## Test, Numerical Model, and Validation of Reinforced Concrete (RC) Waffle-Flat-Plate (WFP) Structure
### Numerical Model of the WFP Structure  
A 3-D numerical model representing the specimen with the shake-table was built in OpenSees v2.5.0. rev 6477 [24]. The model is made up of 1802 nodes and 1810 elements. Columns proved to be the critical elements in the numerical model, since they exhibited the largest non-linear behavior during tests and governed the overall response of the structure. RC columns were modeled using non-linear frame elements. The material properties described in reference [7] were used. The frame element comprises three parts: the two end parts are lumped plastic hinges, while the central part uses fiber elements. The length of the end parts is determined by the plastic hinge length, \(l_{p}\), which is taken here as the depth of the transverse section, i.e., \(l_{p}=160\) mm according to ACI 318M-14 [3]. As for the fiber elements, the transverse section is discretized by a grid of 2x2 mm fibers of concrete, which are replaced by steel when they are occupied by rebars. In addition, the hysteretic behavior of the concrete was defined through the parametric model proposed in [25], adapted to the constitutive model proposed in [26]. For the steel rebars, the Giuffre-Menegotto-Pinto model with isoparametric strain hardening was used. The non-linear behavior of the plastic hinges is characterized by means of the moment-curvature backbone curve, i.e., \(M\)-\(\varphi\), and the corresponding hysteretic law in each main direction. The \(M\)-\(\varphi\) curve is defined by yield moment, \(M_{y}\), and the yield and ultimate curvatures, \(\varphi_{y}\) and \(\varphi_{u}\). \(M_{y}\) was estimated using the empirical expression proposed by [PERSON] [4] with a reduction of 20% to account for the biaxial cyclic loading-interaction factor [27; 28]. First, \(\varphi_{y}\) and \(\varphi_{u}\) were calculated as \(\varphi_{y}\)=\(\theta_{y}\)/\(l_{p}\) and \(\varphi_{u}=\theta_{u}\)/\(l_{p}\), where \(\theta_{y}\) and \(\theta_{u}\) are the yielding and ultimate rotation obtained with empirical formulae [4]. Next, these initial values were modified to fit the results obtained from the tests. The stiffness degradation implemented in the hysteretic law was based on the study carried out by [PERSON] et al. [27]. The waffle-flat-plate is formed by a grid of ribs and solid zones around the columns. The grid of ribs, whose transverse section is shown in Figure 1, was modeled with elastic frame elements having a 20% reduction of the initial elastic stiffness to account for cracking. The solid zones were modeled through shell elements measuring, on average, 42x42 mm; these shell elements support geometric non-linearity. In order to reduce the computational time, non-linearity was adopted only for the shell elements of certain parts of the solid zones around the columns, those showing damage in the test. Shell elements were defined through multilayer shell sections with a total of nine layers. The thickness of each layer depends on the existence (or not) of reinforcement. Rebars at the top and the bottom of the plate cross-section were considered as smeared steel layers of equivalent thicknesses, one in each reinforcement direction. Therefore, complete reinforcement entails four smeared steel layers, two for the upper part and two for the lower. The remaining layers are made up of concrete of variable thickness. The solid zones around the columns were subdivided into different parts according to the heterogeneous distribution of the reinforcement (Figure 2). The constitutive model used for concrete is based on the concept of damage mechanics and the smeared crack model. Cracks are assumed to form when the principal tensile stress exceeds the specified concrete tensile strength. After cracking, concrete is treated as an orthotropic material by smearing the cracks in the finite element. The properties of reinforcing steel are derived from the uniaxial materials for rebars in accordance with the corresponding angles of the steel layer in the model.