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ENGI 1313 Mechanics I

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ENGI 1313 Mechanics I

Lecture 28:Method of Joints

- to understand the method of joints for establishing forces in truss members

- Support Reactions

Ax

Ay

Cy

- Joint Equilibrium
- FBD at a joint
- Particle equilibrium concepts
- Solve for member forces

- Joint Forces
- Tension pulls on joint
- + convention

- Compression pushes on joint
- - convention

- Newton’s 3rd Law
- T pull on member
- C push on member

- Tension pulls on joint

- Two-Force Member
- Coplanar and concurrent force system
- What does this mean?

Automatically Satisfied

Necessary for Equilibrium

- Find Support Reactions
- Typically required but not always necessary

- Draw FBD at Truss Joint
- Select joint with 1 known force and at most 2 unknowns
- Assume forces are tensile (positive scalar) unless obvious by inspection

- Apply Equations of Equilibrium
- Repeat for all Joints

Find Support Reactions

Resolve FCB

Find Support Reactions

Resolve FCB

Resolve FCD

- Determine the force in each member. Indicate whether the member is in tension (T) or compression (C).

500N

FBC

FBA

- Where to Start?
- Examine joints
- # Known Forces?
- # Unknown Forces?

- Examine joints

- Joint B

- Joint C

- Joint A

- Support Reactions
- More than 2 unknowns at each joint then determine reactions first
- For this case not necessary but to show equivalence

Ax

Ay

Cy

- Results Summary

- Hibbeler (2007)
- http://wps.prenhall.com/esm_hibbeler_engmech_1