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STATICS - CASE STUDY

    Introduction


Problem Animation
Click to view movie (480k)

 

A car jack is constructed with four pinned members and a threaded shaft. The shaft must be designed to withstand the tension that results when hoisting a heavy automobile.

What is known:

  • The members of the jack are pinned together at points A, B, C, and D.
  • The length of each member is 0.2 m.
  • The weight of the automobile exerts a force of 1,960 N on the jack.
  • The threaded shaft is pinned to the jack at points C and D.
  • Under normal conditions, the jack is designed to support weight when the bottom members are at an angle between θ = 30° and θ = 60°.
     
    Questions


Force Diagram

 

At what angle θ is the tension in the shaft greatest under normal conditions (30oθ ≤ 60o)? At what angle θ is the tension in the shaft least?

   
  Approach

 
  • Determine the virtual work performed by the weight of the automobile and the tension in the shaft.
  • Knowing that the total virtual work must be equal to zero, derive an equation for the tension T as a function of the angle θ.
  • Use graphic analysis to determine the maximum and minimum values of T under normal operating conditions.