PSI - Issue 78

Alessandro Pisapia et al. / Procedia Structural Integrity 78 (2026) 568–575

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(a) (b) Fig. 4. Influence of the in-plane flexural stiffness on the seismic effects in the case of four vertical frames: Lateral support (a); Central support (b) 3. Validation of the theoretical model In order to evaluate the accuracy of the theoretical model described in the previous section, a numerical model was developed using SAP 2000 software. Specifically, a one-storey three-dimensional structural scheme was modeled, where beams and columns were modelled by beam elements , while the floor diaphragm was modelled by shell elements. All elements are in reinforced concrete with an elastic modulus equal to 31000 and a Poisson ratio equal to 0.20 . The beams have a cross-section of 30x40 , and the floor system consists of a =40 thick reinforced concrete slab. Regarding the column section, the width was set at 30 , while their height was varied in order to modify the lateral stiffness of the vertical frames, and consequently the value of the non-dimensional stiffness parameter .The load was applied to the shell elements of the floor diaphragm and set to 7.50 / 2 . According to the scheme shown in Fig. 5, the depth of the diaphragm was set to = 4.00 , the span between the vertical frames is = 6.00 and the height of the columns is equal to =3.00 . Moreover, by considering that: = 3 12 ; = (5) Moreover, in this case, the shear factor =6/5 and taking into account that = /2(1+ ) , the parameter is equal to: = (1+ 5 ) � � 2 =1.067×10 −1 (6) In order to apply the Eqs. (2) and (3), it is necessary to compute the lateral stiffness of the vertical frames. Generally, it is possible to estimate the horizontal stiffness directly by means of SAP 2000. In fact, according to Fig.6, the stiffness is equal to: = (7) where is the horizontal force and represents the horizontal displacement. As an alternative, the following closed-form relationship can be applied: = 6 3 � 1+6 2+3 � (8) where: = / / (9) where and are the inertia moduli of the column and beam, respectively.