1. Senior Member
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Jan 2007
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## Bending formulas

I'm looking for a couple of offset bending formulas that I've used in the past but cant remember offhand. I don't know enough about trig to find what im looking for.
One was to calculate shrinkage for any given angle, and the other was to determine degrees bent when distance between bends is known for any given depth. Any ideas?

2. KC,
Both are based on the derivations on the hypotenuse equation.
hypotenuse = Square Root of (oppositeside^2 + adjacentside^2 ).

Just a little visualization from a drawing of the right triangle you are working with.
And a little algebra to shift terms around.

The diagram really helps.
(Hypotenuse - OppositeSide) will indicate 'shrink', for example. This is a visualization.
Just draw increasing angles and notice the 'shrink' is (Hyp-Opp).

Given the angles, you can cosine or sine for the length ratios of the side.
But this is too much for 3:00 AM here.

If you work through it, you will be able to apply it on the job,
when you are hot and sweaty.

On the iNet, google for the Benfield Bender calculations.
Well, on checking my old Greenlee and Benfield manuals,
it is obvious they were written for blue collar guys who use look-up tables.
No equations used in these little manuals, just nice diagrams and tables.

Remember, I'll give you a money back guarantee on this.
But this is too much for 3:00 AM here. Good night. :smile:

3. KC,
I checked in UGLY's book, and there are some helpful diagrams.

4. When I was in school the instructor gave everyone a 5' piece of 1/2" and told them to bend a 90 in it and make both legs the same length. All but 2 in the class bent a 30" 90 in it expecting it to come out equal. Me and one other guy who had been doing GRS with an old school guy guessed at how much the growth would be and got pretty close. What amazed me was at the end of our conduit bending session the number of guys that could not grasp where that "extra" conduit came from. As far as offsets go I can get real close on 30's with 1/4" shrinkage per 1" of offset.

5. Originally Posted by masterinbama
When I was in school the instructor gave everyone a 5' piece of 1/2" and told them to bend a 90 in it and make both legs the same length. All but 2 in the class bent a 30" 90 in it expecting it to come out equal. Me and one other guy who had been doing GRS with an old school guy guessed at how much the growth would be and got pretty close. What amazed me was at the end of our conduit bending session the number of guys that could not grasp where that "extra" conduit came from. As far as offsets go I can get real close on 30's with 1/4" shrinkage per 1" of offset.
IIRC, the Benfield book[let] says per inch of offset: 3/16" for 22.5°, 1/4" for 30°, and 3/8" for 45° offsets.

If we were to consider only sharp bends, i.e. no radius, the formula would be...
(1 – cos θ) per offset-inch
It follows to use the cosine of the bend angle because the hypotenuse represents the distance between the bends while the adjacent side of the representative triangle is the longitudinal distance the offset spans. Trigonometry values are based on a hypotenuse of 1 unit.

Another issue to consider is that due to bends having a radius, there is gain at each bend versus our straight line measures. For the smaller diameter conduits, the gain for 45° bends is very small and is usually disregarded. However, when bending larger sized conduits, the gain in offset bends can throw off any pre-calculated final length using just the basic offset formula.

6. Senior Member
Join Date
Jan 2007
Location
Texas
Posts
239
Originally Posted by glene77is
KC,
Both are based on the derivations on the hypotenuse equation.
hypotenuse = Square Root of (oppositeside^2 + adjacentside^2 ).

Just a little visualization from a drawing of the right triangle you are working with.
And a little algebra to shift terms around.

The diagram really helps.
(Hypotenuse - OppositeSide) will indicate 'shrink', for example. This is a visualization.
Just draw increasing angles and notice the 'shrink' is (Hyp-Opp).

Given the angles, you can cosine or sine for the length ratios of the side.
But this is too much for 3:00 AM here.

If you work through it, you will be able to apply it on the job,
when you are hot and sweaty.

On the iNet, google for the Benfield Bender calculations.
Well, on checking my old Greenlee and Benfield manuals,
it is obvious they were written for blue collar guys who use look-up tables.
No equations used in these little manuals, just nice diagrams and tables.

Remember, I'll give you a money back guarantee on this.
But this is too much for 3:00 AM here. Good night. :smile:
Thanks for getting my brain moving, I’ll play with my calculator a little
more for shrink. I think Smart put up the formula I was looking for, but it will take me awhile commit it to memory. I won’t use it much but this plant is old, so sometimes an offset on an odd angle is all that will fit some places. I already use the A^2 plus B^2 thing, but for rolling offsets, it really comes in handy.
I’ve been thinking about getting the benfield manual for awhile, sounds like it might be worth the buy.

