Analytical formulas of beam deflection due to vertical temperature difference

Abstract

This paper presents unified analytical formulas to calculate the vertical temperature difference induced deflection of a prismatic beam with any number of spans. The influences of the structural geometry, material property, and temperature change on the beam deflection are investigated through detailed parametric analysis. A beam with odd-numbered spans has distinct thermal deformation characteristics from that with even-numbered spans. For an equal-span continuous beam, the outermost spans on both ends undergo the largest deformation due to the vertical temperature difference, while the middlemost spans the least. The mid-span deflection of each span converges quickly to the limit value with the increase of the total span number n. The limits for the outermost and middlemost spans are respectively D0·3-1/2 and zero, where D0 is the thermal deflection at mid-span of a simply supported beam with the same span length. This study enhances the understanding of the thermal behaviour of beams.