Issue 74

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

Floor

Column

Beam

( α )=I b /I c

( β 2 )=L/h 2

Section (m)

I C (m 4 ) 0.02

h 2 (m)

Section (m) 0.7  0.7

I b (m 4 ) 0.02

L (m)

0.7  0.7

1 st to 6 th

3

6

1.0

2

Table 1. Geometric and mechanical properties of frame elements adopted for analytical validation.

T calculated (sec) (Eq.28)

m eq (KN.s 2 /m)

k eq (KN/m) 243810

ω (rad/sec)

T FEM (sec) 0.32

Error%

709.8 4% Table 2: The comparison between the fundamental period by the proposed equation with that calculated by FEM. By comparing the results, it was found that the value of the fundamental period obtained from the suggested equation has an error margin of 4% compared to the results from the FEM analysis. This indicates the validity of the derived conclusions and the equations used. Estimation of the fundamental period for a ten-story reinforced concrete frame with uniform member sections In this example, the comparison is conducted on a 10-storey frame, where the floor height for the first five stories is 3.5 meters, and for the remaining five stories, it is 3 meters as shown in Fig.9. The geometric dimensions of the element of the structure are given in Tab. 3. The simplifying process involved nine iterations to convert the building into an equivalent single-story structure. As shown in Tab. 4, the error margin using the equation is approximately 3%, confirming the accuracy of the proposed equation. It can be stated that the proposed formula produces results with high accuracy. 18.7 0.33

Figure 9 : Configuration of RC MRF building.

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