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post #1 of 41 (permalink) Old 02-11-2014, 11:22 AM Thread Starter
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Harness bar strength?

Hi guys,

I don't know if anyone here can help me figure this out, but I am confused by something.

I recently decided to build a harness bar for my Elise. I looked at the OEM and aftermarket ones, and for various reasons didn't like any of them. Most of the options are made from 1.5" DOM tubing in wall thicknesses from .120" to .135". My understanding is the OEM one is similar as well.

Not wanting to just copy this without knowing why, I looked up the requirements, and what I found is this:
For DOT safety, the requirement for seat belt attachment locations (from 49CFR 571.210 if you want to look it up) is that the lap and shoulder belts must simultaneously support 3000lbs for 10s.
I couldn't find an applicable racing requirement for attachments, but for belts it is similar, SFI 16.1 states that shoulder belts must support a load of 3300lbs for 10s, and have a breaking strength of 4500lbs.
Race cars are often designed with a peak deceleration rate used for loading, generally around 15-30g, so 3000lbs to support 1/2 of a 200lb driver seems pretty close to me.


Now, a harness bar in the Elise is about 3.5 feet long, and we can assume the loading from the shoulder belts is symmetrically applied about a foot from each end.

Running the calculations with a 1.5" steel tube, we would find that the tube isn't even CLOSE to being strong enough to support this kind of load. Max bending stresses for a simply supported tube with this loading are on the order of 200ksi (about 3-5 times the strength of steel, depending on grade).

So, my question is, what am I missing here? Are all the available options for harness bars just underbuilt, at least according to these standards? Am I an idiot that can't calculate simple bending, or making some invalid assumption here?
Let me know if anyone has any ideas

Thanks,
Pat

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post #2 of 41 (permalink) Old 02-11-2014, 01:15 PM
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re: Harness bar tube

Common Sense: SCCA spec for roll cage for 1.5"x.125" DOM is 2500lbs car (from memory). Hence, it is very good for our car for harness bar.

I do not understand your calculations either. The bar is attached on both ends of the tube. The belt is 3" wide (SCCA spec). The belt will distribute 3200lbs force very well over the tube. The contact area will be 3x1.5*pi/2 or about 9sq.in. Hence, the pressure is about 350psi under the belt. No problem for .120 wall.

The weak point will be the welds on each side. Assuming 45ksi DOM mild 1018, 3200lbs on each side the weld area should be .071 sq.in. for a weld length of .6" for .120 wall thickness. We have pi*1.5 is about 5", so 10x safety factor.

You are supposed to weld all the way around!

I use 1.375x .095 4130 Chrome Moly in my Lotus. I can almost get away with .080 i.e. 1500lbs size. (I think Canadian standards are a little more lax than SCCA i.e. they are like old SCCA standard).


Anton




Quote:
Originally Posted by pwildfire View Post
Hi guys,

I don't know if anyone here can help me figure this out, but I am confused by something.

I recently decided to build a harness bar for my Elise. I looked at the OEM and aftermarket ones, and for various reasons didn't like any of them. Most of the options are made from 1.5" DOM tubing in wall thicknesses from .120" to .135". My understanding is the OEM one is similar as well.

Not wanting to just copy this without knowing why, I looked up the requirements, and what I found is this:
For DOT safety, the requirement for seat belt attachment locations (from 49CFR 571.210 if you want to look it up) is that the lap and shoulder belts must simultaneously support 3000lbs for 10s.
I couldn't find an applicable racing requirement for attachments, but for belts it is similar, SFI 16.1 states that shoulder belts must support a load of 3300lbs for 10s, and have a breaking strength of 4500lbs.
Race cars are often designed with a peak deceleration rate used for loading, generally around 15-30g, so 3000lbs to support 1/2 of a 200lb driver seems pretty close to me.


Now, a harness bar in the Elise is about 3.5 feet long, and we can assume the loading from the shoulder belts is symmetrically applied about a foot from each end.

