Doctoral Programs – Structural Engineering and Mechanics Group

Structural Engineering Ph.D.

The Structures PhD Field contains subject matter for dissertation research in the areas of structures, structural engineering, and structural mechanics. The student is responsible for the knowledge contained in required core material and additional subject matter approved by the PhD Structures Field Committee.

Prerequisite Preparation for the Major Field

The following topics, normally completed at the undergraduate level, are considered prerequisite material for this field of study; principles of equilibrium, compatibility and force-displacement relationships for structural elements and systems; work and energy principles, mechanical properties of materials, constitutive equations, elementary theories of vibration and stability, basic concepts of design of steel and reinforced concrete structures. (Courses C&EE 130, 135B, 137, 141 or 142. References: P.1, P.2, P.3, P.4,P.5, P.6, P.7)

Topical Outline of the Structures Major Field

I.   Static Analysis

A. (Required) Application to One-Dimensional Structures. Rods, beams, trusses and frames. Fundamental principles: equilibrium, compatibility, force-deflection properties, virtual work, strain energy and complementary strain energy. Matrix methods of analysis. (Course C&EE 235A. References: I.6)

B. Finite Element Analysis of Structures. Systematic formulation of element properties using variational principles. Displacement method, force method and hybrid methods. Interpolation functions and computation aspects. Application of one, two and three dimensional finite elements to beams, membranes, plates and solids. (Course C&EE 235B. References: I.1, I.3, I.5, I.13)

C. Elastic Theory and Two-Dimensional Structures (Plates and Shells). Equations of l linear isotropic elastostatics; two- and three-dimensional problems; torsion and bending. Fundamental principles of plate theory; Kirchoff-Love hypothesis; constitutive equations, equilibrium, compatibility, boundary
conditions, boundary value problems; approximate methods, membrane theory of shells, thermoelastic problems; bending theory of cylinders. (Courses: C&EEM 230, 232. References: I.2, I.4, I.7, I.8, I.9, I.10, I.11, I.12)

II.   Dynamic Analysis

A. (Required) Dynamics of Structures. Hamilton’s principle, variational methods. Lagrange;s equations. Free vibration problem, normal modes in discrete and continuous systems. The structural dynamics eigenvalue problem and its solution. application of beam finite elements in structural dynamics. Approximate methods, Rayleight-Ritz, Galerkin and collocation methods. Proportional damping. Normal mode and frequency response methods, response spectra. (Course: C&EE 237A. References: II.2, II.4, II.5, II.7, II.8)

B. Advanced Dynamics of Structures.
Nonproportional damping. Structural dynamics of two- and three-dimensional structures using approximate and finite element methods. Computational aspects of the structural dynamics eigenvalue problem. Vibrations of Timoshenko beams. Numerical integration schemes for response calculations. Dynamic modelling using substructures and component mode synthesis. (Course: MAE 269B. References: II.5, II.6)

III.   Design

A. Design of steel structures in accord with AISC specifications. Design of reinforced concrete according to ACI requirements. Design for vertical and lateral loads. Load paths and modes of failure in structures. (Courses: C&EE 141, 142, 143, 144, 147, 241, 242, 244. References: III.3, III.4, III.5, III.7, III.8, III.10)

B. Optimum Structural Design. Formulation of structural optimization problems. Fundamentals of solution techniques: linear and nonlinear mathematical programming; numerical implementation. Application to design of components, trusses, frames. Plastic design. Supplementary or alternate methods of structural optimization: approximation concepts; dual methods and optimality criteria. (Courses: C&EEM 140, M240. References: III.1, III.2, III.6, III.9)

IV.   Earthquake Engineering

A. Response of Structures to Ground Motions. Single and multiple degree of freedom idealizations;
numerical methods for solving problems; nonlinear response of singe and multi-degree of freedom systems; earthquake response spectra; reconciliation of measured spectra and building code spectra; combining modal responses with spectra inputs; earthquake response calculations with computer programs. (Courses (C&EE 221 and 246. References: IV.1, IV.3, IV.5, IV.6)

B. Engineering Seismology. Epicenter and fault plane location, source mechanics and fracture mechanics, attenuation, dispersion and diffraction, soil dynamics, and analysis of strong motion data. (Courses: MAE M257B, C&EE 222 and 245. References: IV.2, II.3, IV.4)

V.   Experimental Analysis

A. Experimental methods for determining position, displacement, velocity, stress and strain in structures. Analysis of the limit condition of structures, particularly emphases on fracture mechanics and plasticity. Modal analysis of the structural response of systems to deterministic and nondeterministic loading histories. Computer based testing techniques and analysis, including computer control and computer interactive experiments. (Courses: C&EE 130F, 130L, 137L. 238. References: V.1, V.2, V.3, V.4)

