Bridging formula, My math sucks

yeah, Wyoming plays by a different set of bridge law rules then most states

 

I have a chart, and some state's do have them available if you can get your hands on it. For instance the one I have list the feet down the left side of the cahrt and the number of axles across the top. Measure the center of the hub from whatever axles you want to bridge, obtain the feet. Then count how many axles you are using and let your fingers meet in the middle, hence the weight allowed. The formula will confuse even the brighest brainiacs.

 

Hi there! I hope you all don't mind if I pull up a thread that has been dormant for a year. I'm an engineer and I have studied the bridge formula and its implications earlier in my career.

A couple of other members have posted the correct way to use this equation, but even so, it may be difficult for some to follow. Ronnocomot included two links in his post and the second one is pretty good.

Why do we have the Bridge Formula?

When it comes to building a new road, engineers need to know how much weight they should use to calculate the size of the beams for a bridge. Likewise, the pavement engineers need to know what axle loads, and how close they are from one another, to design the pavement thickness and steel reinforcing.

The Bridge Formula is used to keep the axle loads of a truck spread out so they are not all very close together. For example, a military tank is quite heavy and all of its load is spread over only 20+ feet.

The bridge formula is (thanks to Otter):

W=500 [(LN/N-1) +12N+36]

W= the Maximum weight in pounds that can be carried on a group of two or more axles to the nearest 500 pounds.

L= Spacing in feet between the outer axles of any group of two or more consecutive axles.

N= number of axles being considered.


At this point we can call N and L variables because they depend on the rig someone is driving. Some have 3 axles while others may have 5 or 6 or 7, etc. And the distance between the axles will vary from rig to rig.

First we will check your gross weight. All you need to know to use the Bridge Formula is the number of axles and their spacing and then the Bridge Formula will tell you how much you can weigh.

Let's say that you have a typical 18 wheeler with five axles, a tandem on the trailer and a drive tandem on your truck (I think that's the term you use.) So, all we need is the number of axles, which is 5, and the length from the center of the axle of the first axle (your steering axle) to the center of the last axle on the trailer. Let's say that is 51 ft.

We now have all of the information we need. Your rig has 5 axles and that is "N" in the equation. The distance from the steering axle to the last axle on the trailer is 51 ft, which is "L" in the formula.

So, let's begin.

The Bridge Formula:

W=500 [(LN/N-1) +12N+36]

and N = 5 axles and L = 51 ft.

In math, we do the calculations of the variables inside the inner most parentheses first. In this case it is:

(LN/N-1)

we will put in the values for the variables and we get:

51 x 5 on the top and when we multiply the two we get 255

Next we will do the bottom, N-1:

5 - 1 = 4

Then we put the two together as they were and we have:

255/4 which equals 63.75.

now our Bridge Formula looks like:

W=500 [63.75 +12N+36]

since we know N is 5 we can put that into the equation:

W = 500 [63.75 + 12 x 5 + 36]

In math, when all of the number groups are together in the same parentheses, we always do the multiplication or division first, followed by the addition or subtraction. So we do the multiplication:

15 x 5 = 60

so now our formula looks like:

W = 500 [63.75 + 60 + 36]

In math we always do what is inside the parentheses first, so we add

63.75 + 60 + 36 = 159.75

So we put that into the formula:

W = 500 [159.75]

which is (getting rid of the parentheses):

W = 500 x 159.75

we multiply the two numbers together and get:

W = 79,875 lbs.

So with 5 axles spaced over 51 ft, your legal limit by the Bridge Formula is 79,875 lbs.

You can find a chart like someone mentioned above at this link. This is in pdf format so you will need Acrobat Reader, which most people already have.

Sorry, but I don't have permission to place a link in my posts yet. Link deleted.


So, what we did above was to check your permitted weight by the Bridge Formula using axle 1 (steering) and 5 (last axle on the trailer).

For ease of discussion, let's number the axles: The first axle at the front is axle number 1 and the last axle, at the end of the trailer is axle number 5. So the axles look like (from front to back):

1===2-3=___________4-5_ <===== that's your rig

Now the inspector can check the weight by using any combination of axles and axles spacings. For example, he can check the formula from axle # 2 to axle # 5, or from axle # 1 to axle # 4, etc., etc.

Remember, when two axles are more than 8 ft apart, each axle can carry 20,000 lbs. when they are less than 8 ft apart then they can only carry 17,000 lbs each. This is not for the bridges but for the pavement. As the axles get closer together, the pavement experiences greater stress.

I tried to keep this very simple so everyone could follow it. If you haven't thought about algebra for 20 years, you're bound to forget quite a bit.

Please let me know if you don't understand something or if you have an unusual case. I'll try to help.

krazman - You have the number of axles so now all you need is the spacings between the axles. Once we have the spacings, it is easy to use the Bridge Formula.