Based upon the Von Mises theory, the safety factor for points A and B are 2.77 and 6.22 respectively.
From the diagram of this bar made of AISI 1006 cold-drawn steel shown in the image attached below, we can logically deduce the following parameters:
At point A, the stress is given by this equation:
σx = Mc/I + P/Area
[tex]\sigma_x = \frac{Fl(\frac{d}{2}) }{\frac{\pi d^2}{64} } +\frac{P}{\frac{\pi d^2}{4} } \\\\[/tex]
σx = 32Fl/πd³ + 4P/πd²
Substituting the given parameters into the formula, we have;
σx = 32(550)(0.1)/π(0.02)³ + 4(800)/π(0.02)²
σx = 95.49 MPa.
Next, we would determine the torque:
Mathematically, torque can be calculated by using this formula:
τxy = Tr/J = 16T/πd³
τxy = 16(30)/π(0.02)³
τxy = 19.10 MPa.
From Von Misses theory, we have:
σVM = √(σx² + 3τxy²)
σVM = √(95.49² + 3(19.10)²)
σVM = 101.1 MPa.
Now, we can calculate the safety factor for point A:
n = Sy/σVM
n = 280/101.1
n = 2.77.
At point B, the stress is given by this equation:
σx = 4P/πd²
σx = 4(800)/π(0.02)²
σx = 25.47 MPa.
Next, we would determine the torque:
Mathematically, torque can be calculated by using this formula:
τxy = Tr/J = 16T/πd³ + 4V/3A
τxy = 16(30)/π(0.02)³ + 4(550)/3π(0.02)³
τxy = 21.43 MPa.
From Von Mises theory, we have:
σVM = √(σx² + 3τxy²)
σVM = √(25.47² + 3(21.43)²)
σVM = 45.02 MPa.
Now, we can calculate the safety factor for point B:
n = Sy/σVM
n = 280/45.02
n = 6.22.
Read more on Von Mises theory here: https://brainly.com/question/12976779
#SPJ1
