Analytical calculation of temperature-induced strain of supertall structures

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.