Originally Posted by Smart \$
IIRC, the Benfield book[let] says per inch of offset: 3/16" for 22.5°, 1/4" for 30°, and 3/8" for 45° offsets.

If we were to consider only sharp bends, i.e. no radius, the formula would be...
(1 – cos θ) per offset-inch
It follows to use the cosine of the bend angle because the hypotenuse represents the distance between the bends while the adjacent side of the representative triangle is the longitudinal distance the offset spans. Trigonometry values are based on a hypotenuse of 1 unit.

Another issue to consider is that due to bends having a radius, there is gain at each bend versus our straight line measures. For the smaller diameter conduits, the gain for 45° bends is very small and is usually disregarded.

Thanks for the formula, I’ve found they are easier and quicker for me to use than some methods I’ve tried. Those methods being the bend in the middle cut off both ends method, and the hope it turns out right or do it again method:mad:. To much cutting and threading for me.

Originally Posted by Smart \$
However, when bending larger sized conduits, the gain in offset bends can throw off any pre-calculated final length using just the basic offset formula
Is there any rule of thumb that would account for that? How much would it throw it off for a 4 or 6 inch pipe?

I believe the other one I was looking for was: sin^-1 multiplyed by distance between bends / offset depth, but won’t know until I get back to my toolbox/calculator.

7. Originally Posted by K2500
Originally Posted by Smart \$
However, when bending larger sized conduits, the gain in offset bends can throw off any pre-calculated final length using just the basic offset formula.
Is there any rule of thumb that would account for that? How much would it throw it off for a 4 or 6 inch pipe?
Too many variables to develop a rule of thumb. You either have to have a manufacturer's bending chart which reflects the gain (such as in Greenlee's hydraulic bender manuals when using that particular bender), or rely trial and error (yours or someone before you) and perhaps do the math before the first trial. For 4" rigid, 45° offset, on a Greenlee Cam Track, the gain is approximately 1".

Originally Posted by K2500
I believe the other one I was looking for was: sin^-1 multiplyed by distance between bends / offset depth, but won’t know until I get back to my toolbox/calculator.
sin^-1 is Inverse Sine, also denoted arcsin,and is the correct function. However, if you are trying to determine the angle at which to bend an offset to fit within a certain longitudinal distance (that is, both the bends and the angled section must fit within a certain distance), that formula will leave your offset a bit long because it does not account for the distance the bends occupy. I'll through you a bone for that (you won't find it in any bending manual or handbook).

PS: If you're into using math to better you bending skills, you should pick up a copy of Greenlee's Conduit Bending Handbook.

8. Smart,
Thanks. Good info.
Thanks for distinguishing between 'Run' and other 'Linear' lengths.

I wonder where the creeping shrink comes from?
Could the varying mallability of the conduit become a factor?
I have noticed that 'spring back' is different
for different batches, manufacturers, and ambient temperatures.
I have calculated, and still had to just lay a sample piece on the floor
to measure and tickle.

9. Originally Posted by glene77is
Smart,
Thanks. Good info.
Thanks for distinguishing between 'Run' and other 'Linear' lengths.

I wonder where the creeping shrink comes from?
Could the varying mallability of the conduit become a factor?
I have noticed that 'spring back' is different
for different batches, manufacturers, and ambient temperatures.
I have calculated, and still had to just lay a sample piece on the floor
to measure and tickle.
I'm not certain what you mean by "creeping shrink"...???

Yes, varying malleability is one of the variables I mentioned, as are the others you mention. Even when you do the math to what you believe to be an exacting degree, it will usually get you close, at least closer than outright trial and error. Some methods of doing the math are better than others. But in most cases, close is good enough. Yet it can be frustrating when precision is desired and the result says your math is a little off :wink:

10. Senior Member
Join Date
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Location
Texas
Posts
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Originally Posted by Smart \$

.
Excellent illustration, I’m just not sure how to use it. What does “r” define?

Originally Posted by Smart \$
PS: If you're into using math to better you bending skills, you should pick up a copy of Greenlee's Conduit Bending Handbook.
Thanks, both the greenlee book as well as the benfield book are the next ones on my list.

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