Bridge - Transverse Vibration of Structural Systems

Target of investigations

Unlike other nondestructive evaluation (NDE) techniques used for the condition assessment of individual members, transverse vibration of structural systems aims to provide information about the condition of a structure. This technique is useful because inspecting each member of a structural system is time-consuming, and sometimes accessing wood members can be difficult.(1)


Transverse vibration aims to capture the resonance frequency of a structural system, such as a timber bridge superstructure, and use it to estimate the EI of the system, where E is the elastic modulus, and I is the moment of inertia (inch4 or m4).(1,2) EI represents the system’s condition.

Physical Principle

According to the transverse vibration results from the laboratory and field bridges, the vibration response of single-span bridges can be modeled using the theory for simply supported one-way beams.(2) For a timber beam, the theoretical relationship between E and the resonance frequency (fr) is as follows:

Figure 1. Equation. The theoretical relationship between E and the resonance frequency (fr).

Where W is the beam weight (lb or kg), L is the beam span (inch or m), g is the gravitational acceleration, and n is related to the support condition. For a simply supported beam, n = 2.46, and for a fixed-supported beam, n = 12.65.(1)

For an undamaged system, an agreement between test results and the theoretical value is expected. However, as a structural system deteriorates, its EI tends to decrease, and it deviates from its theoretical value.(1)

Data Acquisition

To estimate the resonance frequency, free or forced vibration can be applied to a structural system. In free vibration, the excitation force is impacted by a large hammer to deflect the structure, while in forced vibration, a motor with an eccentric rotating mass excites the structure. In the forced vibration, the resonance frequency is estimated by changing the speed of the rotating mass to observe the maximum deflection in the structure. The deflection can be estimated using linear variable differential transducers (LVDT) attached to the structure and connected to an oscilloscope.(1,2) Similarly, an LVDT can be used to capture the deflection during the free vibration testing (also known as modal testing.(2))

Data Processing

In practice, the output of the oscilloscope—time-deflection data—is used to estimate the resonance frequency.(1) Using equation 1, the resonance frequency enables estimating the with 95 percent confidence, which allows for variability due to materials and construction. Then, by measuring the floor span (L) and estimating the weight of the flooring, EI can be calculated to represent the condition of the structural system.(1)

Data Interpretation

No data interpretation is required


Transverse vibration of structural systems includes the following advantages:

  • Provides information about the condition of the whole bridge system.
  • Saves time and eliminates accessibility issues compared to individual testing of bridge components.
  • Focuses on the quality of connections, while the majority of NDE techniques focus on the quality of individual members.


Some of the limitations with transverse vibration include the following:

  • The current method of analysis is limited to single-span bridge systems.
  • The test evaluates the overall condition of a structure and fails to provide information about the condition of bridge components.


  1. White, R. H., and R. J. Ross, eds. 2014. Wood and Timber Condition Assessment Manual. 2nd ed. General Technical Report No. FPL-GTR-234. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory.
  2. Wang, X., J. P. Wacker, A. M. Morison, J. W. Forsman, J. R. Erickson, and R. J. Ross. 2005. Nondestructive Assessment of Single-Span Timber Bridges Using a Vibration-Based Method. Research Paper No. FPL-RP-627. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory.