EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Chapter 20, Problem 52P
An experiment is performed to define the relationship between applied stress and the time to fracture for a type of stainless steel. Eight different values of stress are applied, and the resulting data are
| Applied stress x,
|
5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 |
| Fracture time y, hr | 40 | 30 | 25 | 40 | 18 | 20 | 22 | 15 |
Plot these data and then develop a best-fit equation to predict the fracture time for an applied stress of
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100
80
60
40
20
0.002
0.004
0.006
0.008
0.01
0.012
Strain, in/in.
FIGURE P1.17
1.18 Use Problem 1.17 to graphically determine the following:
a. Modulus of resilience
b. Toughness
Hint: The toughness (u) can be determined by calculating the area under
the stress-strain curve
u =
de
where & is the strain at fracture. The preceding integral can be approxi-
mated numerically by using a trapezoidal integration technique:
u, = Eu, = o, + o e, - 6)
%3D
c. If the specimen is loaded to 40 ksi only and the lateral strain was found to
be -0.00057 in./in., what is Poisson's ratio of this metal?
d. If the specimen is loaded to 70 ksi only and then unloaded, what is the
permanent strain?
Stress, ksi
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.
Creep exercises
The following data in the table below was obtained a from rupture test.
Stress (MPa)
Temperature (°C)
Rupture time (hr)
T 550
580
0.75
550
555
5.5
550
540
19.2
550
525
62.0
70
760
2.05
70
730
8.2
70
700
36.5
70
675
134
Assume: C = 46
Establish whether the Larson-Miller parameter is valid for both stresses (550 and 70
MPa).
Was there a change in creep mechanism when changing the stress from 550 to 70 MPa
during rupture test? Motivate your answer with the aid of calculation.
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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