9 e 1.5 2 " = 2 X
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.
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1. **Left Region:**
- The boundary on the left side of this region is defined by the exponential curve \( y = e^x \).
- The region extends horizontally from \( x = 0 \) to \( x = 1.5 \).
- The vertical axis is labeled \( y \), and the horizontal axis is labeled \( x \).
2. **Right Region:**
- This region is a semicircle with a radius \( r = 2 \).
- The semicircle is positioned so that it extends horizontally from \( x = 1.5 \) to \( x = 3.5 \).
3. **Other Details:**
- The height of the exponential curve and the semicircle are joined smoothly at \( x = 1.5 \).
- The entire figure is divided into two main parts: the left part showing the exponential growth, and the right part showing the circular region.
The graph illustrates how different mathematical shapes can be combined to define a particular shaded area."
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