# Correlation of Plastic Strain Energy and Acoustic Emission Energy in Reinforced Concrete Structures
## 2 Cyclic Loading
### Beam-Column Connection  
A 3/5 scale specimen was constructed to represent an exterior wide beam-column connection in a prototype RC moment-resisting frame with six stories and four bays. The prototype building was designed assuming a location in the earthquake-prone southern part of Spain. The specimen corresponds to the second story of the building. The steel yield stress was 404 MPa, and the concrete compressive strength 24.9 MPa [12]. The test model was installed in the loading machine shown in Figure 11, reproducing the actual boundary conditions of the subassemblage within the RC frame under lateral loads. Gravity loading was simulated by the combination of wide beam self-weight and sand bags of total weight 40 kN placed on the beam, plus an axial force applied to the column of 214 kN by means of two post-tensioned rods. Subsequently, cyclic horizontal forced displacements were applied automatically by the actuator following the scheme shown in Figure 12a, which is based on the ATC-24 loading protocol [23], until failure. The amplitude of the cycles was made constant within each set, but it increased with every consecutive set of cycles, following the sequence \(0.5\Delta y\), \(0.75\Delta y\), \(1.0\Delta y\), \(2\Delta y\), \(3\Delta y\), \(4\Delta y\) and so on, where \(\Delta y\) is the quotient between the predicted lateral displacement at the first yielding of the reinforcing steel and the total height of the column (180 cm) expressed as a percentage (drift-ratio). Figure 10: Accumulated AE energy (dashed line) and accumulated hysteretic strain energy (solid line). RC beam with notch. Figure 9: Stiffness degradation of the notched beam. A load cell and a displacement transducer installed on the actuator measured the overall horizontal force, \(Q\), and the corresponding horizontal displacement, \(\delta\), while strain gauges attached to the reinforcing steel measured the corresponding strains (Figure 12b). Six AE low-frequency VS30-V sensors (Figure 11) were placed on each specimen. In all the channels, 25-180 kHz pass filters were used; signals were preamplified 34 dB\({}_{\text{AE}}\), and 40 dB\({}_{\text{AE}}\) was set as the acquisition threshold. Figure 12b shows the strains recorded by the gauges fixed to the longitudinal reinforcing bars of the beam at the column face (_i.e._, at the section of maximum bending moment of the beam). The solid horizontal line indicates the strain corresponding to yielding. It is observed that the steel reinforcement remained elastic (_i.e._, undamaged) during the first two sets of cycles. Figure 13 shows the curves of overall load-displacement, \(Q\)-\(\delta\), obtained from the tests. The solid circle indicates the onset of  
Figure 11: Experimental set up for the beam-column connection subjected to cycling loads. Figure 12: Displacement history applied to beam-column connection (**a**) and corresponding strains in gauges (**b**). plastic deformations in the longitudinal reinforcement, which occurred before the maximum lateral strength was attained. Failure was assumed to occur when the load reached at the peak displacement of a given cycle was lesser than 75% of the maximum load attained by the specimen in previous cycles. This percentage may be considered as the limit of the \"usable\" capacity of the member [24]. The accumulated AE MARSE energy, \(E^{AE}\), was calculated for all sensors. Figure 14 displays with dashed lines the \(E^{AE}\) calculated from the signals recorded by sensors one (on the column) and five (on the beam) [12]. As seen in this figure, the overall plastic strain energy \(W_{p}\) dissipated is superimposed by solid lines. Both \(E^{AE}\) and \(W_{p}\) were normalized by their respective values \(E_{0}^{AE}\) and \(W_{p,0}\) at the onset of yielding in the steel reinforcement, timed at \(t_{0}\). Once again, there is a very good correlation between \(E^{AE}\) and \(W_{p}\) until \(t_{0}\). After this point, however, \(E^{AE}\) is always lower than \(W_{p}\), which is again in very good agreement with Equations (1) and (2).