Analytical and numerical analyses of RC beams exposed to fire adopting a LITS trilinear constitutive law for concrete

A trilinear compressive constitutive law for concretes exposed to fire is proposed. Concrete stress-strain relation as a function of temperature is characterized by means of only two parameters (residual values of concrete compressive strength and modulus of elasticity). The modulus of elasticity is determined through a Load Induced Thermal Strain (LITS) semi empirical model. The compressive strength is established through the design specifications. The constitutive law is implemented in finite element numerical models and in a simplified cross-sectional procedure. In the latter case, a simple methodology is proposed to estimate the residual moment capacity and the midspan deflection at any given time. The uncoupled two-step solution includes a thermal homogenization procedure followed by a sectional analysis. The deflection is estimated considering a constant equivalent stiffness for the RC beam. The case studies included the structural response under transient (hot state) condition of both a reinforced-high strength concrete (R-HSC) beam and a reinforced-ultra-high performance fiber reinforced concrete (R-UHPFRC) beam. The results are compared with experimental tests carried out in literature, showing a good approximation. Moreover, a steady state (after cooling) cross-sectional analysis of a R-HSC beam is performed. The load bearing capacity, the failure type and the midspan deflections are estimated. The analytical results approximate the experimental values, demonstrating the reliability of the proposed simplified procedures for the cases investigated.