Issue 49

S. Pereira et alii, Frattura ed Integrità Strutturale, 49 (2019) 450-462; DOI: 10.3221/IGF-ESIS.49.43 452 Beam Model To model the beam, one uses the Euler-Bernoulli beam theory, according to Eqn. (1) ( ) 4 4 d w EI q x dx = (1) Where q(x) is the distributed transverse load, E is the Young’s Modulus, I is the second moment of area of the cross section of the beam, x is the dimension across the length of the beam and w is the beam’s deflection. Since there are no distributed transverse loads (only point loads due to the imposed displacement), (1) becomes: 4 4 0 d w dx = (2) with the homogenous solution given by (3): ( ) 3 2 1 2 3 4 w x C x C x C x C = + + + (3) Due to the discontinuous nature of the displacement application system, the beam must be divided into four sections, as seen in Fig. 3. Figure 3 : Beam model of the specimen, where x0 is the clamped end of the specimen; x1, x2 and x3 are the positioning pins; and x4 is the free end of the specimen [9]. Section 2 is the constant curvature section. Figure 1 : Test machine with an endodontic file [10]. Figure 2 : Test machine with the tree pins in a testing configuration [10].