Running the calculations with a 1.5" steel tube, we would find that the tube isn't even CLOSE to being strong enough to support this kind of load. Max bending stresses for a simply supported tube with this loading are on the order of 200ksi (about 3-5 times the strength of steel, depending on grade).

So, my question is, what am I missing here? Are all the available options for harness bars just underbuilt, at least according to these standards? Am I an idiot that can't calculate simple bending, or making some invalid assumption here?
Let me know if anyone has any ideas

Thanks,
Pat
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post #3 of 41 (permalink) Old 02-11-2014, 01:56 PM Thread Starter
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^ I am not calculating pressure, but stress.

For a simply supported member, loaded with load 'P' symmetrically a distance 'a' from each end, and with radius 'r' and area moment of inertia 'I' maximum bending stress is:

stress (psi)=P*a*c/I, for this case 3000lb*12"*.75"/.129in^4=209000 PSI.

where I is calculated for a tube as I=(pi)*(OD^4-ID^4)/64 =.129in^4 for 1.5x.125wall DOM.

this is all from Euler-Bernoulli bending, which is about as simple as it gets. What this says is that the stress in the tube at the seat belt location will be about 4x the strength of the tube.

Saying that a roll cage specification has anything to do with a specific loading case in a different application is not "common sense" to me. Furthermore, without doing a lot of research, I have no way of knowing what the intended loading cases are for that specification even if I did want to use it as a comparison. At what speed or with what acceleration, and in what direction are they assuming the car hits the ground?

Your weld calculation also is pointless, as you are assuming shear, not bending. If you doubt this, go weld a 1' bar to something, and apply 3000lbs right at the weld (which is what shear is), then apply the same 3000lb at the other end of the bar. Bending by definition is basically leverage.

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Last edited by pwildfire; 02-11-2014 at 02:16 PM.
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post #4 of 41 (permalink) Old 02-11-2014, 02:02 PM
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It's not a simply supported beam! It's a redundant structure because it is fastened at both ends. Draw a shear moment diagram (distribute the load uniformly across the shoulder straps) and guesstimate end conditions. You can even "pin" them to be super conservative.
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post #5 of 41 (permalink) Old 02-11-2014, 02:06 PM
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Oh...and in a beam, stress is = Mc/I... draw the shear moment diagrams and post them up here. I'll correct them for you.
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post #6 of 41 (permalink) Old 02-11-2014, 02:30 PM
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post #7 of 41 (permalink) Old 02-11-2014, 02:32 PM Thread Starter
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^ I realize it isn't simply supported (although the OEM is pretty close I think with those single shear bolts), but I like to use SS for bending as it is most conservative. IIRC fixed vs simply supported in this case is a factor of 4?, so that still is right at yield for most materials with no safety factor, unless we assume the SF is built into the specifications (which I don't like to do).

I will check what the max stress comes out SS vs pinned vs fixed when I get home.
EDIT: actually, assuming fixed ends reduces stress by 2, not 4, so we are still looking at 100ksi max bending. Still not sure what gives here. Again, I am not saying that everyone's cars are unsafe or anything, only pointing out a discrepancy that I can't figure out.

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post #8 of 41 (permalink) Old 02-11-2014, 02:33 PM Thread Starter
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Quote:
Originally Posted by <@@> View Post
Oh...and in a beam, stress is = Mc/I... draw the shear moment diagrams and post them up here. I'll correct them for you.
And in a SS beam with loads at equal distance (a), Mmax is Pa, so Pac/I, as posted. Thanks for the offer though.

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post #9 of 41 (permalink) Old 02-11-2014, 02:46 PM
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post #10 of 41 (permalink) Old 02-11-2014, 02:59 PM
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re: Stress calculation in a belt bar

I agree with below. It is not a simply supported beam. Hence, my simplistic analysis is valid.

Again, common sense should prevail. There have not been any belt-bar failures in SCCA for the last 50 years. On the other hand, the location of the bar, the width of the webbing has all been 'tested' to failure. Hence, 3" webbing and the regulation that shoulder belt should be horizontal after it leaves the back of the seat.

