` CEVE-MECH 527-427 MATRIX METHODS IN STRUCTURAL MECHANICS

FALL 2009

Ryon 102, Course T TR 1 to 2:20 pm

Office Hours: T TR 2:30 to 3:30 pm

Instructor: Dr. Satish Nagarajaiah

Professor of Civil Eng.

Professor of Mechanical Eng.

213 Ryon Building

713-348-6207, nagaraja@rice.edu

Course

Outline

427 Introduction to matrix structural analysis of beams, trusses, and frames.

527 Introduction to differential and integral formulations: Minimum Principles, Variational Principles, Weighted Residuals, Energy Principles, and Principal of Virtual Work. Boundary, Initial and Eigenvalue problems. Introduction to finite element and finite difference methods for structural mechanics. Applications to static and dynamic truss, beam and frame problems. Use of computer software. 527 UG/Graduate Version. Graduate Version requires extra work: assignments and project.

Text Book: Detailed course notes will be provided: No textbook required.

Homework Policy:

Homework due date will be announced in class. Homework submitted late will receive partial grade at the discretion of the instructor.

Grading Policy:

CEVE / MECH 427	CEVE / MECH 527
HW and MATLAB Assignments 50%	HW and MATLAB Assignments 25%
Computer Software Assign. ETAB/SAP 25%	Computer Software ETABS/SAP/MATLAB 25%
Take Home Exam 25%	Take Home Exam 25%
	Final Computer Project based on MATLAB 25%

COURSE TOPICS:

INTRODUCTORY CONCEPTS IN STRUCTURAL ANALYSIS

· Deflection (Unit load & Moment Area) Methods for Stiffness Matrix Calculation

STIFFNESS METHOD

· Stiffness Method using basic equations

· Element Stiffness

· Coordinate Transformations

· Nodal equilibrium of the structure

· Global stiffness matrix

· Solution of the global stiffness equation

· Nodal displacements & Element forces

· Settlement, initial and thermal strains

· Stiffness Method using principle of virtual work

· Virtual work for deformable bodies

· Element stiffness matrix

· Coordinate Transformations

· Global stiffness matrix

· Solution, nodal displacements, element forces

· Settlement, initial and thermal strains

· Stiffness method for beams and planar frames

· Two dimensional (2D) Beam element

· Stiffness formulation and solution of beam problems

· 2D Plane Frame element

· Stiffness formulation and solution of frame problems

· Settlement, initial and thermal strains

INTRODUCTORY CONCEPTS IN COMPUTATIONAL METHODS IN STRUCTURAL MECHANICS

· Boundary, Initial and Eigenvalue prolems

· Introduction to computational methods in structural mechanics

· Integro-differential equations: Minimum Principles, Variational Principles, Weighted Residuals, Energy Principles, Principal of Virtual Work, Eigenvalue Analysis.

· Introduction to the Finite Element Method (FEM) and Finite Difference Methods (FDM)

· FEM: Static Systems: Boundary Value Problems – Beams and Frames

· FEM/FDM: Dynamic Systems: Initial Value Problems (Eigenvalue Analysis) – Beam and Frames

COMPUTER PROGRAMS

· Computer programs based on MATLAB (427 and 527 students)

· Computer software ETABS and SAP 2000 (427 and 527 students)

CEVE 427 Course Objectives and Outcomes

Course Objectives:

The objective of CEVE 427 is to learn the fundamental concepts of modern matrix structural analysis, such as the stiffness method, and the concepts of modern matrix structural mechanics, such as the finite element method; while, briefly learning the concepts of classical structural analysis such as, energy methods, method of consistent displacement method, slope deflection method, and moment distribution method. The course builds on the fundamental concepts of structural analysis learnt in mechanics of solids and structures course (CEVE 311). The students will:

1. Gain a fundamental understanding of the analysis of statically determinate and indeterminate structures such as trusses, beams and frames

2. Learn the determination of deflections using energy methods

3. Study the classical structural analysis methods, such as energy, compatibility, and equilibrium methods

4. Learn the fundamental concepts of the stiffness method and apply it to a variety of structural problems involving trusses, beams, and frames (two and three dimensional)

5. Understand the introductory concepts of the finite element methods applied to structural mechanics problems such as plates or slabs

6. Learn the use of structural analysis software typically used in structural engineering design firms

Course Outcomes:

Students successfully completing CEVE 427 course will have a clear and thorough understanding of the fundamental concepts of modern structural analysis and sufficient analysis skills for successful professional practice. The students will have the ability to perform advanced structural analysis by hand and by modern computer software. The students will be able to:

1. Apply the concepts of linear algebra (matrices, determinants) to structural analysis and mechanics problems

2. Calculate the deflection of trusses and beams using energy methods

3. Perform the structural analysis of determinate and indeterminate structures using classical compatibility methods, such as method of consistent displacements, and equilibrium methods, such as slope deflection and moment distribution method.

4. Perform structural analysis using the stiffness method. Solve multiple degree of freedom two and three dimensional problems involving trusses, beams and frames

5. Understand basic finite element analysis

6. Analyze complex structures using computer software such as ETABS and SAP2000

7. Document structural analysis results, write detailed project report, and communicate the project findings to the class by making a detailed PowerPoint presentation

Contribution to Meeting the Professional Component:

Engineering Content, 100%, 3 credit hours

Although not a required course, the students are advised to take this course as an essential preparation for professional practice