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A 1,394-lb force is applied to a rotating tool steel bar at a frequency of 3000 cycles/minute. The bar is  is 12.00 in. long. The fatigue curve for the steel used in the bar is shown below. Calculate the diameter of the shaft that would be needed to prevent fatigue failure from ever occurring. Use ±σ=32FLπd3 and report your units in inches.

A 1,394-lb force is applied to a rotating tool steel bar at a frequency of 3000 cycles/minute. The bar is  is 12.00 in. long. The fatigue curve for the steel used in the bar is shown below. Calculate the diameter of the shaft that would be needed to prevent fatigue failure from ever occurring. Use ±σ=32FLπd3 and report your units in inches.

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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A 1,394-lb force is applied to a rotating tool steel bar at a frequency of 3000 cycles/minute. The bar is  is 12.00 in. long. The fatigue curve for the steel used in the bar is shown below. Calculate the diameter of the shaft that would be needed to prevent fatigue failure from ever occurring. Use ±σ=32FLπd3 and report your units in inches.

 

This graph represents the relationship between applied stress and the number of cycles, often referred to as an S-N curve or a Wöhler curve in the context of fatigue analysis. ### Description: - **X-Axis (Horizontal):** The horizontal axis represents the "Number of cycles," marked on a logarithmic scale ranging from \(1.00 \times 10^4\) to \(1.00 \times 10^8\). - **Y-Axis (Vertical):** The vertical axis shows "Applied Stress" measured in ksi (kips per square inch), ranging from 0 to 120 ksi. ### Key Features: - **Data Points:** The curve is represented by blue diamond markers, indicating various levels of applied stress concerning the number of cycles the material can withstand before failure or significant degradation. - **Trend:** The curve shows a downward trend, indicating that as the number of cycles increases, the level of applied stress that the material can withstand decreases. - **Endurance Limit:** Around \(1.00 \times 10^7\) cycles, the curve flattens, suggesting an endurance limit where the material withstands a constant stress level of approximately 50 ksi for an indefinite number of cycles without failure. This S-N curve is essential for designing materials and structures, ensuring they can endure operational cyclic loading over their expected lifespan.
Transcribed Image Text:This graph represents the relationship between applied stress and the number of cycles, often referred to as an S-N curve or a Wöhler curve in the context of fatigue analysis. ### Description: - **X-Axis (Horizontal):** The horizontal axis represents the "Number of cycles," marked on a logarithmic scale ranging from \(1.00 \times 10^4\) to \(1.00 \times 10^8\). - **Y-Axis (Vertical):** The vertical axis shows "Applied Stress" measured in ksi (kips per square inch), ranging from 0 to 120 ksi. ### Key Features: - **Data Points:** The curve is represented by blue diamond markers, indicating various levels of applied stress concerning the number of cycles the material can withstand before failure or significant degradation. - **Trend:** The curve shows a downward trend, indicating that as the number of cycles increases, the level of applied stress that the material can withstand decreases. - **Endurance Limit:** Around \(1.00 \times 10^7\) cycles, the curve flattens, suggesting an endurance limit where the material withstands a constant stress level of approximately 50 ksi for an indefinite number of cycles without failure. This S-N curve is essential for designing materials and structures, ensuring they can endure operational cyclic loading over their expected lifespan.
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