In buildings and civil engineering **structures**, initial local failure can result from the use of inappropriate material or system models, error in construction or excessive loading. They also can result from malevolent or accidental actions such as vehicle, ship or airplane impact; explosions resulting from gas leaks, terrorist attack; or impact and explosion from missile attacks. Environmental actions such as flooding, extreme wind or fire may also lead to local damage. A partial or total redistribution of loads in the structure will result after the occurrence of an initial local failure as the structure tries to reach a new state of equilibrium, relative to its new loading and support conditions. Failure of adjoining structural elements and connections will result if their load and deformation capacities are insufficient in this new state. Progression of damage up to a point where a state of equilibrium is satisfied is commonly referred to as **progressive** **collapse** (Mirzaei, 2010). If there exists a disproportion between the initial triggering event and the final state of the structure which violates defined performance objectives, a disproportionate **collapse** is said to have occurred (Starossek, 2009; DCLG, 2011). The insensitivity of building and civil engineering **structures** to initial local failure is a characteristic commonly referred to as structural robustness. It is a property, designers aim to incorporate into **structures** so as to minimize secondary structural damages (which can lead to **progressive** **collapse**) and other consequential losses which could result from an initial local damage triggering event.

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This paper presents an analytical model based on the Critical Shear Crack Theory which can be applied to ﬂ at slabs subjected to impact loading. This model is particularly useful for cases such as **progressive** **collapse** **analysis** and ﬂat **slab**-column connections subjected to an impulsive axial load in the column. The novelty of the approach is that it considers (a) the **dynamic** **punching** shear capacity and (b) the **dynamic** shear demand, both in terms of the **slab** deformation (**slab** rotation). The model considers in- ertial effects and material strain-rate effects although it is shown that the former has a more signiﬁcant effect. Moreover, the model allows a further physical understanding of the phenomena and it can be applied to different cases (slabs with and without transverse reinforcement) showing a good correlation with experimental data.

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(Mitchell and Cook, 1984) investigated the **response** of **slab** **structures** after initial failures due to **punching** shear and flexure. They presented analytical models for predicting **post**-failure **response** of slabs and the predictions were compared with existing experimental results. These models along with the experimental investigation enabled the development of simple design and detailing guidelines for bottom steel reinforcement which are capable of hanging the **slab** from the columns after failure. They concluded that the bottom bars which are well anchored and effectively continuous provide not only a means of preventing **progressive** **collapse** but also provide a means of preventing initiation of **punching** shear failure.

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Buildings are generally designed according to the design standards which usually consider dead, imposed, wind and earthquake loads etc. and their combinations. There are allowances for other loads, such as impact and explosion. Civil engineering **structures** can be subjected to loads due to natural disasters like earthquakes, hurricanes, tornadoes, floods, fires and man-made and artificial disasters, such as explosion and impact, during their lifetime. However, there are still circumstances that are unforeseeable at design stage. On the other hand, every project has a budget and engineers should meet the design requirements while producing an economical design within the allocated budget. The building will be **collapse** if one of the important structural members gets fail. Due to the failure of one structural member (local failure), the load on the other members in the vicinity of it increases and that member is going to fail if an increased load goes beyond the capacity of the member. Likewise, failure will transfer from one member to another which leads to **collapse** of the whole structure. Such type of failure of structure is known as **progressive** **collapse** or cascade failure.Xinzheng Lu and Kaiqi Lin (2016) [19] has studied that increasing the **slab** reinforcement by expanding the **slab** thickness marginally improved the **collapse** resistance under the catenary mechanism but contributed little to that under the beam mechanism. J M Russel, J S Owen and I Hajira (2015) [8] has studied that ultimate failure is **punching** shear failure of the corner columns. The **dynamic** **response** of the system is altered by force distribution and damage. Meng et al (2012)[11] has studied Demand to capacity ratios are calculated to check out the susceptibility of structure for **progressive** **collapse**. Finally, it is concluded that the GSA linear static **analysis** of the building has a low potential for **progressive** **collapse**. SewerynKokat et al (2012)[15]hasstudied the behavior of RC **flat** **slab** frame building under a **progressive** **collapse**. From the results of SAP linear **dynamic** **analysis**, it is observed that the structure would still be susceptible to the **progressive** **collapse** of the central column removal case but not necessarily for exterior column removal case. MengHao Tsai et al (2011)[12] has observed that if any one neglect panel type walls, then **collapse** resistance will be overestimated and wing type walls may bring less adverse effect on the building **response** under column losses.

