Chapter 6: Problem 51
Upon what three criteria are factors of safety based?
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 6: Problem 51
Upon what three criteria are factors of safety based?
These are the key concepts you need to understand to accurately answer the question.
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Get started for freeDemonstrate that Equation 6.16 , the expression defining true strain, may also be represented by $$\epsilon_{T}=\ln \left(\frac{A_{0}}{A_{i}}\right)$$ when specimen volume remains constant during deformation. Which of these two expressions is more valid during necking? Why?
An aluminum bar \(125 \mathrm{mm}(5.0\) in.) long and having a square cross section \(16.5 \mathrm{mm}(0.65 \text { in. })\) on an edge is pulled in tension with a load of \(66,700 \mathrm{N}\left(15,000 \mathrm{lb}_{\mathrm{f}}\right),\) and experiences an elongation of \(0.43 \mathrm{mm}\left(1.7 \times 10^{-2} \text {in. }\right) .\) Assuming that the deformation is entirely elastic, calculate the modulus of elasticity of the aluminum.
A cylindrical specimen of a nickel alloy having an elastic modulus of \(207 \mathrm{GPa}\left(30 \times 10^{6}\right.\) psi) and an original diameter of \(10.2 \mathrm{mm}\) \((0.40 \text { in. })\) will experience only elastic deformation when a tensile load of \(8900 \mathrm{N}\left(2000 \mathrm{lb}_{\mathrm{f}}\right)\) is applied. Compute the maximum length of the specimen before deformation if the maximum allowable elongation is \(0.25 \mathrm{mm}\) \((0.010 \text { in. })\).
A cylindrical rod of steel \((E=207 \mathrm{GPa}, 30 \times\) \(\left.10^{6} \text { psi }\right)\) having a yield strength of \(310 \mathrm{MPa}\) \((45,000 \mathrm{psi})\) is to be subjected to a load of \(11,100 \mathrm{N}\left(2500 \mathrm{lb}_{\mathrm{f}}\right) .\) If the length of the rod is \(500 \mathrm{mm}(20.0 \text { in. }),\) what must be the diameter to allow an elongation of \(0.38 \mathrm{mm}(0.015 \text { in. }) ?\)
For a brass alloy, the stress at which plastic deformation begins is \(345 \mathrm{MPa}(50,000 \mathrm{psi})\) and the modulus of elasticity is 103 GPa \(\left(15.0 \times 10^{6} \mathrm{psi}\right)\). (a) What is the maximum load that may be applied to a specimen with a cross- sectional area of \(130 \mathrm{mm}^{2}\left(0.2 \text { in. }^{2}\right)\) without plastic deformation? (b) If the original specimen length is \(76 \mathrm{mm}\) \((3.0 \text { in. }),\) what is the maximum length to which it may be stretched without causing plastic deformation?
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