ABSTRACT
Since structural deterioration or weakening is an unavoidable process that bridges undergo during its lifetime, Structural Health Monitoring (SHM) has been an important research topic. A Finite-Element (FE) model updating method is widely used for identifying structural integrities such as support conditions and material properties. However, it is still difficult to properly estimate support conditions using limited number of data. Boundary condition is an important variable in model updating, since it is very sensitive to bridge responses. There are several studies however that considers the effect of the boundary conditions in the model updating method. Tu and Lu (2008) and Gordis and Papagiannakis (2011) presented a general algorithm (GA) based methodology making use of artificial boundary condition frequencies for model updating to enlarge the data set, increasing its sensitivity (Gordis & Papagiannakis 2011; Tu & Lu 2008).
As a bridge ages, its supports deteriorate. The deteriorated bridge support may restrain the bridge movement. During this state, the bridge support condition is neither simple nor fixed but in between. The restraining effect of the deteriorated support can be expressed by an artificial rotational spring.
Principle of superposition is used to calculate the rotational angles of both ends and the displacement at a certain location L/2 as follows.
The resulting equation (1) shows a linear relationship between the spring constant and response ratio, regardless of the magnitude of the load. Simple Beam Load Configuration. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315207681/cd556cd4-4dcf-4efe-8e29-56fc67b8bfbd/content/fig318_1.tif"/> () K A = 1008 E I 48 L 2 { 8 7 δ x θ A − L 3 ( 1 + θ B 7 θ A ) } K B = 1008 E I 48 L 2 { 8 7 δ x θ B − L 3 ( θ A θ B + 1 7 ) } https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315207681/cd556cd4-4dcf-4efe-8e29-56fc67b8bfbd/content/eq170.tif"/>
Equation (1) is only valid for a simple beam with homogenous cross section and material. Therefore it cannot be applicable to real bridges with complex structural properties such as multiple girders, slab, cross beams, varying cross sections and various material properties. Basically, it uses the linear relationship between the rotational spring constants at both ends and measured response ratio, displacement over rotational angle. An initial FE model is created based on drawings. Initial values of spring constant are assumed and the corresponding displacement and rotational angles are calculated. The relationship between the response ratios (displacement/rotational angle) and assumed spring constants is established using sensitivity analysis. From this relationship, we can estimate the spring constant of a bridge using measured displacement and rotational angles. The verification of the proposed method was carried out through numerical analysis and laboratory test.
