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.

Characterization of the effect of nitrogen deficiency on above-ground plant phenotypes in relation to root complexity in maize

Nitrogen (N) is an essential plant nutrient in maize production, and if considering only natural sources, is often the limiting factor world-wide in terms of a plant’s grain yield. For this reason, many farmers around the world supplement available soil N with synthetic man-made forms. Years of over-application of N fertilizer have led to increased N in groundwater and streams due to leaching and run-off from agricultural sites. In the Midwest Corn Belt much of this excess N eventually makes its way to the Gulf of Mexico leading to eutrophication (increase of phytoplankton) and a hypoxic (reduced oxygen) dead zone. Growing concerns about these types of problems and desire for greater input use efficiency have led to demand for crops with improved N use efficiency (NUE) to allow reduced N fertilizer application rates and subsequently lower N pollution. It is well known that roots are responsible for N uptake by plants, but it is relatively unknown how root architecture affects this ability. This research was conducted to better understand the influence of root complexity (RC) in maize on a plant’s response to N stress as well as the influence of RC on other above-ground plant traits. Thirty-one above-ground plant traits were measured for 64 recombinant inbred lines (RILs) from the intermated B73 & Mo17 (IBM) population and their backcrosses (BCs) to either parent, B73 and Mo17, under normal (182 kg N ha-1) and N deficient (0 kg N ha-1) conditions. The RILs were selected based on results from an earlier experiment by Novais et al. (2011) which screened 232 RILs from the IBM to obtain their root complexity measurements. The 64 selected RILs were comprised of 31 of the lowest complexity RILs (RC1) and 33 of the highest complexity RILs (RC2) in terms of root architecture (characterized as fractal dimensions). The use of the parental BCs classifies the experiment as Design III, an experimental design developed by Comstock and Robinson (1952) which allows for estimation of dominance significance and level. Of the 31 traits measured, 12 were whole plant traits chosen due to their documented response to N stress. The other 19 traits were ear traits commonly measured for their influence on yield. Results showed that genotypes from RC1 and RC2 significantly differ for several above-ground phenotypes. We also observed a difference in the number and magnitude of N treatment responses between the two RC classes. Differences in phenotypic trait correlations and their change in response to N were also observed between the RC classes. RC did not seem to have a strong correlation with calculated NUE (ΔYield/ΔN). Quantitative genetic analysis utilizing the Design III experimental design revealed significant dominance effects acting on several traits as well as changes in significance and dominance level between N treatments. Several QTL were mapped for 26 of the 31 traits and significant N effects were observed across the majority of the genome for some N stress indicative traits (e.g. stay-green). This research and related projects are essential to a better understanding of plant N uptake and metabolism. Understanding these processes is a necessary step in the progress towards the goal of breeding for better NUE crops.