Transcript Home Work #1

Home Work #5
Due Date:25 Mar, 2010
(Turn in your assignment at the mail box
of S581 outside the ME general office)
The solutions must be written on single-side A4 papers only.
HW 3-Problem #1
A solid circular bar ABC consists of two segments, as shown in the figure.
One segment has diameter d1=50mm and length L1=1.25m; the other
segment has diameter d2=40mm and length L2=1.0m.
What is the allowable torque Tallow if the shear stress is not to exceed
30MPa and the angle of the twist between the ends of the bar is not to
exceed 1.5 °.(Assume G=80Gpa)
Solution to Problem #1
377
HW 3-Problem #2
A solid circular bar ABCD with fixed supports at ends A and D is acted
upon by two equal and oppositely directed torque To, as shown in the
figure. The torques are applied at ponits B and C, each of which is
located at distance x from on end of the bar.(The distance x may vary
from zero to L/2.)
(a) For what distance x will the angle of twist at points B and C be a
maximum?
(b) What is the corresponding angle of the twist Φmax?(Hint: Use Eqs.346a and b of example 3-9 to obtain the reactive torques.)
Solution to Problem #2
HW 3-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
diameter of the two parts are d1=40mm for the brass core and d2=50mm for the steel
sleeve. The shear moduli of elasticity are Gb=36GPa for the brass and Gs=80GPa for
the steel.
Assuming that the allowable shear stresses in the brass and steel are τb=48MPa and
τs=80MPa, respectively, determine the maximum permissible torque Tmax that may be
applied to the shaft.(Hint: Use Eqs.3-44a and b to find the torque.)
Solution to Problem #3
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Solution to Problem #3
1521