CEVE 427 MATRIX METHODS IN STRUCTURAL
MECHANICS
FALL 2005
Ryon 231, MW
Instructor:
Prof. S. Nagarajaiah
Depts. of Civil & Env.
216 Ryon Building
713-348-6207, nagaraja@rice.edu
Office
Hours: TBD
TA:
219 Ryon Building
713-348-2217, sonmeze@rice.edu
Course Description:
Introduction to
matrix structural analysis and finite element method, applied to trusses,
beams, frames and two dimensional elasticity problems. Use of
computer programs for structural analysis.
Prerequisite: CEVE
311
Corequisite: None
Knowledge Prerequisite: Analysis of statically
determinate trusses and beams. Applying equilibrium,
compatibility, and force-deformation relationships to structural elements.
Ability to calculate axial forces, shear forces, bending moments, and the
calculation of deflection of statically determinate beams.
Textbooks
and/or other required Material:
Text Book: Ronald Sack, Matrix Structural
Analysis, Waveland Press, 1994
ISBN:
0881338249
Recommended Reference:
William McGuire, Richard
H. Gallagher, Ronald D. Ziemian, Matrix Structural
Analysis, John Wiley, 2000, ISBN: 0471129186
Grading Policy:
Home Work and
Computer
Assignments - 20%
First Exam (in
class)
- 25%
Second Exam (Take Home)
- 25%
Final
Project - 30%
Homework Policy:
Homework
due date will be announced in class. Homework submitted late will receive
partial grade at the discretion of the instructor.
Course Topics
1. Introductory Concepts in Structural Mechanics
Linear
Algebra; Matrices and Determinants; Introduction to MATLAB; Basic differential equations
for one and two dimensional elasticity problems; Minimum principles, and
Principle of virtual work and complementary virtual work
2. Introductory Concepts in Structural Analysis
Unit load Method;
Deflection of trusses using complementary virtual work method; Deflection of
beams and frames using complementary virtual work method; Classical
compatibility methods: Method of consistent displacements; and Classical
equilibrium methods-Slope deflection method and Moment Distribution method.
3. 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; and Settlement, initial and thermal
strains.
4. 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.
5. 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.
6. Stiffness Method for Three Dimensional Structures
Space
trusses; Grid structures; Space Frames.
7. Introduction to Finite Element Method
8. Computer Software ETABS and SAP 2000
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