Compound Structures 2010-11 - Structural Analysis IV...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Structural Analysis IV Virtual Work – Compound Structures 4th Year Structural Engineering 2010/11 Dr. Colin Caprani Dr. C. Caprani 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Structural Analysis IV Contents 1. Introduction . ........................................................................................................ 4 1.1 Purpose . ........................................................................................................... 4 2. Virtual Work Development. ............................................................................... 5 2.1 The Principle of Virtual Work. ........................................................................ 5 2.2 Virtual Work for Deflections. .......................................................................... 9 2.3 Virtual Work for Indeterminate Structures. ................................................... 10 2.4 Virtual Work for Compound Structures. ....................................................... 12 3. Basic Examples . ................................................................................................. 15 3.1 Example 1 . ..................................................................................................... 15 3.2 Example 2 . ..................................................................................................... 22 3.3 Example 3 . ..................................................................................................... 32 3.4 Example 4 . ..................................................................................................... 39 3.5 Problems . ....................................................................................................... 47 4. Advanced: Ring Beam Examples. .................................................................... 51 4.1 Example 1 . ..................................................................................................... 51 4.2 Example 2 . ..................................................................................................... 56 4.3 Example 3 . ..................................................................................................... 63 4.4 Example 4 . ..................................................................................................... 71 4.5 Example 5 . ..................................................................................................... 80 4.6 Review of Examples 1 – 5. .......................................................................... 101 5. Advanced: Grid Examples. ............................................................................. 112 5.1 Example 1 . ................................................................................................... 112 5.2 Example 2 . ................................................................................................... 118 5.3 Example 3 . ................................................................................................... 127 6. Appendix – Past Exam Questions. ................................................................. 137 6.1 Sample Paper 2007 . ..................................................................................... 137 6.2 Semester 1 Exam 2007 . ............................................................................... 138 Dr. C. Caprani 2
Background image of page 2
Structural Analysis IV 6.3 Semester 1 Exam 2008 . ............................................................................... 139 6.4 Semester 1 Exam 2009 . ............................................................................... 140 6.5 Semester 1 Exam 2010 . ............................................................................... 141 7. Appendix – Trigonometric Integrals. ............................................................ 142 7.1 Useful Identities. .......................................................................................... 142 7.2 Basic Results. ............................................................................................... 143 7.3 Common Integrals . ...................................................................................... 144 8. Appendix – Volume Integrals. ........................................................................ 151 Dr. C. Caprani 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Structural Analysis IV 1. Introduction 1.1 Purpose Previously we only used virtual work to analyse structures whose members primarily behaved in flexure or in axial forces. Many real structures are comprised of a mixture of such members. Cable-stay and suspension bridges area good examples: the deck- level carries load primarily through bending whilst the cable and pylon elements carry load through axial forces mainly. A simple example is a trussed beam: Other structures carry load through a mixture of bending, axial force, torsion, etc. Our knowledge of virtual work to-date is sufficient to analyse such structures. Dr. C. Caprani 4
Background image of page 4
Structural Analysis IV 2. Virtual Work Development 2.1 The Principle of Virtual Work This states that: A body is in equilibrium if, and only if, the virtual work of all forces acting on the body is zero. In this context, the word ‘virtual’ means ‘having the effect of, but not the actual form of, what is specified’. There are two ways to define virtual work, as follows. 1. Virtual Displacement: Virtual work is the work done by the actual forces acting on the body moving through a virtual displacement. 2. Virtual Force: Virtual work is the work done by a virtual force acting on the body moving through the actual displacements. Virtual Displacements A virtual displacement is a displacement that is only imagined to occur: virtual displacements must be small enough such that the force directions are maintained. virtual displacements within a body must be geometrically compatible with the original structure. That is, geometrical constraints (i.e. supports) and member continuity must be maintained. Dr. C. Caprani 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Structural Analysis IV Virtual Forces A virtual force is a force imagined to be applied and is then moved through the actual deformations of the body, thus causing virtual work.
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 151

Compound Structures 2010-11 - Structural Analysis IV...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online