Anton


Quote:
Originally Posted by <@@> View Post
It's not a simply supported beam! It's a redundant structure because it is fastened at both ends. Draw a shear moment diagram (distribute the load uniformly across the shoulder straps) and guesstimate end conditions. You can even "pin" them to be super conservative.
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post #11 of 41 (permalink) Old 02-11-2014, 04:48 PM Thread Starter
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Quote:
Originally Posted by ageshelin View Post
I agree with below. It is not a simply supported beam. Hence, my simplistic analysis is valid.

Anton
So, you think that since the real world case is *more* complex than my assumptions, that means that your simplistic and totally inaccurate analysis is correct? Sorry, the world doesn't work that way.

Yes, I realize that 1.5" harness bars are standard, but when I take the time to design and build something, I like to know what assumptions I am following, and 'everyone does it that way' is not one that works for me.

This is actually something that I am really trying to understand, and no offense, but your comments do nothing to that end. <@@>'s comments may be a little condescending, but at least they are valid, I'll take that any day.

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post #12 of 41 (permalink) Old 02-11-2014, 06:44 PM
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I can't answer the calculation - but I can comment on the SF point. It is easy to add contingency and safety factors (including assessing it as SS which it isn't) to the point of making anything (or any project) too heavy and/or uneconomic.
That said according to your info
Quote:
Originally Posted by pwildfire View Post
...
is that the lap and shoulder belts must simultaneously support 3000lbs for 10s.
...
this structure could fail at 11s and thus the SF at that load = 1.0
Quote:
Originally Posted by pwildfire View Post
...unless we assume the SF is built into the specifications (which I don't like to do).
...
That question is answered - no additional FoS need be applied.
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post #13 of 41 (permalink) Old 02-11-2014, 07:04 PM
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Keep up the good work. I want to know more, but as it related to the calculations...
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post #14 of 41 (permalink) Old 02-11-2014, 07:41 PM
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The other thing that you are missing out on is that the center of mass of a human body is right about the waist line (if I remember correctly). That means that just about all of the 3K force will be taken up by the lap belts at 1500-lbs each anchor point. That doesn't leave much for the shoulder harnesses to support. Say conservatively 50-lbs at your 15Gs is just 750-lbs divided by the two shoulder straps, that's only 375-lbs. Now you are at approximately 1/10th the load and very reasonable loading.
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post #15 of 41 (permalink) Old 02-12-2014, 06:44 AM Thread Starter
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Quote:
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I can't answer the calculation - but I can comment on the SF point. It is easy to add contingency and safety factors (including assessing it as SS which it isn't) to the point of making anything (or any project) too heavy and/or uneconomic.
True, but it is similarly easy to do the opposite, ie assuming it is fixed, which it isn't, and underdesign something.

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this structure could fail at 11s and thus the SF at that load = 1.0

That question is answered - no additional FoS need be applied.
Well, no, not really. All the calculations I am doing are static loading, which means that assuming I am not making a mistake in calculations, the structure would yield during the ramp up phase, before even reaching 3000lbs.

And, yes, one can assume that no FoS is needed, but the problem is, that number is based on physical testing, and does not specify what the design FoS is. Assuming that the same FoS is appropriate for rough calculations is not a valid answer. If they specified the FoS that was included in the test, then I could evaluate whether it is appropriate, but since they don't, we don't know if it is 1.1, or 1.5, or 3. A FoS of 1.3 is often used for proof tests (see ASME B30.20 for example), but I wouldn't want to design something for FoS of 1.3 without a lot more in depth analysis, and/or physical testing.

