## 2 Experimental Data  
In the present paper, the assessment of the in situ compressive strengths of the concrete structural elements of an existing building is discussed. In [7] the authors showed that the concrete strength may alter from one floor level to another and/or even from one structural element to another of the same typology within the same structure. In the case of using conventional destructive testing to evaluate existing conventional buildings, the extraction of concrete cores and the subsequent calibration of empirical models may be difficult because, on the one hand, a high value for the coefficient of variation of the concrete strength (\(Cov_{fc}\)) may be recorded, and on the other hand, extending the destructive tests to a sufficient number of locations may be difficult or even impossible due to economic and logistic reasons. Therefore, to acquire detailed information on the structure, the use of non-destructive tests (NDTs) is quite useful. This is also confirmed by the experimental tests here investigated which have been conducted on a building located in Bari (Italy). The building was built in the 1970s and it is composed of five floors. The experimental tests have been performed on some walls and repeated on the same walls on each floor; the walls have been chosen, as often happens in practical applications, based on some logistic constraints mainly due to the possibility of drilling a core on each investigated wall. Although the transversal section of the tested walls varies on each floor, there is one dimension that remains constant and equal at 35 cm, which ultimately determined the direction of the performed tests. The structure does not manifest cracks or damage. The rebound tests have been performed by means of a Schmidt concrete test hammer type N, oriented orthogonally to the investigated elements and thus laying in a horizontal direction, in accordance with the manufacturer's instructions. The testing method consists in provoking the impact of a standardized mass against the surface of the structural element under testing and in measuring the height of the rebound, the measurement is expressed in terms of the percentage of the rebound height compared to the distance traveled by the moving mass between the instant it is released and when it hits the concrete surface, this percentage is called the rebound index and is measured on a scale numbered from 10 to 100. It is worth noting that the presence of internal voids, cracks, aggregates, etc., in correspondence with the point on which the hammer is positioned for the execution of the test, may be responsible for the overestimation or underestimation of the concrete strength. Therefore, the rebound index related to each investigated element has been evaluated as the mean value of the measurements acquired in the nine points of a grid fixed upon the element's surface, in this way the impact of possible \"local\" conditions on the assessed strength may be attenuated. The RH tests have been performed in a single day, to reduce the influence of environmental conditions on the acquired measurements. The surface had been rubbed off with an abrasive stone before testing, in order to guarantee the smoothness of the test surface and to minimize the influence of carbonatation. Moreover, the points of impact have been chosen as far as possible from edges and corners, and the tests have been performed in dry-air conditions inside the building. After the rebound hammer tests, a core has been drilled on each investigated element, and subjected in a laboratory to compression tests, in accordance with prescriptions of [18; 19]. In detail, the cylindrical cores have been extracted with a diameter of 100 mm and a ratio height/diameter equal to 2; afterward, the load-bearing surfaces of the cores have been prepared to improve the contact with the loading machine and ensure uniaxial compression conditions. In detail, 28 cores have been drilled and subjected to compression laboratory tests.