Problem $3$

The structural part of a setup to measure net belt tensions in pulleys is shown in the figure. The belt tensions

at both sides of the pulley at $B($radius $10$ cm $)$ are $P$ and $F={0\mathrm{.}1}^{**}P$ along $z$ and a reaction force is measured

from the pulley at $C($radius $2$ cm $),$ which is connected to a load cell at $E$ with an axial member parallel to

$x.$ Pulleys are rigidly attached to rod $AD,$ which is made with a ductile steel rod $60$ cm long and $1\mathrm{.}27$ cm in

diameter. Length $AB=0\mathrm{.}20m,$ and length $DC=0\mathrm{.}15m.$ There is a spherical hinge at A and a plane hinge at

$D.$ The latter constrains motion in the $x-z$ plane only.

a$.-$ Draw bending moment and torsion diagrams for this structure as functions of the unknown tension

and use them to draw a diagram of the critical section showing internal loads $($bending and torsion moments$)$

and the critical points.

b$.-$ Use your results from part a to determine the maximum normal stress due to bending and the maximum

shear stress due to torsion in terms of the unknown tension $P.$ Calculate the maximum value that $P$ can have

if only bending stresses are considered $($with ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=350$MPa $)$ and then if only torsion stresses are

considered $($with ${}_{\text{a}\text{l}\text{l}\text{o}\text{w}}=175$MPa $).$