Stress concentration factor and notch sensitivity in a shaft

In summary: N force is still acting on the shaft and will contribute to the bending moment. Therefore, we cannot disregard this force when calculating the bending moment. It's also worth noting that the point of highest stress may change depending on the loading conditions and the specific notch geometry.In summary, we have clarified the question, identified key information, and discussed the importance of using the correct values for D/d, r/d, and Kt. We have also addressed the student's questions about which Kt value to use and the location of the point of highest stress. It's important to carefully consider all factors when approaching a problem in order to arrive at an accurate and valid solution.
  • #1
ridiculoid
19
0

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!
 
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  • #2


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
 

1. What is the stress concentration factor in a shaft?

The stress concentration factor in a shaft is a dimensionless factor that represents the ratio of the maximum stress at a notch or discontinuity in the shaft to the nominal stress at a smooth section of the shaft under the same loading conditions. It takes into account the geometry and material properties of the shaft.

2. How does the stress concentration factor affect the strength of a shaft?

The stress concentration factor can significantly reduce the strength of a shaft, as it causes high stress concentrations at notches or discontinuities. This can lead to premature failure of the shaft, especially under cyclic or dynamic loading conditions.

3. What factors influence the stress concentration factor in a shaft?

The stress concentration factor in a shaft can be influenced by various factors such as the geometry of the notch or discontinuity, the material properties of the shaft, the type of loading applied, and the surface finish of the shaft. It is important to consider all of these factors in order to accurately determine the stress concentration factor.

4. What is notch sensitivity in a shaft?

Notch sensitivity in a shaft refers to the extent to which the stress concentration factor affects the strength of the shaft. Some materials are more notch-sensitive than others, meaning they are more susceptible to the effects of stress concentration factors. This is an important consideration in material selection for shafts in high-stress applications.

5. How can the stress concentration factor and notch sensitivity be reduced in a shaft?

The stress concentration factor and notch sensitivity in a shaft can be reduced by using design modifications such as fillets or gradual transitions in geometry, improving the surface finish of the shaft, and selecting materials that are less notch-sensitive. Finite element analysis can also be used to optimize the design and minimize stress concentrations in the shaft.

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