yes / This paper reports the testing of fifteen reinforced concrete deep beams with openings. All beams tested had the same overall geometrical dimensions. The main variables considered were the opening size and amount of inclined reinforcement. An effective inclined reinforcement factor combining the influence of the amount of inclined reinforcement and opening size on the structural behaviour of the beams tested is proposed. It was observed that the diagonal crack width and shear strength of beams tested were significantly dependent on the effective inclined reinforcement factor that ranged from 0 to 0.318 for the test specimens. As this factor increased, the diagonal crack width and its development rate decreased, and the shear strength of beams tested improved. Beams having effective inclined reinforcement factor more than 0.15 had higher shear strength than that of the corresponding solid beams. A numerical procedure based on the upper bound analysis of the plasticity theory was proposed to estimate the shear strength and load transfer capacity of reinforcement in deep beams with openings. Predictions obtained from the proposed formulas have a consistent agreement with test results.

Yes / Nine continuous concrete deep beams reinforced with glass fibre reinforced polymer (GFRP) bars were experimentally tested to failure. Three main parameters were investigated, namely, shear span-to-overall depth ratio, web reinforcement and size effect. The experimental results confirmed the impacts of web reinforcement and size effect that were not considered by the strut-and-tie method (STM) of the only code provision, the Canadian S806-12, that addressed such elements. The experimental results were employed to evaluate the applicability of the methods suggested by the American, European and Canadian codes as well as the previous studies to predict the load capacities of continuous deep beams reinforced with GFRP bars. It was found that these methods were unable to reflect the influences of size effect and/or web reinforcement, the impact of which has been confirmed by the current experimental investigation. Therefore, a new effectiveness factor was recommended to be used with the STM. Additionally, an upper-bound analysis was developed to predict the load capacity of the tested specimens considering a reduced bond strength of GFRP bars. A good agreement between the predicted results and the experimental ones was obtained with the mean and coefficient of variation values of 1.02 and 5.9%, respectively, for the STM and 1.03 and 8.6%, respectively, for the upper-bound analysis. / Higher Committee of Education Development in Iraq (HCED)

Many programs are executed according to the conventional, eager execution order, for which verification of execution costs is well-understood. However, there are other execution orders in use. One such order in common use is lazy execution or lazy evaluation, which is mostly demand-driven. Laziness supports better decompositions of algorithms, e.g., into modular producers and consumers, which enables compositional reasoning of answer correctness, but then timing correctness is more elusive. This thesis gives a formal method for verifying lazy timing, compositional with respect to program structure; it is an extension of a predicative programming theory. Predicative programming theories are formal methods that unify both specifications and programs as predicates or boolean-typed expressions over memory state and other quantities of interest. Their strengths are mathematical simplicity and support of program development and verification by incremental refinements. Among these theories, Hehner's a Practical Theory of Programming has the further strength of leaving termination and timing open rather than a built-in, and therefore is a flexible substrate for various timing schemes corresponding to various execution strategies. We use this substrate for our method for lazy timing. This thesis also proves soundness of the eager timing scheme in Hehner's work with respect to an eager operational semantics, and our lazy timing scheme with respect to a lazy operational semantics. Thus, if refinements promise an upper time bound, then execution actually stops within that time. Lastly, this thesis outlines a space of more operational semantics. It is possible ground for more execution strategies.

Many programs are executed according to the conventional, eager execution order, for which verification of execution costs is well-understood. However, there are other execution orders in use. One such order in common use is lazy execution or lazy evaluation, which is mostly demand-driven. Laziness supports better decompositions of algorithms, e.g., into modular producers and consumers, which enables compositional reasoning of answer correctness, but then timing correctness is more elusive. This thesis gives a formal method for verifying lazy timing, compositional with respect to program structure; it is an extension of a predicative programming theory. Predicative programming theories are formal methods that unify both specifications and programs as predicates or boolean-typed expressions over memory state and other quantities of interest. Their strengths are mathematical simplicity and support of program development and verification by incremental refinements. Among these theories, Hehner's a Practical Theory of Programming has the further strength of leaving termination and timing open rather than a built-in, and therefore is a flexible substrate for various timing schemes corresponding to various execution strategies. We use this substrate for our method for lazy timing. This thesis also proves soundness of the eager timing scheme in Hehner's work with respect to an eager operational semantics, and our lazy timing scheme with respect to a lazy operational semantics. Thus, if refinements promise an upper time bound, then execution actually stops within that time. Lastly, this thesis outlines a space of more operational semantics. It is possible ground for more execution strategies.