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A nine story **reinforced** **concrete** building frame was selected for performing **progressive** **collapse** **analysis**. This **reinforced** **concrete** frame was a real building with slight modification to simplify the **analysis** and design process. The building has six spans in longer direction and three spans in shorter direction. The story height is 3.3m. The building plan is showing with dimension is given in figure 2. The beam sizes are (457mm x406mm), (457mm x457mm) and (635mm x457mm) and column sizes are (457mm x406mm) and (533mm x 533mm) are considered for the building. The walls having 115mm thickness is present on all the beams. The characteristics compressive strength of **concrete** (f c ´)

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further developed to speciﬁc constitutive **concrete** models. The popular models include disturbed stress ﬁeld model for **reinforced** **concrete** (Vecchio and Shim 2004) and micro- plane model (Bazant et al. 2000). For the numerical mod- elling, the fracture-plastic material model is selected in the research. The material models themselves differ mainly in the number of required input information on the **concrete**. The compressive strength and modulus of elasticity are insufﬁcient information. Typically it is necessary to deter- mine the **concrete** tensile strength and fracture-mechanical parameters where the basis for their determination can be found also in Model Code 2010 (2012). Certain information is provided also in ISO 2394 (1998) and JCSS (2016). The determination of material parameters are subject of many research projects. A particularly difﬁcult task is to deter- mine the **concrete** tensile strength (Sarfarazi et al. 2016). The results often show high spread of measured data. The latest advanced methods include identiﬁcation of material properties combining laboratory tests and inversion analy- ses with computers modelling using sophisticated algo- rithms. The methods comprise stochastic modelling, application of neuron networks, multiple-criteria decision **analysis**, etc.

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Shear wall 0.010373 0.001005 0.001004 CL wt. SW 0.010153 0.001012 0.001011 Similarly 10 15 storey buildings of regular plan and three types of modified buildings Lateral displacement were taken. By observing the drift of 5, 10, and 15, regular and irregular buildings some of the building models shows excessive drift which exudes IS code limit. The code allows limits the drift to 4% of the storey height only. And some are not cross the limit. Although hear all buildings are modified to bring the drift to lower level. They are altering the stiffness of the ground storey by increasing the size of the column. Lateral resisting forces is increased by providing **concrete** shear wall at the corner of the buildings. By this process all buildings shows least drift for different cases as compared to early stages. Hear we observe that in case of regular buildings it shows least drift for column modification with shear wall next shear wall provision finally for column modification it shows minimum liming of drift. For all irregular buildings re- entrant, vertical geometrical irregular, mass irregular and torsion irregular. Maximum drift can be controlled by providing shear wall at ground storey only. If you increase the stiffness of Colum with shear wall it will not alter anything. By increasing only the column stiffness small amount of drift reduction takes place.

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Specimen MB2 [18] was **reinforced** with No. 13 high strength bars like specimen MU2 [18] except that the reinforcing bars were banded together near the column. The reinforcement ratio in the band was 1.36% which is similar to MU1 (ρ=1.18%). It had been shown previously that slabs with a banded distribution of reinforcement have a higher **punching** shear strength than companion slabs with uniform reinforcing. The experimental results though show the opposite; the capacity of MU2 was higher than MB2. The authors contributed this irregularity to bond failure of the bars whereby the combined effect of closely spaced bars and the high strength over-stressed the **concrete** surrounding the bars and the bars subsequently de-bonded from the **concrete**. The authors proposed that this failure could be remedied with longer development lengths of the bars. The steel bar to **concrete** bond interaction is beyond the scope of this FEA model. Rather, this model assumes that the bars are properly detailed for development and assigns a ‘perfect’ bond between the two elements. Therefore, the results of this model show the load-deflection results that Yang et al. would have experienced if their **slab** did not fail

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Figure 12 presents the crack patterns at Stage 1 of the tests (SLS). Photos captured by the Aramis camera are superimposed with rendered images indicating the strains measured on the specimens. From these ren- dered images the crack patterns are clearly visible. The location of the major cracks in all four systems corresponds to the position and shape of the construction joint of the particular system used. All the specimens recorded one major crack of between 0.1 mm and 0.4 mm, with Model A recording the widest crack of 0.4 mm. This crack was observed on the rear side of the wall and is therefore not visible in Figure 12. Apart from this crack, all the other cracks fell within the general limit of 0.3 mm for **structures** exposed to a serviceability load (SANS 2000).

