How do they know the load limit on bridges? (And please don’t tell me that they put heavier and heavier trucks on the bridge until it falls and build it back up again) This question has been plaguing me ever since I read it.
It’s basically physics. Or physical engineering, or some such. If you know the tensile strength of your building materials, and the mathematics behind the shape and structure of the bridge you’re building, you can compute how much it should hold.
Doubtless an engineer will come along to explain it better.
You’ll have much better luck getting an engineer to answer the question if you ask a mod to change the thread title to something descriptive of the question you are asking.
How can I do that?
Use the “Report this post to a moderator” feature, in the lower right hand corner of the post.
I’ve changed the title for you.
DrMatrix - GQ Moderator
Qadgop is on the right track. The structure is designed to resist particular loads (some are specified, such as traffic loads, others are calculated as part of the design process, such as the weight of the structure itself).
You need to know a lot about the mechanical properties of the materials that make up the structure and you have to analyze the structure itself to know what stresses will result in which locations when you apply a given load to the structure.
On top of all this safety factors are applied when analyzing the strength of the structure - live & dead loads (like traffic and weight of the bridge) are multiplied by a certain amount and the strength of the materials used is decreased by a certain amount.
A lot of the info used in this does come from empirical tests (i.e. the strength of structural steel comes from actual tests on pieces of metal) but generally speaking you don’t load the finished product up to failure.
This is really the “thirty thousand foot” view, for a better understanding hop on down to your local university and enroll as a civil engineering major. I highly recommend my alma mater the U of I in Champaign/Urbana 
The load limit of a bridge can also be measured. In fact, our lab recently designed and built a wireless data acquisition system for determining the load rating of bridges…
I’m not an engineer, but I WAS a Combat Engineer. Being in the Army and not in college we had a method not nearly as complicated. One of our missions was to “classify” bridges (determine the weight class, but on a simpler scale). I don’t remember the details, though. Not much help to you, I know, but just a side-note.
Funny you should mention that… I’m taking Statics right now, which includes calculating loads. Without going into too much detail, different materials have different standard yield strengths. When the stress on the material becomes greater than the yield strength, the material either breaks or starts buckling in a manner that cannot be accurately predicted. Builders routinely incorporate safety factors into their designs as well, so that even if the bridge’s expected load is exceeded, it won’t immediately break/buckle. Of course, calculating this stuff is fairly complicated and tedious. However, it can be calculated without resorting to experimental means.
(Of course, any degreed engineers are welcome to come along and correct/refine this.)
Degreed engineer checking in to say that you folks are doing just dandy without us.
Haj
They keep increasing the amount of weight on it till it collapses. Then they rebuild it and post a sign 10 pounds less than the amount that broke it.
(I can’t believe no one came up with this ‘Calvin and Hobbes’ solution.)
::Snigger:: Hehe, he said “Ridged member analysis”. Yeah, that joke got really old, really fast.
Hey, Postcards, check out the discussion about the threads’ title in the OP.
:smack:
I opened this thread for the sole purpose of saying what Calvin’s dad told him, postcards, but you beat me to it.
I should’ve known this thread was open too long for me to be the first one to pop in with Calvin and Hobbes in mind…
Well, I’m no engineer, but as a physicist, I can tell you what I’d do (given an existing bridge, not starting from the drawing board). First, I’d put strain meters all over the bridge: These are devices which basically tell you how much the bridge-parts are stretching and squishing. Then, I’d look up the ultimate strain tolerances of the various materials which make up the bridge: That is to say, how much those materials can be stretched or squished before failing. Then, I’d load up the bridges until one of my strain gauges read half of the maximum strain. I would then take double the value I had loaded up, and call that the weight limit.
I’d probably also include some sort of safety factor, but I’m not sure how much is considered appropriate. It probably depends on why you’re measuring the bridge.
Assumptions in this method:
1: That the stress-strain tensor (which tells you how much things stretch or squish, given how much you pull or push on them) is linear in the regime of interest. Probably my least-justified assumption.
2: That the ultimate strain is above the detection threshhold of my gauges.
3: That I have a gauge at or sufficiently near each probable failure point.
Engineers, is this a sound method?
While I’m no civil engineer, I’ve done some reading about bridge design. A couple of friends of mine did civil engineering, though none build bridges. Design of structures like bridges is a specific course in civil engineering. In layman’s terms, off the top of my head, this is what I’ve gathered. (any Civil engineer is welcome to correct me).
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There are known limits of what specific parts of the bridge can handle, and by relatively simple analysis of forces you can calculate whether (given a specific load) specific parts will be overloaded.