This research aims to investigate the behaviour of glass fibre reinforced polymer bars (GFRP) reinforced continuous concrete deep beams. For this purpose, experimental, analytical and numerical studies were conducted. Nine continuous concrete deep beams reinforced with GFRP bars and one specimen reinforced with steel bars were experimentally tested to failure. The investigated parameters included shear span-to-overall depth ratio (𝑎/ℎ), size effect and web reinforcement ratio. Two 𝑎/ℎ ratios of 1.0 and 1.7 and three section heights of 300 mm, 600 mm and 800 mm as well as two web reinforcement ratios of 0% and 0.4% were used. The longitudinal reinforcement, compressive strength and beam width were kept constant at 1.2%, ≈55 MPa and 175 mm, respectively. The web reinforcement ratio achieved the minimum requirements of the CSA S806-12. The experimental results highlighted that the web reinforcement ratio improved the load capacities by about 10% and 18% for specimens having 𝑎/ℎ ratios of 1.0 and 1.7, respectively. For specimens with web reinforcement, the increase of 𝑎/ℎ ratio from 1.0 to 1.7 led to reductions in the load carrying capacity by about 33% and 29% for beams with overall depths of 300 mm and 600 mm, respectively. Additionally, a considerable reduction occurred in the shear strength due to the increase of the section depth from 300 mm to 600 mm. The experimental results confirmed the impacts of web reinforcement and size effect that were not considered by the strut-and-tie method (STM) of the only code provision, the Canadian S806-12, that addressed such elements. In this study, the STM was illustrated and simplified to be adopted for GFRP RC continuous deep beams, and then, the experimental results obtained from this study were employed to assess the performance of the effectiveness factors suggested by the STMs of the American (ACI 318-2014), European (EC2-04) and Canadian (S806-12) codes as well as those factors recommended by the previous studies to predict the load capacities. It was found that these methods were unable to reflect the influences of member size and/or web reinforcement reasonably, the impact of which has been confirmed by the current experimental investigation. Therefore, a new effectiveness factor was recommended to be used with the STM. Additionally, an upper bound analysis was developed to predict the load capacities of the tested specimens considering a reduced bond strength of GFRP bars after assessing the old version recommended for steel RC continuous deep beams. A good agreement between the predicted results and the measured ones was obtained with the mean and coefficient of variation values for experimental/calculated results of 1.02 and 5.9%, respectively, for the STM and 1.03 and 8.6%, respectively, for the upper-bound analysis. A 2D finite element analysis using ABAQUS/Explicit approach was carried out to introduce a model able to estimate the response of GFRP RC continuous deep beams. Based on the experimental results extracted from the pullout tests, the interface between the longitudinal reinforcement and concrete surface was modelled using a cohesive element (COH2D4) tool available in ABAQUS. Furthermore, a perfect bond between the longitudinal reinforcement and surrounding concrete was also modelled to evaluate the validity of this assumption introduced by many previous FE studies. To achieve a reasonable agreement with the test results, a sensitivity analysis was implemented to select the proper mesh size and concrete model variables. The suitability and capability of the developed FE model were demonstrated by comparing its predictions with the test results of beams tested experimentally. Model validation showed a reasonable agreement with the experiments in terms of the failure mode, total failure load and the load-deflection responses. The perfect bond model has overestimated the predicted results in terms of stiffness behaviour and failure load, while the cohesive element model was more suitable to reflect the behaviour of those specimens. The validated FE model was then employed to implement a parametric study for the key parameters that govern the behaviour of beams tested and to achieve an in depth understanding of such elements. The parametric study showed that the higher the 𝑎/ℎ ratio the more pronounced the effect of web and the longitudinal reinforcements and the lower the effect of concrete compressive strength; and vice versa when 𝑎/ℎ ratio reduces.