Page 32 - Reinforced concrete voided slabs subjected to gravity and seismic actions

32Reinforced concrete voided slabs subjected to gravity and seismic actionsFigure 1.26. Example of a section of voided slab with U-Boot Beton® truncated pyramid-shaped elements1.4. Modelling: structural theoriesBelow are described two classic structural theories for analysis of the slab systems: the Kirchhoff isotropic continuous slab model and a discrete equivalent model.1.4.1. Kirchhoff slabAttention is focused on the response of the slab under vertical loads with different peri- meter conditions, constraints, forces and torques applied . It is assumed it is possible not to consider shear deformations. Only the flexural behaviour is considered as the bending and membrane problems are uncoupled under the assumption of small displacements and symmetry of construction in relation to the middle plane of the slab.1.4.1.1. Calculation AssumptionThe following calculation assumptions are formulated:• small displacements and deformations;• decoupling between bending and membrane problem (symmetry of the slab in rela-tion to the middle surface);• negligible shear deformation ;• linear, homogeneous and isotropic elastic material;• normal forces on the middle surface negligible.1.4.1.2. Kinematic modelConsider a flat floor of consistent thickness, h. The position of a generic point of the struc- ture can be conveniently described in a Cartesian reference (O, x, y, z) defined in such a way that the axes (x, y) lie on the middle plane (see figure 1.27).U-Boot Beton® fillersIntegrative reinforcement 3Ø16 in the x and y directionDistributed reinforcement Ø8/20x20cmup © Dalifoform Group © Daliform Grouup © Daliform Group © Daliform Group © Dalifoform Group © Daliform Group © Daliform Group © Daliform Grouup © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Dalifoform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Grouup © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Dalifoform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Grouup © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Dalifo form Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Grou© Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Dalifo iform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Grouup © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Daliform Group © Dalifo form Group © Daliform Group © Daliform Group © Daliform Group © Daliform Grouup © Daliform Group © Daliform Group © Daliform Group © Dalifoform Group © Daliform Group © Daliform Grouup © Daliform Group © Dalif form Grou