PSI - Issue 79

Albena Doicheva et al. / Procedia Structural Integrity 79 (2026) 370–378

374









for cross section 30/30 cm,

for cross section 75/75 cm and

2 3 10,05 cm 5 16 А N  

2 29,11 cm 10 16 N

A

A

А  

2

2

3

represent the areas of the bottom and top reinforcement for two sections, and the moduli of

3 39,000 kN / cm

E Е  

2

2

elasticity, respectively; 3cm e  — the cover of the reinforcement; 200cm L  — the length of the beam; 2 1 1700kN/ cm E  — the modulus of elasticity for normal concrete and

2 1 4200kN/ cm E  for high-strength

concrete;

1 1   — multiplier for reduced tensile/compressive stiffness of the concrete section; 2 1   and 3 1   — multiplier for reduced tensile/compressive stiffness of the reinforcing bars; 0.05 kN/cm' q  — for all numerical results on section 5. The distance   cm b varies in the interval   , 0 C z and is monitored by the ratio / h b .

h=75 cm

h=30 cm

-0,20 0,00 0,20 0,40 0,60 0,80 1,00 1,20

-0,50 0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50

H1/(qL/2) H2/(qL/2) H3/(qL/2)

H1/(qL/2) H2/(qL/2) H3/(qL/2)

H1/qL/2; H2/qL/2; H3/qL/2

H1/qL/2; H2/qL/2; H3/qL/2

1,9

2,3

3,0

4,4

7,7

1,9

2,2

2,7

3,5

4,8

7,8

h/b

h/b

34,0

20,7

a)

b)

2 1 1700kN/cm E  ; a) 75/75 cm; b)

Figure 3. The parameters of the three support reactions for a beam with asymmetrical cross-section and

30/30 cm, calculated by Equations (5) – (7).

Figure 3 shows the variation in the parameters of the three support reactions, calculated by Equations (5) – (7), 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. 3a), before the appearance of a crack, 2 1.08 /2 H qL  , 3 0.84 /2 H qL  and 1 0.11 /2 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 0.45 /2 qL , while 3 H slightly increases to   3 / 2.1 0.85 / 2 b h H qL   and then decreases to 0.41 /2 qL . The support reaction parameter 1 ( /2) H qL increases to a value of 0.98 /2 qL . For section 30/30cm, Fig. 3b), before the appearance of a crack, 2 3.21 /2 H qL  , 3 2.27 /2 H qL  and 1 0.37 /2 H qL  . After the appearance of a crack 2 H decreases to 2.01 /2 qL , while 3 H slightly increases to   3 / 2.3 2.34 / 2 b h H qL   and then decreases to 1.67 /2 qL . The support reaction parameter 1 /2 H qL increases to a value of 1.48.

h=30 cm

h=75 cm

-0,50 0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50

-0,10 0,40 0,90 1,40 1,90

H1/(qL/2) H2/(qL/2) H3/(qL/2)

H1/(qL/2) H2/(qL/2) H3/(qL/2)

H1/P; H2/P; H3/P

1,9

2,2

2,7

3,5

4,8

7,8

1,9

2,3

3,0

4,4

7,7

20,7

h/b

H1/qL/2; H2/qL/2; H3/qL/2 h/b

34,0

a)

b)

2 1 4200kN/cm E  ; a) 75/75 cm; b)

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

30/30 cm, calculated by Equations (5) – (7).

Figure 4 shows the variation in the parameters of the three support reactions, calculated by Equations (5) – (7), while the crack between the beam and the column grows, and 2 1 4200kN/cm E  . A comparison of the results of Fig.3 and