Estimating temperature-induced strain is of critical importance for structural safety assessment. Most previous studies estimated the temperature-induced strain by statistical analysis, resulting in the unexplainable physical meaning of the obtained model coefficients. In this paper, an analytical formula for the temperature-induced strain of supertall structures is derived based on the simulated temperature field. First, a supertall structure is simplified as a cantilever column, and the theoretical relationship between the sectional two-dimensional temperature field and strain is derived. Afterwards, the structure is extended to a generalised cantilever column bounded by springs at the top end, and the theoretical relationship of temperature and strain is derived as well. The formula shows that the sectional strain is composed of the sectional average temperature-induced strain and the gradient temperature-induced strain along two horizontal directions. A finite element (FE) model is established to verify the derived strain formula. Finally, the formula is applied to a real supertall structure, the Wuhan Yangtze River Navigation Centre, on which a long-term structural health monitoring system has been installed. The temperature field of the whole structure is obtained by the FE heat transfer analysis, and the temperature-induced strain is calculated according to the derived formula. The average difference between the theoretically derived and measured strains is less than 7 με. This study provides a simple theoretical formula for calculating the temperature-induced strain of supertall structures, avoiding the complicated FE structural analysis.

中文翻译：

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超高层结构温度致应变的解析计算

估计温度引起的应变对于结构安全评估至关重要。以往的研究大多通过统计分析来估计温度引起的应变，导致所获得的模型系数的物理意义无法解释。本文基于模拟温度场推导出超高层结构温度致应变的解析公式。首先，将超高层结构简化为悬臂柱，推导出截面二维温度场与应变的理论关系。之后，将结构扩展为顶端以弹簧为边界的广义悬臂柱，并推导出温度和应变的理论关系。由公式可知，截面应变由截面平均温度诱发应变和沿两个水平方向的梯度温度诱发应变组成。建立有限元（FE）模型来验证导出的应变公式。最后，将该公式应用于实际的超高层结构——武汉长江航运中心，其上安装了长期结构健康监测系统。通过有限元传热分析得到整个结构的温度场，并根据推导出的公式计算温度致应变。理论得出的应变和测量的应变之间的平均差异小于 7 με。本研究为计算超高层结构的温度致应变提供了一个简单的理论公式，