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# ENGI 1313 Mechanics I - PowerPoint PPT Presentation

ENGI 1313 Mechanics I. Lecture 28:Method of Joints. Lecture 28 Objective. to understand the method of joints for establishing forces in truss members. Recall 2D Rigid Body Equilibrium. Support Reactions. A x. A y. C y. Method of Joints. Joint Equilibrium FBD at a joint

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ENGI 1313 Mechanics I

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## ENGI 1313 Mechanics I

Lecture 28:Method of Joints

### Lecture 28 Objective

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

### Recall 2D Rigid Body Equilibrium

• Support Reactions

Ax

Ay

Cy

### Method of Joints

• Joint Equilibrium

• FBD at a joint

• Particle equilibrium concepts

• Solve for member forces

### Method of Joints (cont.)

• Joint Forces

• Tension pulls on joint

• + convention

• Compression pushes on joint

• - convention

• Newton’s 3rd Law

• T pull on member

• C push on member

### Method of Joints Equilibrium Equations

• Two-Force Member

• Coplanar and concurrent force system

• What does this mean?

Automatically Satisfied

Necessary for Equilibrium

### Procedure for Method of Joints

• 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

### Coordinate Axes Orientation

Find Support Reactions

### Coordinate Axes Orientation (cont.)

Resolve FCB

Find Support Reactions

Resolve FCB

Resolve FCD

### Example 28-01

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

500N

FBC

FBA

### Example 28-01 (cont.)

• Where to Start?

• Examine joints

• # Known Forces?

• # Unknown Forces?

• Joint B

• Joint C

• Joint A

### Example 28-01 (cont.)

• 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

### Example 28-01 (cont.)

• Results Summary

### References

• Hibbeler (2007)

• http://wps.prenhall.com/esm_hibbeler_engmech_1