Issue 50

S. R. Pereira et alii, Frattura ed Integrità Strutturale, 50 (2019) 242-250; DOI: 10.3221/IGF-ESIS.50.20 245 The concrete used in the production of the models had its strength tested at 28 days of age and its average compressive strength was 33.5 MPa. All models had four longitudinal 12.5 mm CA-50 reinforcement bars and 5 mm transverse reinforcement bars spaced every 150 mm. Specimens were submitted to a concentrated eccentric force applied at a fixed point on the consoles to impose a combined bending and compression situation on the column. The column is simply supported on both ends, being one of them supported on a reaction block and the opposite one subjected to a point load applied by a hydraulic jack, as shown in Figs. 2 and 3. For force application, a hydraulic jack equipped with a load cell was used, which enabled monitoring of the forces applied throughout the tests. To obtain the lateral displacements of the column, a displacement transducer was positioned at the midspan. When the column was close to rupture, the sensor was removed and displacement was measured with a tape. Four tests were conducted with different eccentricities. Tests E1 and E2 had eccentricities of 82 mm and 310 mm in the x direction (see Fig. 1) and tests E3 and E4 had eccentricities of 72 mm and 264 mm in the x’ direction, rotated 45° in relation to x (see Fig. 1), as shown in Tab. 1. Test Axis direction Eccentricity [mm] 1 x 82 2 x 310 3 x’ 72 4 x’ 260 Table 1 : Overall characteristics of the tests performed. T HEORETICAL A NALYSIS theoretical model considering the stress-strain relationships of steel and concrete presented by the ABNT NBR 6118:2014, first presented by Pereira et al. (2013) [20] was adapted to evaluate the tested columns in serviceability. This model considers the physical nonlinearities due to rheological behaviour of concrete, such as shrinkage, creep and cracking and, not only the variations of properties over time, but also the loading history of the concrete structural element. Computationally, the structure is longitudinally divided into elements, each of which may have different physical properties, as well as different loading histories. Several assumptions are adopted in the development of this model. First, the column cross section, the applied loads and the deformations remain in a plane. Secondly, the loading plane corresponds to an element symmetry plane. Also, the column is slender, that is, its length is much larger than its lateral dimensions and the cross-section and longitudinal displacements are infinitesimal. Only the deformations parallel to the longitudinal direction of the column are considered and physical properties in each cross section can vary from element to element. Finally, the model allows a variation of column geometry along its length and over time and applied loads and boundary conditions can also vary over time. There seems to be no use in a model that considers rheological properties in the assessment of a column tested under short- term loading, but the state of coercion imposed on the structure by shrinkage that occurs since casting of the concrete, which produces tensile stresses in the concrete and compressive stresses on the reinforcements, can be considered through this model. The stress and strain states are iteratively calculated for each increment of time and bending moment and axial force resultants of these stresses are compared to the actual applied loads to assess convergence in each cross section. To ensure the convergence of the iterative search process present in the theoretical model, the compressive strength of concrete and steel stress must consider unlimited. Since the theoretical model is applicable to the verification of structures in the service limit state, the stresses are less than limit of the strength of the materials, and therefore the non-verification of the stress values is acceptable. However, for ultimate limit state verification, materials stress checking with strength limits is paramount. More details on the theoretical model and equations necessary for its implementation can be obtained in Pereira et al. (2013) [20] . Since the proposed model does not consider the effects of geometric nonlinearities, a simplified alternative to consider these effects was used: the displacements of the previous step were used to determine an increment of the bending moment corresponding to the product of the applied force by the second-order eccentricity. A