Theory Damage Detection

In order for a damage detection procedure to be practical to implement it must use easy to obtain information. Static response data, i. e. displacements resulting from static loads, can be obtained using electronic distance meters and can even be automated. Therefore it seems natural that static response data can serve well as a basis for a damage detection procedure. The measured displacements are a function of the loads applied to the structure and also the stiffness matrix of the structure. Damage must be quantified using the variables obtained from static response data.

What is damage?

Structural damage is usually associated with the inability of a structure to support loads. As a result, large displacements occur that normally would have been minimal. It is natural to associate the increased displacements of a structure with a decrease in overall stiffness. Therefore damage is defined as a reduction in stiffness of a structure. For this reason, the change in structural properties that comprise the stiffness matrix must be used as a measure for the location and severity of damage.

Structural Elements

The problem presented in this paper utilizes bending elements to construct the two dimensional frame structures. The stiffness matrix of a bending element is of the form:

12 EI

6EI

-12 EI

6EI ‘

L

6EI

L2

4EI

L

– 6 EI

L2

2EI

L2

12 EI

L

– 6EI

L2

12 EI

L

– 6EI

Eq(1)

L

6EI

L2

2EI

L

– 6 EI

L2

4EI

L2

L

L2

L _

By utilizing bending elements, the stiffness matrix is dependent on only the length, modulus of elasticity, and moment of inertia of each element. In reality the length of each element can be determined either from structural drawings or direct measurement of each member and the modulus of elasticity can be taken as the industry standard. Therefore, these values can be considered constant for both the healthy and damaged element. On the other hand, the moment of inertia of each element can change between the healthy and damaged member. By assembling the global stiffness matrix of the damaged structure and extracting the moment of inertia values, comparison with the healthy stiffness matrix values allows damage to be located and quantified.