free-body diagrams, equations of equilibrium & constraints for a rigid body todays objective:...
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FREE-BODY DIAGRAMS, EQUATIONS OF EQUILIBRIUM & CONSTRAINTS FOR A RIGID BODY
Today’s Objective:
Students will be able to:
a) Identify support reactions in 3-D and draw a free body diagram, and,
b) apply the equations of equilibrium.
In-Class Activities:
• Check Homework, if any
• Reading Quiz
• Applications
• Support Reactions in 3-D
• Equations of Equilibrium
• Concept Quiz
• Group Problem Solving
• Attention quiz
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READING QUIZ
1. If a support prevents rotation of a body about an axis, then the support exerts a ________ on the body about that axis.
A) couple moment B) force
C) Both A and B. D) None of the above.
2. When doing a 3-D problem analysis, you have ________ scalar equations of equilibrium.
Enter a number corresponding to your answer.
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3D Rigid Body Equilibrium (Ch 5)
6 equations 6 unknowns that can be solved
for a single rigid body in 3D
∑ �⃑�=0
∑ �⃑�𝑃=0
∑ 𝐹 𝑥=0∑ 𝐹 𝑦=0∑ 𝐹 𝑧=0
∑ 𝑀𝑃𝑥=0∑ 𝑀𝑃𝑦=0∑ 𝑀𝑃𝑧=0
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roller or smooth surfacesingle F normal to surface
Support Reactions in 3D
Ball-and-socket jointFx, Fy and Fz
fixed supportFx, Fy, Fz and Mx, My, Mz
*more complete table in text
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Real Supports
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The Door Hinge & “Proper Alignment”
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FBD Example 1 in 3D
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FBD Example 2 in 3D
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FBD Example 3 in 3D
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CONCEPT QUIZ
1. The rod AB is supported using two cables at B and a ball-and-socket joint at A. How many unknown support reactions exist in this problem?
1) 5 force and 1 moment reaction
2) 5 force reactions
3) 3 force and 3 moment reactions
4) 4 force and 2 moment reactions
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FBD Example 4 in 3D
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FBD Example 5 in 3D
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Solution to Example 5 in 3D (cont)Determine the reaction forces at A and the tension in the cable, if F = 120N.
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Solution to Example 5 in 3D (cont)
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Solution to Example 1 in 3DDetermine the reaction forces at O and tension in cables AB and AC if the plant weighs 30 lb.
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ATTENTION QUIZ
1. A plate is supported by a ball-and-socket joint at A, a roller joint at B, and a cable at C. How many unknown support reactions are there in this problem?
A) 4 forces and 2 moments
B) 6 forces
C) 5 forces
D) 4 forces and 1 moment
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ATTENTION QUIZ
2. What will be the easiest way to determine the force reaction BZ ?
A) Scalar equation FZ = 0
B) Vector equation MA = 0
C) Scalar equation MZ = 0
D) Scalar equation MY = 0