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.

Incomplete information games of conflict and collective action

My thesis consists of three essays that investigate strategic interactions between individuals engaging in risky collective action in uncertain environments. The first essay analyzes a broad class of incomplete information coordination games with a wide range of applications in economics and politics. The second essay draws from the general model developed in the first essay to study decisions by individuals of whether to engage in protest/revolution/coup/strike. The final essay explicitly integrates state response to the analysis. The first essay, Coordination Games with Strategic Delegation of Pivotality, exhaustively analyzes a class of binary action, two-player coordination games in which players receive stochastic payoffs only if both players take a ``stochastic-coordination action''. Players receive conditionally-independent noisy private signals about the normally distributed stochastic payoffs. With this structure, each player can exploit the information contained in the other player's action only when he takes the “pivotalizing action”. This feature has two consequences: (1) When the fear of miscoordination is not too large, in order to utilize the other player's information, each player takes the “pivotalizing action” more often than he would based solely on his private information, and (2) best responses feature both strategic complementarities and strategic substitutes, implying that the game is not supermodular nor a typical global game. This class of games has applications in a wide range of economic and political phenomena, including war and peace, protest/revolution/coup/ strike, interest groups lobbying, international trade, and adoption of a new technology. My second essay, Collective Action with Uncertain Payoffs, studies the decision problem of citizens who must decide whether to submit to the status quo or mount a revolution. If they coordinate, they can overthrow the status quo. Otherwise, the status quo is preserved and participants in a failed revolution are punished. Citizens face two types of uncertainty. (a) non-strategic: they are uncertain about the relative payoffs of the status quo and revolution, (b) strategic: they are uncertain about each other's assessments of the relative payoff. I draw on the existing literature and historical evidence to argue that the uncertainty in the payoffs of status quo and revolution is intrinsic in politics. Several counter-intuitive findings emerge: (1) Better communication between citizens can lower the likelihood of revolution. In fact, when the punishment for failed protest is not too harsh and citizens' private knowledge is accurate, then further communication reduces incentives to revolt. (2) Increasing strategic uncertainty can increase the likelihood of revolution attempts, and even the likelihood of successful revolution. In particular, revolt may be more likely when citizens privately obtain information than when they receive information from a common media source. (3) Two dilemmas arise concerning the intensity and frequency of punishment (repression), and the frequency of protest. Punishment Dilemma 1: harsher punishments may increase the probability that punishment is materialized. That is, as the state increases the punishment for dissent, it might also have to punish more dissidents. It is only when the punishment is sufficiently harsh, that harsher punishment reduces the frequency of its application. Punishment Dilemma 1 leads to Punishment Dilemma 2: the frequencies of repression and protest can be positively or negatively correlated depending on the intensity of repression. My third essay, The Repression Puzzle, investigates the relationship between the intensity of grievances and the likelihood of repression. First, I make the observation that the occurrence of state repression is a puzzle. If repression is to succeed, dissidents should not rebel. If it is to fail, the state should concede in order to save the costs of unsuccessful repression. I then propose an explanation for the “repression puzzle” that hinges on information asymmetries between the state and dissidents about the costs of repression to the state, and hence the likelihood of its application by the state. I present a formal model that combines the insights of grievance-based and political process theories to investigate the consequences of this information asymmetry for the dissidents' contentious actions and for the relationship between the magnitude of grievances (formulated here as the extent of inequality) and the likelihood of repression. The main contribution of the paper is to show that this relationship is non-monotone. That is, as the magnitude of grievances increases, the likelihood of repression might decrease. I investigate the relationship between inequality and the likelihood of repression in all country-years from 1981 to 1999. To mitigate specification problem, I estimate the probability of repression using a generalized additive model with thin-plate splines (GAM-TPS). This technique allows for flexible relationship between inequality, the proxy for the costs of repression and revolutions (income per capita), and the likelihood of repression. The empirical evidence support my prediction that the relationship between the magnitude of grievances and the likelihood of repression is non-monotone.