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Chiven Coupling V = 0.290). is 4340-HT Steel (E = 205 [C+Pa], G+ = 80 cpa, 6y = 470 GPa, 6₂ = 7195 ² u diameter is D=19.62.com &- d Diameter of bolt hole is 1 cm / out side diameter of flange is 00 = 25 cm = - Find the thickness of the thing flange t such that the maximum bearing, and shear and normal stresses do not exceed allownable limits? T a 00 bolt pattern and applied torque is 4.00e + 04 [N-m] ODEd Of DOD

Chiven Coupling V = 0.290). is 4340-HT Steel (E = 205 [C+Pa], G+ = 80 cpa, 6y = 470 GPa, 6₂ = 7195 ² u diameter is D=19.62.com &- d Diameter of bolt hole is 1 cm / out side diameter of flange is 00 = 25 cm = - Find the thickness of the thing flange t such that the maximum bearing, and shear and normal stresses do not exceed allownable limits? T a 00 bolt pattern and applied torque is 4.00e + 04 [N-m] ODEd Of DOD

Elements Of Electromagnetics
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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**Problem Statement: Design of a Flange Coupling** **Given Data:** - Material: 4340-HT Steel - Modulus of Elasticity, \( E = 205 \, \text{GPa} \) - Ultimate Tensile Strength, \( \sigma_u = 30 \, \text{GPa} \) - Yield Strength, \( \sigma_y = 470 \, \text{GPa} \) - Shear Strength, \( \tau = 745 \, \text{MPa} \) - Poisson's Ratio, \( \nu = 0.290 \) - Diameter of bolt hole, \( d = 1 \, \text{cm} \) - Bolt pattern diameter, \( D = 19.6 \, \text{cm} \) - Outside diameter of flange, \( OD = 25 \, \text{cm} \) - Applied torque, \( T = 4.00 \times 10^4 \, \text{N-m} \) **Objective:** Determine the thickness of the flange, \( t \), such that the maximum bearing, shear, and normal stresses do not exceed allowable limits. --- **Diagram Explanation:** - The diagram shows a flange coupling with a central shaft and bolted connection pattern. - The flange has several bolt holes marked by the pattern diameter, \( D \). - The outer diameter of the flange is labeled \( OD \). - The shaft is subjected to an applied torque, \( T \), around its axis, illustrated by an arrow. - The thickness of the flange is represented by \( t \). This initial setup aids in calculating and ensuring the structure's safety under the given mechanical conditions.
Transcribed Image Text:**Problem Statement: Design of a Flange Coupling** **Given Data:** - Material: 4340-HT Steel - Modulus of Elasticity, \( E = 205 \, \text{GPa} \) - Ultimate Tensile Strength, \( \sigma_u = 30 \, \text{GPa} \) - Yield Strength, \( \sigma_y = 470 \, \text{GPa} \) - Shear Strength, \( \tau = 745 \, \text{MPa} \) - Poisson's Ratio, \( \nu = 0.290 \) - Diameter of bolt hole, \( d = 1 \, \text{cm} \) - Bolt pattern diameter, \( D = 19.6 \, \text{cm} \) - Outside diameter of flange, \( OD = 25 \, \text{cm} \) - Applied torque, \( T = 4.00 \times 10^4 \, \text{N-m} \) **Objective:** Determine the thickness of the flange, \( t \), such that the maximum bearing, shear, and normal stresses do not exceed allowable limits. --- **Diagram Explanation:** - The diagram shows a flange coupling with a central shaft and bolted connection pattern. - The flange has several bolt holes marked by the pattern diameter, \( D \). - The outer diameter of the flange is labeled \( OD \). - The shaft is subjected to an applied torque, \( T \), around its axis, illustrated by an arrow. - The thickness of the flange is represented by \( t \). This initial setup aids in calculating and ensuring the structure's safety under the given mechanical conditions.
Expert Solution
Step 1

Given:

The Elastic modulus of the material used, E = 205 GPa

The shear modulus of the material used, G = 80 GPa

The yield strength of the material used, σy = 470 MPa

The ultimate strength of the material used, σu = 745 MPa

The poison ratio, ν = 0.29

The diameter of bolt hole, d = 1 cm

The diameter of bolt pattern, D = 19.62 cm

The outside diameter of the flange, D′ = 25 cm

The torque applied, T = 4x104 N.m

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