Determine the stress concentration factor in a 0.2 inch thick flat bar with two symmetric grooves (semi-circular notches) of radius 0.3 inches and width 2.6 inches. Use the graph in Fig. 2. 3.0 Nolched rectangular bar in lension or simple compression. a0 = F/A, where A = dt and is the thickness. Awld =3 2.6 15 2.2 12 K, 1.1 1.8 1.05 14 1.0 0.05 0.10 0.15 0.20 0.25 0.30 rid
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.
![**Problem 2**
*For this problem, use the graph below, also given at the end of the notes on stress concentration.*
Determine the stress concentration factor in a 0.2-inch thick flat bar with two symmetric grooves (semi-circular notches) of radius 0.3 inches and width 2.6 inches. Use the graph in Fig. 2.
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### Explanation of the Diagram:
The diagram provided, labeled as Fig. 2, is a graph used to determine the stress concentration factor (\( K_t \)) for a notched rectangular bar under tension or simple compression. The stress concentration factor is used to quantify how much stress is increased due to the presence of notches or grooves.
- **Axes of the Graph:**
- The x-axis represents the ratio of notch radius to notch width (\( r/d \)).
- The y-axis represents the stress concentration factor (\( K_t \)), ranging from 1.0 to 3.0.
- **Curves on the Graph:**
- Several curves are plotted, corresponding to different \( w/d \) ratios (width of the bar over diameter of the notch) with one labeled as \( w/d = 3 \).
- The curves indicate how \( K_t \) changes based on the ratio \( r/d \).
- **Inset Image:**
- The inset illustrates a notched rectangular bar with symmetric grooves under tension, showing dimensions and load directions.
- **Equation Provided:**
- \( \sigma_0 = F/A \), where \( A = dt \) and \( t \) is the thickness.
To solve for the stress concentration factor using your specific dimensions, locate the point on the curve that corresponds to your \( r/d \) value and read off the associated \( K_t \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd12c1cb2-e3a7-4517-8219-a3d85d32f034%2Ffc2e0b8e-8a23-4d3e-b21f-dc408cc9af63%2F2a1l80l_processed.jpeg&w=3840&q=75)
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