Stress concentration factor and notch sensitivity in a shaft

[ridiculoid]

Homework Statement

[/B]
I can't seem to get the image links to work sorry! Also, I think the question is supposed to say 2.5mm radius notch, not 10mm

https://imgur.com/Klxw4gG

https://imgur.com/C9d81Rl

https://imgur.com/7H421ou

Homework Equations

[/B]
q = Ka - 1 / Kt - 1
M = Fd
(σa / σ'e) + (σm / σy) = 1/FoS

The Attempt at a Solution

[/B]
From the stress concentration and notch sensitivity graphs, I found that D/d is 1.82, r/d 0.114 and q = 0.82. From this, Kt for the shaft under tension is 2.25 and Kt for the shaft under bending is 1.88.

For question part (c), I need to use the equation q = Ka-1 / Kt-1 rearranged to Ka = 1 + q(Kt - 1).
What I am wondering is which value of Kt I need to use, my first thought is to use 2.25 because this will give higher stress values which you would need when designing.

I am also stuck with question part (e). With all other examples I have done in class or from worksheets, the shaft has been a single step with a fillet or something similar. I am struggling to find any source material for a notched shaft under tension. I need to take moments around the point of highest stress, I am just unsure where that point is in a notched shaft. My initial thought is the center of the notch but on a single stepped shaft with a fillet, it is at the top edge but wouldn't this mean that you would disregard the 5kN force as M = Fd, M = 5 x 0?

Any help would be greatly appreciated!

 

[anathema]

it's important to approach problems systematically and logically. Let's start by clarifying the question and identifying the key information we have been given. The question mentions a 2.5mm radius notch and the images show a notched shaft under tension and bending. We also have the equations for stress concentration and notch sensitivity, as well as the attempt at a solution provided by the student.

First, we need to confirm the value of the radius of the notch. The student mentions that the question may have a typo and should say 2.5mm instead of 10mm. If this is the case, we should use the correct value of 2.5mm in our calculations.

Next, let's make sure we understand the equations for stress concentration and notch sensitivity. The stress concentration factor (Kt) tells us how much the stress is amplified at the notch compared to the average stress in the unnotched section. The notch sensitivity factor (q) tells us how sensitive the material is to notches - a higher q value means the material is more likely to fail at a notch.

Based on the given information, we can calculate the values of D/d, r/d, and q as the student has done. However, we need to be careful when using these values to calculate the stress concentration factor (Kt). The student has used D/d = 1.82 and r/d = 0.114 to calculate Kt values of 2.25 and 1.88 for the shaft under tension and bending, respectively. However, these values are only valid for the specific notch geometry shown in the images. If the notch geometry were to change, these values would also change. Therefore, it's important to clearly state the assumptions we are making and the limitations of our calculations.

Now, let's address the student's question about which value of Kt to use for part (c). As mentioned earlier, the value of Kt depends on the specific notch geometry. Since we are dealing with a notched shaft under tension and bending, we should use the appropriate Kt values for each loading condition. This means using Kt = 2.25 for the shaft under tension and Kt = 1.88 for the shaft under bending.

Moving on to part (e), the student is correct in thinking that the point of highest stress will be at the center of the notch. However, it's important to remember that the 5