Respuesta :
Answer:
nf=1.11 (Goodman criterion)
ny=2.41 (factor of safety for fatigue)
Explanation:
From the table A-20 Deterministic ASTM minimum tensile and yield strengths for HR and CD steels, we have approximately:
Sut=120 kpsi
Sy=66 kpsi
Due Sut<1400 Mpa, the endurance limit is:
[tex]Se=0.5Sut=0.5*120=60 kpsi[/tex]
The surface condition modification factor is:
[tex]ka=a(Sut)^{b}=2.7(120)^{-0.265} =0.759[/tex]
The effective diameter is:
[tex]de=0.37d=0.37*2.09=0.7733 in[/tex]
The size factor is:
[tex]kb=0.879de^{-0.107} =0.879(0.7733)^{-0.107} =0.9[/tex]
The endurance limit at critical location is:
[tex]See=ka*kb*kc*kd*kd*ke*kf*Se=0.759*0.9*1*60=40.986 kpsi[/tex]
[tex]\frac{D}{d}=\frac{2.32}{2.09} =1.11\\\frac{r}{d}=\frac{0.117}{2.09} =0.056[/tex]
From Figure A-15-15 chart, the Kf = 2.1
The notch sensitivity is:
[tex]\sqrt{a}=0.246-3.08(10^{-3})Sut+1.51(10^{-5})Sut^{2}-2.67(10^{-8})Sut^{3}[/tex]
[tex]\sqrt{a}=0.246-3.08(10^{-3})(120)+1.51(10^{-5})(120^{2})-2.67(10^{-8})(120^{3})=0.048[/tex]
[tex]q=\frac{1}{1+\frac{\sqrt{a} }{\sqrt{r} } }=\frac{1}{1+\frac{0.048}{\sqrt{0.117} } }=0.877[/tex]
The fatigue stress is:
[tex]Kf=1+q(Kt-1)=1+0.877(2.1-1)=1.96[/tex]
The moment of inertia is:
[tex]I=\frac{\pi }{64} d^{4}=\frac{\pi }{64} (2.09^{4})=0.936 in^{4}[/tex]
The maximum stress is:
[tex]omax=\frac{M*c}{I}=\frac{25000*\frac{2.09}{2} }{0.936} =27911.32 psi=27.911 kpsi[/tex]
The mean stress is:
[tex]om=Kf\frac{omax+omin}{2} =1.96\frac{27.911+0}{2}=27.35 kpsi[/tex]
The alternate stress is:
[tex]oa=Kf|\frac{omax-omin}{2}|=27.35 kpsi[/tex]
The fatigue factor using Goodman is:
[tex]\frac{1}{nf}=\frac{oa}{See}+\frac{om}{Sut}\\\frac{1}{nf}=\frac{27.35}{40.986}+\frac{27.35}{120}[/tex]
nf=1.11
the factor of safety is:
[tex]ny=\frac{Sy}{omax}=\frac{66}{27.35} =2.41[/tex]
The infinite life cannot be predicted with this data.
Given, D= 2.1, d (diameter) = 1.892, r= 0.117
Endurance limit for the material= Se'= 60 kpsi
According to the goodman relation= nf= 0.833
Yielding factor of safety: ny= Sy/σmax= 66/36.828
ny= 1.792
Learn more about goodman relation:
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