-ху —D 10 5 4 3 1 x(m) 4 6 4 I, = 105 X m" Iy 35 x m4 m %3D =
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.
![**Determine the Second Moments of Area and Radii of Gyration**
This educational content focuses on the calculation of second moments of area, denoted as \( I_x \) and \( I_y \), in \( \text{m}^4 \) and the radii of gyration in meters for a given shaded area. The area in question is illustrated in a graph with a distinct yellow region, bounded by the curve \( xy = 10 \).
### Graph Explanation:
- **Axes:** The graph displays the x-axis and y-axis, both labeled in meters (m). The x-axis ranges from 0 to 6, and the y-axis ranges from 0 to 6 as well.
- **Shaded Area:** The yellow region is the area of interest, representing the shape for which the calculations are being conducted. This area is bound by the horizontal line at \( y = 6 \), the vertical line at \( x = 2 \), and the curve \( xy = 10 \).
### Given Values:
- \( I_x = 105 \, \text{m}^4 \)
- \( I_y = 35 \, \text{m}^4 \)
### Unknown Values:
- \( k_x = \) m
- \( k_y = \) m
These unknown values, \( k_x \) and \( k_y \), represent the radii of gyration which need to be determined based on the given moments of area.
### Problem Statement:
Determine the second moments of area in \( \text{m}^4 \) and the radii of gyration in meters for the shaded area shown about the x-axis and the y-axis.
This exploration into moments of area and radii of gyration is fundamental in understanding the distribution of areas in structural elements and is crucial for structural engineering calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf4a0e0b-2125-467b-b1bc-8bc81e995df8%2F76b1e821-e319-4451-990e-3e89c9564eee%2Fv5oe362f_processed.png&w=3840&q=75)
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