In: Mechanical Engineering

A circular shaft, 100 mm diameter is subjected to combined
bending moment and torque, the bending moment being 3 times the
torque. If the direct tension yield point of the material is 300
MN/m2 and the factor of safety on yield is to be 4, calculate the
allowable twisting moment by the three following theories of
failure:

(a) Maximum principal stress theory

(b) Maximum shear stress theory

(c) Maximum shear strain energy theory.

(c)according to maximum shear strain energy theory shear strain energy per unit volume at failure is equal to maximum shear strain energy in uniaxial loading.

A 100mm shaft is loaded with a torque of 100Nm and a bending
moment of 50Nm. As a designer you need to select a material to find
a suitable material for size, weight and cost. Using Von-Mises
stress and the distortion energy failure theory determine the
sizing / weight and cost for each of the three materials below.
Complete the table with your answers and show all work.
Yield Strength
Density (kg/m^3)
Cost ($/kg)
Required Diameter (mm)
Weight (kg)
Cost...

A circular solid shaft rotating at n=1000n=1000 rpm suports a
bending moment M=200M=200 klbf*in. Compute the life NN for shafts
having four different diameters
d1=2.6,d2=2.32,d3=1.93d1=2.6,d2=2.32,d3=1.93, and d4=4.16d4=4.16
inches. Material properties: SUT=200SUT=200 kpsi, Se=50Se=50 kpsi,
f=0.8,Nt=103,Ne=106f=0.8,Nt=103,Ne=106.

A horizontal shaft of 75mm diameter projects from a bearing and,
in addition to the torque transmitted, the shaft carries a vertical
load of 8 kN at 300 mm from the bearing. If the safe stress for the
material, as determined in a simple tension test, is 135 MN/m2 find
the safe torque to which the shaft may be subjected using as a
criterion
(a) The maximum shearing, stress,
(b) The maximum strain energy per unit volume.
Poisson’s ratio ?...

A particular manufacturing design requires a shaft with a
diameter between 21.91 mm and 22.018 mm. The manufacturing process
yields shafts with diameters normally distributed, with a mean of
22.003 mm and a standard deviation of 0.006 mm. Complete parts (a)
through (c).
a. For this process what is the proportion of shafts with a
diameter between 21.91 mm and 22.00 mm question mark The proportion
of shafts with diameter between 21.91 mm and 22.00 mm is
nothing.
b. For...

bending moment of 4 kN m is found to cause elastic failure of a
solid circular shaft. An exactly similar shaft is now subjected to
a torque T. Determine the value of T which will cause failure of
the shaft according to the following theories:
(a) Maximum principal stress;
(b) Maximum principal strain;
(c) Maximum shear strain energy. ?= 0.3.)
Which of these values would you expect to be the most reliable and
why?

1. An aluminum circular cylinder 50 mm in diameter with ends
insulated is initially at 100◦C. Approximate the temperature at the
center of the cylinder after 2 s if the lateral surface is kept at
0◦C.For aluminum, k = 8.6 × 10−5m2 /s.
2. A circular cylinder 1 m in radius is completely insulated and
has an initial temperature distribution 100r ◦C. Find an expression
for the temperature as a function of r and t. Write integral
expressions for at...

A particular manufacturing design requires a shaft with a
diameter of 17.000 mm, but shafts with diameters between 16.988 mm
and 17.012 mm are acceptable. The manufacturing process yields
shafts with diameters normally distributed, with a mean of 17.004
mm and a standard deviation of 0.004 mm.
Complete parts (a) through (d) below.
a. For this process, what is the proportion of shafts with a
diameter between 16.988mm and 17.000 mm?
The proportion of shafts with diameter between 16.988 mm...

The propeller shaft of a large ship has an outside diameter of
350 mm and inside diameter 250mm. the shaft is rated for a maximum
of shear stress 62 MPa.
1) if the shaft is runnning at 500 rpm what is the maximum power
that can be transmitted without exceeding allowable stress.
2) if the rotational speed of the shaft is doubled but the power
requirements unchanged what happens to the shear stress in the
shaft? calculate valures.

3.7-4 A solid steel shaft ABC with diameter d=40 mm is driven at
A by a motor that transmits 75kW to the shaft at 15 Hz. The gears
at B and C drive machinery requiring power equal to 50kW and 25 kW,
respectively. Compare the maximum shear stress and angle of twist
in the shaft between the motor at A and the gear at C. Assume that
G=75 GPa.

A 580-mm long tungsten wire, with a 0.046-mm-diameter circular
cross section, is wrapped around in the shape of a coil and used as
a filament in an incandescent light bulb. When the light bulb is
connected to a battery, a current of 0.526 A is measured through
the filament. (Note: tungsten has a resistivity of 4.9 × 10-8 ? •
m.) How many electrons pass through this filament in 5 seconds?
How many electrons pass through this filament in 5...

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