Long-term deflections in cracked reinforced concrete flexural members

Long-term deflections, especially in cracked and slender R/C flexural members, may cause delayed damage in non-structural elements, so they must be accurately estimated at the design stage. The time-dependent response of cracked sections is complex, since creep and shrinkage produce a shift of the neutral axis, and the delayed curvature is significantly affected by the amounts of tensile and compressive reinforcements. In this paper, a simplified method for the calculation of long-term curvatures and deflections in flexural members is proposed, which is based on the mechanics of reinforced concrete, and explicitly incorporates the most important parameters governing the time-dependent behavior of RC sections and elements. Constant stress in the tensile reinforcement under sustained load is assumed, according to experimental observations and the results of numerical simulations on the time-dependent behavior of cracked sections. The results of the simplified proposed formulae fit very well those obtained by a general non-linear and time-dependent analysis of a large number of hypothetical beams. Good agreement has also been obtained with the results of 217 previously tested beams under sustained load, available in the literature. Better approximation and lower scatter than the long-term deflections calculated with other widely used simplified methods have been obtained. It is concluded that, in order to accurately predict the delayed deflections at any time of the service life of normal and high strength concrete structures, loaded at any age, creep coefficient and shrinkage strain must explicitly appear in the simplified formulae, as those derived in the proposed method.