Problem $5.$ Rotor blade hub connection

Figure. $3$ shows a potential design for the attachment of a rotor blade to the rotorcraft hub. The yoke

consists of two separate pieces each of which connects the rotor blade to the hub, and the spindle also

connects the rotor blade to the hub through an elastomeric bearing. As the rotor blade spins, a large

centrifugal force $F$ is applied to the assembly, which can be idealized as three parallel bars of length L$,$

which connect the blade to the hub. The two bars modeling the yoke each have an axial stiffness $(EA{)}_y,$

while the spindle has an axial stiffness $(EA{)}_y.$ The elastomeric bearing is idealized as a very short spring

of stiffness $k_b$ in series with the spindle. $(1)$ Calculate and plot the non$-$dimensional forces in the yoke,

$\frac{F_y}{F},$ and in the spindle, $\frac{F_s}{F},$ as a function of the non$-$dimensional bearing stiffness,

$0L\frac{k_b}{(EA{)}_s}25.(2)$ For what value of the stiffness constant $k_b$ is all the centrifugal load carried by

the yoke? $(3)$ Find the maximum load that can be carried by the spindle. What is the corresponding

value of $k_b?(4)$ For what value on $L\frac{k_b}{(EA{)}_s}$ do the yoke and spindle carry equal loads? Use the

following data: $\frac{(EA{)}_y}{(EA{)}_s}=0\mathrm{.}8$

Fig. $3.$ Rotor blade connection to the hub by means of a yoke and spindle.