EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 17, Problem 24P
A material is tested for cyclic fatigue failure whereby a stress, in MPa, is applied to the material and the number of cycles needed to cause failure is measured. The results are in the table below. When a log-log plot of stress versus cycles is generated, the data trend shows a linear relationship. Use least-squares regression to determine a best-fit equation for these data.
N, cycles | 1 | 10 | 100 | 1000 | 10,000 | 100,000 | 1,000,000 |
Stress, MPa | 1100 | 1000 | 925 | 800 | 625 | 550 | 420 |
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A tensile test was performed to find the stress-strain curve of a metal sample.Here are the results
provided by the tensile testing machine.Suppose the results are free of errors.
Elongation, 0
AL (cm)
Applied
force , F(N)
4.086
5.448
2.724
6.81
1.362
55571.1
61710.1
52930.5
68018.1
39498.3
Additional information :
Lo : the length of the extensometer
Lo = 5.42 cm
A= 5.342
Questions :
a) At. Using the 0.2% yield strength method, calculate the tensile strength of the metal sample.
b) Find the modulus of resilience of the material under test.
c) Calculate the allowable load for an object made of this metal using the parameters following:
* Maximum stress: elastic limit
Cross section: 10 mm2
Safety factor (or margin): 7
Calculate numerically with a minimum of four decimal places.
Chapter 17 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 17 - Given these data 8.8 9.5 9.8 9.4 10.0 9.4 10.1 9.2...Ch. 17 - Given these data 29.65 28.55 28.65 30.15 29.35...Ch. 17 - 17.3 Use least-squares regression to fit a...Ch. 17 - 17.4 Use least-squares regression to fit a...Ch. 17 - 17.5 Using the same approach as was employed to...Ch. 17 - Use least-squares regression to fit a straight...Ch. 17 - Fit the following data with (a) A...Ch. 17 - Fit the following data with the power model...Ch. 17 - 17.9 Fit an exponential model...Ch. 17 - 17.10 Rather than using the base-e exponential...
Ch. 17 - 17.11 Beyond the examples in Fig. 17.10, there are...Ch. 17 - 17.12 An investigator has reported the data...Ch. 17 - An investigator has reported the data tabulated...Ch. 17 - 17.14 It is known that the data tabulated below...Ch. 17 - 17.15 The following data are...Ch. 17 - Given these data x 5 10 15 20 25 30 35 40 45 50 y...Ch. 17 - 17.17 Fit a cubic equation to the following...Ch. 17 - Use multiple linear regression to fit x1 0 1 1 2 2...Ch. 17 - Use multiple linear regression to fit x1 0 0 1 2 0...Ch. 17 - Use nonlinear regression to fit a parabola to the...Ch. 17 - 17.21 Use nonlinear regression to fit a...Ch. 17 - 17.22 Recompute the regression fits from Probs....Ch. 17 - Develop, debug, and test a program in either a...Ch. 17 - A material is tested for cyclic fatigue failure...Ch. 17 - The following data show the relationship between...Ch. 17 - 17.26 The data below represents the bacterial...Ch. 17 - The concentration of E. coli bacteria in a...Ch. 17 - 17.28 An object is suspended in a wind tunnel and...Ch. 17 - 17.29 Fit a power model to the data from Prob....Ch. 17 - Derive the least-squares fit of the following...Ch. 17 - 17.31 In Prob. 17.11 we used transformations to...
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