Beam ABC has a mass of 73 kg centered at the middle of the b

Beam ABC has a mass of 73 kg, centered at the middle of the beam (not necessarily point B). The winch at C has a mass of 35 kg. A rope attaches at B and passes over a frictionless, small-diameter pulley at D. The rope is taken up by the winch, which lies directly below the pulley in the position shown (i.e. rope segment CD is vertical). Find the tension in the rope and the magnitude and direction of the reaction force at A, given the dimensions shown below. Dimensions: Reaction: (the force that the support exerts on the beam) ||R_A|| = @ direction = (measured as an angle between -180 and +180 degrees from the positive x axis: counterclockwise positive) Rope Tension: T_rope =

Solution

The angled beam ABC in the figure is composed of segments AB and BC joined at B at a 90 angle. Both segments have length L and uniform section stiffness EI. The beam is fixed at C and loaded by a downward concentrated force, P, applied at its free end A.

The thin wall shaft is fixed at and loaded by concentrated torques at sections and of direction and magnitude indicated in the figure. The shaft is composed of three segments, and of equal lengths m, and diameters indicated in the figure. The three segments are hollow tubes .