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In this project phase, the behavior of elements resisting combined blast and fragment loading was studied further both in regard to reinforced concrete and sandwich structures. Firstly, a further study was conducted on reinforced concrete slabs. In this case, the residual capacity was calculated on the basis of fixed support conditions, as these would be more common in practical designs. The results of this study were then used to derive a single degree of freedom model which could describe the behavior of the slabs accounting for the projectile damage. Following this, the behavior of the sandwich and purely steel panels was studied further, repeating the quasi static tests performed on them in the past with a higher loading limit. Finally, additional impact tests were performed on sandwich panels to consider the effects of a different projectile shape.

This document mostly reports on the efforts to determine whether the steel and sandwich structures were affected by the combined blast and fragment loading to the same extent as was seen for the RC structures. Of especial importance was to determine whether the impacts, besides transmitting significant momentum to the system, also affected its overall stiffness and capacity due to the localized damage. To achieve this, blast tests and quasi static tests were performed and modeled.

In this context, it was decided to consider the performance of steel vertical structures, composed of several steel universal beam (UB) sections welded together, with additional protective steel plates on each face. Additionally, a steel-concrete sandwich panel type was also included. It was decided that they would be included in the study to assess their performance with realistic charges. To fully consider the behaviour of these structures and to inform modelling techniques to be used to facilitate their design, it was decided to conduct a series of experiments, including both impact and blast tests. These would then be used to validate detailed numerical models, with a special attention to developing blast tests prediction capabilities.

Real design scenarios are likely to differ in several respects from the analysed situations. One of these is the boundary condition. In the cases considered previously, the slabs were always simulated as simply supported, since this was the condition generally used during the tests. In realistic structures it is more likely that the concrete elements will have fixed boundary conditions, as these better represent the reinforcement ties generally included in design. Additionally, lower stand-offs and more concentrated fragment distributions are also likely to be required when design conditions are determined. Therefore, it was decided that the ability of modelling such different situations was an important parameter to assess the capability of the modelling method developed.

The residual capacity of structural elements after they are damaged by explosions or other catastrophic events is an important parameter in the design of structures. This is especially the case for key defensive elements, which need to be able to satisfy their original function though they might be targeted specifically.

Very low stand-off explosions of real ammunition can produce significant amounts of shrapnel, which will be propelled at high velocities onto structures. The impact of these fragments can represent a significant loading of structural elements, and its effects will be compounded to the damage caused by the blast shock wave. Therefore, designing structures to resist low stand-off blast loads requires an understanding of these combined phenomena to ensure that the proposed solutions will provide the desired level of protection in an efficient and cost effective manner.

In this study, experiments were carried out to investigate the influence of welding on the strength of high performance steels including the reheated, quenched and tempered (RQT) high strength steel in grade S690 and thermos-mechanically controlled processed (TMCP) normal strength steel in grade S385. Firstly, a special welding program was designed and performed on the RQT and TMCP steel plates to induce welding heat input to the materials. These welding affected plates were subsequently fabricated into smaller specimens for tensile test and metallurgical examination including microstructure observation and Vickers hardness test. Secondly, two T-stub joints made of these two material were manufactured and tested in tension. By comparing the first yield resistances of the T-stub specimens and the design plastic resistances obtained by using equations provided by EC3, the strength of the high performance steel T-stub joints are evaluated. The results showed that welding softened the heat affected zone (HAZ) of S690 high strength steel significantly but its effect on the normal strength steel S385 was insignificant. Accepted version

When analyzing reinforced concrete (RC) framed structures under monotonic loading—for example, progressive collapse and pushover analysis—besides flexural deformation, the so-called “fixed end” rotations induced by longitudinal bar slips at the beamcolumn ends connected to the joints can be significant and may result in additional vertical deformations not accounted for in the conventional analysis. Hence, it is important to quantify the deformations arising from the fixed end rotations. In this paper, shortcomings of existing bond stress-slip models are discussed in terms of application limitation and prediction accuracy. A new analytical model based on the bond stress integration along the bar stress propagation length is proposed to predict the bar-slip behavior in RC beam-column joints under monotonic loading. The phenomena of combined axial pullout and transverse dowel action at the joints are considered. The proposed model is validated with experimental studies from published literature and is shown to be simple, yet reliable. Published version

A high gradient of displacement field occurs when a yield line is formed in a plate with elasto-plastic material. For such applications, the Extended Finite Element Method (XFEM) has shown to be an effective numerical method to capture the behavior of a plate with a locally non-smooth displacement field, as well as a displacement field with a high gradient. In this article, a 6-node isoparametric plate element with XFEM formulation is presented to capture the elasto-plastic behavior of a plate in small-deformation analyses. The Hermite function is adopted at the element level to enrich both the translational and the rotational displacement approximation fields so that non-smoothness in displacement fields near a yield line can be simulated. Accepted version

