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 $D_0·\left(\sqrt{3}-1\right)/2$ 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.

本文提出了统一的解析公式，用于计算任意跨度的棱柱形梁在垂直方向上的温差引起的挠度。通过详细的参数分析，研究了结构几何形状，材料特性和温度变化对梁挠度的影响。具有奇数跨度的梁具有与具有偶数跨度的梁不同的热变形特性。对于相等跨度的连续梁，由于垂直温度差，两端的最外跨度承受的变形最大，而最中跨度则承受的变形最小。随着总跨度数n的增加，每个跨度的中跨挠度迅速收敛到极限值。最外面和最中间范围的限制分别是$d_0·\left(\sqrt{3}--\mathrm{1个}\right)/\mathrm{2个}$ 和零，哪里 $d_0$是具有相同跨距长度的简单支撑梁在中跨处的热变形。这项研究增强了对梁的热行为的理解。