Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Gait analysis of the hind limb in Labrador Retrievers with and without cranial cruciate ligament disease

Cranial cruciate ligament (CCL) deficiency is the leading cause of lameness affecting the stifle joints of large breed dogs, especially Labrador Retrievers. Although CCL disease has been studied extensively, its exact pathogenesis and the primary cause leading to CCL rupture remain controversial. However, weakening secondary to repetitive microtrauma is currently believed to cause the majority of CCL instabilities diagnosed in dogs. Techniques of gait analysis have become the most productive tools to investigate normal and pathological gait in human and veterinary subjects. The inverse dynamics analysis approach models the limb as a series of connected linkages and integrates morphometric data to yield information about the net joint moment, patterns of muscle power and joint reaction forces. The results of these studies have greatly advanced our understanding of the pathogenesis of joint diseases in humans. A muscular imbalance between the hamstring and quadriceps muscles has been suggested as a cause for anterior cruciate ligament rupture in female athletes. Based on these findings, neuromuscular training programs leading to a relative risk reduction of up to 80% has been designed. In spite of the cost and morbidity associated with CCL disease and its management, very few studies have focused on the inverse dynamics gait analysis of this condition in dogs. The general goals of this research were (1) to further define gait mechanism in Labrador Retrievers with and without CCL-deficiency, (2) to identify individual dogs that are susceptible to CCL disease, and (3) to characterize their gait. The mass, location of the center of mass (COM), and mass moment of inertia of hind limb segments were calculated using a noninvasive method based on computerized tomography of normal and CCL-deficient Labrador Retrievers. Regression models were developed to determine predictive equations to estimate body segment parameters on the basis of simple morphometric measurements, providing a basis for nonterminal studies of inverse dynamics of the hind limbs in Labrador Retrievers. Kinematic, ground reaction forces (GRF) and morphometric data were combined in an inverse dynamics approach to compute hock, stifle and hip net moments, powers and joint reaction forces (JRF) while trotting in normal, CCL-deficient or sound contralateral limbs. Reductions in joint moment, power, and loads observed in CCL-deficient limbs were interpreted as modifications adopted to reduce or avoid painful mobilization of the injured stifle joint. Lameness resulting from CCL disease affected predominantly reaction forces during the braking phase and the extension during push-off. Kinetics also identified a greater joint moment and power of the contralateral limbs compared with normal, particularly of the stifle extensor muscles group, which may correlate with the lameness observed, but also with the predisposition of contralateral limbs to CCL deficiency in dogs. For the first time, surface EMG patterns of major hind limb muscles during trotting gait of healthy Labrador Retrievers were characterized and compared with kinetic and kinematic data of the stifle joint. The use of surface EMG highlighted the co-contraction patterns of the muscles around the stifle joint, which were documented during transition periods between flexion and extension of the joint, but also during the flexion observed in the weight bearing phase. Identification of possible differences in EMG activation characteristics between healthy patients and dogs with or predisposed to orthopedic and neurological disease may help understanding the neuromuscular abnormality and gait mechanics of such disorders in the future. Conformation parameters, obtained from femoral and tibial radiographs, hind limb CT images, and dual-energy X-ray absorptiometry, of hind limbs predisposed to CCL deficiency were compared with the conformation parameters from hind limbs at low risk. A combination of tibial plateau angle and femoral anteversion angle measured on radiographs was determined optimal for discriminating predisposed and non-predisposed limbs for CCL disease in Labrador Retrievers using a receiver operating characteristic curve analysis method. In the future, the tibial plateau angle (TPA) and femoral anteversion angle (FAA) may be used to screen dogs suspected of being susceptible to CCL disease. Last, kinematics and kinetics across the hock, stifle and hip joints in Labrador Retrievers presumed to be at low risk based on their radiographic TPA and FAA were compared to gait data from dogs presumed to be predisposed to CCL disease for overground and treadmill trotting gait. For overground trials, extensor moment at the hock and energy generated around the hock and stifle joints were increased in predisposed limbs compared to non predisposed limbs. For treadmill trials, dogs qualified as predisposed to CCL disease held their stifle at a greater degree of flexion, extended their hock less, and generated more energy around the stifle joints while trotting on a treadmill compared with dogs at low risk. This characterization of the gait mechanics of Labrador Retrievers at low risk or predisposed to CCL disease may help developing and monitoring preventive exercise programs to decrease gastrocnemius dominance and strengthened the hamstring muscle group.