Bickford's strength reduction factor 2

[electricpete]

The above graph shows strength reduction factor for thread bending which is supposed to reduce thread strength when using materials of unequal strengths (based on the discussion). The minimum of the figure occurs at 1.0 (equal strengths where thread stengths should be the highest), which suggests maybe we are supposed to invert the ratio to determine a "correction factor" for strength of threads?.....

But then here is an example calculation using that figure

http://books.google.com/books?id=gT...when the nut material is 25% stronger&f=false

which states

SR2 = strength reduction factor when the nut material is 25% stronger = 1.1 (from figure 3.8)

Now I'm really confused. If I enter figure 2.8 using strength ratio = 1.25 on the horizontal axis, I read around 0.975 on the vertical axis. If I invert that I get 1.025, not 1.1. Why heck would I ever have a factor of 1.1 which as applied in the example suggests the threads are stengthened by the unequal material strengths?

Now an even weirder twist. The above comes from 3rd ed. If you have the 4th edition, read on... else ignore this last paragraph since it'll be too hard to follow. In the 4th edition he writes 4th SR2=1.1 the same way. Then when he plugs it into the final formula he changes it (witout explanatio) to 0.975 instead of 1.1. OK, I feel a little more comfortable since that's what I read off the graph. But that doens't make sense. If we used that same approach if we had strength ratio (horizontal axis) of 1.6, we'd read a number of 1.1 on the vertical axis again (improvement in strength due to unequal materials).

Either I am totally missing something, or this is just gibberish. Any light that can be shed would be appreicated.

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[electricpete]

The above graph...

Whoops I forgot to include a link to the graph at beginning of my post. Here it is:

http://books.google.com/books?id=gT...h reduction factor for thread bending&f=false

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[CoryPad]

My discussion regards the 3rd edition, Revised and Expanded for this book. On page 72, I see the same example that you link above. However, SR2 = 0.9 in my book, which agrees with the graph in Figure 3.8.

There is no need to invert anything - the SR factors are in the numerator for the F equation.

If you want to double-check these calculations, you can use the ones in VDI 2230. They are similar, but a little different in form.

 

[electricpete]

Thanks for the response.

My discussion regards the 3rd edition…. However, SR2 = 0.9 in my book

1 - So your 3rd edition book is different than the linked 3rd edition book which lists SR2=1.1 ?

2 – How do we come up with 0.9 using 1.25 to enter Figure 3.8 ?

There is no need to invert anything

So…. if my strength ratio is 1.5 (horizontal axis), then I should use SR2 = 1.1 based on Figure 3.8 ?

I appreciate your patience. At this point I don’t see any logic, just a bunch of inconsistencies.


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[CoryPad]

1. Yes, mine is different. The cover calls it "Third Edition, Revised and Expanded", so I imagine this example is part of the "revised" content.

2. I wasn't paying enough attention, 0.9 is wrong, it should be 0.975 or so like you said in your first post. Yes, you should use 1.1 if your strength ratio is 1.5.

 

[electricpete]

Aha. Thanks.

Yes, you should use 1.1 if your strength ratio is 1.5

4. Thanks. In that case, according to the graph then, the more different are the strengths of our nut and bolt, the higher multiplier which increases the thread stripping strength. (Right?).

I can buy that (I remember hearing it is good for nut to be softer than bolt). But it seems somewhat in conflict with Bickford’s description for the figure 3.8 which reads as follows:

Relative strength of nut-to-bolt threads [14–16]. As we have seen, the relative strength
always determines which members will fail. If there is too big a difference between the two
materials, another factor must be considered: The weaker of the two threads will deflect under
the relatively stiff action of the other, creating a form of thread disengagement that again
reduces the area supporting shear stress. Note that it doesn’t matter which thread—nut or
bolt—is substantially weaker than the other. The result is shown in Fig. 3.8

5. Would you agree that the quote from Bickford suggests that difference in strength reduces the thread stripping strength? (which seems in conflict with an affirmative answer to question 4).

6. Does the SR = 1.1 factor apply to both nut thread stripping calc and bolt thread stripping calculations (regardless of which is stronger)?


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[CoryPad]

4. Figure 3.8 is for the thread bending factor, not overall thread stripping strength.

5. If you have a really weak nut material and a really strong bolt material, that is bad and will result in a reduced thread stripping strength. You always have the area (engagement length) factor to overcome material strength issues.