VI.   Stability and Nonlinear Analysis

A. Stability of Structures. Bucking of bars, frames, and trusses. Fundamental concept of buckling,
beam-column effects. Buckling as an eigenvalue problem. Energy concepts in stability analysis. The Rayleigh-Ritz method, geometric stiffness matrix. Coupled lateral and torsional buckling effects. Inelastic buckling. Introduction to plate buckling. (Course: C&EE 236. References: VI.4, VI.5)

B. Nonlinear Structural Analysis. Large strain-displacement relations, elasto-plastic behavior of metals and geologic materials, finite element representation of nonlinear solid and structural systems. Numerical solution of nonlinear algebraic equations, implicit and explicit time integration techniques, stability and accuracy of nonlinear solution algorithms. Discrete element systems.(Courses: C&EE 231, 235C. References: VI.1, I.1, VI.2, VI.3)

VII.   Mechanics of Structural Materials

A. Mechanical Behavior of Metals and Polymers. Constitutive relation, deformation maps. Failure criteria, fatigue, corrosion. Fracture mechanics. Viscoelasticity, temperature-time-moisture equivalence. (Courses: C&EE 234 and MAE 256F. References: V.1, V.3)

B. Mechanical Behavior of Frictional materials. Stress-strain and strength behavior of frictional materials such as soils, rock, concrete, and ceramics; effective stress principle; volume change and pore pressure developments as functions of void ratio and confining pressure; compositional and
environmental factors affecting the behavior of frictional materials; critical state concepts; three-dimensional behavior. Constitutive modeling, elasto-plastic material models, nonassociated flow, work-hardening plasticity theory, failure criteria, stability and instability of frictional materials. (Courses: C&EE 220 and 229. References: miscellaneous technical reports and papers)

Major Field Requirements

Each student who selected Structures as his or her major field is expected to have a background equivalent to the material contained in the courses listed under prerequisite preparation for the major field. The student is also required to acquire proficiency in the subject matter listed in paragraphs IA and IIA, and in elective subject matter covered in at least xix additional graduate courses listed in this syllabus. The student is expected to acquire this knowledge in at least four of the seven topics contained in the syllabus. Each student must submit to the Departmental Graduate Advisor, a Proposal of Fields of Study for the Ph.D. Degree containing a list of the required subject matter.

Each student in this major field will be required to pass a closed book written examination based on the subject matter contained in the prerequisite courses, C&EE 235A, C&EE 237A, and any three elective graduate courses from her os his major field. The format of the examination is contained in the Appendix. Additional detail are available from the Chair of the Structures Ph.D. Field Committee.

Breadth Requirements

Each student selecting Structures as his/her major field will be held responsible for the body of knowledge contained in two independent PH.D. Minor Fields which complement the Structures Ph.D. Major Field. Each Minor Field is defined by a body of knowledge contained in three courses, at least two of which are at the graduate level. (Fields other than established Minor Fields in the School of Engineering and Applied Science are subject to the approval of the Structures Ph.D. Field Committee.) One of these Minor Fields may be selected from one of the seven topics contained in this Syllabus, provided the selected topical area is clearly distinct from the subject matter specified in the major field. The breadth requirement is satisfied by earning a 3.25 GPA in the courses listed in each of the Minor Fields.
The student may petition the Structures Ph.D. Field Committee for permission to show proficiency in a body of knowledge which differs from the above recommended norm.

Minor Field Requirements

A student selecting Structures as his/her Minor Field will be held responsible for the body of knowledge contained in C&EE 235A and C&EE 237A and any other course listed in this Syllabus (including prerequisite courses).
Students who select any of the courses listed in the Syllabus to satisfy requirements of a field other than Structures may not use that course as part of the Structures Minor Field.
Students who wish to satisfy the Minor Field written examination requirement by grades in courses must achieve at least a 3.25 GPS in the courses used to satisfy Minor Field requirements.
Students may petition the Structures PhD Field Committee for permission to show proficiency in a body of knowledge which differs from the above recommended norm.

List of References


P.1 Beer, F.P., and Johnston, E.R., Vector Mechanics for Engineers Statics and Dynamics, McGraw-Hill, 1972.
P.2 Popov, E.P., Engineering Mechanics of Solids, McGraw-Hill, 1990.
P.3 Ferguson, P., Breen, J., and Jirsa, J., Reinforced Concrete Fundamentals,5th Ed, Wiley, 1988.
P.4 Norris, C.H., Wilbur, J.B., and Utku, S., Elementary Structural Analysis, McGraw-Hill, 1976.
P.5 Salmon, C.G. and Johnson, J.E., Steel Structures: Design and Behavior, Intext Education Publisher, Current Edition.
P.6 Timoshenko, S.P., Young, D.H., and Weaver, W., Jr., Vibration Problems in Engineering, Wiley, 1974.
P.7 Ugural, A.C. and Fenster, S.K., Advanced Strength and Applied Elasticity, Elsevier, 1981.

