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°.

Force Diagram

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

• 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.