Question 6.113: The aircraft-hangar door opens and closes slowly by means of...
The aircraft-hangar door opens and closes slowly by means of a motor, which draws in the cable AB. If the door is made in two sections (bifold) and each section has a uniform weight of 300 lb and height L = 10 ft, determine the force on the cable when u = 90°. The sections are pin connected at C and D and the bottom is attached to a roller that travels along the vertical track.
Equations of Equilibrium: Referring to the FBD of member CD shown in Fig. a,
\hookrightarrow +\Sigma M_D=0 ; \quad 300 \cos 45^{\circ}(5)-C_y\left(10 \cos 45^{\circ}\right)-C_x\left(10 \sin 45^{\circ}\right)=0C_x+C_y=150 (1)
Referring to the FBD of member AC shown in Fig. b
\hookrightarrow +↑\Sigma M_A=0 ; \quad 300 \cos 45^{\circ}(5)+C_y\left(10 \cos 45^{\circ}\right)-C_x\left(10 \sin 45^{\circ}\right)=0C_x – C_y = 150 (2)
Solving Eqs. (1) and (2) yields
C_x=150 \mathrm{lb} C_y=0
Using these results to write the force equations of equilibrium along y axis
+↑ \Sigma F_y=0 ; \quad T_{A B}-300=0 \quad T_{A B}=300 \mathrm{lb}
