PSI - Issue 78

Franco Braga et al. / Procedia Structural Integrity 78 (2026) 285–292

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where: • α is the degree of interlocking at the level of each deck ( α is 12 for shear type frames, 10 for frames with emerging beams, 6 for frames with thick beams, 3 for columns without beams); • E c is the modulus of elasticity of concrete; • I is the moment of inertia of the square section of the column considered, equal around X and around Y; • h int is the storey height. The cross-section of the pillars, as already mentioned assumed to be square (to simplify processing), was assumed to be equal to the ratio between the axial load and a reference tension f cp = 7 MPa which, for the Italian standards prior to O.P.C.M. n. 3274/2003, was approximately equal to half the calculation resistance of the concrete in current use. Since the expected stresses on the slab are the greater the greater the difference in stiffness between the columns, the stresses on the slab were evaluated on the end of the slab, the part indicated as "Block 1" in ( Fig.2 a) because, as is the case for almost all existing buildings designed prior to 2003, the year in which the first Italian regulations came into force which envisaged criteria for the hierarchy of resistances, the edge columns (alignment 1) are expected to have a significantly smaller cross-section than the internal columns (alignment 2).

Fig.2 . (a) Identification of block 1, (b) forces acting on block 1.

The slab stresses were evaluated in the initial unformed configuration, based on the system of forces acting on block 1 shown in Fig.2 b. Therefore, the following were considered • the force F corresponding to the seismic action; • the forces transmitted by the lower floor columns V pi and upper floor columns V ps ; • the force V representing the shear action induced on "block 1" by the part of the floor outside "block 1". By imposing the equilibrium of forces in the direction Y V+V =F+V (2) we obtain V=F − V +V (3) Among the calculation assumptions, it should also be noted that: • the moment T∙DX, which guarantees the equilibrium of block 1, is supported by the edge beams, a likely hypothesis, especially in the case of a floor with an unreinforced slab, since the only elements capable of resisting the traction T are the beams themselves, since they are provided with longitudinal reinforcement;