Probabilistic analysis of cracking moment of ferrocement flexural members

Abstract

Characteristic cracking moment equations for the design of ferrocement flexural members are proposed. These are derived based on the results of a detailed Monte Carlo simulation (MCS) studies. In simulation, the strengths of cement mortar and reinforcement and, dimensions of reinforcements and ferrocement members are considered as random variables. The preliminary cross-sections considered for MCS are of realistic dimensions and are those of 37 ferrocement flexural members. The probability density functions of ultimate strengths of weld mesh and steel bars, required in MCS, are determined from the uni-axial tension tests on 187 weld mesh bars, 200 specimens of 4 mm diameter and 80 specimens of 6.8 mm diameter steel bars. Two deterministic equations, proposed earlier by the authors, are used in MCS. It is noted that the statistical variations in compressive strength of cement mortar has significant effect on coefficient of variation of cracking moment, and that the cracking moment follows a normal distribution at 5% significance level. A more rational equation is derived for cumulative distribution function of cracking moment and it satisfies the condition that cracking moment can not be negative. A detailed review of literature on strength and behaviour of ferrocement flexural members is included as supplementary material.