# Shaft strength

#### elmariachi

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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#### Astronuc

Staff Emeritus
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? [Broken]

I believe it is the same journal, but I have not referenced it recently.

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#### FredGarvin

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.

#### RigidBody

what is the average shaft length? im doing an experimental plan.

is it around 7 inches?

help much appreciated

#### Astronuc

Staff Emeritus
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.

#### acceler8

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

#### acceler8

oh and bending will affect a wide shaft less so take this into account.

#### RigidBody

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! :-)

"Shaft strength"

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