PSI - Issue 66

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

440

8

h=75 cm

h=25 cm

-0,50 0,00 0,50 1,00 1,50 2,00

-1,00 1,00 3,00 5,00 7,00

H1/qL H2/qL H3/qL

H1/qL H2/qL H3/qL

2,0 H1/qL; H2/qL; H3/qL 2,4 2,9

3,8 h/b

5,6

10,0

50,0

2,0 H1/qL; H2/qL; H3/qL 2,4

2,9

3,8 h/b

5,6

10,0

50,0

a)

b)

2 1 1700kN/cm E = ; and a) 75/75 cm; b)

Figure 4. The parameters of the three support reactions for a beam with symmetrical cross-section and

25 /25 cm, calculated by Equations (12)–(14).

Figure 4 shows the variation in the parameters of the three support reactions, calculated by Equations (12)–(14), while the crack between the beam and the column grows, and 2 1 1700kN/cm E = . The three support reactions increase as the dimensions on the cross section of the beam decreases. For section 75/75cm, Fig. 4a), before the appearance of a crack, 2 1.7 H qL = , 3 1.2 H qL = and 1 0.19 H qL =− . Therefore 1 H is on a tensile state before the appearance of a crack. After the initiation of a crack 2 H decreases to 1.29 qL , while 3 H slightly increases to ( ) 3 / 2.7 1.23 b h H qL = = and then decreases to 1.00 qL . The support reaction parameter 1 H qL increases to a value of 0.58 . For section 25/25cm, Fig. 4b), before the appearance of a crack, 2 6.26 H qL = , 3 4.27 H qL = and 1 0.5 H qL =− . After the appearance of a crack 2 H decreases to 5.48 qL , while 3 H slightly increases to ( ) 3 / 2.9 4.37 b h H qL = = and then decreases to 4.01 qL . The support reaction parameter 1 H qL increases to a value of 0.82. For all sections H 1 there are values smaller than those of the other two support reactions, H 2 and H 3 .

h=25 cm

h=75 cm

2,00

-1,00 1,00 3,00 5,00 7,00

H1/qL H2/qL H3/qL

H1/qL H2/qL H3/qL

1,00

0,00

2,0

2,4

2,9

3,8 h/b

5,6

-1,00

H1/qL; H2/qL; H3/qL

10,0

50,0

2,0

2,4

2,9

3,8 h/b

5,6

10,0

50,0

H1/qL; H2/qL; H3/qL

a)

b)

2 1 3700kN/cm E = ; and a) 75/75 cm; b)

Figure 5. The parameters of the three support reactions for a beam with symmetrical cross-section and

25 /25 cm, calculated by Equations (12)–(14).

Figure 5 shows the variation in the parameters of the three support reactions, calculated by Equations (12)–(14), while the crack between the beam and the column grows, and 2 1 3700kN/cm E = . For section 75/75cm, Fig. 5a), before the appearance of a crack, 2 1.64 H qL = , 3 1.26 H qL = and 1 0.16 H qL =− . After the appearance of a crack 2 H decreases to 0.98 qL , while 3 H slightly increases to ( ) 3 / 2.4 1.28 b h H qL = = and then decreases to 0.82 qL . The support reaction parameter 1 H qL increases to a value of 1.06 . For section 25/25cm, Fig. 5b), before the appearance of a crack, 2 6.15 H qL = , 3 4.37 H qL = and 1 0.61 H qL =− . After the appearance of a crack 2 H decreases to 4.66 qL , while 3 H slightly increases to ( ) 3 / 2.4 4.47 b h H qL = = and then decreases to 3.65 qL . The support reaction parameter 1 H qL increases to a value of 1.75. A comparison of the results of Fig.4 and Fig. 5 shows that as the modulus of elasticity of concrete increases, the support response H 1 increases while H 2 decreases. The support response H 3 is larger for higher concrete modulus until the crack opening around b/h=2.1 to 3, where there is an extremum and then decreases rapidly to values smaller than those before the crack opening.