Issue 74

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

Figure 2: Equivalent cantilever column.

Figure 3: Configuration of MRF with simplification procedures. To develop the shear stiffness matrix of the two-storey MRF, considering the stiffness of the beams and anti-symmetry, the flexibility matrix is developed first by applying two horizontal forces separately and calculating the horizontal deformations. The stiffness matrix of the frame due to translational and rotational degrees of freedom takes the form:

EIc

EIc

EIc

EIc

EIc

EIc

24

24

12

12

24

12

           

           

1

2

1

2

2

2









3

3

2

2

3

3

h

h

h

h

h

h

1

2

1

2

2

2

EIc

EIc

8 EIb EIc

EIc

EIc

EIc

12

12

8

8

12

4

1

2

1

2

1

2

2







2

2

2

L h

h

h

h

h

h

2

1

2

1

2

2

(8)

K=

EIc

EIc

EIc

EIc

24

12

24

12

2

2

2

2



3

2

3

2

h

h

h

h

2

2

2

2

EIc

EIc

EIc

8 EIb EIc

12

4

12

8

2

2

2

2

2





3

2

h

L h

h

h

2

2

2

2

To obtain the flexibility matrix, the horizontal deformations due to horizontal unit forces are obtained as follows:

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