In: Mechanical Engineering

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 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.

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?

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 steel shaft is to be manufactured either as a solid
circular bar or as a circular tube. The shaft is required to
transmit a torque of 1200 N_m without exceeding an allowable shear
stress of 40 MPa nor an allowable rate of twist of0.75°/m. (The
shear modulus of elasticity of the steel is 78 GPa.).
Determine the required outer diameter do of the solid
shaft [58.8 mm]
Determine the required diameter d2of the hollow shaft
if thethickness t of...

A
machine with a rotating shaft has a total weight of 200 lbs, and is
supported by springs. The damping constant for the system is found
to be 3 lb.sec/in. The resonant speed is determined exprimentally
to be 1200 rpm, and the corresponding amplitude of the main mass of
the machine is 0.50 inches. (a) Determine the amplitude for a speed
of 2400 rpm. (b) Determine the fixed value which amplitude will
eventually approach at high speed. (c) Determine the...

A disk cam rotating at 200 rpm lifts a radial roller follower
with simple harmonic motion through a maximum displacement of 2.5
in. while the cam rotates through 90°. There is then a dwell of the
follower for 180° of cam rotation, followed by a return of the
follower in simple harmonic motion in the remaining 90° of cam
rotation. For a follower weight of 8 lb, determine the inertia
force of the follower for each 15° of cam rotation...

Find the moment of inertia of a circular disk of radius R and
mass M that rotates on an axis passing through its center. [Answer:
½ MR2]
Step 1: Pictorial representation: Sketch a neat picture to
represent the situation.
Step 2: Physical representation: 1) Cut the disk into many small
rings as it has the circular symmetry. 2) Set up your coordinate
system and choose its origin at the pivot point (or the axle
location) for convenience. Then choose a...

A solid disk of mass M and radius R is rotating on the vertical
axle with angular speed w. Another disk of mass M/2 and radius R,
initally not rotating, falls coaxially on the disk and sticks. The
rotational velocity of this system after collision is:
w
w/2
2w/3
3w/2
2w

A circular coil (830 turns, radius = 0.087 m) is rotating in a
uniform magnetic field. At t = 0 s, the normal to the coil is
perpendicular to the magnetic field. At t = 0.021 s, the normal
makes an angle of 45o with the field because the coil has made
one-eighth of a revolution. An average emf of magnitude 0.075 V is
induced in the coil. Find the magnitude of the magnetic field at
the location of the...

Determine the shear stress developed on a 3-m circular shaft
with D=250 mm, G = 83GPa applied with the torque, T = 100 kN-m,
a. at the center of the cross-section
b. at a point 50 mm away from the center
c. at a point 100 mm away from the center
d. maximum distance from the center

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