Mechanical Behavior of Materials 5th. Edition by Norman E. Dowling, Stephen L. Kampe, Milo V. Kral | 9781292279350 | 1292279354

Mechanics of Materials

Mechanical Behavior of Materials

1 SOLVED PROBLEMS

89 SOLVED PROBLEMS

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 ...

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The constants for this material’s cyclic stress–st...

Question: 13.1

Some test data points on the monotonic stress–strain curve of 7075-T651 aluminum for uniaxial stress are given in Table E13.1. Obtain values of the constants for a stress–strain curve of the Ramberg–Osgood form, Eq. 13.12, that fits these data. ...

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The elastic modulus E is needed, as are the consta...

Question: 13.2

A material has the Ramberg–Osgood uniaxial stress–strain curve given by the constants of Fig. 13.9. Write the equation relating the principal stress and strain σ1 and ε1 for the case of plane stress, σ3 = 0, with λ = σ2/σ1 = 1.0. ...

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Equation 13.39 applies. The following constants fo...

Question: 13.3

A thin-walled tubular pressure vessel of radius r and wall thickness t has closed ends and is made of a material having a uniaxial stress–strain curve of the Ramberg–Osgood form, Eq. 13.12. If the internal pressure p is increased monotonically, derive an equation for the relative change in radius, ...

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The principal stresses are

\sigma_{1}=\frac...

Question: 13.4

Consider the state of stress σ2 = σ3 = 0.5σ1 applied to a material that follows the Ramberg–Osgood uniaxial stress–strain curve, Eq. 13.12. Derive an equation for the strain ε1 in the direction of σ1 as a function of σ1 and material constants E, H, and n from the uniaxial curve, as well as ...

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Since this is not a case of plane stress, Eqs. 13....

Question: 13.5

A material has the uniaxial stress–strain curve given by the constants in Fig. 13.9. Assume that this curve also applies for cyclic loading and that the stress–strain behavior is similar to that of a multistage spring-slider model. Then estimate the stress–strain response for starting from zero and ...

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The stress–strain response for this example is the...

Question: 13.6

Table E13.6(a) gives the strain history that is repeatedly applied for the stress-strain response example of Fig. 13.24. Estimate the stress response for stable behavior after cyclic softening in this material is complete. The AISI 4340 steel (σu = 1158 MPa) has fitting constants for its stable ...

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Behavior similar to a spring and slider rheologica...

Question: 13.7

Let the strain history of Fig. 13.24(a) be replaced by that of Fig. E13.7, which differs only in that the cycle from G to H and return to G is now repeated 20 times. Simulate the stress response for this revised strain history (a) according to a spring and slider rheological model, and (b) ...

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(a) Behavior according to a spring and slider mode...

Question: 14.1

Consider a beam in pure bending having a rectangular cross section, with depth 2c and thickness t, as in Fig. 14.3. Let the material have a simple power-hardening stress–strain relationship with no elastic region: σ = H2ε^n2 Derive an equation giving the bending moment M as a function of the strain ...

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From the linear strain distribution of Eq. 14.4, w...

Question: 14.2

Consider a beam in pure bending having a rectangular cross section, with depth 2c and thickness t, as in Fig. 14.3. Let the material have the elastic, perfectly plastic stress–strain relationship of Eq. 13.1. Derive an equation giving the bending moment M as a function of the strain εc at y = c and ...

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The behavior of the beam is shown in Fig. 14.5. Up...

Question: 14.3

Consider a beam in pure bending having a rectangular cross section, with depth 2c and thickness t, as in Fig. 14.3. Let the material have the Ramberg–Osgood stress–strain relationship ε = f (σ) of Eq. 13.12. Derive an equation giving the bending moment M as a function of the stress σc at y = c and ...

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The integral of Eq. 14.9 applies, but the form of ...