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These days mostly anything is calculated with computers (finite elements method).
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For taking care of dynamic factors (Tacoma bridge, anyone?), windtunnel simulation is occasionally used. Computers used to have a hell of a time to calculate/simulate these effects, but I’ve heard they manage this quite well these days.
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When designing the bridge, the designers are commonly given a load that it should be able to handle. They always multiply by a safety factor of two, just to be sure. (this is not a joke, although a lot of jokes are made about this. The precise factor may differ these days because of advances in computer calculation).
Hence they calculate the load when designing the bridge, they don’t do measurements. Heavy loading/overloading of the bridge would seriously compromise the quality of the structure, so that is not recommended.
I’d be able to look up some things at home. Additionally, for those who are interested, there is a fun program which simulates simple bridge design (and shows what happens with a load that is too heavy) with the West Point Bridge Design Contest
A quick Google on ‘bridge design’ got me this site which explaines some things in relatively simple terms. You might check the other links in Google as well.
I am a bridge engineer with 25 years experience. Finally a subject I can discuss intelligently.
There are three accepted methods for design and rating of structures, those being Allowable Stress (or working stress), Load Factor (LF), and Load and Resistance Factor Design (LRFD). For design purposes, any of these may be used. For reporting capacity to the Federal Highway Administration (FHWA), ONLY LF is allowed. However, the states may use any methodology to determine posting.
A brief overview of each design methodology- For Allowable stress, the members are sized as to limit the stress to values that we know the steel is good for. For example, your modern steel typically has a tensile yield stress of 50,000 psi, we would size the member such that under dead load and live load combined, the stress never exceeds 27,000 psi. So for AS, we take actual loads and make sure the member is stressed well under its capacity. Load Factor takes a different tack. Here we compute the full ultimate strength of the section, but we multiply the loads by factors (hence the name) to ensure that the member has adequate strength. Additionally, we reduce the computed strength by multiplying by a factor (generally 90% for members in bending). Basically the load factor is 1.3 (DL + 5/3 LL). So we take the live load (traffic) on the structure, multiply by 5/3, add the dead load (self weight) and then multiply the sum by 1.3. This is kept less than 90% of the computed strength of the section. LRFD is a new approach and much more complicated, basically it is a probabilistic approach where we assume the loads have a certain uncertainty and the strength has a certain uncertainty, we take these bell shaped curves and ensure that the risk of the loads exceeding the strength is very small.
Back to load rating- two terms you need to know are Inventory Rating (the loads a structure can take repeatedly) and Operating Rating (the loads that can be passed infrequently). The states have the option to use either IR or OR for posting their bridges. The basic formula is RF = (C-A1D)/A2(L+I) That is: The Rating factor = the capacity minus a factor A1 times the Dead Load all over another factor A2 times the Live Load + Impact. So we compute the capacity, we know the effects of dead load and the live load effect for a given truck, thus we can compute a Rating Factor. If RF>1, the bridge can pass the truck. If not, you need to post. The capacity of the section is computed from the dimensional and material properties of the members. Your garden variety bridge may have steel stringers and a concrete deck that acts compositely, it is more than I can get into here but we can compute a capacity in terms of moment. Moment is merely a measure of the bending in a member and the English units are ft-k where a k is a kip, or 1000 lbs.
Simple example- we know our truck weighs 50 T and for the span in question causes a bending moment per lane of 800 ft-k. Let’s say the dead load of the structure causes 1200 ft-k of moment per beam. Let’s say the capacity of the member at the center of span is 2400 ft-k. The beams are spaced at 5’-6" on centers. How do we proceed?
First thing is we look up in our spec book and see that the distribution factor is S/11, so we take the 800 ft-k of LL moment and multiply by 5.5 and divide by 11. We get 400 ft-k per beam. We compute the impact factor for the span length, assume it’s 30%. Now we go right to our formula:
Inventory Rating : A1 = 1.3, A2 = 2.17
RF = (2400-1.3*1200) / (2.17 * 400 * 1.3) = 0.74
Since 0.74 < 1, the Inventory Rating for this bridge for this truck is 0.74 * 50T = 37T
Operating Rating: A1 = 1.3, A2 = 1.3
RF = (2400-1.3*1200) / (1.3 * 400 * 1.3) = 1.24
Since RF > 1, this truck may pass the bridge under operating rating.
Depending on the policy of the agency, if it uses Inventory Rating it would post the bridge at 37T. If operating rating is used, then the bridge would not be posted.
In practice, we would not do this by hand. We have software that models the structure and knows all about the specifications.