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.

Effects of supplemental osteopontin on intestinal development and serum antibody responses to rotavirus vaccination in piglets

Milk contains numerous bioactive substances including immunoglobulins, cytokines, growth factors and components that exert antibiotic and prebiotic activity (Field, 2005). Little is known about the biological effects of individual milk bioactives, despite the fact that natural milk improves intestinal development and immune system functions in neonates (Donovan et al., 1994; Field, 2005) relative to milk formula. Characterization of the biological effects of such components is important for optimal production of infant milk formulas to be used when mother’s milk is not available. Milk components with preliminary evidence of positive effects on the intestinal growth and mucosal immunity include osteopontin (OPN). Osteopontin is a phosphorylated acidic glycoprotein expressed by a number of different immune and non-immune cells and tissues (Sodek et al., 2000). It is also present in body fluids including blood, bile and milk (Sodek et al., 2000). Osteopontin is a multifunctional protein that is implicated in a wide number of biological processes including cell survival, bone remodeling, and immune modulatory functions (Sodek et al., 2000). Furthermore, Schack and colleagues (2009) demonstrated that the concentration of OPN in human milk is considerably higher than in bovine milk and infant formulas. Taken together, it is likely that OPN plays a role in the early development of gastrointestinal tract and mucosal immune responses in infants. Since the neonatal pig shares anatomical, physiological, immunological, and metabolic similarities with the human infants (Moughan, et al., 1992), they were selected as the animal model in our studies. Our first aim was to investigate the effects of OPN on piglet intestinal development. Newborn, colostrum-deprived piglets (n=27) were randomized to receive three treatments: formula with bovine OPN (OPN; 140 mg/L); formula alone (FF); or sow reared (SR) for 21 days. Body weight, intestinal weight and length, mucosal protein and DNA content, disaccharidase activity, villus morphology, and crypt cell proliferation were measured. Statistical significance was assigned at P<0.05. No significant effects of OPN were observed for body weight, intestinal weight and length. Mucosal protein content of SR piglets was lower than FF and OPN piglets in the duodenum, but higher than FF and OPN piglets in the ileum. No significant effects of diet in mucosal DNA content were detected for the three regions of the small intestine. Lactase and sucrase activities of SR piglets were higher than the two formula-fed groups in the duodenum, lower in the ileum. No significant effects of diet on lactase and sucrase activities were noted between two formula-fed groups in the duodenum and ileum. Jejunal lactase activity of FF piglets was higher than SR piglets, whereas no significant effect of diet was observed in jejunal sucrase activity among the three groups. Duodenal and ileal villus height and villus area of SR piglets were lower than two formula-fed groups, while OPN piglets did not differ from FF piglets. There was a significant effect of diet (P<0.0001) on jejunal crypt cell proliferation, with proliferation in OPN piglets being intermediate between that of FF and SR. In summary, supplemental OPN increased jejunal crypt cell proliferation, independent of evident morphological growth, and had a minor impact on disaccharidase activity in the small intestine of neonatal piglets. Rotavirus (RV) is the most common viral cause of severe gastroenteritis in infants and young children worldwide (Parashar et al., 2006). Maeno et al. (2009) reported that OPN knockout (OPN-KO) suckling mice were more susceptible to RV infection compared to wild-type (WT) suckling mice. To detect the role of OPN in intestinal immune responses of neonates, the goal of the second study was to evaluate whether supplemental OPN influenced the serum antibody responses to RV vaccination in neonatal piglets. Newborn, colostrum-deprived piglets were randomized into two dietary groups: formula with bovine OPN (OPN; 140 mg/L) and formula alone (FF) for 35 days. On d7, piglets in each dietary group were further randomized to receive rotavirus (RV) vaccination (Rotarix®) (FF+RV and OPN+RV) or remained non-vaccinated (FF+NV and OPN+NV). Booster vaccination was provided on d14. Blood samples were collected on d7, 14, 21, 28 and 35. RV-specific serum immunoglobulin (Ig) G, IgA, IgM and total serum IgG, IgA, IgM were measured by ELISA. Statistical significance was assigned at P<0.05, with trends reported as P<0.10. Body weight gain was unaffected by diet and/or vaccination. No significant effect of oral OPN supplementation was observed for RV-specific antibody responses and total Igs levels. After the combination of dietary groups, RV piglets had significantly higher RV-specific IgM concentrations compared to NV piglets. Although there were higher means of RV-specific IgG and RV-specific IgA concentrations in RV group than their counterparts in NV group, the difference did not reach statistical significance. RV-specific IgM reached a peak at d7 post booster vaccination (PBV), whereas the RV-specific IgG and IgA peaked later at PBV 14 or 21. Total Igs were unaffected by RV vaccination but were significantly increased over time, following similar pattern as RV-specific Igs. In summary, neonatal piglets generated weak antibody responses to RV vaccination. Supplemental OPN did not enhance RV-specific serum antibody responses and total serum Igs levels in neonatal piglets with or without RV vaccination. In conclusion, we observed normal developmental changes in the small intestine and serum Igs levels in neonatal piglets over time. Oral OPN supplementation showed minimal impacts on intestinal development and no effect on serum Igs levels. The role of supplemental OPN on the growth and development of infants is still inconclusive. Future studies should measure other physiological and immunological parameters by using different models of vaccination or infection.