Thermal stresses in rectangular concrete beams, resulting from constraints at microstructure, cross-section, and supports

Abstract

Concrete beams carrying flat roofs are subjected to daily temperature cycles. Thermal eigenstrains at different scales of observation may be constrained or even prevented. This may apply to the entire beam and its support conditions, to the cross-sections of the beam, the microstructure of concrete, consisting of coarse aggregates embedded in a mortar matrix, and to the microstructure of mortar, consisting of fine aggregates embedded in a cement paste matrix. Scale transitions from the entire beam to the cross-sectional scale and further down to the microstructural scales of concrete and mortar are based on standard equations of the linear theory of slender beams and on the concentration-influence relations between the macroscopic and the microscopic strains, taken from continuum micromechanics. This multiscale approach is used for computing thermal stresses of concrete and of its constituents. Sensitivity analyses are carried out w.r.t. the support conditions, the type of coarse aggregates, the internal relative humidity, the speed of the temperature change, and the height of the cross-section. It is demonstrated that even if thermal stresses appear to be reasonably small at the scale of concrete, there may be significant microstructural stress fluctuations. They are the larger, the greater the difference between the thermo-elastic properties of the individual microstructural constituents. It is concluded that the thermal insulation of flat roofs, as promoted by the United Nations environment program to reduce energy consumption in buildings, is also important to obtain smaller daily cycles of stresses of beams carrying flat roofs.