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As a simply-supported T beam of the girder grid system, the damage of the bridge deck will inevitably change the overall stiffness of the bridge, and then affect the natural dynamic characteristics of the bridge. The variation of the first-order natural frequency of the bridge before and after the damage of the T beam flange was analyzed by using the finite element analysis method, and the influence law of the T beam flange damage on the natural frequency of the simply supported T beam bridge was obtained. The analysis results showed that the damage of T beam flange will bring about a significant change in the first-order natural frequency. Taking the natural frequency test of multi-span simply supported beams in practical engineering as an example, the first order natural frequency of the undamaged span and the damaged span of the bridge deck were tested respectively, and the influence of the damage on the first order natural frequency was analyzed. Results showed that the first order natural frequency decreases by 15.63 % under the condition that the single T beam is completely damaged in the mid-span position. Therefore, the damage of T bridge can be preliminarily judged by the change of the natural frequency of simply supported beam bridge in practical engineering.

The equivalent effective length parameter is introduced into the vibration equation of short cable; that is, the boundary condition that affects the test accuracy of short cable force is equivalent to the calculated length of cable. By attaching an additional mass block to the cable, new parameters are introduced to identify the tension force. Vibration differential equations are established for cable with and without addition mass block, taking new parameters into account, such as equivalent effective length and added mass. By solving the equations using the RITZ method, the analytical relationship between the natural frequency of cable and equivalent effective length before and after a mass block is added can be developed. It can also develop an analytical method to identify the equivalent effective length depending on whether the added mass block is attached. Then, tension force of short length cable can be evaluated by measuring its natural frequency based on equivalent effective length. The method is verified by field tests. The tests results indicate the new method mentioned in this paper is going to largely improve the accuracy of tension force measurement of short length cable.