PSI - Issue 84

Alessandro Lipari et al. / Procedia Structural Integrity 84 (2026) 1087–1094

1092

= 4 + 4 ( − )

(10)

in which d t and ρ t are the effective depth to and the ratio of the transverse reinforcement.

Fig. 3. Typical reinforcement arrangements.

5. Results and discussion In order to make a comparison with the experimental results, in Eq. (1) it is considered γ V = 1, f ck = f cm =0.82 f cm,cube , as done in Lantsoght et al. (2014), and f yd = f ym , besides d dg = 40 mm. Doing so an average value of the shear stress resistance is found, τ R,c , rather than its design value τ Rd,c . Similarly, all the loads are unfactored. From the model, the results for v E,x , v E,y , m E,x , m E,y and m E,xy are extracted at d from the load on a section parallel to the support line for further analysis. The values are taken in the element centers, as recommended by Rombach (2011).

Table 2. Shear forces, moments and shear resistances.

Specimen

S75N1Auc S60N1Auc S45N1Auc S60O1Auc

Shear force along x -axis, v E,x [kN/m] Shear force along y -axis, v E,y [kN/m] Maximum principal shear force, v E [kN/m] Direction of maximum principal shear force, α v [°] Average shear force over the control section, v E,av [kN/m] Average shear stress over the control section, τ E,av [N/mm 2 ]

1626.0 -304.2 1654.2 -10.60

776.2 -380.8 864.6 -26.13 423.6 213.1 102.0 -73.9 249.3 -26.53 222.4 0.261 0.525 0.185 0.533 1.80

435.5 -301.4 554.4 -33.60 312.6 1.35 71.2 68.4 -56.0 125.7 -44.28 106.7 0.258 0.341 0.148 0.237

742.8 -364.4 827.3 -26.13 405.6 97.5 -70.9 238.8 -26.53 213.1 0.261 0.525 0.185 0.549 1.72 204.1

538.3

2.27

Bending moment along x -axis, m E,x [kNm/m] Bending moment along y -axis, m E,y [kNm/m]

313.4 162.8 -59.8 333.2 -19.23 284.9 0.264 0.529 0.187 0.825

Twisting moment, m E,xy [kNm/m]

Moment across the control section, m E [kNm/m]

Direction of principal moment, α m [°]

Average moment over the control section, m E,av [kNm/m]

Effective depth, d [m]

Effective shear span, a cs [m] Mechanical shear span, a v [m]

Equivalent reinforcement ratio across the control section, ρ [%]

Minimum shear stress resistance, τ Rc,min [N/mm 2 ] * Shear stress resistance (using a v ), τ R,c [N/mm 2 ] * Shear stress resistance (using d ), τ R,c [N/mm 2 ] *

1.49 (1.52) 1.44 (1.25) 1.53 (0.88) 1.49 (1.16) 1.43 (1.59) 1.21 (1.49) 1.03 (1.31) 1.25 (1.38) 1.28 (1.78) 1.08 (1.67) 0.86 (1.58) 1.11 (1.55)

* In parenthesis, ratio of tested-to-predicted shear stress resistance.

Firstly, from Table 2 it can be seen that the direction of the maximum principal shear force α v aligns reasonably well with the skew angle of the member (negative angles mean anti-clockwise). This can also be seen from Fig. 4, which shows the principal shear forces at the peak and surrounding elements (two above and two below the peak) for two specimens, along with their components in the direction perpendicular and parallel to the control section. Even when the direction of the maximum principal shear force α v deviates appreciably from the perpendicular to the control