CARACTERÍSTICAS DE LA PROVIDENCIA CAUTELAR

The approach adopted in the analytical modelling of asymmetric post-punching shear response was similar to that adopted for modelling symmetric cases. Modelling asymmetric post-punching shear response analytically was carried out by considering four sectors projected from each column face. Behaviour of each sector differed at various phases of the connection’s response, hence, their contributions to the post-punching shear resistance were also considered to vary. This variation was modelled analytically taking into consideration the shape of the post-punching shear cone and the application of a displacement factors at each side of the column face.

At the critical face (Figure 3.13) a single inclination surface was adopted for the punching shear cone, with an inclination angle of 45o (instead of 35o for conventional cases). This was to simulate the enhanced activation of flexural and integrity reinforcement during the post- punching phase. The angle of inclination for the other faces were as adopted in the symmetric assessment (i.e. 35o_).

Displacement factors were also applied in summation of the contribution of the various sectors to post-punching shear resistance. Average displacement factors of 0.65 and 0.75, for the opposite and adjacent sides respectively were again adopted for the purpose of compatibility of

the various slab sectors (see Section 3.2.3). Varying the slab displacement factors applied to each side of column face also allowed for the early activation of post-punching shear on the critical side of the connection relative to others. The sum of the post-punching resistance of flexural and integrity reinforcements from the various sectors gave the total post-punching shear resistance of the slab.

Figure 3.37: Asymmetric PM4: Load

displacement curve- Analytical

Figure 3.38: Asymmetric PM12: Load displacement curve- Analytical

The post-punching load-displacement curves were obtained analytically for the asymmetric response based on specimens PM4 and PM12. Analytical asymmetric responses were close to those obtained numerically as shown in Figure 3.37 and Figure 3.18. Though the drop in post- punching shear resistance, after fracture of integrity reinforcement (Figure 3.37) at the critical side of specimen PM12 was more pronounced in the numerical model than it was the analytical, numerical post-punching capacity rose to within a 10.5% difference from the analytical value at the end of the analysis. This confirmed the suitability of the analytical approach for the modelling of asymmetric post-punching shear response. Asymmetric post-punching tests are not available in the literature and further validation of the proposed approach with test data would be an area of future work to confirm these results. However, the consistent numerical and analytical predictions provide some confidence on the main findings obtained.

3.4

Conclusions

Chapter three of this thesis assessed numerically cases of symmetric and asymmetric post- punching shear responses of slab-column connections. It extended existing analytical models for prediction of symmetric response to take into consideration the activation and deactivation of flexural reinforcement. It also proposed an approach through which the progressive destruction of concrete around reinforcement connecting the slab to the punching shear cone was the basis for calculation of shear transferred to the column and the slab displacement during post- punching. lab connection after punching shear. The analytical model developed was also extended to cases of asymmetric post-punching shear failure. These strength parameters obtained analytically included the residual shear strength after punching as well as peak post punching shear strength. These parameters are relevant as they influence redistribution of gravity loads after local damage of slab-column connections in flat slab structures.

Results from numerical modelling gave predictions of punching shear capacity for the various specimens with percentage differences between 0.03 and 2 percent from results of tests found in literature. Residual shear strengths after punching gave percentage differences between 0.03 and 21 percent, while peak post-punching shear strength gave percentage differences between 0.03 and 3 percent. In tests PM9 and PM10, numerical simulations predicted the fracture of some integrity reinforcements which were as reported in tests. Asymmetric FE models gave post- punching shear strength values lower than those obtained in symmetric models whereas the residual shear strengths immediately after punching were higher. The numerical approaches are extended to flat slab system analysis in Chapter 4.

Results from analytical modelling gave predictions of peak post punching shear strength with differences between 0.062% and 19.3% from test results. Results obtained analytically such as the residual shear strength after punching, as well as overall connection post-punching response

were also adequate. Extension of the analytical models developed to asymmetric cases of post- punching was considered analytically through the shape of the punching shear cone and variations in slab displacements around the four sides of the connections. This led to early activation of post-punching mechanism at the opposite side and higher values of residual shear strength after punching. During asymmetric post-punching, difference in the angle of inclination of the punching shear cone also leads to variations in the number of flexural rebar activated (𝑛_{𝑏𝑟𝑒𝑎𝑘}), due to reductions in the width of the punching shear cone (𝑏_{𝑓𝑙𝑒𝑥}). This generally led to lower values of peak post-punching shear strength during the non-symmetric response. Values of residual strength after punching and peak post-punching shear strength obtained numerically agreed with those obtained analytically. The proposed analytical model for post-punching is applied in Chapter 5 and Chapter 6.

Numerical modelling of slab-column subsystem

and flat slab system

4.1 Introduction

Flat slab systems tend to respond differently from isolated slab specimens assumed in tests. These differences in response are due to continuity characteristics of flat slab systems. Continuity leads to higher values of strength and stiffness at flat slab connections (Jurgen Einpaul, 2016). Compressive membrane action develops internally within a continuous flat slab system due to the horizontal restraint provided by the slab and its supporting members, leading to an increase in strength and flexural stiffness.

Redistribution of gravity loads occur after the total or partial loss of capacity of a vertical load bearing member (i.e. columns or slab-column connections). Such member loss could be due to punching shear around the connection resulting from over loading, explosion or impact leading to column loss, or any other form of malevolent or accidental event. Due to numerous possibilities of malevolent and accident events, event independent scenarios such as the sudden column removal scenario, are adopted in structural robustness design.

Sudden loss of vertical load bearing members tends to initiate a dynamic response in adjoining supports as well as the overall system. This dynamic effect is due to the sudden redistribution of gravity loads to adjoining connections as well as the sudden change in deformed shape as the structure tries to attain a new state of equilibrium through the activation of velocities and accelerations. Hence, there is a need to adequately model the dynamic response of slab-column connections to assess potential progressive collapse of flat slab structures.

This chapter aims to develop a novel numerical approach to model flat slab systems using a combination of solid and shell elements. Slab-column connections will be modelled explicitly using solid (for concrete) and beam (for reinforcement) elements, as presented in Chapter 3 for static cases, to effectively simulate flexural, punching shear and post-punching shear responses. Numerical models of slab-column connections will be validated for dynamic load scenarios

using test cases available in literature. Models of slab-column connections will be incorporated into a flat slab system model and assessed based on a sudden column removal scenario. The analyses will be carried out using permanent, quasi-permanent and frequent load combinations of the Eurocode 1 (CEN, 2010b). The numerical approach developed predicts the response of flat slab systems after the sudden loss of an internal column while taking into the account and investigating the various load actions, their interactions and dynamic effects. The numerical approach developed will also serve as a basis for the verification of the analytical approaches, for slab-column connection subsystem and flat slab system presented in Chapter 5 of this Thesis.