Mecanica de materiales

1. Problem 1
Four gears are attached to a circular
shaft and transmit the torques shown in
the figure.
The allowable shear stress in the shaft is 10,000 psi.
(a) What is the required diameter d of the s
haft if it has a solid cross section? R// d=1.78 in
(b) What is the required outside diameter d
if the shaft is hollow with an inside
diameter of 1.0 in.? R// d=1.83 in

3. Problem 2
A motor delivers 275 hp at 1000 rpm to
the end of a shaft (see figure). The gears at B
and C take out 125 and 150 hp, respectively.
Determine the required diameter d of the
shaft if the allowable shear stress is 7500 psi
and the angle of twist between the motor a
nd gear C is limited to 1.5°.
(Assume G = 11.5E6 psi, L1 = 6 ft,
and L2 = 4 ft.) R// d=2.75 in

6. Problem 3
The composite shaft shown in the figure
is manufactured by shrink-fitting a steel sleeve
over a brass core so that the two parts act as a
single solid bar in torsion. The outer diameters
of the two parts are d1 _ 40 mm for the brass
core and d2 _ 50 mm for the steel sleeve. The
shear moduli of elasticity are Gb _ 36 GPa for
the brass and Gs _ 80 GPa for the steel.
Assuming that the allowable shear stresses in
the brass and steel are tb _ 48 MPa and
ts _ 80 MPa, respectively, determine the
maximum permissible torque Tmax that may
be applied to the shaft. R// T=1520 Nm