I.   Static Analysis

I.1 Bathe, K-J. and Wilson, E.L., Numerical Methods in Finite Element Analysis, Prentice Hall, 1976.
I.2 Boley, B.O. and Weiner, J.G., Theory of Thermal Stresses, R. E. Krieger, 1985.
I.3 Cook, R., Concepts and Applications of Finite Element Analysis, 1974.
I.4 Flugge, W., Stresses in Shells, Springer Verlag, 1960.
I.5 Gallagher, R., Finite Element Analysis, Prentice Hall, 1975.
I.6 Ghali, A. and Neville, A.M., Structural Analysis, Third Edition, Chapmand and Hall, 1980.
I.7 Gladwell, G.M.L., Contact Problems in Classical Theory of Elasticity, 1981.
I.8 Kraus, W., Thin Elastic Shells, 1967.
I.9 Mura, T., Micromechanics of Defects in Solids, 2nd Ed. 1987.
I.10 Szilard, R., Theory and Analysis of Plates, Prentice Hall, 1974.
I.11 Timoshenko, S.P. and Woinowsky-Krieger, S., Theory of Plates & Shells, McGraw-Hill, 1959
I.12 Zienkiewicz, OC., The Finite Element Method, Third Edition, McGraw-Hills, 1977.

II.   Dynamic Analysis

II.1 Achenbach, J.D., Wave Propagation in Elastic Solids, North Holland, Amsterdam, 1973.
II.2 Clough, R. and Penzien, J., Dynamics of Structures, McGraw-Hills, 1975.
II.3 Ewing, W.M., Jardetzky, W.S., and Press, F., Elastic Waves in Layered Media, McGraw-Hills, 1957.
II.4 Hurty, W.C. and Rubinstein, M.F., Dynamics of Structures, Prentice Hall, 1964.
II.5 Meirovitch, L., Analytical Methods in Vibrations, MacMillan Co., 1967
II.6 Meirovitch, L., Computational Methods in Structural Dynamics, Sijhoff & Noordhoff, 1980.
II.7 Thompson, W.T., Vibration Theory and Applications, Prentice Hall, 1975.
II.8 Berg, G.V., Elements of Structural Dynamics, Prentice Hall, 1989.

III.   Design

III.1 Atrek, E., Gallagher, R.H., Ragsdell, K.M., and Zienkiewicz, O.C., (Editors), New Directions in Optimum Structural Design, John Wiley, NY, 1984
III.2 Haftka, R.T., Gurdal, Z., and Kamat, M.P., Elements of Structural Optimization, Second
Edition, Kluwar Academic Publishers, Boston, 1990.
III.3 Lin, T.Y., Design of Prestressed Concrete Structures, Wiley, 1963.
III.4 MacGregor, J.G., Reinforced Concrete, Prentice Hall, 1988
III.5 McCormac, J.C., Structural Steel Design (LRFD Method, Harper & Row, 1989
III.6 Morris, A.J., (Ed.), Foundations of Structural Optimization: A Unified Approach, John Wiley, NY, 1982.
III.7 Park, R. and Paulay, T., Reinforced Concrete Structures, Wiley, 1974.
III.8 Seismological Committee of the Structural Engineers Association of California, Recommended Lateral Force Requirements and Commentary, Current Edition.
III.9 Vanderplaats, G.N.,Numerical Optimization Techniques for Engineering Design with Applications, MacGraw-Hills, NY, 1984.
III.10 Wang, C.K. and Salmon, C.G., Reinforced Concrete Design, 4th Edition, Harper & Row, 1979.

IV.   Earthquake Engineering

IV.1 Englekirk, R.E. and Hart, G.C., Earthquake Response of Structures, Prentice Hall 1982.
IV.2 Dobrin, M.B., Introduction to Geophysical Prespecting, McGraw-Hill, 1974.
IV.3 Hart, G.C., Uncertainty Analysis, Loads, and Safety in Structural Engineering, Prentice Hall, 1982.
IV.4 Jacobs, J.A., Russell, R.D., and Wilson, J. T., Physics and Geology, McGraw-Hill, 1974
IV.5 Newmark, N.M. and Rosenbleuth,E., Fundamentals of Earthquake Engineering, Prentice Hall, 1971.

