Calculating Strength of Hollow Shaft with Notch & Holes

In summary, Fred's Hollow Shaft will have a 15% reduction in strength compared to a Solid 2" Shaft due to the drilled tranverse holes and the notch. Roark's Formulas for Stress and Strain can be used to calculate stress concentrations for bending and torsion for a notch and hole in a shaft. The average shaft length is 7 cm, not inches.
  • #1
elmariachi
6
0
Hi all,
I have a hollow shaft of 2" outside dia to 1.25" inside dia, about 1.5 ft in length.I also have a notch going around the outside periphery of the shaft. The shaft also has 2 holes drilled tranversely through the shaft
The shaft will be rotating and will have torsion and probably bending load. I already calculated that the strength of this hollow shaft will reduce by about 15% compared to a solid 2" shaft.How can I further calculate the reduction in strength taking into consideration the drilled tranverse holes & the notch.Thanks in advance.


john
 
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  • #2
The stress resulting from holes and notches in a shaft are generally handled by stress concentration factors, and the classic work is that of R. E. Peterson, "Stress Concentration Factors," Wiley, New York, 1974.

Unfortunately, I do not have a copy at the moment.

Some texts, like Richard G. Budynas's "Advanced Strength and Applied Stress Analysis" may have graphs or tables taken from Petersen's text (which does have stress concentration factors for semicircular notches in a solid shafts) or journal articles, particularly in Machine Design, in which Petersen published a series of articles on stress concentration factors in Feb-July, 1951.

This might be of use -
http://www.machinedesign.com/asp/index.asp?

I believe it is the same journal, but I have not referenced it recently.
 
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  • #3
I can't type all of it here, but if you have access to Roark's Formulas for Stress and Strain, stress concentrations that you require are in table 37, pages 737 and 739 in my copy deal exactly with your situation.

For the notch, it it is a 3rd order polynomial that is a function of notch depth and notch radius (makes sense).

For the hole is another 3rd order polynomial that is a function of hole radius and shaft OD.
 
  • #4
what is the average shaft length? I am doing an experimental plan.

is it around 7 inches?

help much appreciated
 
  • #5
I have the 7th edition of Roark's Forumulas for Stress and Strain.

The data that Fred described are in Table 17.1 on page 790-792, and show stress concentration factors for bending and torsion.
 
  • #6
the average shaft length is 7 cm, not inches. a common misconception. 7 inches is aroundabout 3 cm. it depends what instruments shaft youre measuring, and whether length really plays a key part. for many methods a wide shaft performs better and gives more consistent results than a long shaft. bear this in mind for your shaft experiment!

enjoy

xxxx Gareth
 
  • #7
oh and bending will affect a wide shaft less so take this into account.
 
  • #8
acceler8 said:
the average shaft length is 7 cm, not inches. a common misconception. 7 inches is aroundabout 3 cm. it depends what instruments shaft youre measuring, and whether length really plays a key part. for many methods a wide shaft performs better and gives more consistent results than a long shaft. bear this in mind for your shaft experiment!

enjoy

xxxx Gareth

oh thanks! i remember hearing about the length but not having actually measured one before, i was lost! :-)
 

1. How do I calculate the strength of a hollow shaft with notches and holes?

To calculate the strength of a hollow shaft with notches and holes, you will need to consider the material properties, dimensions of the shaft, and the location and size of the notches and holes. The formula for calculating the bending stress is σ=Mc/I, where σ is the bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia. You will also need to consider the stress concentration factor at the notches and holes, which can be found in a table based on the geometry of the notch or hole.

2. What is the difference between a notch and a hole in terms of calculating strength?

A notch is a cut or indentation in the surface of the shaft, while a hole is a void or opening through the shaft. Notches typically have a larger effect on the strength of the shaft than holes, as they create a stress concentration point. Holes, on the other hand, distribute the stress evenly along the edges of the hole, resulting in a lower stress concentration factor.

3. How do I determine the stress concentration factor for a notch or hole?

The stress concentration factor can be found in a table based on the geometry of the notch or hole. This table typically includes factors for different notch or hole shapes, depths, and radii. You will need to determine the appropriate factor based on the specific dimensions of your notch or hole.

4. Can I use the same formula for calculating the strength of a solid shaft?

No, the formula for calculating the strength of a hollow shaft with notches and holes is different from that of a solid shaft. This is because the presence of notches and holes significantly affects the stress distribution and concentration in the shaft. Therefore, it is important to use the correct formula for the type of shaft you are analyzing.

5. How can I improve the strength of a hollow shaft with notches and holes?

There are a few ways to improve the strength of a hollow shaft with notches and holes. One option is to increase the thickness of the shaft, which will increase its moment of inertia and reduce the stress on the shaft. Another option is to use a different material with higher strength properties. Additionally, you can also modify the shape and size of the notches and holes to reduce the stress concentration factor. It is important to carefully consider all of these factors in order to design a strong and reliable hollow shaft.

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