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# Lecture6c

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### Lecture6c

1. 1. Today: Virtual Work Book: Chapter 11.1-11.3 + hand-out on Blackboard
2. 2. a) Calculate the reactions in A and B b) Calculate the normal forces in DD’ and EE’ with the correct signs for tension and compression. c) Draw the N, V and M lines for CDSEGA B E’ ED D’ C S G
3. 3. + + -
4. 4. A few tips… • When drawing N,V and M lines, clearly denote the jumps and kinks in the lines. Give the values of ‘special’ points on the curves (maxima, transition points).
5. 5. A few tips… • Use enough paper, work neatly. It will reduce the number of unnecessary mistakes. • Before filling in the answering sheet, draw the N,V and M diagrams on a piece of scrap paper.
6. 6. Work of a force (infinitesimal movement) The work done by a force F acting on a particle with a differential displacement dr is defined as: dW d= ×F r W = [Nm] = kg m2 /s2 ] = [J]
7. 7. Work of a force (infinitesimal movement) The work done by a force F acting on a particle with a differential displacement dr is defined as: cosdW d α= F r
8. 8. Work of a force (finite movement) ( )x x y y z zW d F dr F dr F dr= = + +∫ ∫F r
9. 9. Static equilibrium of a particle
10. 10. The principle of virtual work (particle) A particle is in equilibrium when for any virtual displacement, the virtual work is equal to zero. 0x x y y z zW u F u F u Fδ δ δ δ= + + =∑ ∑ ∑
11. 11. Work of a concentrated moment
12. 12. Work of a concentrated moment A B
13. 13. Small-Angle approximations
14. 14. Work of a concentrated moment A B
15. 15. The principle of virtual work (body in two dimensions) A particle is in equilibrium when for any variational displacement and/or rotation, the virtual work is equal to zero. 0i i i ix x y y i iW u F u F Mδ δ δ δθ= + + =∑ ∑ ∑
16. 16. Calculate the reaction forces and moment in A using the principle of virtual work.A B
17. 17. Calculate the reaction forces and moment in A. Vertical reaction A B
18. 18. Calculate the reaction forces and moment in A. Horizontal reaction A B
19. 19. Calculate the reaction forces and moment in A. Moment A B
20. 20. Calculate the reaction in B A C B
21. 21. Calculate the reaction in B Replace hinge B by a reaction force.A C B
22. 22. Calculate the reaction in B Replace hinge B by a reaction force. Due to the absence of hinge B, the beam can rotate A C B
23. 23. Calculate the reaction in B Replace hinge B by a reaction force. Due to the absence of hinge B, the beam can rotate Express all virtual rotations in terms of A C B
24. 24. Calculate the reaction moment in A B A S
25. 25. Calculate the internal moment in C B A C
26. 26. Calculate the internal moment in CBA C BA
27. 27. Internal moment • Hinge: only different rotation angles on either side of the cut. • Reaction moments M
28. 28. Calculate the shear force in C B A C
29. 29. Calculate the shear force in CBA BA
30. 30. Shear force • Shear hinge: only different displacements perpendicular to the member on either side of the cut. • Reaction forces V
31. 31. Calculate the normal force in member FG of this truss structure. B A C D E F G H
32. 32. Calculate the normal force in member FG of this truss structure.B A C D E F G H
33. 33. Normal force • Telescope hinge: only different displacements parallel to the member on either side of the cut • Reaction forces N