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# Lecture3c(1)

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### Transcript

• 1. Today: Trusses continued - Method of sections - Rigid trusses - Frames Book: Chapter 6.4 & 6.6
• 2. A B C D E F G H K L M Determine the zero-force members of this structure under the given load.
• 3. A B C D E F G How many zero-force members does this structure have for the given external load? A) 0 B) 1 C) 4 D) 5
• 4. A B C D E G How many zero-force members does this structure have for the given load? A) 0 B) 3 C) 5 D) 7 H F
• 5. What are zero-force members good for? - In case the structure is loaded in a different way - To prevent buckling
• 6. Two Methods to Analyze Trusses 1) Method of joints 2) Method of sections
• 7. Method of joints Determine the force in the members by calculating the equilibrium of the joints 1. Draw Free Body Diagram 2. Determine the reaction forces at the supports of the whole structure 3. Calculate the forces in a joint with max. 2 unknowns 4. Proceed to the next joint with max. 2 unknowns until all joints are analyzed
• 8. Determine the force in member DE.
• 9. 1) Determine the force in member DE. 2) Determine the force in member DL.
• 10. Method of sections Determine the force in a members by dividing the structure in two sections by cutting the members and calculating the equilibrium of one of the sections. 1) Determine the section by cutting just three members (in general) 2) Use the moment equilibrium equation in a clever way.
• 11. A B C D E G Calculate the forces in members CE, DE, DF H F K L M N R Q
• 12. A B C D E G Calculate the forces in member HG H F K L M N R Q
• 13. Rigid truss Flexible truss (mechanism) 3 members, 3 joints 4 members, 4 joints
• 14. 3 members, 3 joints 5 members, 4 joints 7 members, 5 joints
• 15. Rigid truss consisting of triangular elements Where s = number of members k = number of joints
• 16. Non-rigid truss Rigid truss This is a necessary condition, but not sufficient!!
• 17. Rigid or non-rigid?
• 18. Rigid or non-rigid?
• 19. Rigid or non-rigid?
• 20. Rigid or non-rigid?
• 21. Rigid or non-rigid?
• 22. Constraints
• 23. Constraints
• 24. Constraint truss structure Where n = difference between number of unknowns and equations r = number of constraints s = number of members k = number of joints
• 25. Constraint truss structure n < 0 kinematically indeterminate (mechanism) n >= 0 kinematically determinate (necessary, not sufficient) n = 0 statically determinate n > 0 statically indeterminate
• 26. Statically determinate?