PSI - Issue 66

Albena Doicheva et al. / Procedia Structural Integrity 66 (2024) 433–448 Author name / Structural Integrity Procedia 00 (2025) 000–000

443

11

6. Shear force

The magnitudes of the forces ′ are already known (Figure 9). Then, the determination of the shear force in RC internal beam–column connections will be determined by Equation (28) instead of Equation (1). 3 2 1 , and H H H ′

Figure 9. The joint shear in interior RC beam–column connection, with the determined exact forces from the beam.

3 j c V H H H V ′ ′ = + + − 2 1

(30)

If joint is symmetric and other conditions are equal, we will achieve the equality of 1 1 H H = ′ , 2 2 H H ′ = and

3 3 H H ′ =

. Then, Equation (30) becomes Equation (31)

3 j c V H H H V = + + − 2 1

(31)

The advantage of the proposed solution is that the exact magnitudes of shear forces are considered, taking into account a significant number of parameters affecting the magnitudes of the support reactions entering the beam– column joint. To verify the proposed solution, a comparison with the approximate solution recommended in the literature and codes is made. Equation (5.22) of Eurocode (2004) gives us the magnitude of the shear force: ( ) 1 2 jhd Rd s s yd c V A A f V γ = + − (32)

where yd f [kN/cm

2 ]—design value of the yield strength of steel;

Rd γ should not be taken less than 1.2. The comparison of Equations (31) with (3) and (32) is expressed in the comparison shown in Equation (33).

′

M M

?

?

(

)

;

(33)

3 s yd H H H A A f γ + + = + 2 1 1 2 Rd s

H H H

b + + = +

b

′

3

2

1

j

j

b

b

where is the moment of the beam on the face of the column. The spring coefficients 1 k , 2 k and 3 k of the three supports are reduced to the tension/compression stiffness of the beam by the 1 ζ , 2 ζ and 3 ζ multipliers. When we consider the rigid support between structural elements using static schemes, we assume that the connections between them do not allow the sections to move and to rotate. This was implied in Equation (10) and (20). For this reason, multipliers 1 ζ , 2 ζ and 3 ζ will be assumed equal to 1. b M qL = 2 / 2