In Part 1 of this study, an experimental investigation on the residual stress distributions near the weld toe of high strength steel box section T-joints is conducted. Two specimens fabricated by welding at ambient temperature and at a preheating temperature of 100°C were studied. The effects of preheating on the residual stress distribution near the weld toe of the T-joints were investigated by applying the standard ASTM hole-drilling method. A study was also conducted to evaluate the corner effect of the welding and the brace-to-chord width ratio of the box section T-joint on the residual stress distribution near the weld toe of the T-joint. Accepted version

A high gradient zone (HGZ) comes into existence in both rotation and deflection displacement fields in the vicinity of a yield line in a plate structure with elasto-plastic material. This HGZ makes the displacements non-smooth locally around the yield line. The Extended Finite Element Method (XFEM) has been proved to be an effective numerical method to capture the behavior of a structure with a locally non-smooth displacement field. In this article, a 6-node triangular and a 9-node quadrilateral Mindlin-Reissner plate element with the XFEM formulation are presented to trace the elasto-plastic behavior of a plate in small-deformation analyses. Regularized enrichments are employed to enrich the rotation and the deflection displacement approximation fields simultaneously so that the non-smoothness in a displacement field near a yield line can be captured. The discrete shear gap method (DSG) is adopted to alleviate shear locking phenomena in the present XFEM plate element. Several plate bending examples are simulated to show the robustness of the enrichment in capture the high gradient zone resulted from yield lines and the effectiveness of the application of DSG method in controlling the shear locking in the XFEM plate element. Accepted version

In the second part of this study, the reliability of the geometrical models and the mesh generation procedure developed in Part 1 are validated by comparing the modelling results with full scale tests results. Static tests were applied to study the stress concentration factors while fatigue tests were applied to study the stress intensity factor and the fatigue life of the joints. The results obtained indicated that the uncracked joint model could lead to reliable stress concentration factor estimations while the cracked joint models could lead to conservative stress intensity factor and residual fatigue life predictions close to experimental results. Accepted version

In this study, an adaptive refinement procedure using the element free Galerkin method (EFGM) for the solution of 2D elastostatic problem is suggested. This refinement procedure is based on the well-known Zienkiewicz and Zhu (Z–Z) error estimator for the a posteriori error estimation and a simple point refinement scheme for new point mesh generation. The presentation of the work is divided into two parts. In Part I, concentration will be paid on the stress recovery and the a posteriori error estimation processes for the EFGM. A comprehensive study on the theories and natures of some commonly used recovery schemes for the EFGM is given. The essential features and relationships among the studied recovery schemes are highlighted. It will be demonstrated that all these recovery schemes are particular cases of a general recovery scheme called the weighed continuous moving-least-square over stationary least square (MLS-SLS) recovery scheme. A numerical experience has also been carried out to study the performances of a number of different MLS-SLS recovery procedures generated by applying different fitting parameters to the continuous MLS-SLS recovery scheme. In Part II of the study, attention will be focused on the mesh refinement and the development of the adaptive algorithms for the proposed automatic adaptive EFGM procedure. Accepted version

In this paper, an adaptive refinement procedure using the element free Galerkin method (EFGM) for the solution of 2D linear elastostatic problems is suggested. Based on the numerical experiments done in Part I of the current study, in the proposed adaptive refinement scheme, the Zienkiewicz and Zhu (Z-Z) error estimator using the TBelytschko (TB) stress recovery scheme is employed for the a posteriori error estimation of EFGM solution. By considering the a priori convergence rate of the EFGM solution and the estimated error norm, an adaptive refinement strategy for the determination of optimal node spacing is proposed. A simple point mesh generation scheme using pre-defined templates to generate new nodes inside the integration cells for adaptive refinement is also developed. The performance of the suggested refinement procedure is tested by using it to solve several benchmark problems. Numerical results obtained indicate that the suggested procedure can lead to the generation of nearly optimal meshes and the effects of singular points inside the problem domain are largely eliminated. The optimal convergence rate of the EFGM analysis is restored and the effectivity indices of the Z-Z error estimator are converging towards the ideal value of unity as the meshes are refined. Accepted version

This report is written in the form similar to a conference proceeding. It discussed the three dimensional finite element modelling of reinforced concrete structures.

This report discussed the numerical simulation & experimental verification of structural responses. RGM 9/01

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Due to increasing threats from terrorism in the past decades, progressive collapse modeling of buildings is gaining popularity with objective of simulating collapse process of the whole or partial structural system, in order to give useful insight to improve existing design for the structure against progressive collapse. In this thesis, a novel modeling framework for progressive collapse of reinforced concrete (RC) frame structures is proposed. A set of damage assessment criteria to identify and quantify flexural, shear and axial damages and failures of RC members is suggested. This set of damage criteria incorporates axial-shear-flexural interactions of the structure during the analysis and it is capable of tracing cracking and crushing of concrete, yielding and fracture of reinforcement as well as final failures of cross-sections within RC members. Direct member removal algorithm is developed to simulate the process of collapse at member level, based on combined flexural/shear/axial failures of RC members. With developing a specially designed searching scheme, a new algorithm to monitor substructure collapse is also proposed. Locations and magnitudes of impact loads of the collapsed partial structure are also identified and calculated, according to rigid-body kinematics and energy principle. In addition, inelastic and oblique impact effects are properly considered. To efficiently simulate progressive collapse of large-scale buildings, superelement technique which separates the structure into linear and nonlinear zones is employed to reduce the computational time. As buildings in progressive collapse may undergo large rigid-body rotations of the structure, a rigid-body rotation correction to improve conventional superelement formulation is proposed for a more accurate large deformation analysis using superelement. Further, in order to consider nonlinearity spread during progressive collapse analysis, an adaptive superelement algorithm to automatically identify the propagation of nonlinear zone and then update the definition of superelement is proposed. By incorporating direct member removal algorithms as well as model regeneration procedure, an efficient adaptive superelement modeling procedure is developed for progressive collapse of RC frame structures. Numerical examples are given to show the advantages and effectivity of the suggested damage criteria and modeling procedures, through comparison with the results obtained from physical tests or standard nonlinear finite element analysis. Doctor of Philosophy (CEE)

