Damage Diagnosis of Bridge Girders via Modal Flexibility Deflections, Inertia Force vectors, and strain energies

Document Type : Invited by Davoud Younesian


1 Quchan University of Technology

2 Civil Engineering Department, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran

3 Assistant Professor, Civil Engineering Department, Retired, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Mashhad, Iran



This paper presents a new method for identifying damage in bridge girders based
on modal flexibility deflections. Using modal inertia forces for spatial load
distribution vector, a new approach for obtaining modal flexibility deflections is
presented. A two-stage damage identification method is then proposed for beamlike structures using these flexibility deflections. In damage severity estimations,
the concepts of static beam deflections are utilized. The abilities of the proposed method are demonstrated using experimental modal data of two full-scale bridge girders. Four damage scenarios of a steel plate girder and the surface damages in a pre-stressed concrete box girder are selected and discussed. The influence of uniform load surface and the number of vibration modes on damage patterns are studied. The results show that the localization resolution declines 15%-30% when applying the uniform load surface method, and the first two vibration modes are very influential on the damage patterns. In most cases, the predictions based on the flexibility deflections due to the modal inertia forces are found to closely (above 90%) agree with the actual damage of the bridge girders. Finally, the performance of the proposed method in the presence of modelling errors and noisy data is investigated. The results indicate that the proposed method is efficient in damage identification of beam-like structures.


  • A new spatial load distribution vector consisting of modal inertia forces is suggested.
  • The abilities of the vector of uniform load surface method are investigated.
  • Damage severity is estimated by the concepts of static deflections.
  • A new two-stage damage identification method is proposed.


Main Subjects

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