PSI - Issue 72

Albena Doicheva / Procedia Structural Integrity 72 (2025) 235–242

241

The biger difference is at h/b = 3.2 – 14.51%. For concrete with E 1 = 4000 kN/cm 2 , the biger difference is at h/b = 3.5 – 10.59%. The comparison of the exact method with the Eurocode shows a large margin in favor of the Eurocode's safety.

h=30 cm

h=30 cm

1,50 2,50 3,50 4,50 5,50 (H1+H2+H3)/qL/2

1,40 2,40 3,40 4,40 5,40

(H1+H2+H3)/qL/2 2×(Mb/jb)/qL/2 Eurocode

(H1+H2+H3)/qL/2 2×(Mb/jb)/qL/2 Eurocode

h/b

(H1+H2+H3)/qL/2

2,0 2,2 2,5 2,9 3,5 4,3 5,6 7,9

h/b

a)

b)

Figure 6. Comparison of the parameters on Equation (12) calculated by Equations (5) – (7): ( a ) 2 1 4000kN/ cm E  . Figure 6 shows the variation in the sum with respect to the parameters of the three support reactions, H 1 / qL + H 2 / qL + H 3 / qL , calculated by Equations (5) – (7), while the crack between the beam and the column grows. The results show the differences between the exact method ( H 3 + H 2 + H 1 ) and the approximate method ( M b / j b + M ' b / j ' b ) used in Equation (1), and with Eurocod. For sections with E 1 = 1700 kN/cm 2 for concrete the biger difference is at h/b = 3.8 – 2.3%. For concrete with E 1 = 4000 kN/cm 2 , the biger difference is at h/b = 3.3 – 6.16%. The comparison of the exact method with the Eurocode shows a large margin in favor of the Eurocode's safety. A comparison of the exact method with the Eurocode shows a big difference: h/b = 3.8 – 73.4% for sections with E 1 = 1700 kN/cm 2 and h/b = 3.3 – 74.6%. The comparison shows that the calculated exact magnitudes of the forces for the considered static loading forces are close to those predicted by Eurocode. Designing according to Eurocode includes several calculated safety factors and values of the exact method greater than those set in Eurocode cause concern. 7. Conclusions A solution for a cantilever beam with a special arrangement of the supports was developed. The actual dimensions of the beam were taken into account. The beam was loaded with uniformly distributed load. The derived expressions for the reactions of the horizontal supports yielded results that clearly show the distribution of the forces along the height of the beam. The formulas were derived for the limit stage and enabled us to determine the distribution of forces before and after the appearance of a crack between the beam and the column. The resulting expressions for the support reactions take into account the influence of both the geometry of the beam and the material properties of all its components. This makes it possible to trace the variation in the forces acting on the beam and entering the beam – column connection with different data combinations of the included quantities. A comparison was made between the contribution of beam forces to the shear force value in RC internal beam – column connections and those known from the literature and from Eurocode. The results showed that the proposed exact method gives results that differ from the adopted one by 4% to 15%, depending on the stage of crack development. The difference between the new exact method and that of the Eurocode ranges from -82% to +75%, based only on the largest shear force value determined by the exact method. Eurocode specifies the force that the intended reinforcement could withstand, while the new formulas show how big the forces 2 1 1700kN/ cm E  ; ( b )

actually are. References

Alaee, P., Li, B., 2017, High-strength concrete interior beam – column joints with high-yield-strength steel reinforcements. J. Struct. Eng., 143, 4017038. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001773