This section provides an overview of the different results taken from the models . De- tails of how each value was obtained and its uses are stated.
6.4.1 Displacement values
During every simulation, vertical displacements were monitored for the slab. In each case these were normalised against the slab thickness to allow comparison between different arrangements. For the static push down tests, the displacement values were recorded as the loading was increased, primarily at the column loss location, but also in the middle of nearby bays. This provides information into the extent of damage that is occurring due to the lost support, as well as considering how much of the structure is affected by the removal.
For the dynamic loss situation, the normalised displacement against time was recorded at the column loss location. This was sampled at 250Hz, as was used in previous simu- lations. This rate ensures that the sudden changes immediately after a column loss are captured. As well as comparing the maximum deflection between models, a Fourier Transform of the displacement-time response provides the frequency of oscillation for the model, which can be compared to the results from a modal analysis. As the modal analysis is based on the elastic response, the difference in oscillation frequency is due to a reduction in stiffness. Additionally, as the major energy dissipation method speci- fied is based on the plasticity and damage of the concrete, included in the CDP model, and from yielding of the reinforcement, the damping ratio can be extracted from the response. Both these results provide an indication into the level of damage that the slab has undergone.
6.4.2 Reaction forces
All the nodes at the base of each column were restrained vertically, and the reaction forces for these locations were recorded throughout the analysis. For static analyses, that is the static push down condition and the pre-load for the dynamic, the sum of the reactions were taken at each load increment for each column. Similarly, after the column was removed dynamically, the sum of the reaction forces was recorded against time. This method provides the total vertical force transmitted via that column, but does not account for the moment effect. As only a single floor is considered, this force represents the shear force that is transferred around the slab-column connection. How-
CHAPTER6: PARAMETERSTUDY ONDIFFERENTFLOORVARIABLES
ever, the shear stresses required for assessing punching shear failure are dependant also on the transfer of bending moments into the column. Due to the construction of the model, these values could not be accurately determined and therefore an exact de- scription of the potential of failure cannot be specified. Despite this limitation, a strong indication into the areas that may be susceptible to such failures can be determined by considering the change in vertical force demand at that support. This is achieved by taking the vertical reaction while the model is fully supported and carrying load wac.
The reaction forces after a column loss can then be expressed as a percentage of this value, less than 100% indicates that demand has reduced for that column. However, anything over 100% should be considered carefully for progressive shear failure as the column loss event has increased the shear force at that location and may now exceed the designed capacity.
6.4.3 Steel strain rates
In order to assess the influence of strain rate effects in changing the material properties of the concrete after a dynamic column loss, the strain rates in the steel reinforcement were recorded with time. While the strains in the concrete will be slightly different from the steel, the large number of concrete elements are more computationally demanding to monitor and will be of the same order of magnitude as the steel rates. At every sampled time step, the maximum strain rate in the steel is recorded, this provides an indication into the most critical values, and an upper bound for a DIF of the tensile strength of concrete.
6.4.4 Tensile damage to the concrete
The most common form of damage that RC structures experience is flexural cracking of the concrete, and therefore should be suitably considered. The CDP model used, described in Section 4.3.1, represents cracks as a region of plastic deformation and as a region with reduced elastic stiffness according to its damage index. During the static loading the regions of the concrete that undergo tensile failure, due to the increased hogging and sagging moment demand on surrounding supports and midspans respec- tively, can be visualised indicating the progression of cracks. This highlights how much of the structure is affected by the column loss and regions that may be susceptible to flexural failure.
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6.4.5 Fundamental frequencies
A modal analysis of each model was conducted. This was based on the elastic proper- ties of the structure after the relevant column has been removed, and includes the load, and associated mass, from the accidental load case, wac from Equation 6.2.5. The ad-
ditional mass from imposed loading was applied as a uniformly distributed nonstruc- tural mass to the concrete elements, in the same manner described in Section 4.2.6. As the modal analysis provides the fundamental frequency of the linear elastic, undam- aged structure, comparisons to the frequency of oscillation during the dynamic analysis gives an indication into the reduction in stiffness, due to concrete or steel damage.