Free Body Diagrams Mechanical Engineering Notes | EduRev

Engineering Mechanics - Notes, Videos, MCQs & PPTs

Mechanical Engineering : Free Body Diagrams Mechanical Engineering Notes | EduRev

The document Free Body Diagrams Mechanical Engineering Notes | EduRev is a part of the Mechanical Engineering Course Engineering Mechanics - Notes, Videos, MCQs & PPTs.
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Equilibrium of Bodies in 3D space

  • Draw the FBD
  • Equations of equilibrium are given by

 

Free Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev

 

  • 6 scalar equations are required to express the conditions for the equilibrium of a rigid body in the general three dimensional case.

∑Fx = 0  ∑Fy = 0  ∑Fz = 0
∑Mx = 0 ∑My = 0 ∑Mz = 0 

  • 6 unknown reactions can be solved for.

Some unknown reactions in 3D: 

Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev

 

Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev

 

Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev
Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev

 

Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev
Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev

 

Free Body Diagrams Mechanical Engineering Notes | EduRev

Examples 4.7

Free Body Diagrams Mechanical Engineering Notes | EduRev

Given W = Ladder + Person 

= 100 * 9.81 = 981 N

The wheels at A & B are flanged while the wheel at C is unflanged.

Determine reactions at A, B and C

Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev

Example 4.8

Given W = 270 lbs

Determine 

  • Tensions in AE and BD.
  • Reactions at A.

Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev

Example 4.9

Given mass of the cover: 30 kg Assume no axial reaction at B.

Find Tension in CD and reactions at A & B.

Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev

Example 4.10

Given W = 450 lb.

Find 

  • Location of G so that the tension EG is minimum
  • This minimum value of tension

Free Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRevFree Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev  

Free Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev

Free Body Diagrams Mechanical Engineering Notes | EduRev

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