ENGI 1313 Mechanics I

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ENGI 1313 Mechanics I

• Lecture 26 3D Equilibrium of a Rigid Body

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Schedule Change

• Postponed Class
• Friday Nov. 9
• Two Options
• Use review class Wednesday Nov. 28
• Preferred option
• Schedule time on Thursday Nov.15 or 22
• Please Advise Class Representative of Preference

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Lecture 26 Objective

• to illustrate application of scalar and vector
  analysis for 3D rigid body equilibrium problems

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Example 26-01

• The pipe assembly supports the vertical loads
  shown. Determine the components of reaction at
  the ball-and-socket joint A and the tension in
  the supporting cables BC and BD.

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Example 26-01 (cont.)

• Draw FBD

Due to symmetry TBC TBD
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Example 26-01 (cont.)

• What are the First Steps?
• Define Cartesian coordinate system
• Resolve forces
• Scalar notation?
• Vector notation?

F1 3 kN
F2 4 kN
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Example 26-01 (cont.)

• Cable Tension Forces
• Position vectors
• Unit vectors

F1 3 kN
F2 4 kN
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Example 26-01 (cont.)

• Ball-and-Socket Reaction Forces
• Unit vectors

F1 3 kN
F2 4 kN
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Example 26-01 (cont.)

• What Equilibrium Equation Should be Used?
• ?Mo 0
• Why?
• Find moment arm vectors

F1 3 kN
F2 4 kN
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Example 26-01 (cont.)

• Moment Equation

Due to symmetry TBC TBD
F1 3 kN
F2 4 kN
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Example 26-01 (cont.)

• Moment Equation

F1 3 kN
F2 4 kN
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Example 26-01 (cont.)

• Force Equilibrium

F1 3 kN
F2 4 kN
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Example 26-01 (cont.)

• Force Equilibrium

F1 3 kN
F2 4 kN
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Example 26-01 (cont.)

• Force Equilibrium

F1 3 kN
F2 4 kN
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Example 26-02

• The silo has a weight of 3500 lb and a center of
  gravity at G. Determine the vertical component of
  force that each of the three struts at A, B, and
  C exerts on the silo if it is subjected to a
  resultant wind loading of 250 lb which acts in
  the direction shown.

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Example 26-02 (cont.)

• Establish Cartesian Coordinate System
• Draw FBD

W 3500 lb
F 250lb
Bz
Cz
Az
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Example 26-02 (cont.)

• What Equilibrium Equation Should be Used?
• Three equations to solve for three unknown
  vertical support reactions

W 3500 lb
F 250lb
Bz
Cz
Az
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Example 26-02 (cont.)

• Vertical Forces

W 3500 lb
F 250lb
Bz
Cz
Az
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Example 26-02 (cont.)

• Moment About x-axis

W 3500 lb
F 250lb
Bz
Cz
Az
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Example 26-02 (cont.)

• Moment About y-axis

W 3500 lb
F 250lb
Bz
Cz
Az
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Example 26-02 (cont.)

• System of Equations
• Gaussian elimination

W 3500 lb
F 250lb
Bz
Cz
Az
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Example 26-02 (cont.)

• System of Equations
• Gaussian elimination

W 3500 lb
F 250lb
Bz
Cz
Az
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References

• Hibbeler (2007)
• http//wps.prenhall.com/esm_hibbeler_engmech_1