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Mechanics of Materials
Mechanical Behavior of Materials
86 SOLVED PROBLEMS
Question: 15.8
A rectangular beam made of S-590 alloy has depth 2c = 50 mm and thickness b = 20 mm. It is loaded with a moment of M = 1.50 kN·m at a temperature of 725°C. At this temperature, and for stresses in the range 100 to 400 MPa, constants for Eq. 15.71 are m = 10.74 and B = 3.91 × 10^−29, where t is in ...
Verified Answer:
The stress at the edge of the beam is obtained dir...
Question: 15.7
A beam is simply supported over a length of L = 100 mm and is loaded at its center with a transverse load of P = 50 N. Its cross section has width b = 15 mm and depth 2c = 10 mm. The material has linear viscoelastic behavior with elastic and steady-state creep strains, similar to the model of ...
Verified Answer:
Due to the linear viscoelastic behavior, stresses ...
Question: 15.6
For a given material and temperature, the uniaxial creep behavior follows Eq. 15.39(b). A thin-walled tubular pressure vessel of radius r and wall thickness b has closed ends and is made of this material. Develop an equation for the relative change in radius, Δr/r , as a function of time t and a ...
Verified Answer:
we first generalize the uniaxial stress–strain cur...
Question: 15.5
Consider the situation of Ex. 15.2 and 15.3, where a component made of alloy S-590 is subjected to a stress of 200 MPa at a temperature of 600°C. (a) Repeat the rupture life calculation of Ex. 15.3, using the Eq. 15.20 fit for PLM. (b) If the desired service life is 1.5 years, what are the safety ...
Verified Answer:
(a) From Table 15.3, the S-590 alloy constants for...
Question: 15.4
The creep–rupture data for alloy S-590 plotted in Fig. 15.8 are given in Table E15.4(a), where, for each test, the temperature T, stress σ, and rupture time tr are listed. Employ these data as follows: (a) On the basis of Eq. 15.19, obtain a fitted equation relating the Sherby–Dorn parameter to ...
Verified Answer:
(a) First calculate x = log σ and
P_{SD}[/l...
Question: B.1
The results of a number of fracture toughness tests on dolomitic limestone are given in Table B.1. Determine the sample values of the mean, standard deviation, and coefficient of variation. ...
Verified Answer:
Equations B.1 to B.3
\bar{x}=\frac{1}{n} \s...
Question: 15.3
Consider again Example 15.2, using the Larson–Miller parameter. ...
Verified Answer:
The logic is the same as before, except that now [...
Question: 15.2
An engineering component made of the heat-resisting Fe-Cr-Ni-Co alloy S-590 is subjected in service to a static stress of 200 MPa at a temperature of 600°C. What creep–rupture life in days is expected? ...
Verified Answer:
Figure 15.21 provides the needed stress versus [la...
Question: 15.1
Consider nickel with the same grain size and processing as the material of Fig. 15.16. This material is subjected to a tensile stress of 6 MPa at a temperature of 900°C. What is the approximate strain rate, and what creep mechanism is dominant? ...
Verified Answer:
To enter the map, we need τ and G from Eqs. 15.12 ...
Question: 14.4
A shaft made of hot-rolled and normalized SAE 1045 steel is loaded in bending and has a diameter change, as in Fig. A.12(b) of Appendix A. The stress concentration factor for the fillet radius is kt = 3.00, and the member is repeatedly subjected to the history of net section nominal stress shown in ...
Verified Answer:
The constants for this material’s cyclic stress–st...
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