Question

Spring CD remains in the horizontal position at all times due to the roller at D. If the spring is unstretched when  =0° and the bracket achieves its equilibrium position when  =30°, determine the stiffness k of the spring and the horizontal and vertical components of reaction at pin A.

                             

Answer 1

Solution

Spring Force Formula : At the equilibrium position , the spring elongates.

x = 0.6 sin 30 ° m . Using the spring force formula , the force in spring CD is found to be F_sp= kx = 0.3k .

Equations of Equilibrium : From the free - body diagram of the bracket , Fig . a , the stiffness k of spring CD and Ay can be obtained by writing the moment equation of equilibrium about point A and the force equation of equilibrium along the x axis , respectively .

Using the result k = 1327.35 N / m and writing the force equation of equilibrium along the x axis ,