Analytical formulas of beam deflection due to vertical temperature difference: Fid-Bau Portal

Analytical formulas of beam deflection due to vertical temperature difference

Zhou, Yi / Xia, Yong / Fujino, Yozo

Highlights • Analytical formulas of beam deflection due to differential temperature are derived. • Essential relation between thermal deflection and structural properties is revealed. • The thermal deflection limits are determined as the span number approaches infinity.

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 $D_{0} \cdot (\sqrt{3} - 1) / 2$ and zero, where $D_{0}$ 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.