Composite action phenomenon

The stiffness of RC elements under different loading conditions is a function of steel behaviour, concrete behaviour, and the interaction between them. Although many studies on the mechanical behaviour of RC elements have been conducted, research work in this area is ongoing due to the complexity arising from the composite nature of the materials

(Marfia et al., 2004). Thus, an investigation on the relationship between the dynamic and static properties of RC elements should take into consideration the behaviour of each material under different conditions, the interaction between steel bar and concrete, and its influence on the overall element stiffness.

The relationship between the dynamic and static properties i.e. the natural frequency and the stiffness of the structural elements is expressed in the equation for transverse free vibration of a simply supported Bernoulli-Euler beam given by:

(3.44)

where f is the natural frequency, n is the mode number, m is the mass per unit length, and L is the span length. Rewriting Equation 3.44, and representing the flexural rigidity, EI by the symbol K and assuming the mass and length are constant, the expression below is obtained, (3.45) implying that a change in flexural rigidity causes changes in natural frequency.

For elements comprising either steel or plain concrete only, K is a function of their respective material properties, where the boundary conditions effect is ignored. For a

composite element, such as RC, the stiffness, K, is a function of both the individual material properties as well as the interaction between the materials. Thus, for RC, the following equation applies:

K RC = K concrete + K steel + K bond (3.46)

Concrete stiffness is dependent on its behaviour under different loading conditions. For RC beams under flexural loading, the concrete stiffness is represented by its behaviour in compression as well as in tension as given below:

K concrete = K tension + K compression (3.47)

For RC beams under shear loading, the concrete stiffness will presented by its behaviour in compression, tension, and at the shear interface zone and as given below:

K concrete = K tension + K compression + K shear (3.48)

The steel stiffness for an RC beam (i.e. Ksteel) is the stiffness of steel under tension loading

conditions only, since the steel is normally positioned in the tension zone. When a load is applied, the concrete stiffness will change according to the loading level and its behaviour under compression or tension. Cementitious materials are characterized by a softening response, which can vary depending on its strength in compression and tension.

Bond action at the interface between the steel bar and the surrounding concrete during loading and unloading can be explained by means of an interaction force. The interaction force is assumed to have no bonding action (BA) at the initial stages when no load is applied. As load is applied, bonding action will begin to grow as a compression-bond action (CBA) force at the interface between the steel and the surrounding concrete, and it will try to resist the tensile force in the steel bar. This compression-bond action force is affected by applied load, steel bar diameter, steel bar perimeter, steel bar shape, compressive strength, and steel bar properties.

When the applied load increases, the tensile force in the steel bar will also increase, resulting in an increase in the compression-bond action force at the interface to resist slipping. Under the same applied load, when the bar diameter increases, the tensile stress in the steel bar will decrease, which then leads to a decrease in resisting the compression-bond action force. In addition, when the bar diameter increases, the mean increase in bonding area will cause a decrease of compression-bond action force per unit area. For smooth bars with the absence of ribs, the compression-bond action force will decrease, and this can lead to slipping. When compressive strength increases, this will lead to more shear force action from the surrounding concrete, which leads to an increase in the compression-bond action force.

Problems on the steel surface, such as corrosion, will lead to a decrease in the compression- bond action force, and this can cause slipping. Figure 3.4 shows the longitudinal section in a simply supported RC beam, and Figure 3.5 shows the development of compression-bond action force on the steel bar perimeter under loading. When the applied load is released, tensile force in the concrete will be reduced. This will lead to growth in shear force resistance at the interface between the steel and the surrounding concrete. This shear force, which is in the form of tension-bond action (TBA) force, will lead to an increase in tension stiffness of the RC element. Figure 3.6 shows the development of tension-bond action resistant force on the steel bar perimeter.

Figure 3.4. Longitudinal section in a simply supported RC beam under loading and un- loading

Figure 3.5. Development of compression-bond action (CBA) force in deformed bar

3.5 Summary

This chapter covered the analytical background of the damage detection algorithms, where it highlighted both damage severity and damage location algorithms. For each algorithm, it suggested the modification to the original form of the existing algorithms (which was described in Chapter 2), and subsequently developing new algorithms. The first section highlighted the damage severity algorithms, by presenting a new developed algorithm, which is perceive to be more sensitive in quantifying the damage severity compared to existing algorithms. Moreover, in this section a weighting method is proposed that is based on the area under the curve of the mode shape, which can assist in averaging the sensitivity of different modes. The second section covered the damage location algorithms, where the modifications to the original form of the existing algorithms were suggested. Developed algorithms have been proposed, which are believed to be more sensitive than the existing algorithms. Moreover, this section proposed an elimination procedure that is needed to cut- off the anomalies along the beam length. Finally, it is suggested to use the same proposed weighting method for the damage severity algorithm, for averaging of different modes to derive the overall crack patterns.