Design Against Fluctuating Loads
Machine elements are subjected to varieties of loads, some components are subjected to static loads, while some machine components are subjected to fluctuating loads, whose load magnitude tends to fluctuate. The components of a machine, when rotating at a high speed, are subjected to a high degree of load, which fluctuates from a high value to a low value. For the machine elements under the action of static loads, static failure theories are applied to know the safe and hazardous working conditions and regions. However, most of the machine elements are subjected to variable or fluctuating stresses, due to the nature of load that fluctuates from high magnitude to low magnitude. Also, the nature of the loads is repetitive. For instance, shafts, bearings, cams and followers, and so on.
Design Against Fluctuating Load
Stress is defined as force per unit area. When there is localization of huge stresses in mechanical components, due to irregularities present in components and sudden changes in cross-section is known as stress concentration. For example, groves, keyways, screw threads, oil holes, splines etc. are irregularities.
![Learning Goal:
To use the vector cross product to calculate the moment produced by
a force, or forces, about a specified point on a member.
Part A - Moment due to a force specified by magnitude and endpoints
The moment of a force F about the moment axis passing through O
and perpendicular to the plane containing O and F can be expressed
using the vector cross product, Mo =r x F. In a properly
constructed Cartesian coordinate system, the vector cross product can
be calculated using a matrix determinant:
As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B.
(Figure 1)
The force has magnitude F = 180 N and is directed as shown. The dimensions are ¤1 = 0.350 m, x2 = 1.90 m, y1 = 2.30 m, and z1 = 1.20 m.
What is the moment about the origin due to the applied force F?
j
M=r x F =|rz
i
k
Express the individual components of the Cartesian vector to three significant figures, separated by commas.
Ty
Tz
F, F, F:
• View Available Hint(s)
Notice that the order of the elements of the matrix determinant is
important; switching rows 2 and 3 of the determinant would change the
sign of the moment from positive to negative (or vice versa.)
I vec
?
Mo =[
i, j, k] N · m
Submit
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Part B - Moment due to a force specified as a Cartesian vector
As shown, a member is fixed at the origin, point O, and has an applied force F, the tension in the rope, applied at the free end, point B.
(Figure 2)
Figure
< 1 of 3 >
The force is given by F = 130NI- 135 Nj+ 70 Nk. The dimensions are ¤1 = 1.35 m, y1 = 1.90 m, and z = 1.05 m.
What is the moment about the origin due to the applied force F?
Express the individual components of the Cartesian vector to three significant figures, separated by commas.
• View Available Hint(s)
vec
Mo =|
i, j, k] N · m
Submit
Previous Answers
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