Nonlinear Deformation Model for Analysis of Temperature Effects on Reinforced Concrete Beam Elements

The results of the study are aimed at developing a nonlinear strain model for reinforced concrete beam elements in the general case of force actions and temperature effects for different durations. As a rule, temperature effects on structures involve temperature drops, causing heterogeneity of mechanical and rheological properties of concrete and reinforcement. The article has approximating expressions needed to take into account the effects of temperature and heating time on the values of temperature-induced strain and mechanical and rheological properties of heavy concretes with C30-C60 strength classes. The properties of concrete and rebars are heterogeneous from top to bottom and across the width of the cross section. A physically nonlinear problem is solved using the method of elastic solutions combined with the method of stepwise increases in temperature and force loading. The cooling of a heated reinforced concrete element to normal temperature is considered a short-term effect. Strength criteria of portions of a concrete cross section, crack closure conditions, and the ability of cracked sections to take loads in compression amid a change in the sign of stresses are determined. The stress-strain state (SSS) analysis of reinforced concrete beams, made according to the proposed method, is compared with the experimental studies using (i) values of thermal bending moments in statically indeterminate structures, (ii) cracking forces, and (iii) values of deformations (elongations and curvatures) of the elements in the longitudinal axis. Good agreement between the calculated and experimental values of controllable criteria confirms the reliability of physical relationships (i) developed for heterogeneous reinforced concrete beam elements and (ii) applied to the complex cases of temperature and force effects.