3 Attachment(s)

Stress concentration factor and notch sensitivity in a shaft

Hey everyone,

I cant seem to get the image links to work sorry! Also, I think the question is supposed to say 2.5mm radius notch, not 10mm

[ATTACH]2155[/ATTACH]

[ATTACH]2156[/ATTACH]

[ATTACH]2157[/ATTACH]

Equations used:

q = Ka - 1 / Kt - 1

M = Fd

(σa / σ'e) + (σm / σy) = 1/FoS

My working so far:

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 wouldnt this mean that you would disregard the 5kN force as M = Fd, M = 5 x 0?

Any help would be greatly appreciated!