# Damage Evolution Analysis in a \"Spaghetti\" Bridge Model Using the Acoustic Emission Technique
## 3 Application: The Bridge Model Analysis  
The technique was applied to a small-scale bridge model made from spaghetti sticks, built by undergraduate students taking part in a contest, in order to illustrate the effectiveness of the global parameters' evolution obtained from an AE analysis method as predictors of structure collapse. The idea of spaghetti bridge contests was initially proposed in the Okanagan College in 1980 [40], to motivate the students in the basic concepts of building  
Figure 5: The Bundle Model. (**a**) Parallel bar model where a prescribed displacement \(u_{x}\) is applied and the reaction \(P_{x}\) is measured, (**b**) evolution of the load during the damage process in typical Bundle Model.  
Figure 6: The avalanches distribution in the Bundle Model, defining avalanche as the number of bars that break simultaneously. (**a**) When the prescribed displacement is continuously increased, but the test is stopped before complete failure (i.e., \(u_{xi}<u_{x\,\text{max}}\)). (**b**) When \(u_{x}\) is applied in discrete steps with amplitude \(\delta u\).  
actual structures. Nowadays, similar initiatives occur in several educational institutions around the world. The structure that was analyzed here was built for the contest at the Engineering School of Federal University of Rio Grande do Sul (UFRGS), which occurs twice a year since 2004. Participation in the context is mandatory for Civil Engineering students, but it is also open to students from all other Engineering programs. This bridge model complies with all guidelines for the contest (geometric restrictions, mass limits, load application, etc.), described in detail in [41; 42], and its main geometric parameters appear in Figure 7.  
The collapse loads for all bridges evaluated in the contest are informed in Figure 8, with four winning designs being highlighted in the same figure and depicted in Figure 9. It is noticed that the average collapse load increases for the first six years, tending to an approximately constant value after that. This is due to the increased tendency of most contestants to adopt the topology that is depicted in Figure 9c, which is theoretically optimal for stiffness [43].  
Figure 8: Evolution of collapse loads for the UFRGS Spaghetti Bridge contestants, data from [42].  
Figure 7: Geometric restrictions for the University of Rio Grande do Sul (UFRGS) Spaghetti Bridge contest (adapted from [42]).  
Figure 10 depicts the spaghetti bridge used in the AE test, undergoing its load test during the contest, and its corresponding collapse load is also highlighted (in red) in Figure 8. This bridge was 1.08 m long, 0.15 m wide and 0.45 m high, with 1.40 kg of mass. Load was increasingly applied manually to its center line, with increments in 10 s intervals until collapse occurred at \(t=235\) s, with 784.80 N. Two accelerometers [44] were installed on the spots that are marked as \(S_{1}\) and \(S_{2}\) in Figure 10a, for acquiring the AE signals. The sensors were located at the bridge arc, in the regions most expected to present AE events: \(S_{1}\) near one of the bridge supports and \(S_{2}\) at mid-length, where the loads were applied. The AE analysis uses the signals from \(S_{2}\), with \(S_{1}\) as a secondary reference to confirm the identification of AE events. The sensors are piezoelectric accelerometers, with frequency measurement in lineal range from 5 kHz to 60 kHz. Their signal was acquired through a data acquisition module Bruel & Kjaer(r) PULSE(tm) 3035, at a sampling rate of 65.54 kHz. A Nyquist-type filter with a cutoff frequency of 30 kHz was used in order to reduce noise and to avoid aliasing.