Essentials of Materials Science and Engineering, SI Edition
Essentials of Materials Science and Engineering, SI Edition
4th Edition
ISBN: 9781337672078
Author: ASKELAND, Donald R., WRIGHT, Wendelin J.
Publisher: Cengage Learning
Question
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Chapter 7, Problem 7.66DP
Interpretation Introduction

Interpretation:

The shaft design using the appropriate material for given condition should be determined.

Concept introduction:

Endurance strength is the value of maxium reveresed bending stress that a material can withstand without failure for finite number of cycle.

The following condition are specified based on number of cycle, If number of cycles are more than 106, the corresponding endurance is known as Endurance limit.If number of cycles are less than 106, the corresponding endurance is known as Endurance Strength.

Endurance Ratio:

It is defined as the ratio of endurance limit to tensile strength, the relationship is given below:

  EnduranceRatio=EnduranceLimitTensileStrength

It helps to estimate the properties of fatigue using tensile test. The value of endurance limit for metallic material is 0.3 to 0.4.

Relationship for endurance limit is shown below:

  ±σ=5.092FLd3

Where,

σ is fatigue strength in psi.

F is the applied load in pounds.

L is the length I inch.

D is the diameter in inch.

Expert Solution & Answer
Check Mark

Answer to Problem 7.66DP

Magnesium-Manganese alloy is best suitable material for shaft designing based on the value of fatigue strength.

Explanation of Solution

Given Information:

The value of load is 15000lb.

The material used along with the values of fatigue strength is shown in table below:

  Essentials of Materials Science and Engineering, SI Edition, Chapter 7, Problem 7.66DP

The required values are shown in table,

The relationship for Endurance limit is,

  ±σ=5.092FLd3

Considering the case for Aluminum manganese alloy,

The amount of load applied is 15000lb.

The value of fatigue strength for aluminum- manganese alloy is 110MPa.

Value of fatigue strength in psi is 15954.15 psi.

Assuming the value of length as 100inch.

Substituting the values in the above formula,

  15954.15=5.09215000×100d3d=7.8229inch

Thus, the required value of diameter for shaft designing is d=7.8229inch.

Considering the case for Aluminum magnesium and zinc alloy,

The amount of load applied is 15000lb.

The value of fatigue strength for aluminum- manganese alloy is 225MPa.

Value of fatigue strength in psi is 32633.5 psi.

Assuming the value of length as 100inch.

Substituting the values in the above formula,

  32633.5=5.09215000×100d3d=6.162inch

Thus, the required value of diameter for shaft designing is d=6.162inch.

Considering the case for Aluminum- Beryllium alloy,

The amount of load applied is 15000lb.

The value of fatigue strength for aluminum- manganese alloy is 295MPa.

Value of fatigue strength in psi is 42786.1 psi.

Assuming the value of length as 100inch.

Substituting the values in the above formula,

  42786.1=5.09215000×100d3d=5.630inch

Thus, the required value of diameter for shaft designing is d=5.630inch.

Considering the case for Magnesium- Manganese alloy,

The amount of load applied is 15000lb.

The value of fatigue strength for aluminum- manganese alloy is 80MPa.

Value of fatigue strength in psi is 11603 psi.

Assuming the value of length as 100inch.

Substituting the values in the above formula,

  11603=5.09215000×100d3d=8.69inch

Thus, the required value of diameter for shaft designing is d=8.69inch.

Considering the case for Beryllium alloy,

The amount of load applied is 15000lb.

The value of fatigue strength for aluminum- manganese alloy is 180MPa.

Value of fatigue strength in psi is 26106.8 psi.

Assuming the value of length as 100inch.

Substituting the values in the above formula,

  26106.8=5.09215000×100d3d=6.638inch

Thus, the required value of diameter for shaft designing is d=6.638inch.

Considering the case for Tungsten alloy,

The amount of load applied is 15000lb.

The value of fatigue strength for aluminum- manganese alloy is 320MPa.

Value of fatigue strength in psi is 46412.1 psi.

Assuming the value of length as 100inch.

Substituting the values in the above formula,

  46412.1=5.09215000×100d3d=5.480inch

Thus, the required value of diameter for shaft designing is d=5.480inch.

The required values are shown table,

AlloysFatigue Strength (MPa)Calculated diameter in inch
Al-Mg1107.8229
Al-Mg-Zn2256.162
Cu-Be2955.630
Mg-Mn808.69
Be1806.638
W3205.480

Designing of shaft is based on the stress level. On comparing, the values of fatigue strength the alloys of magnesium and manganese gives the lower value of fatigue strength as compared to other.

Thus, based on the fatigue strength value, Mg-Mn is suitable for designing of the shaft.

Conclusion

The best suitable material for shaft designing based on the value of fatigue strength is Magnesium-Manganese alloy.

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