 20% of members. To provide a database and reliable results, 1000 analyses were carried out (a total of 24000 analyses) using the MATLAB software for each combination. Comparative studies were conducted for both shear- and flexure-deficit beams under four-point loading and results were compared using finite element software where relevant. Capability of lattice modeling was highlighted as an efficient tool to account for uncertainty in statistical studies. Results showed that the number of deficient members had a more significant effect on beam capacity compared to the level of strength deficiency. The scatter of random load-capacities was higher in flexure (range: 0.680-0.990) than that of shear (range: 0.795-0.996). Finally, nonlinear regression relationships were established with coefficient of correlation values (R-2) above 0.90, which captured the overall load-deflection response and level of load reduction.