# CE445/545 - Matrix Analysis of Structures

### Text: Matrix Structural Analysis, 2nd ed. by McGuire, Gallagher & Ziemian

Details of class organization and Engineering Outreach and Contact Information (Dr. Nielsen's Homepage)
 Class Date Topic Reading Assignment 1 Jan 15 Introduction - Review of Structures Links for the class notes are available through Blackboard 1.1-1.2 2 Jan 17 Degrees of Freedom & Coordinate Systems 2.1-2.3, 13.1 Jan 20 Human Rights Day 3 Jan 22 Axial Force Elements, Matrix Condensation, Matrix Condensation Example 2.4 2.12, 14 - These problems don't require matrix methods, but they do illustrate flexibility and stiffness concepts. Think about which approach is best for each problem.  (Submit assignments through Blackboard) 4 Jan 24 Axial Force Elements - Global Equations 2.5-2.6 5 Jan 27 Direct Stiffness Method 3.1 2.5, 2.6 6 Jan 29 Mathcad Background - 2 member truss 3.2-3.4 7 Jan 31 Stress & Strain - Work & Energy 4.1-4.4 8 Feb 3 Axial Force & Torsional Elements 4.5.1-4.5.2 3.3, (you can use MASTAN2, RISA, SAP, etc. to analyze the truss) 4*, 7* (*Provide "manual" solution, w/o Mastan2, RISA, etc.) 9 Feb 5 Beam Elements 4.5.3-4.5.5 10 Feb 7 Frame-Truss Example 11 Feb 10 3D Coordinate Transformations 4.6, 5.1.1 3.15 (the "computer program" may be MASTAN, RISA, SAP, etc.), [4.1b-e]*, 6* (*Provide a "manual" solution) 12 Feb 12 Coord. Transformation, Space Truss 5.1.2-5.1.4 13 Feb 14 Member End Releases - Hinge Example 4. 10*, 14, 16*, 5.3* (*Provide a "manual" solution) Feb 17 Presidents' Day 14 Feb 19 Virtual Displacements 6.1-6.5 5.10a 15 Feb 21 Displaced State of Elements - Shape Functions 7.1 16 Feb 24 Element Stiffness from Virtual Displacements 7.2 17 Feb 26 EXAM #1 18 Feb 28 Stiffness Matrices from Virtual Work 19 Mar 3 Non-nodal Forces from Virtual Displacements, Background 7.5 7.1, 6 20 Mar 5 Thermal & Prestrain Loads by Virtual Work 7.6 21 Mar 7 Nonuniform Elements, Tapered Element Example, Tapered Element/Log Shape Function 7.3 5.8a, b, f* (include axial deformations), 10b*, 13* (*Provide a "manual" solution) 22 Mar 10 Nonuniform Torsion 7.4 23 Mar 13 Nonuniform Torsion 2D vs. 3D Comparison 24 Mar 14 Uniform Torsion, 8-Element Nonuniform Torsion Project Assignment Mar 17-21 Spring Break 25 Mar 24 Shear Deformations, Shear Deformation Example 8.1.1-8.1.2 7.12, 19 26 Mar 26 Nonlinear Analysis 8.1.3 27 Mar 28 Nonlinear Examples 8.1.4 7.13 28 Mar 31 EXAM #2 Presentation Topic Proposal 29 Apr 2 Plastic Hinge Example 8.2-8.3 8.1, 4 30 Apr 4 Matrix Non-linear Analysis 9.1 31 Apr 7 Geometric Stiffness Matrices for 2D 9.2 8.6, 8 32 Apr 9 Geometric Stiffness Matrix Example 1 9.3 33 Apr 11 Geometric Stiffness Matrix Example 2 9.4 Presentation Outline 34 Apr 14 Nonlinear Material Behavior 10.1 35 Apr 16 Nonlinear Material Example, Postscript 10.2 9.5, 9.10 (both can be done with MASTAN2) 36 Apr 18 Eigenvalue Buckling Analysis 10.3 37 Apr 21 Eigenvalue Buckling Examples 10.4 38 Apr 23 Partially Restrained Joints 13.1-13.2 Presentation Progress Report 39 Apr 25 Member End Offsets 13.3 10.12, 9.2 (both can be done with MASTAN2) 40 Apr 28 Restraint/Offset Example 13.5 41 Apr 30 Structural Optimization 42 May 2 Structural Optimization 43 May 5 Presentations 13.20, 23 44 May 7 Presentations 45 May 9 Presentations 49 May 14 EXAM #3

The reading assignments should be completed before each lecture.

The homework problems are due on the dates shown.