Circular hollow sections (CHS) are widely adopted in fixed jacket and topside structures due to their excellent structural and mechanical properties. Virtually in almost all off-shore structures, one of the main design considerations when using CHS is to optimize the structural joints which are susceptible to fatigue failure due the dynamic and cyclic loading natural of the structures. Recently, partially overlapped CHS tubular K-joints become more and more popular due to their optimum strengths when compared to other alternative joint configurations such as non-overlapped (gapped) or completely overlapped K-joints. However, in the past, few research works were carried out to study the fatigue behaviour of partially overlapped CHS K-joints. In fact, currently, only a very limited information regarding the fatigue life of CHS overlapped K-joints are available. Hence, there is a need to investigate the stress concentration factors (SCF) and the hot spot stress (HSS) distributions of this kind of joints in the current research. Doctor of Philosophy (CEE)

The objective of current research is to numerically investigate the deformation behaviour of reinforced concrete (RC) beam-column framed structures subjected to destructive external loading. Firstly, besides the conventional uniaxial concrete models to predict flexural failures, a unified plasticity concrete model is proposed to accurately simulate shear deformations of beams. Secondly, a three dimensional co-rotational beam finite element is formulated with considerations of material nonlinearities for both steel and concrete. The proposed co-rotational beam formulation is shown to be capable of predicting steel and reinforced concrete framed structures with satisfactory accuracy and efficiency. Thirdly, a component-based mechanical model is proposed to simplify two dimensional RC beam-column joints, where three types of components are considered, viz., the bond-slip component, shear-panel component and interfacial shear component. Analytical models are respectively proposed to reasonably calibrate the bond-slip component and the shear-panel component, and an empirical model is summarized for the interfacial shear component based on extensive experimental results and design regulations. Fourthly, as an integrated system, the proposed concrete models, the co-rotational beam element and the component-based joint model are studied at the system level to show the prediction accuracy, computational efficiency and robustness in numerical algorithms. Advantages and disadvantages of different concrete models are also discussed. Finally, a superelement concept is proposed for structural analysis of large-scale structures. Compared with models without superelement, significant saving in computational cost and satisfactory prediction accuracy can be obtained without any loss in critical information of structural responses. This aspect is particularly crucial for progressive collapse analysis of structures subjected to localized damage. Doctor of Philosophy (CEE)

The application of extended finite element method (XFEM) formulation for nonlinear structural analyses is presented in this thesis. It aims to capture accurately the elastic response of a beam with an internal pin connection and the elasto-plastic response of a beam or a plate structure at a relatively low computational cost by utilizing the XFEM Timoshenko beam and Reissner-Mindlin plate elements. In the XFEM formulation for an internal pin, a step function is employed in the enriched rotation approximation field and an absolute level set function is adopted in the enriched translation approximation field. The enrichment function for a plastic hinge is formulated by using Hermite function over the high gradient zone resulted from the plastic hinge. The Hermite function regularizes the discontinuous enrichment function for an internal pin to be a continuous function with a high gradient zone. The strain fields derived from the enriched displacement approximation fields remain continuous inside an element. As the absolute level set function is constructed by standard finite element shape functions, such an enrichment function is also called ‘local’ enrichment function. The local enrichment function is applied in the XFEM plate element in this thesis. However, it is found that such local enrichment function is not suitable for the formulation of a 9-node quadrilateral plate element. Hence a global enrichment function is proposed. The global enrichment function is constructed on the structure level and independent of mesh scheme. Thus, it is applicable for both triangular and quadrilateral plate elements. Shear locking mitigation method is one of the major concerns in the present XFEM formulation. Two methods, including reduced integration and assumed shear strain methods, are employed to control shear locking in this thesis. In the assumed shear strain method, the mixed interpolation of tensorial components (MITC) technique and the discrete shear gap (DSG) technique are adopted in the XFEM plate elements. Numerical examples are given for different applications including an internal pin in a beam, a plastic hinge in a beam and a yield line in a plate. The numerical results show that the XFEM formulation is able to capture the discontinuous displacement over an internal pin connection and the locally high gradient displacement resulting from a plastic hinge or a yield line. It is also shown that shear locking can be controlled effectively by the reduced integration method and the assumed shear strain method. Doctor of Philosophy (CEE)