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Analysis of Structures. TrussesDesigned to support loadsConsist entirely of two-force membersFramesDesigned to support loadsInclude one or more multi-force membersMachinesDesigned to transmit and/or modify forcesInclude one or more multi-force members. Two-Force Members. Pinned at both ends
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1. ES220 Statics Exam III Review Notes
2. Analysis of Structures Trusses
Designed to support loads
Consist entirely of two-force members
Frames
Designed to support loads
Include one or more multi-force members
Machines
Designed to transmit and/or modify forces
Include one or more multi-force members
3. Two-Force Members Pinned at both ends (both joints)
No applied forces between joints
No applied moments
Line of action of forces is directed along a line drawn between the two joints
4. Trusses Consist entirely of straight two-force members, connected at joints
5. Trusses Example on board: decompose truss into two-force members and joints, and show how forces meet at joints
6. Trusses: Method of Joints Typically used to find forces in all or several of the members
Each joint is a particle
Particle equilibrium in 2D:
For each joint, we have 2 equations, therefore, we can solve for 2 unknowns
Must start process at a joint with only 2 unknown forces
7. Trusses: Method of Joints Find a joint with only two unknown forces
First, may need to draw an FBD of the entire truss and find support reactions
Draw FBD of selected joint
Draw each force along the direction of the member
Draw in tension (away from joint)
Find angle of force from truss geometry
Resolve angled forces into x, y components
8. Trusses: Method of Joints Apply equilibrium, to solve for 2 unknown forces
A + sign: the force is tension (T)
A – sign: the force is compression (C)
Find the next joint that has only 2 unknown forces and repeat the process
Typically this is adjacent to the prior joint
Repeat with additional joints until all member forces are known.
Remember to specify (T) or (C) for each force!
9. Special Cases
10. Trusses: Method of Joints Example
11. Trusses: Method of Joints Example
12. Trusses: Method of Sections Typically used when only 1 or a few member forces are needed
Since a section consists of multiple joints and multiple members, it is a rigid body
Rigid body equilibrium in 2D
For each section, have 3 equations, therefore, can solve for 3 unknown forces
13. Trusses: Method of Sections Identify the member(s) for which we will determine the forces
Can determine up to 3 forces for each section
Create a separable section by cutting through the member(s)
May need to cut additional members to cut loose a section
Decide which portion of the truss to keep
14. Trusses: Method of Sections Draw a free body diagram of the section
Replace cut members with forces directed along the direction of the cut members
Draw unknown forces in tension (pointed away from the joint)
Include externally applied forces and support reactions
First, you may need to draw an FBD of the entire truss to find support reactions
Include dimensions needed to sum moments
15. Trusses: Method of Sections Determine angles from truss geometry
Resolve angled forces into x, y components
Apply equilibrium,to solve for 3 unknown forces
A + sign: the force is tension (T)
A – sign: the force is compression (C)
16. Trusses: Method of Sections Cut the member for which you are finding the force
If possible, choose the other cuts such that the extra unknown forces (but not the force you need) pass through a single joint
Sum the moment about that joint
17. Trusses: Method of Sections Example
18. Frames Contain at least one multi-force member
Objective: Find some or all forces acting on members and/or find support reactions
19. Frames: Method of Analysis Draw a FBD of the entire frame, showing applied loads and support reactions
20. Frames: Method of Analysis Draw a FBD for each member of the frame
Find any two-force members
Pinned at both ends, no applied moments or loads
Draw forces directed along line connecting the two joints
21. Frames: Method of Analysis Multi-force members:
Pin connections: x and y reaction forces
Where two members connect, draw forces equal and opposite
22. Frames: Method of Analysis Draw forces on connecting members equal and opposite
Draw forces due to two-force members in the known direction
23. Frames: Method of Analysis FBD of entire frame is a rigid body
A multi-force member is a rigid body
For each rigid body, can solve for three unknowns, using 2D equilibrium
Using 2 or more of these rigid bodies, can find all the desired forces and reactions
24. Frames: Method of Analysis Example
25. Machines Transmits or modifies forces
Contain one or more multi-force members
26. Machines: Method of Analysis Similar to method for frames
27. Machines
28. Machines
29. Machines
30. Machines