Issue 74

E. Sharaf et alii, Fracture and Structural Integrity, 74 (2025) 262-293; DOI: 10.3221/IGF-ESIS.74.17

A comparison of the equation's results is made using five different configurations in terms of beam-to-column cross sections. Each model has a different beam cross-section compared to the column cross-section; however, this difference remains consistent throughout the building's height, as shown in Tab. 6. The analysis of models in Tab.7 demonstrates that a reduction in the alpha coefficient value, which represents the beam-to column inertia ratio, results in a greater difference between the value derived from the proposed equation and the value calculated by FEM. When the alpha value was 0.14, the difference between the two values reached 10%. Therefore, a correction was made to the seismic mass coefficient to obtain the corrected ratio (f/f 0 ) as a function of alpha to achieve more accuracy. Fig. 12 shows the corrected seismic mass coefficient as a function of the alpha ratio used. To simplify the steps and obtain results quickly and with high accuracy, an equation was derived as a function of alpha to facilitate access to results faster and with higher accuracy, as stated in Eqn. (29).

Model number

1

2

3

4

5

Number of storeys

10

15

20

25

30

I b (m I c (m

0.0341 0.0341

0.0833 0.0833

0.02 0.02

1.33 1.33

1.33 1.33

4

)

4

)

L (m)

8.0

7.0

6.0

8.0

8.0

m eq (KN.s

2 /m)

3420

16140

32701.5 24099790

526309 24099790 12107600

1309360 24099790 14946270

E (KN/m 2 )

24099790

24099790

K eq (KN/m) (Eq.16)

371262 10.417

937408

684556

ω (rad/s)

7.62 0.82 0.78 5%

4.57 1.373 1.39

5.24

3.37 1.85 1.95

T(sec) (Eqn.28)

0.6

1.2 1.3 6%

T FEM (sec) Error (%)

0.57 5%

2% 5% Table 5: Accuracy assessment of the proposed period estimation formula for frames with varying numbers of storeys.

Figure 11 : Configuration of MRF concrete structures.

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