= A solid 4340 HR Steel tie rod with diameter drod = 27.5 mm and length Irod = 950 mm is employed to compress a 2024-T4 aluminum bushing with outer diameter do 75 mm and length Lbushing = 600 mm as shown. If F = 50 kN, determine the minimum wall thickness of the bushing based on the below design requirements: • the displacement of the bottom of the tie rod with respect to the fixed horizontal surface may not exceed Stotal = 0.9 mm • the normal stress of the bushing may not exceed the yield strength of the bushing material Lbushing tmin =, number (rtol-0.01, atol=1e-05) do drod F mm Lrod
= A solid 4340 HR Steel tie rod with diameter drod = 27.5 mm and length Irod = 950 mm is employed to compress a 2024-T4 aluminum bushing with outer diameter do 75 mm and length Lbushing = 600 mm as shown. If F = 50 kN, determine the minimum wall thickness of the bushing based on the below design requirements: • the displacement of the bottom of the tie rod with respect to the fixed horizontal surface may not exceed Stotal = 0.9 mm • the normal stress of the bushing may not exceed the yield strength of the bushing material Lbushing tmin =, number (rtol-0.01, atol=1e-05) do drod F mm Lrod
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Educational Content: Analysis of Tie Rod and Bushing System**
**Problem Description:**
A solid 4340 HR Steel tie rod with diameter \(d_{\text{rod}} = 27.5 \, \text{mm}\) and length \(L_{\text{rod}} = 950 \, \text{mm}\) is employed to compress a 2024-T4 aluminum bushing with outer diameter \(d_o = 75 \, \text{mm}\) and length \(L_{\text{bushing}} = 600 \, \text{mm}\) as shown in the diagram. If \(F = 50 \, \text{kN}\), determine the minimum wall thickness of the bushing based on the following design requirements:
- The displacement of the bottom of the tie rod with respect to the fixed horizontal surface may not exceed \(\delta_{\text{total}} = 0.9 \, \text{mm}\).
- The normal stress of the bushing may not exceed the yield strength of the bushing material.
**Diagram Explanation:**
The diagram showcases a vertical arrangement where the tie rod moves downward, compressing the bushing against a surface. The components and measurements indicated are:
- **Tie Rod**: Represented with a solid circle at the bottom, indicating force \(F\) acting downwards. The length \(L_{\text{rod}}\) and diameter \(d_{\text{rod}}\) are marked.
- **Bushing**: The bushing is represented as a hollow cylinder surrounding the tie rod, with the length \(L_{\text{bushing}}\) and outer diameter \(d_o\) specified. The minimum wall thickness is to be calculated.
**Objective:**
Calculate the minimum wall thickness \(t_{\text{min}}\) that satisfies:
- Total displacement requirement of \(0.9 \, \text{mm}\).
- Stress requirements under the applied force of \(50 \, \text{kN}\).
**Formula:**
\[ t_{\text{min}} = \text{number (rtol=0.01, atol=1e-05)} \, \text{mm} \]
This presents a computational representation indicating how to determine \(t_{\text{min}}\) with a relative tolerance of 1% and an absolute tolerance of \(1 \times 10^{-5}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee563bfe-badf-4a9d-9a7e-d47066dc4e0e%2F1f435f2b-426e-45f5-b8cf-a0f6c9bc7433%2Flxbh1qk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Content: Analysis of Tie Rod and Bushing System**
**Problem Description:**
A solid 4340 HR Steel tie rod with diameter \(d_{\text{rod}} = 27.5 \, \text{mm}\) and length \(L_{\text{rod}} = 950 \, \text{mm}\) is employed to compress a 2024-T4 aluminum bushing with outer diameter \(d_o = 75 \, \text{mm}\) and length \(L_{\text{bushing}} = 600 \, \text{mm}\) as shown in the diagram. If \(F = 50 \, \text{kN}\), determine the minimum wall thickness of the bushing based on the following design requirements:
- The displacement of the bottom of the tie rod with respect to the fixed horizontal surface may not exceed \(\delta_{\text{total}} = 0.9 \, \text{mm}\).
- The normal stress of the bushing may not exceed the yield strength of the bushing material.
**Diagram Explanation:**
The diagram showcases a vertical arrangement where the tie rod moves downward, compressing the bushing against a surface. The components and measurements indicated are:
- **Tie Rod**: Represented with a solid circle at the bottom, indicating force \(F\) acting downwards. The length \(L_{\text{rod}}\) and diameter \(d_{\text{rod}}\) are marked.
- **Bushing**: The bushing is represented as a hollow cylinder surrounding the tie rod, with the length \(L_{\text{bushing}}\) and outer diameter \(d_o\) specified. The minimum wall thickness is to be calculated.
**Objective:**
Calculate the minimum wall thickness \(t_{\text{min}}\) that satisfies:
- Total displacement requirement of \(0.9 \, \text{mm}\).
- Stress requirements under the applied force of \(50 \, \text{kN}\).
**Formula:**
\[ t_{\text{min}} = \text{number (rtol=0.01, atol=1e-05)} \, \text{mm} \]
This presents a computational representation indicating how to determine \(t_{\text{min}}\) with a relative tolerance of 1% and an absolute tolerance of \(1 \times 10^{-5}\).
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