Bridges are designed for the loads that come from the vehicles that are expected to cross them. This includes the weight the vehicle and any dynamic loads that may be introduced from movement of the vehicle. Dynamic loads may be from "bouncing" or from hitting a joint or pothole.

Initially it would seem obvious that more load is applied to a bridge while the vehicles are in motion (weight of vehicle plus dynamic load). The dynamic loads are proportional to the travelling speed of the vehicles, but as vehicles go faster, they typically are spaced farther apart.

When vehicles are stopped, they typically are much more closely spaced than when they are moving.

  • Can there be a situation where more load is on a bridge because of closely spaced parked vehicles than from moving vehicles that are farther apart?
  • Are these two situations covered in bridge design?
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    $\begingroup$ I suspect that the case of a slowly moving traffic jam (motion plus tight spacing) is the worst case static load. When cars hit potholes etc, they may give higher transient loads (mitigated by the suspension) but if you assume that cars are 3x closer when in a jam vs in normal traffic, and that they are not on average experiencing a 3g acceleration due to potholes, you can see that the tightly packed case wins. Nose-to-tail trucks is the thing you have to worry about. I am sure bridge designers have figured that out too... $\endgroup$
    – Floris
    Feb 17 '15 at 16:01

Parked vehicles vs moving vehicles

Closely spaced parked (or slow moving) vehicles are definitely more onerous, as stated on page 89, Appendix 2.A, Clause 2.A.1 of the South African bridge design code TMH7:

It is generally accepted and can readily be shown that except in the very small span range, the worst loading condition occurs under congested (bumper to bumper) conditions caused by a traffic blockage and that the dispersion of traffic at speed caused by increased vehicular inter-spacing, more than off-sets the effects of impact.

However, this is only true by inspection for an unlimited number of vehicles of the same weight per unit length. If an unusual extremely heavy vehicle is crossing a bridge, then we can’t apply this rule, as we only have one of this vehicle and it can’t be bumper to bumper with itself. So we turn to bridge design codes to consider relevant configurations.

Bridge design codes

When it comes to bridge design every country seems to come up with their own bridge loading in their design code. I have read a lot of these codes - a significant proportion of my job is programming these bridge loading codes into bridge design software. Most design codes have various loading configurations to be checked, although they rarely specify that they are for "parked vehicles" or "moving vehicles". The closest I know of is the United Kingdom's BD86 standard.

BD86 is for assessment of existing UK bridges to carry exceptionally heavy vehicles (named SO or SOV loads). Clauses 3.20 to 3.25 gives two different configurations. Either (i) the SO/SOV moves at normal speed, with a dynamic factor, and normal loading is not allowed within 25m of the SO/SOV; or (ii) the SO/SOV moves at low speed, with no dynamic factor, but the normal loading is allowed closer (not within 5m).

But what about all the other design standards across the world? On the basis that I haven't heard of any bridges failing due to the standard design load being too low, I think it is a safe assumption that the design standards definitely consider the worst case. So, whatever it is that is designed for, it must represent the worst case out of either moving load or closely spaced static load.

Most countries' highway loading standards consider two configurations which must be designed for: a configuration of a single vehicle (or a single vehicle per lane), and a configuration of a uniformly distributed load (i.e. a load per area that is applied wherever it adds to the effect being designed for). This second configuration could be the closely spaced parked vehicles, or it could represent many lorries/trucks spaced apart but their weight averaged out over the total length. I suspect that it may in fact represent both of these situations.

An important fact here is the relative weight of a lorry/truck compared to a car. In the UK, a normal lorry (i.e. one not requiring special permission for its journey) has a maximum weight of 44 metric tonne, and has a length of about 12m. This gives 3.7t/m. A typical car (I've picked the Vauxhall Astra) is about 2 tonne and 4.5m long giving 0.45t/m.

I suggest that in a moving load situation you might get lorries/trucks fairly well spaced out, but in a traffic jam situation, when lorries and cars tend to mix, the lorry/truck spacing is about the same because the gaps are filled with cars. With the cars producing little load per length compared to a lorry/truck, the average load per unit length may be about the same whether traffic is moving or stationery.

