PSI - Issue 78

Pier Paolo Rossi et al. / Procedia Structural Integrity 78 (2026) 726–733

731

To obtain the magnitude of the transverse normal stress on the compressed uncracked concrete of the considered failure surface, the above stress is first calculated at two points of the compressed zone of the failure cross-section. Then, the obtained resultant of the transverse stresses on the compressed zone is averaged over the area of all the compressed zone of the failure cross-section to obtain a single value of the transverse normal stress in this zone. To obtain the transverse stress caused by the single strut, the intersection of the upper line L F and the compressed part of the failure surface is first sought. If the upper line L F does not intersect the compressed part of the failure surface, the contribution of the considered strut to the transverse normal stress is null. If this is not the case, the intersection point is named P (1) (Fig. 5) and the distance of this point from the top of the member is indicated as (2)  h . The transverse normal stress at this point is given by the following relation

V,i F b z 

(1) y,i  

(i=1 or 2)

(4)

(1) σi

σ  z is the amplitude, along the z

where F v is the transverse component of the axial force of the single strut and (1)

axis, of the fan of the compressive stresses at point P (1) . Then, the intersection point of the lower line L F and the compressed part of the failure surface is sought. If the lower line L F does not intersect the compressed part of the failure surface (as for example in the close-up in Fig. 5), the transverse normal stress at the lower end of the vertical part of the failure surface exists. In particular, the point at the lower end of the vertical part of the failure surface is named P (2) and the transverse normal stress at this point is calculated with regard to the amplitude of the fan at a distance from the top of the beam equal to the depth x of the compressed part of the failure surface. Instead, if the above point of intersection exists within the depth of the compressed part of the failure surface, the point of intersection is named P (2) (see Fig. 5) and its distance from the top of the member is indicated as (2)  h . In any case, the transverse compressive stress at point P (2) is where (2) σ  z is the amplitude, along the z-axis, of the fan of the compressive stresses at point P (2) . Finally, the average transverse stress over the compressed part of the failure surface is given by the relation     (1) (2) (2) (1) y,i y,i y,i ,i ,i 0.5 /         h h x (i=1 or 2) (6) Once a failure surface has been assigned, the above calculation of the transverse normal stresses is carried out with reference to the two abovementioned struts originating from the loading plate and from each of the transverse rebars on the right of the considered failure surface. To obtain the total transverse normal stress on the vertical part of the assigned failure surface, all the above contributions to the total transverse normal stress are summed up. V,i F b z  (2) y,i   (2) σ,i (i=1 or 2) (5)

Fig. 5 Determination of the transverse compressive stresses at an assigned vertical cross-section