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strength of **concrete** slabs: 1- increasing the **slab** thickness in the vicinity of the column by providing a drop panel or a column head; 2- Providing shear reinforcement. Sometimes, after the construction of some building, the increase of **punching** shear resistance for **reinforced** **concrete** **slab**-column connection may be needed. The strengthening of **slab**-column connection against **punching** shear resistance by using traditional methods (steel plates, steel stirrups, steel studs, or increasing **concrete** dimensions) was studied [3-5]. Few studies concerned with using the FRP strengthening systems for **flat** slabs [6]. The present study aims to evaluate the using of FRP materials to increase the **punching** shear resistance of **concrete** **slab**-column. The values of **punching** shear strength were predicted taking into account the contribution of the applied strengthening systems. The calculated values were compared with the corresponding experimental results in order to evaluate the used equations.

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been a necessary in the recent past. The structural systems that are adopted world over, beam less **slab** type of construction is popular and getting into the veins of the builders due to the cost effective construction with respect to clearer distance, lesser utility usage and lesser height of the system for a given occupancy. However, the absence of the beams, in the system makes it vulnerable to lateral forces; both wind and seismic, but seismic forces by variable nature increases the vulnerability of the system.

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Figure 4.17 plots the vertical displacement of Node 11 over time, after its supporting column has been removed suddenly. Initially the displacement increases rapidly until a peak displacement of - 168.5 mm is reached at t = 64.9 ms. After this the structure recovers slightly and starts to vibrate harmonically about an equilibrium displacement of approximately -163.1 mm, where the amplitude of the vibration can be seen to gradually decrease with each cycle as damping takes effect. The degree of recovery observed after the first oscillation is dependent on the elasticity of the frame at that time. In this case, the beams in the central two bays of the structure have formed plastic hinges at their ends and have undergone significant irrecoverable permanent plastic deformations. This prevents the vertical displacement from reducing further. In a more elastic structure (i.e. where the permanent plastic deformations are significantly smaller), and after the initial load redistribution phase, the nonlinear **dynamic** **response** would vibrate about a lesser equilibrium displacement with greater amplitude. Comparing the peak vertical displacement predicted using nonlinear static and **dynamic** **analysis** illustrates the influence of **dynamic** effects in **progressive** **collapse** and highlights underestimated deformations computed using nonlinear static **analysis**. In this case, the peak vertical displacement predicted using nonlinear **dynamic** **analysis** (-168.5 mm) is more than three times that predicted using nonlinear static **analysis** (-50.9 mm). The horizontal displacement of Node 8 (computed using nonlinear **dynamic** **analysis**) follows a similar pattern to the vertical displacement at Node 11, reaching a peak of 4.30 mm at t = 65.1 ms and subsequently vibrating about an equilibrium position of circa 4.01 mm (Figure 4.18). As before, this displacement is underestimated by nonlinear static **analysis** which predicts a maximum horizontal displacement of 0.23 mm. Although these displacements are small, they have a notable influence on the magnitude of the internal forces in the connected members.

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It has been shown that Eq. (20) predicts the steel-**reinforced** **slab** test results in a better way than Design Codes with a smaller standard deviation [16]. Furthermore, Ospina et al (steel **slab** SR-1) [1] and Matthys and Taerwe (steel slabs R1, R1′, R2 and R3) [5], cast these steel reference slabs for comparison purposes to their FRP- **reinforced** slabs. Applying Eq. (20) (not shown here) to the above mentioned steel slabs one can find predicted-to-test strength ratios of 0.945 for **slab** SR-1 and 0.850 (on the mean) for slabs R1, R1′, R2 and R3. It is to be pointed out that these ratios are of comparable magnitude to those (on the mean) of the corresponding FRP-**reinforced** slabs of these researchers.

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Nonetheless, an abrupt increase of the axial load in vertical elements neighbouring an axially failing column takes place – in addition to potential increase of shear or deformation demands – and they ought to be checked in order to perform an accurate assessment of the ability of the structure to arrest **progressive** **collapse**. Xu & Ellingwood (2011) accounted for this via **considering** the potential buckling of neighbouring vertical elements in a design procedure against **progressive** **collapse** of steel buildings. However, only in one noteworthy study of R/C buildings has it been attempted to account for this effect, modelling shear and axial failure of the columns of an R/C frame building that were judged as the most critical based on preliminary analyses (Murray & Sasani, 2013). Their shear strength model could take the variation of axial load into consideration. Nonetheless, the **post**-peak shear strength degradation rate was assigned a value based on results from similar columns cycled under constant axial load, without **considering** the effect of axial load increase or decrease. Additionally, the onset and rate of axial strength degradation were also assumed based on past experimental results. Furthermore, although the structure was representative of older construction, the anchorage slip as well as shear deformations were not taken into account in the analyses. Naturally, the effect of vertical load redistribution can be readily taken into account using member-type elements that account for axial-flexure interaction, in the case of flexure-critical elements. However, this is not the case for shear or flexure-shear critical elements of older R/C **structures** – which are the focus of this thesis – modelled through beam-column models explicitly accounting for shear **response**, where this effect has not been modelled appropriately yet.

