Master's Program Course Schedule

Basic solid mechanics for structural engineers. Stress, strain and constitutive laws. Linear elasticity and viscoelasticity. Introduction to nonlinear mechanics. Static, dynamic and thermal stresses. Specialization of theory to one- and two-dimensional cases: plane stress and plane strain, rods, and beams. Work and energy principles; variational formulations.

Covers probabilistic computational modeling in civil engineering and mechanics: Monte Carlo simulation, sampling methods and variance reduction techniques, simulation of stochastic processes and fields, and expansion methods. Applications to stochastic finite element, uncertainty quantification, reliability analysis, and model verification and validation.

Matrix methods for the analysis of statistically indeterminate structures such as beams, plane and space trusses, and plane and space frames. Stiffness and flexibility methods. Linear elastic analysis and introduction to nonlinear analysis.

This course will cultivate broad knowledge of the use of engineering principles in the art of architecture. Fundamental definitions of architecture in the basic provision of shelter and social use are paired with aesthetics and cultural heritage. The course emphasizes structural frameworks and systems within the Civil Engineering curriculum, while expanding upon their critical intersections with the highly varied specialized components and systems of modern architecture, and the corresponding community of specialists that represent them. Topics include a historical view of the evolution of specialization in architecture, a quantitative review of loads and resistance systems, architectural and structural determinants of form, the function and aesthetics of building surface, and an introduction to environmental systems and their role in design sustainability. The class will include a trip to Fallingwater, the house designed by Frank Lloyd Wright, in western Pennsylvania, which stands as an iconic example of American architecture and a complex example of architectural engineering. This course is co-listed with EN.560.421.

The renovation of existing buildings often holds many advantages over new construction, including greater economy, improved sustainability, and the maintenance of engineering heritage and architectural character in our built environment. Yet, the renovation of existing structures presents many challenges to structural engineers. These challenges include structural materials that are no longer in widespread use (e.g., unreinforced masonry arches and vaults, cast iron, and wrought iron) as well as structural materials for which analysis and design practices have changed significantly over the last half-century (e.g., wood, steel, and reinforced concrete).This course will examine structures made of a wide variety of materials and instruct the student how to evaluate their condition, determine their existing capacity, and design repairs and/or reinforcement. The investigation and analysis procedures learned from this course may then be applied to create economical and durable structural alterations that allow for the reuse of older buildings. Site visits near Homewood campus will supplement lectures. co-listed with 560.429.

Concepts of stability of equilibrium, stability criteria, work energy and variational methods. Elastic buckling of columns, beams, frames, and plates. Introduction to inelastic and dynamic buckling.

Why do buildings deteriorate, and how do we address this problem? This course examines the deterioration (by human and nature) of building materials and systems. Through lectures and a field trip, students will learn how to set up and execute an investigation, study the symptoms, diagnose the problems, determine what kinds of tests are needed, design the necessary repairs, and maintain existing systems. This course is co-listed with Engineering for Professionals EN.565.633.

Seminar series of speakers on various aspects of civil engineering. Different speakers are invited each semester. Full time civil engineering graduate students must enroll in the seminar course every semester unless excused by the Department.

This course revolves around the grid integration of renewable energy systems and operations of energy systems with renewables. The main emphasis is on grid level effects of renewable energy, particularly solar and wind power systems, and how these effects can be analyzed using mathematical modeling and modern software tools. The course begins with an introduction to basic power system concepts (transmission/distribution system modeling, power transformers, conventional and renewable generation technologies) along with power flow analysis and optimization. Following that, the course considers applications of optimal power flow and its variants to electricity market operations. An important component of this course is a guided project that will be carried out by students in small groups; each group will choose a real-world energy system to research and analyze and will present their findings at the end of the semester. Prior knowledge of circuits (including operations with complex numbers), linear algebra, calculus, and optimization is helpful, but not required. This course is co-listed with EN.560.449.

An introduction to operations research and its applications. The course will review the basics of mathematical modelling, linear programming, primal and dual Simplex methods, post-optimization analysis, decomposition methods, and heuristic methods along with sample applications. Recommended course background (EN.553.291 or AS.110.201) and AS.110.109 or equivalent. This course is co-listed with EN.560.450

Many real-world problems can be modeled using network structures, and solved using tools from network theory. For this reason, network modeling plays a critical role in various disciplines ranging from physics and mathematics, to biology and computer science, and almost all areas of social science. This course will provide an introduction to network theory, network flow algorithms, modeling processes on networks and examples of empirical network applications spanning transport, health and energy systems.

Planning for manufacturing and service industries is critical for efficiently utilizing resources to produce cost-effective goods and services. This course delves into the fundamentals, models, and techniques required for planning, controlling, and optimizing the performance of manufacturing systems. The curriculum focuses on the trade-offs between key measures, like costs, cycle time, throughput, capacity, work-in-process, inventory, and variability. The course utilizes analytical approaches (linear programming, simulation, probability, and statistics) and coding (Python). Co-listed EN.560.479. Recommended courses that cover topics on probability and coding.

Additive Manufacturing (AM) removes many geometric constraints imposed by traditional manufacturing processes. Resultingly, systems can be designed to support and improve multiple design objectives, which has the potential to alter the way products are designed. While this allows for the fabrication of more complex and often unprecedented geometries, it also increases the complexity designers face. In addition, engineers must not only understand AM technologies and materials, they must also be able to synthesize its economic and environmental impacts on a manufacturing value chain. Additive Manufacturing and Design will provide an in-depth overview of the most common – and promising – AM technologies, materials, and design methods by including examples from state-of-the-art research. A particular emphasis is placed on Design for Additive Manufacturing (DfAM), where the different topics will converge to fully utilize the newly created design space.

Variational methods and mathematical foundations, Direct and Iterative solvers, 1-D Problems formulation and boundary conditions, Trusses, 2-D/ 3D Problems, Triangular elements, QUAD4 elements, Higher Order Elements, Element Pathology, Improving Element Convergence, Dynamic Problems.