PSI - Issue 66

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

441

9

5.2. Asymmetrical cross section The numerical results are calculated for beams with a trapezoidal cross-section, as shown in Figure 3b. The shape of the cross-section is tentatively adopted, to meet the asymmetric cross-section condition. The short base has a size equal to the height 25cm h = of the trapezoid, and the long base has a size of

1 2 1 5   × +    

(28)

.

h

The position of the support, in which the support reaction

1 H occurs, varies in the interval

(

) 38 60 72 120 h − −

  

   

h h

(29)

; 0

b z

= =

c

measured from the bottom edge of the beam.

h=25 cm

h=75 cm

-0,70 -0,20 0,30 0,80 1,30 1,80

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

H1/qL H2/qL H3/qL

H1/qL H2/qL H3/qL

H1/qL; H2/qL; H3/qL

1,9 H1/qL; H2/qL; H3/qL 2,2 2,7

3,5

4,8

7,8

1,9

2,2

2,7

3,5

4,8

7,7

20,7

h/b

20,1

h/b

a)

b)

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

Figure 6. The parameters of the three support reactions for a beam with asymmetrical cross-section and

25 /25 cm, calculated by Equations (22)–(24).

Figure 6 shows the variation in the parameters of the three support reactions, calculated by Equations (22)–(24), while the crack b6tween 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. 6a), before the appearance of a crack, 1 H

,

2 1.74 H qL = and

3 1.12 H qL = . H qL = ) 3 1.15

0.24

qL

=−

(

2 H decreases to 1.33 qL , while

3 H slightly increases to

After the appearance of a crack

/ b h

2.7

=

and then decreases to 0,95 qL . The support reaction parameter 25/25cm, Fig. 6b), before the appearance of a crack, 1 H =−

1 H qL increases to a value of 0.55 . For section

,

3 3.94 H qL = . After the

2 6.40 H qL = and

0.62

qL

(

)

2 H decreases to 5.65 qL , while

3 H slightly increases to

and then

appearance of a crack

/ b h

3.0

4.08 H qL =

=

3

1 H qL increases to a value of 0.69. For all sections H 1 there

decreases to 3.78 qL . The support reaction parameter

are values smaller than those of the other two support reactions, H 2 and H 3 .