6. Yes

 

[electricpete]

Thanks again. I remain really confused.

4. Thanks. In that case, according to the graph then, the more different are the strengths of our nut and bolt, the higher multiplier which increases the thread stripping strength. (Right?).

4. Figure 3.8 is for the thread bending factor, not overall thread stripping strength

I thought Figure 3.8 is for the thread bending factor, which IS used precisely to calculate a correction to thread stripping strength and nothing else. This is based on:
A – The heading of the section is "Things that modify that static strength of threads".
B – "To compute the modified potential strength of a nut thread, therefore, one multiplies the apparent strength in pounds by the appropriate nut factor from Figure 3.7, and by the approximate thread bending factor from Figure 3.8"
C – The example calculation which I have summarized below (direct quotes in italics):
Fst = Su * Ats
Where
Ats = thread stripping area
Fst = "force required to strip the threads of the bolt"
"The Reduced estimate for the strength of our threads is now
Fst' = SR1*SR2*SR3*SR4*Fst"
Where SR2 is read directly from Figure 3.8.

7. After reading the above, can you agree with me that Figure 3.8 is a correction for thread stripping strength? And therefore it predicts that a larger difference in material strengths results in a correction which increases stripping strength?

8. If answer to 7 is no (Figure 3.8 is not a correction for thread stripping strength), then what is the purpose of Figure 3.8?

5. If you have a really weak nut material and a really strong bolt material, that is bad and will result in a reduced thread stripping strength. You always have the area (engagement length) factor to overcome material strength issues.

9. Doesn't this put us on the far left of Figure 3.8 where the correction factor is >1 indicating improved strength? As an example:
Case A: Synut = 40ksi, Sybolt = 40ksi, StrengthRatio = 1, SR2=0.9
Case B: Synut = 40ksi, Sybolt = 100ksi, StrengthRatio = 0.4, SR2=1.2
According to figure 3.8 and accompanying discussion, the nut thread stripping strength should be higher in case B by a factor of 1.2/0.9 ~1.3, correct?

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[CoryPad]

You are correct, Figure 3.8 is the thread bending factor, and you have the equations correct.

7. Yes, I agree it is a correction and provides a numerically higher factor when the strength ratio varies away from 1.

9. Yes, that would be on the left of that chart.

But my point is that there is more to stripping strength than SR2 (or any of the other SR's). Stripping strength is directly proportional to material shear strength and shear area: F = S * A. So, if you decrease nut material strength, you decrease stripping strength. It is a balancing act with all of the factors, which you have shown in previous posts.

What you will find is that you usually are forced into a certain nut material strength for reasons completely unrelated to fastening. Then, you trade off thread depth (and hence shear area) with bolt strength/property class.

 

[electricpete]

Thanks for your patience. I think I am getting closer.

10 – Would you agree there is a conflict between Figure 3.8 (which implies that difference in relative strengths results in a correction that increases the stripping strength) and the following discussion (which states/explains that difference in relative strengths decreases the stripping strength)

Relative strength of nut-to-bolt threads - As we have seen, the relative strength always determines which members will fail. If there is too big a difference between the two materials, another factor must be considered: The weaker of the two threads will deflect under the relatively stiff action of the other, creating a form of thread disengagement that again reduces the area supporting shear stress. Note that it doesn't matter which thread—nut or bolt—is substantially weaker than the other. The result is shown in Fig. 3.8

11 – Assuming answer to 10 is yes, the resolution of the conflict as I understand is that we believe Figure 3.8 Specifically, we believe that the difference in material strengths of male and female threads results in a correction which increases thread stripping strength beyond what we would calculate without considering opposite thread strength. The text quoted above doesn't explain why this would be the case (it explains the opposite). What is the explanation for this behavior?


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[electricpete]

Let's start with #10. Is there anyone out there in the world who agrees that the linked figure is not consistent with the quoted text?

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[CoryPad]

10. I don't think the word conflict is correct; it is a case of multiple variables. Figure 3.8 shows one factor, SR2, but the text is referring to the overall behavior (eq. 3.10, F' = F x SR1 x SR2 x SR3 x SR4).

11. I look to equation 3.10 - there is the primary factor F, which relates to stress and area, then the secondary factors (SR1, etc.).