The P-delta effect, which is a second order effect, is experienced by a structure mostly when the structure is subjected to lateral forces like earthquake and wind. In addition to earthquake and wind loads, when the structure is subjected to various live load patterns other than symmetrical loading, the structure experiences side sway or lateral translation. In this thesis, P-delta effects due to symmetrical and asymmetrical live loads is studied on a three-bay, two-story steel moment frame. The main objective of this research is to investigate P-delta effects on the column which is subjected to critical load case. The effect is analyzed based on the value of the moment magnification factor, B2. Besides, the story drift due to asymmetrical loading is also investigated. For the purpose of this study, “Approximate Second-Order Analysis” specified in “Appendix 8” of AISC Steel Construction Manual (AISC 2011) is used to amplify the first order effects to account for the second-order effects in the steel moment frame. Additionally, computer software is used to calculate the first order moments and axial forces.

Uncertainty analysis is crucial to any thorough analysis of an engineering system. Traditional uncertainty analysis can be a tedious task involving numerous steps that can be error prone if conducted by hand. If conducted with the aid of a computer, these tasks can be computationally expensive. In either case, the process is quite rigid. If a parameter of the system is modified or the system configuration is changed, the entire uncertainty analysis process must be conducted again giving more opportunities for calculation errors or computation time. Modular uncertainty analysis provides a method to overcome all these obstacles of traditional uncertainty analysis. The modular technique is well suited for computation by a computer which makes the process somewhat automatic after the initial setup and computation errors are reduced. The modular technique implements matrix operations to conduct the analysis. This in turns makes the process more efficient than traditional methods because computers are well suited for matrix operations. Since the modular technique implements matrix operations, the method is adaptable to system parameter or configuration modifications. The modular technique also lends itself to quickly calculating other uncertainty analysis parameters such as the uncertainty magnification factor, and the uncertainty percent contribution. This dissertation will focuson the modular technique, the extension of the technique in the form the uncertainty magnification factor and uncertainty percent contribution, and the application of the modular technique to different type of energy systems. The modular technique is applied to an internal combustion engine with a bottoming organic Rankine cycle system, a combined heat and power system, and a heating, ventilation, and air conditioning system. The results show that the modular technique is well suited to evaluate complex engineering systems. The modular technique is also shown to perform well when system parameters or configurations are modified.

Every moment of every day, at least hundreds of thousands of tires roll across a surface throughout the world. Tires are indisputably important in our daily life. The tire's primary component is rubber, which consumes energy when it rotates on a substrate due to the viscoelastic material's internal friction: a phenomenon referred to as rolling resistance. The interaction between the tire and the road surface is one of the most intricate and crucial phenomena in an automobile, because it is responsible for creating forces, moments, and deformation in the tire. Additionally, the road's roughness interacts with the tire and contributes significantly to its performance. This dissertation aims to develop a comprehensive physics-based model for predicting the rolling resistance of a viscoelastic material due to dynamic deformations caused by tire rotation using an analytical approach. The model was developed by proposing a Gaussian wave function propagating across a tire circumference's viscoelastic medium. The wave function was selected to describe the displacement field produced by tire-road interaction. Additionally, by adopting a multi-scale modeling technique, the model was upgraded to estimate rolling resistance while taking into account surface roughness at all length scales, from macroscopic to microscopic. Additionally, another mathematical model was developed using the Fourier series approach to evaluate the steady-state stress response and energy dissipation for any harmonic and non-harmonic periodic strain signals. Additionally, the dissertation strove to build a continuum damage mathematical model using a combined testing/modeling methodology to predict the aging of Styrene-Butadiene Rubber (SBR) after continuous exposure to the atmosphere. The obtained model was developed through the implementation of optimization techniques while formulating a mathematical model, which was then combined with a physics-based model to predict rolling resistance while taking into account rubber aging. Calibration of hyperelastic and viscoelastic material models with testing data was performed using an optimization technique that yielded sufficient results. The results of all mathematical models obtained in this dissertation are reported subsequently. The stress response of a viscoelastic material under harmonic and non-harmonic strain input yielded good agreement with the FEA model obtained using ABAQUS. The rolling resistance behavior under various operating conditions, including texture and aging effects, was reported, and the results aligned with the experimental results found in the literature. / Doctor of Philosophy / Every moment of every day, hundreds of thousands of automobile tires roll across a surface somewhere in the world. A tire is an undeniably important part of everyday life. Rubber is the tire's main component, and when it rotates on a surface, it loses energy, resulting in a force that resists motion, known as rolling resistance force. The contact between the tire and the road is one of the most complicated and important phenomena that happens in an automobile because it is responsible for the vehicle's dynamic performance in areas such as acceleration, stopping distance, and stability. Another factor that affects tire and car performance and should be taken into account is the road's roughness. This dissertation used an analytical method to come up with an accurate physics-based model for predicting the rolling resistance force of a viscoelastic material caused by tire rotation. The model was developed by assuming a Gaussian wave function would move across the tire circumference. Additionally, using a multi-scale modeling technique, the model was improved so that it could calculate the value of rolling resistance force considering surface roughness in all lengths of scale. This project also developed an additional mathematical model using the Fourier series method to determine how the stress response and energy dissipation would behave for any harmonic and nonharmonic periodic strain signals. Additionally, the dissertation presents the developing of a continuum damage mathematical model that could predict the material property of styrene-butadiene rubber (SBR) after being exposed to the air for a long time (i.e., aged). The model was developed based on experimental data and optimization techniques. This model was then combined with a physics-based model to predict rolling resistance force while taking aging into account. The material models were defined using an optimization method that yielded good results. The stress response of a viscoelastic material when it was subjected to harmonic and non-harmonic strain was in good agreement with the Finite Element Analysis (FEA) model made with ABAQUS. Rolling resistance behavior was observed, and the results were consistent with those found in the literature.