Thermally induced uniform strains and curvatures calculated using equivalent linear temperature distributions

Highlights: ► Changes of temperature distributions were investigated using the FE heat transfer analyses. ► Validity of thermal curvature calculated using linear thermal gradient was examined. ► Thermal gradient in ACI 349 can be used for concrete sections with reinforcing steel. ► Thermal gradient in ACI 349 underestimates curvature of a section with liner. ► The proposed thermal gradient takes into account the effect of liner on thermal curvatures. - Abstract: Thermal effects due to varying temperature are considered in the design of reinforced concrete structures for nuclear power plants. The commentary to Appendix E of ACI 349 provides a method of converting a nonlinear temperature distribution to an equivalent linear temperature distribution. The linear temperature distribution consists of two components: (1) a uniform temperature change and (2) a thermal gradient. Each component of the linear temperature distribution is used for calculating free thermal uniform strain and curvature. Further, thermal-induced loads can be estimated by taking into account the degree of restraints. The ACI 349 method for calculating free thermal uniform strain and curvature using a linear temperature distribution is developed based on a pure concrete section. As a result, the calculated free thermal uniform strain and curvature do not account for the effect of steel liner plate and reinforcing bars. The objective of this paper is to examine free thermal uniform strains and curvatures calculated using equivalent linear temperature distributions. Concrete sections with different thickness and the existence of steel liner plate and reinforcing bars were considered. Finite element analyses were performed and free thermal uniform strain and curvature were obtained. These results were compared with those calculated by the ACI 349 method. It was found that the equivalent linear temperature distribution method in ACI 349 can be used for predicting free thermal uniform strains and curvatures for pure concrete sections and concrete sections with steel reinforcement if rebars are equally placed on both faces of a concrete section or the steel area ratio is less than 1%. However, when a steel liner is attached to concrete, free thermal curvature can be significantly underestimated. Modified expression for the equivalent linear temperature distribution was proposed to account for concrete sections with liner.