Although it comes at it from a different angle, I believe AASHTO's Manual for Bridge Evaluation; commentary clause C6B.7.2.2 implies something like this. It says:

The probability of having a series of closely spaced heavy vehicles of the maximum allowable weight becomes greater as the maximum allowed weight for each unit becomes less. That is, it is more likely to have a train of light-weight vehicles than to have a train of heavy-weight vehicles.

I assume this can be applied to the parked/moving situation. That is, the more vehicles you have on the bridge at once, the lower the probable average weight of vehicle.


Which is more significant depends upon the bridge in question, certainly its length and the characteristics of the loading applied. For this discussion I am assuming highway traffic loading.

The question refers to dynamic effects, and it is worth noting that this is more than just impact from striking a pothole. If an elastic single span simple beam is instantaneously loaded with a force, the peak deflection that results is twice the deflection under the same force in the static case, and this effect is unrelated to the effect of instantaneous spikes in applied loading due to vehicles hitting surface irregularities (potholes etc).

For most highway bridges, I believe the dynamic effect is more significant. Fast-but-spaced-out traffic is more onerous than slow-and-bunched traffic. However, this conclusion is based upon the observation that there are more short bridges (spans of up to tens of metres) than long bridges - there is not a general principle that gives one universal answer.

It's relatively simple to determine that for a very short bridge whether the traffic is queuing or not is irrelevant - if the bridge is shorter than one vehicle, only one vehicle (or one axle) will be on the bridge, so whether there is a queue or not does not influence the number of vehicles loading the structure or the loading. Conversely it's easy to imagine that a very long bridge (several hundreds of metres long), one vehicle hitting a pothole will have a negligible effect, since even if the load from that one vehicle doubles instantaneously, if there are hundreds of vehicles on the deck it won't have a proportionately great effect.

In UK practice, trunk road bridges are designed and assessed to Highways Agency documents (so-called 'BD's and 'BA's). The vehicular highway loading is in two 'flavours' - HA is 'normal' traffic, and HB is an arbitrary loading used to examine the characteristics of the bridge under abnormal loading. HA loading for design is defined in BD37 and the derivation includes allowance for impact - read Appendix A: "the impact effect of an axle on highway bridges can be as high as 80% of the static axle weight and an allowance of this magnitude was made in deriving the HA loading", though the influence of impact reduces as the span becomes greater.

Traffic queues not only give rise to nose-to-tail bunching, they potentially give rise to vehicles squeezing closer side-to-side. In the BDs this is referred to as 'lateral bunching', which is where more vehicles crowd onto the structure.

BD37 allows for both impact and lateral bunching simultaneously - ie, it assumes that you have a tightly-packed traffic jam that's also travelling at high speed. This obviously doesn't happen, but is what the code encapsulates.

When assessing existing structures, however, the UK standards don't apply both effects together. BD21 is the code for assessing structures. Clause 5.23 specifically addresses this question (UDL and KEL are two component parts of HA loading):

"The HA UDL and KEL have been derived using a lateral bunching factor to take into account the possibility that, in slow moving situations, more lanes of traffic than the marked or notional lanes could use the bridge. Probabilistic analysis shows that maximum impact effects, which occur at high speeds, should not be considered together with maximum lateral bunching. Comparison of the effects of alternative traffic speed and bunching situations have led to the conclusion that high speed high impact effect with no lateral bunching is the most onerous criterion for bridge loading. The HA UDL and KEL are therefore to be adjusted in order to eliminate the lateral bunching factor by dividing by the following Adjustment Factor (AF)"

The adjustment factor is a relatively large number for loaded lengths up to 20m, but tails off to 1.0 (ie divide by 1.0, so don't change the value) at 40m loaded length.

