Example 7: For the beam and loading shown, determine the tension in the cable and the support reactions at A. Neglect the size of the pulley at C.
Solution: We begin the analysis by first drawing the free-body diagram of the beam. We remove the support A to reveal the reaction forces at that point. We also cut the cable at B and D to reveal the tension force in the cable.
Note that the cable is wrapped around a frictionless pulley, therefore, the tension in the cable is constant at every point along its length as indicated in the free-body diagram. We proceed by writing the equations of equilibrium and solving for the unknown forces. The distance between points C and D is . Summing moments about point A gives
The horizontal component of tension at D passes through point A, hence, it does not appear in the moment equation. Solving the above equation for T gives
Having found the tension in the cable, we can now find the reaction forces at A by using the two force equilibrium equations.
The negative sign in front of RAy indicates that it is directed in the opposite direction to that shown in the FBD.