Concept explainers
A round cold-drawn 1045 steel rod has a mean strength
(a)
The reliability corresponding to
The diameter of cold-drawn 1045 steel rod for
Answer to Problem 19P
The reliability corresponding to
The diameter of cold-drawn 1045 steel rod for
Explanation of Solution
Write the expression for coefficient of variance for strength.
Here, the coefficient of variance for strength is
Write the expression for coefficient of variance for stress.
Here, the coefficient of variance for stress is
Write the expression for transform variable.
Here, the design factor is
Write the expression for axial stress.
Here, the axial stress is
Calculate the reliability for steel rod.
Here, the reliability for steel is
Calculate the diameter of steel rod.
Substitute
Conclusion:
Substitute
Substitute
Substitute
Write the formula of interpolation.
Here, the variables denote by
Refer to table A-10 “Cumulative distribution function of Normal distribution” and obtain the value given in Table below.
y | |
Table (1)
Substitute
Substitute
Thus, the reliability of steel rod is
Substitute
Thus, the diameter of steel rod is
(b)
The reliability corresponding to
The diameter of cold-drawn 1045 steel rod for
Answer to Problem 19P
The reliability corresponding to
The diameter of cold-drawn 1045 steel rod for
Explanation of Solution
Write the expression for coefficient of variance for strength.
Write the expression for coefficient of variance for stress.
Write the expression for transform variable.
Write the expression for axial stress.
Calculate the reliability for steel rod.
Calculate the diameter of steel rod.
Substitute
Conclusion:
Substitute
Substitute
Substitute
Write the formula of interpolation.
Here, the variables denote by
Refer to table A-10 “Cumulative distribution function of Normal distribution” and obtain the value given in Table below.
y | |
Table (2)
Substitute
Substitute
Thus, the reliability of steel rod is
Substitute
Thus, the diameter of steel rod is
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Chapter 1 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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