V.   Experimental Analysis

V.1 Barsom, J.M. and Rolfe, S.T., Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics 2nd Edition, Prentice Hall, 1977.
V.2 Dally, J.W. and Riley, W.F.,Experimental Stress Analysis, 2nd Ed., McGraw-Hill, 1971.
V.3 Hellan, K., Introduction to Fracture Mechanics, McGraw-Hill, 1984
V.4 Holman, J.P., Experimental Methods for Engineers, McGraw-Hills, 1971.

VI.   Stability and Nonlinear Analysis

VI.1 Bathe, K.J., Ozdemir, H., and Wilson, E.L., Static and Dynamic Geometric and Material
Nonlinear Analysis, University of California, Berkeley, Structural Engineering Lab, Report No. UCSESM 74-4, 1974.
VI.2 Kachanov, L.M., Foundations of the Theory of Plasticity, MIR Publishers, 1974.
VI.3 Lin, T.H., Theory of Inelastic Structures, Wiley, 1968.
VI.4 Simiteses, G.J., An Introduction to the Elastic Stability of Structures, Prentice Hall, 1976.
VI.5 Timoshenko, S.P. and Gere, T., Theory of Elastic Stability, McGraw-Hill, 1976.
VI.6 Bazant, Z.P. and Cedolin, L., Stability of Structures, Oxford University Press, 1991.

VII.   Mechanics of Structural Materials

Professional Journals:

ASCE Journal of Structures
ASCE Journal of Engineering Mechanics
Bulletin of the Seismological Society of American EERI Monograph Series
Journal of Earthquake Engineering and Structural Dynamics
Journal of Geophysics Proceedings of World Conferences on Earthquake Engineering
Earthquake Spectra
International Journal of Solids and Structures
Journal of Applied Mechanics
AIAA Journal
Journal of The Masonry Society
International Journal for Numerical Methods in Engineering

Example Programs

Example 1

Major Field

C&EE 235 (I. Static Analysis), C&EE 237A (II. Dynamic Analysis) and six (6) courses C&EE 235B (I. Static Analysis) C&EE 235C (VI. Stability and Nonlinear Analysis) C&EE M240 (III. Design) C&EE 241 (III. Design) C&EE 242 (III. Design) C&EE 244 (III. Design)
Note: The four specialized areas are I, II, III, and IV.


(1) Geotechnical Engineering C&EE 220 C&EE 221 C&EE 223
(2) Earthquake Engineering (Specialized Area IV) C&EE 222 C&EE 245 C&EE 246

Example 2

Major Field

C&EE 235 (I. Static Analysis) C&EE 237A (II. Dynamic Analysis) and six (6) courses C&EE 232 (I. Static Analysis) C&EE 235B (I. Static Analysis) C&EE 235C (VI. Stability and Nonlinear Analysis) C&EE 236 (VI. Stability and Nonlinear Analysis) C&EE 240 (III. Design) MAE 269B (II. Dynamic Analysis
Note: The fours areas of specialization are I, II, III, and VI.


(1) Mechanics of StructuralMaterials (Specialized Area VII) C&EE 233 C&EE 234 MSE 250A
(2) Any Appropriate Established Ph.D.Minor Field; e.g., Operations Research Applied Dynamic Systems Dynamics


Format for Written Preliminary Ph.D. Major Field Examination in the Field of Structures. The written Preliminary Ph.D. Exam in the field of Structures is a closed-book exam, given in two parts on separate days.

Part I is a five hour exam consisting of at least five questions covering the prerequisite subject matter contained in courses C&EE 130, C&EE 135B, C&EE 137, and C&EE 141 or C&EE 142.

Part II is a five hour examination covering the subject matter contained in courses C&EE 235A and C&EE 237A plus subject matter contained in at least three additional courses from each student’s study llist.

Prior to the examination, each student will be asked to specify three elective courses from his/her study list for inclusion of related subject matter on the examination; the Sstructures Ph.D. Field Committee will prepare an examination covering subject matter in the specified subject areas.

Each student will submit answers to a total of five questions from Part I and five questions from Part II. Two of the five questions answered in Part II must be those related to the subject matter in courses C&EE 235A and C&EE 237A.

In order to pass the examination a student must receive a passing grade on a total of seven questions, with not less than three passing grads in each Part.

Students may elect to take the Written Preliminary Ph.D. Major Field Examination to satisfy the comprehensive examination requirement in the program leading to the Master of Science in Civil Engineering (Plan II).

Studentsare permitted only two (2) attempts at passing the Written Preliminary Ph.D. Major Field Examination, including any attempts made to satisfy the M.S. comprehensive examination requirements using this examination.