A 220 kg box is hanging from a steel wire with a Young's modulus of 200 GPa. You have a design criteria of gallowed = 125 MPa. What is the minimum diameter of the wire? Diameter = unit B) If the length of the wire is 1.0 m, what is the elongation of the wire after loading? Assume you use the diameter of the wire from part A. Elongation = AL = unit
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 Description
A 220 kg box is suspended from a steel wire with a Young's modulus of 200 GPa. The design criteria require that the allowed stress \( \sigma_{\text{allowed}} \) is 125 MPa. The tasks are as follows:
**A) Determine the minimum diameter of the wire.**
**Diameter = ________ unit ______**
**B) Given the length of the wire is 1.0 m, calculate the elongation of the wire after loading, using the determined diameter from part A.**
**Elongation \( \Delta L \) = ________________ unit ______**
### Diagram Explanation
The diagram accompanying the text represents a vertical system where a box is hanging from a wire. A horizontal line represents a support holding the wire. Below the wire, a rectangular box represents the load. The diagram visually indicates the setup described in the problem, where a load (220 kg box) is supported by a vertical wire suspended from a fixed point.
This setup is typically analyzed in mechanical and structural engineering to ensure materials can support the given load without exceeding stress limits or undergoing excessive deformation.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa572c903-8f29-4a18-ba49-8181d6c8cb85%2F5772f215-a94d-4dc9-8897-b49694b0f67b%2Fcd0f39n_processed.png&w=3840&q=75)
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