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This paper investigates new damage detection method for bridges to ensure their safety. The idea of using displacement data of two symmetrical points for multiple damage detection is presented for the first time. After introducing the concept of Equivalent Element, a novel index termed as 'Symmetrical Displacement Difference Index (SDDI),' is proposed. The displacement under static load is used for constructing the new index. Then the relationship between the local flexural stiffness change caused by damage and SDDI value is generated. In application, SDDI values can be plotted after the measurement of displacement. The relative changes between the intact state and the damage state in the curve shapes can be used to indicate the position of damage. This new damage detection method based on SDDI is flexible enough to be applied to real-world bridges with inherent random uncertainty and actual support condition. Numerical and experimental examples have been conducted to examine the suitability of the method. This paper provides a simple, convenient, cost-effective, and nondestructive damage detection method for bridges. [ABSTRACT FROM AUTHOR]