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rising number of multi-storey **reinforced** **concrete** (RC) buildings in the commercial districts of the country. It is important to investigate the seismic behavior of these multi- storey buildings especially those situated in high seismic regions. The effect of seismic forces on a structure vary depending on the selected load bearing system. Layout of the shear walls in the plan, selected floor system and structural irregularities affect the seismic performance of the structure **Flat** **slab** systems are commonly adopted for many buildings in Erbil city due to economic advantages over conventional **slab**. They also present some disadvantages as lack of resistance to lateral loads. Adding shear walls in **flat** **slab** buildings leads to improve their seismic performance especially in higher seismic zones. The main aim of this study is to investigate the seismic performance of purely **flat** **slab**, and **flat** **slab** with shear walls at five different locations. A five-storey residential building is analysed by using Equivalent Lateral Force Method (ELFM) using Extend Three Dimension **Analysis** of Building System (ETABS) software package as per Iraqi Seismic Code (ISC- 2017) in Erbil city. The results achieved from static **analysis** is presented in the form of horizontal displacement, base shear, time period and storey drift. Based on the **analysis**, the results show that the position of shear wall close to the center of the building gives the best performance.

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Full three-dimensional models including the impacting projectile are developed here. The **reinforced** **concrete** slabs are represented by solid elements for **concrete**, beam elements for bending and stirrup reinforcement (Figure 1). The impacting projectile is modelled by shell elements and the supporting bars between the **slab** and the supporting frame are modelled using solid elements. Eight-node hexahedron constant stress solid elements and two-node beam elements are used for the modelling. Slabs are represented by a mesh size of 15mm×15mm, where 20 elements are defined through the wall thickness (12.5mm thick).

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NLFEA is carried out using multi-layered shell elements and the PARC_CL 2.0 crack model (Belletti et al., 2017) implemented in Abaqus as a user subroutine. PARC_CL 2.0 crack model is a new release of previous models (PARC for monotonic loading (Belletti et al., 2001) and PARC_CL 1.0 for secant unloading (Belletti et al., 2013)), which is able to account for hysteretic loops and plastic deformations in the case of cyclic loading. PARC_CL 2.0 is total strain fixed, meaning that after cracking, the 1,2-coordinate system remains fixed at the integration point, Figure 2(a). The reinforcement is assumed to be smeared in the hosting **concrete** elements. Nonlinear stress –strain relationships for **concrete** and steel, multiaxial state of stress for **concrete** and aggregate interlock are considered. Since the PARC_CL 2.0 crack model is suit- able for a plane stress state, the thickness of the **slab** is subdi- vided into layers. Four Gauss integration points in the plane of the shell and three Simpson integration points in the thickness

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appealing solution. **Flat** slabs system of construction is one in which the beams used in the conventional methods of constructions are done away with. The **slab** directly rests on the column and load from the **slab** is directly transferred to the columns and then to the foundation. To support heavy loads the thickness of **slab** near the support with the column is increased and these are called drops, or columns are generally provided with enlarged heads called column heads or capitals.

MRV. After generating the value of an MRV, the values related to dierent members are generated by taking into account its specic median and standard deviation. The sensitivity of IDA outcomes (target variables, TVs) to the dened MRVs can now be comfortably assessed. In this regard, the MRVs are systematically perturbed several times following the Box-Wilson cen- tral composite design method [15] and the IDA process is performed each time. According to Box-Wilson method, the MRVs are perturbed from their median by either 1.7 or 1.2 times their standard deviation. The 1.7 coecient is used when all MRVs except the one being perturbed are set to their medians. The 1.2, on the other hand, is used when two or more MRVs are per- turbed simultaneously. The data points obtained for each TV using the sensitivity analyses are used, at the next step, for establishing polynomials that correlate the TVs to the MRVs through multivariate regression equations. The obtained polynomial established for a TV is called \**response** surface" and can reasonably substitute for the IDA for generating the TV values. A Monte Carlo simulation is used, next, for predicting the TVs corresponding to thousands of MRVs generated randomly. The random society generated in this way for the TVs is nally regarded for extracting proba- bilistic performance quantities in which modeling and Record-To-Record (RTR) uncertainties are combined.

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