Structure analysis II Matrix Stiffness Method Pdf
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Contents
Matrix Stiffness Method
4.1 Introduction ......................................................................................................... 3
4.1.1 Background .................................................................................................... 3
4.1.2 Basic Concepts............................................................................................... 4
4.1.3 Computer Programs to Support Learning...................................................... 6
4.2 Basic Approach .................................................................................................. 10
4.2.1 Individual Element ...................................................................................... 10
4.2.2 Assemblies of Elements ............................................................................... 12
4.2.3 Example 1 .................................................................................................... 14
4.2.4 General Methodology .................................................................................. 20
4.2.5 Member contribution to global stiffness matrix .......................................... 22
4.2.6 Interpretation of Stiffness Matrix ................................................................ 27
4.2.7 Restricting a Matrix – Imposing Restraints ................................................. 29
4.3 Plane Trusses ..................................................................................................... 32
4.3.1 Introduction .................................................................................................. 32
4.3.2 Truss Element Stiffness Matrix ................................................................... 35
4.3.3 Element Forces ............................................................................................ 40
4.3.4 Example 2: Basic Truss ............................................................................... 43
4.3.5 Example 3: Adding Members ...................................................................... 52
4.3.6 Example 4: Using Symmetry ....................................................................... 56
4.3.7 Self-Strained Structures ............................................................................... 59
4.3.8 Example 5 – Truss with Differential Temperature ...................................... 63
4.3.9 Example 6 – Truss with Loads & Self Strains ............................................ 69
4.3.10 Problems ................................................................................................... 74
4.4 Beams .................................................................................................................. 77
4.4.1 Beam Element Stiffness Matrix ................................................................... 77
4.4.2 Beam Element Loading ............................................................................... 82
4.4.3 Example 7 – Simple Two-Span Beam ......................................................... 84
4.4.4 Example 8 – Non-Prismatic Beam .............................................................. 88
4.4.5 Problems ...................................................................................................... 92
4.5 Plane Frames ...................................................................................................... 95
4.5.1 Plane Frame Element Stiffness Matrix ........................................................ 95
4.5.2 Example 9 – Simple Plane Frame ............................................................. 104
4.5.3 Example 10 –Plane Frame Using Symmetry............................................. 109
4.5.4 Problems .................................................................................................... 115
4.6 Appendix .......................................................................................................... 120
4.6.1 Plane Truss Element Stiffness Matrix in Global Coordinates ................... 120
4.6.2 Coordinate Transformations ...................................................................... 129
4.6.3 Past Exam Questions ................................................................................. 137
4.7 References ........................................................................................................ 148
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