It's not possible to make definitive statements from this (ie, you can't say "below 20m it's dynamic, above 40m it's traffic queues"), because the loading is to some degree empirical and derived after a probabilistic analysis, and includes guesswork (described as "by estimation" in the standard) with allowance for the findings of sensitivity analysis. Again, BD371 Appendix A has discussion of this:

"For long loaded lengths, the main factors affecting the loading are the traffic flow rates, percentage of heavy vehicles in the flows, frequency of occurrence and duration of traffic jams and the spacing of vehicles in a jam. These parameters were determined by studying the traffic patterns at several sites on trunk roads, by load surveys at other sites and, where the required data was unobtainable, by estimation. A statistical approach was adopted to derive characteristic loadings from which nominal loads where obtained. Sensitivity analyses were carried out to test the significance on the loading of some of the assumptions made."

It is worth noting that the above is a bit non-rigorous with respect to spans. The length that matters with respect to load derivation is the 'loaded length', which is not always the same thing as the span. For a single simply-supported span, if you're examining the bending effect, the two are synonymous, but very many bridges are more complex than that (eg, multiple continuous spans, or integral abutments etc). Loaded length is the length over which the element of structure is loaded, and when designing you should choose the length that gives rise to the most onerous effect for the element you are designing for doing the calculations with respect to that particular element. This is often the whole length of a span, but there are cases where (eg) loading a shorter length has a greater effect, particularly in continuous structures, partly because the shorter the loaded length used, the greater the intensity of load to be applied.

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    $\begingroup$ Or to put it more simply - the Highways Agency assessment code says the impact effect is more significant than the crowding effect, and you can apply just the impact allowance when assessing an existing bridge, but when designing a new one you assume teh worst and have high speed and crowded vehicles. Did you even read the entire paragraph to understand the context for the relevant statement in BD37/01 Appendix A that you quoted? It says for short loaded lengths, applied to the highest axle load and only included in a single vehicle loaded case. $\endgroup$ Mar 14 '15 at 2:13
  • $\begingroup$ I stand by what I wrote as absolutely true - BD37 (the loading code for design) explicitly states that it does include an allowance for dynamic effects (which can be very significant in some cases) and BD21 (the assessment code) says that the dynamic effect is more significant than the crowding effect. This are factual statements about the content of the codes, and the links are provided. $\endgroup$
    – achrn
    Mar 14 '15 at 10:55

If you are talking about vertical live load only, the case where you have traffic jam would be more governing to the design of the bridge deck. The momentary increase and decrease in vertical force due to bumps from uneven roadway can be neglected since:

  • the magnitude would be small for a properly maintained roadway
  • the magnitude would still be small for a badly maintained roadway as drivers tend to slow down if they have difficulty driving straight
  • such sporadic occurrences tend to cancel out globally as they don't occur in synchrony

An established highway bridge design code such as BD37 do not make any explicit consideration for the dynamic bumps that you mentioned.

Where you have vehicles moving on the bridge, traction and braking effects would generate a longitudinal horizontal force that is governing to the design of the bridge substructure.

Through the proper use of load combinations (as shown in table below) and their corresponding load factors which have already been rigorously studied and tested, it is possible for all loading scenarios to be considered to achieve a safe design.

Load Combination Table

  • $\begingroup$ It is interesting that BD37 doesn't take into consideration impact loading. AASHTO (USA highway bridge code) does include a separate Impact loading. $\endgroup$
    – hazzey
    Feb 22 '15 at 15:58
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    $\begingroup$ @hazzey - I am always surprised at highway loading codes which feel the need to specify impact loading separately, when it is applied to all live loading - why not just roll it up into the magnitude of loading specified? $\endgroup$
    – AndyT
    Feb 23 '15 at 13:56
  • $\begingroup$ @Question - a poor road surface does increase loading. See BD21/01, which uses loading based on BD37/01, and gives higher loads when assessing bridges with "poor surface" compared to "good surface". $\endgroup$
    – AndyT
    Feb 23 '15 at 13:57
  • $\begingroup$ @AndyT If impact is a separate number, you can reduce it for things like speed or depth through soil or just superstructure vs substructure. $\endgroup$
    – hazzey
    Feb 23 '15 at 13:59
  • $\begingroup$ @hazzey - good point. Also, I've been reading AASHTO Standard Specs 17th edition today, and the impact in there is not a simple constant factor to be applied, hence it makes sense accounting for it separately. $\endgroup$
    – AndyT
    Feb 23 '15 at 19:09

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