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post #16 of 41 (permalink) Old 02-12-2014, 06:49 AM Thread Starter
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Quote:
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The other thing that you are missing out on is that the center of mass of a human body is right about the waist line (if I remember correctly). That means that just about all of the 3K force will be taken up by the lap belts at 1500-lbs each anchor point. That doesn't leave much for the shoulder harnesses to support. Say conservatively 50-lbs at your 15Gs is just 750-lbs divided by the two shoulder straps, that's only 375-lbs. Now you are at approximately 1/10th the load and very reasonable loading.
Actually, this is what I am assuming the difference probably is. The problem is that according to both of the posted regulations, the 3K load is for the shoulder belts explicitly, and there is a separate load for the lap belt.
It seems like a lot of this may be based on SCCA roll cage specs, which do specify a 1.5" harness bar, but I would like to see what loading was in their design, as it doesn't jive with the 3K requirements. It is easy to believe that they are using something similar to what you just said, but that would not be very good communication between them and SFI if the belts are designed 10x stronger than what they are attached to.

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post #17 of 41 (permalink) Old 02-12-2014, 01:36 PM
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Quote:
Originally Posted by <@@> View Post
The other thing that you are missing out on is that the center of mass of a human body is right about the waist line (if I remember correctly). That means that just about all of the 3K force will be taken up by the lap belts at 1500-lbs each anchor point. That doesn't leave much for the shoulder harnesses to support. Say conservatively 50-lbs at your 15Gs is just 750-lbs divided by the two shoulder straps, that's only 375-lbs. Now you are at approximately 1/10th the load and very reasonable loading.
The human body is not a rigid body. For this analysis, I suggest that it would be appropriate to assume that the belts are locating a hinge (waist), resisting the deceleration of all body mass below the waist and some of the mass above the waist. The shoulder harness(es) handle the mass above the waist not handled by the lap belt.

Biggest complication to this is proper installation and tightening of all elements of the restraint system. For example shoulder harness too loose would force the lap belts to do most of the work not to mention allowing potentially dangerous upper body kinematics. Also, perhaps I am missing something but does the 3000 lb requirement for shoulder harness and lap belt apply to each attachment of the belt or a total for the belt, i.e., is the lap belt system supposed to handle 6000 lb or 3000?

Anyway, kudos to the OP for trying to analyze the system. I did not set out to stir up the pot, so I will stop now with the comment that the harness bar probably is marginally OK if all belts are properly tightened. If the shoulder harness is not tight, the loads in an actual crash will be much higher than for the tight case and the Lotus harness bar probably is under-designed.


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post #18 of 41 (permalink) Old 02-12-2014, 02:15 PM Thread Starter
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It is total load, as in 1500lb per anchorage. For anyone who cares to read, you can find the specs at:
www.schroth.com/download/sfi161.pdf

and
49 CFR 571.210 - Standard No. 210; Seat belt assembly anchorages.

Another issue to consider is that static loading is really not relevant to a crash situation, so it is possible that although the bar would yield, it could still restrain the occupants and provide some energy dissipation as it deforms, but who knows how to quantify that.
I think it is beyond the scope of what I can accomplish to figure out what an appropriate design load is from scratch, so really what I am trying to figure out is why, based on strength calculations for this bar, it seems that both roll cage and harness bar common practice seems to be at odds with these documented design requirements. I am assuming that if I knew that answer, then I could determine whether it was safe to go with standard practice of 1.5x120 wall DOM, or whether there is a reason to design the system for 3000lb static load.

Also, to add to the mix, I did a quick FEA in Catia today, and based on 1500lbs distributed evenly across each of 4x 3" wide shoulder belts, max von mises stress at the ends of the bar came out at 132ksi for fixed end supports, which is slightly more than what I calculated from beam bending, and still ~3x the strength of a typical DOM bar.

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post #19 of 41 (permalink) Old 02-12-2014, 09:34 PM
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You need an automotive engineer... can I suggest you ask simply sports cars to supply you their harness bar along with the certification of compliance. That way you know it was designed by an automotive engineer and conforms to the required standard.

Simply Sports Cars -SSC Lotus Harness Bar- Lotus

The cost of the bar will be less than the cost of engineering a custom one
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post #20 of 41 (permalink) Old 02-12-2014, 10:08 PM
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I never trust people that constantly edit their own posts.

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