EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 20, Problem 61P
The data below were obtained from a creep test performed atroom temperature on a wire composed of 40% tin, 60% lead, andsolid core solder. This was done by measuring the increase in strainover time while a constant load was applied to a test specimen. Using a linear regression method, find (a ) the equation of these line that bestfits these data and (b ) the
If the line does not pass through the origin, force it to do so. Does thisnew line represent the data trend? Suggest a new equation that satisfies zero strain at zero time and also represents the data trend well.
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The following data were collected from a standard 0.505-in. diameter test specimen of a copper alloy (initial
length (lo) = 2.0 in.):
%3D
Load (Ib)) 0.0
3000
6000
7500
9000
10500
12000
12400
11400
41 (in) 0.0 0.00167
0.00333
0.00417
0.009
0.040
0.26
0.50
1.02
After fracture, the total length was 3.014 in. and the diameter was 0.374 in. Plot the engineering stress-strain
curve and calculate.
(a) the 0.2% offset yield strength;
(b) the tensile strength;
(c) the modulus of elasticity3;
3. A strip of chicken skin was excised for mechanical testing in tension. The initial
dimension of the rectangular specimen was 30 mm long and 15 mm wide, with
average thickness of 3 mm. The mechanical testing was conducted at a rate of 5
mm/sec. The following data were obtained:
gauge length, mm
20
22
24.2
26.3
27.9
30.1
force, N
0
0.8
2.7
7.9
12.9
19.6
a. Calculate the engineering stresses and strain from the information given and
plot the stress-strain curve. Assume that 5 mm of the specimen length is
clamped by the testing grip at each end, such that the initial gauge length of
the specimen is 20 mm.
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 20 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 20 - 20.1 Perform the same computation as in Sec. 20.1,...Ch. 20 - You perform experiments and determine the...Ch. 20 - 20.3 It is known that the tensile strength of a...Ch. 20 - Prob. 4PCh. 20 - 20.5 The specific volume of a superheated steam is...Ch. 20 - Prob. 6PCh. 20 - In Alzheimers disease, the number of neurons in...Ch. 20 - 20.8 The following data were taken from a stirred...Ch. 20 - Prob. 9PCh. 20 - Concentration data were taken at 15 time points...
Ch. 20 - Prob. 11PCh. 20 - The molecular weight of a polymer can be...Ch. 20 - 20.13 On average, the surface area A of human...Ch. 20 - 20.14 Determine an equation to predict metabolism...Ch. 20 - 20.15 Human blood behaves as a Newtonian fluid...Ch. 20 - 20.16 Soft tissue follows an exponential...Ch. 20 - 20.17 The thickness of the retina changes during...Ch. 20 - 20.18 The data tabulated below were generated from...Ch. 20 - The shear stresses, in kilopascals (kPa), of nine...Ch. 20 - 20.20 A transportation engineering study was...Ch. 20 - The saturation concentration of dissolved oxygen...Ch. 20 - For the data in Table P20.21, use polynomial...Ch. 20 - 20.23 Use multiple linear regression to derive a...Ch. 20 - 20.24 As compared to the models from Probs. 20.22...Ch. 20 - 20.25 In water-resources engineering, the sizing...Ch. 20 - 20.26 The concentration of total phosphorus and...Ch. 20 - 20.27 The vertical stress under the corner of a...Ch. 20 - Three disease-carrying organisms decay...Ch. 20 - 20.29 The mast of a sailboat has a cross-sectional...Ch. 20 - 20.30 Enzymatic reactions are used extensively to...Ch. 20 - 20.31 Environmental engineers dealing with the...Ch. 20 - An environmental engineer has reported the data...Ch. 20 - The following model is frequently used in...Ch. 20 - 20.34 As a member of Engineers Without Borders,...Ch. 20 - 20.35 Perform the same computations as in Sec....Ch. 20 - 20.36 You measure the voltage drop V across a...Ch. 20 - Duplicate the computation for Prob. 20.36, but use...Ch. 20 - The current in a wire is measured with great...Ch. 20 - 20.39 The following data was taken from an...Ch. 20 - It is known that the voltage drop across an...Ch. 20 - Ohms law states that the voltage drop V across an...Ch. 20 - 20.42 Repeat Prob. 20.41 but determine the...Ch. 20 - 20.43 An experiment is performed to determine the...Ch. 20 - Bessel functions often arise in advanced...Ch. 20 - 20.45 The population of a small community on the...Ch. 20 - Based on Table 20.4, use linear and quadratic...Ch. 20 - 20.47 Reproduce Sec. 20.4, but develop an equation...Ch. 20 - 20.48 Dynamic viscosity of water is related to...Ch. 20 - 20.49 Hooke’s law, which holds when a spring is...Ch. 20 - 20.50 Repeat Prob. 20.49 but fit a power curve to...Ch. 20 - The distance required to stop an automobile...Ch. 20 - An experiment is performed to define the...Ch. 20 - The acceleration due to gravity at an altitude y...Ch. 20 - The creep rate is the time rate at which strain...Ch. 20 - 20.55 It is a common practice when examining a...Ch. 20 - The relationship between stress and the shear...Ch. 20 - The velocity u of air flowing past a flat surface...Ch. 20 - 20.58 Andrade’s equation has been proposed as a...Ch. 20 - Develop equations to fit the ideal specific heats...Ch. 20 - 20.60 Temperatures are measured at various points...Ch. 20 - 20.61 The data below were obtained from a creep...
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