Vibration-Based Estimation of Tension Stress in Steel Eyebars

Abstract

To support the repair and maintenance of steel eyebars in bridges, tension stresses are sometimes estimated from the observed member natural frequencies. Although the ends of such eyebars are often essentially fixed, a pin-ended model has typically been used to predict tensions because closed-form solutions do not exist for any other end conditions. An approximation that reflects vibrating stretched wires with fixed ends has also been used, but this still incurs considerable error at lower member slenderness and stress levels. To provide for better estimates of eyebar tensions from observed vibrations, this paper presents exact tabular solutions for determining the direct tension stress in undamped steel bars, generalized for any length or thickness, where both ends of the member are fixed or where one end is fixed and the other pinned. Approximation equations derived from these exact solutions are also developed. Examples demonstrate the application of these new tools and the potential increase in accuracy over the former methods.