A bridge too far? - covered bridge hidden capacity for live load
Those who work with historic covered bridges have repeatedly encountered the frustrating conundrum of apparent hidden capacity for live load. Routine analytical evaluations indicate the bridges should have fallen down long ago, yet they support vehicles with no apparent distress. Why is this? Drawing on his 40 years’ experience working with timber buildings and bridges, Phillip Pierce investigates.
While most of the world’s remaining covered bridges were built after the basics of engineering analysis had been established in the mid 19th Century, there were no standard design speciﬁcations at the point of construction. Those that remain have survived for a variety of reasons, but not because they were built in accordance with modern design practices.
Standardisation of timber speciﬁcations did not commence in earnest until the late 1930s, with a subsequent big push due to World War II, after almost all of the remaining covered bridges had been built. Builders sized bridges based on past experience or their own numerical instincts and were astute enough to place the best quality old-growth timber where they would be exposed to the highest forces.
Much debate has taken place over the modiﬁcation of these old structures, challenging today’s engineers to balance public safety with maintaining standards of care of the industry. However, it would seem that a lack of appreciation of the complexity of the bridge structure and the nature of timber is a major problem.
Like metal, timber structural elements react to loading in a generally predictable, linear, elastic manner up to a certain point, after which the relationship of stress to strain becomes non-linear as it is loaded to failure. Unlike metal, timber is anisotropic with signiﬁcantly different stress/ strain properties depending on the direction of loading with respect to grain. Timber contains a variety of variables that affect its strength – most notably the extreme difference between cross-grain and parallel-to-grain cell structures.
Addressing the challenges
Because timber is a product of nature, one of the ﬁrst challenges when developing design standards is to confront the variability of the material. One way to establish design guidelines is to select a particular species of tree for which standardised information is desired, choose individual trees to represent the forest and proceed to test them in largescale protocols, using statistics and probability to determine appropriate design values.
An alternative way to establish design guidelines (and one that is much more practical) involves an extensive testing programme of small, clear specimens of the species, made up of prepared samples measuring 5x5x76cm with straight grain and no knots or other apparent imperfections. This served as the starting point for the basis of adoption of predicted strength. Each species for which a design parameter was required had to have a sufﬁcient number of samples and tests to produce a statistically reliable value. A 5% exclusion rule was adopted, meaning that statistically 95 of 100 elements have greater strength than the value used for design (sizing of elements). The next question to consider was the degree of conﬁdence in the normal distribution curve adequately representing the true strength of the group. Investigation shows that the number of tested specimens for a given grouping was selected so that the normal distribution curve would represent a 75% conﬁdence level in the results. This means design of new structures and the corresponding sizing of elements should be based on a 95% exclusion rule with a 75% conﬁdence level. This relates to the design of new elements, making them as big as needed to carry the loads.
Like metal and concrete, early timber design speciﬁcations were based on an allowable stress methodology. This was derived from a stress-strain curve and statistical analysis similar to the one described above, but with an appropriate reduction by a factor of safety to produce an acceptable allowable stress for comparison with calculated actual stresses. These published stresses, reduced by the factor of safety, are commonly referred to as reference design values. For example, the value for tension can be thought of as equivalent to 55% of yield stress for the allowable design stress of a steel element – a value readily recognised by bridge engineers. It is important to note that in timber, the factor of safety developed via this statistical process is not consistent. In general, the average factor of safety is in the order of 2.5, but due to the variability of wood the factor may be larger or smaller. It is reported that in 99% of cases, the factor will be greater than 1.25 and for 1% the factor will exceed 5.
The evaluation of the bridge begins with determination of forces and corresponding stresses for the various types of loading that can be applied to a structure, as well as the potential combinations, with their corresponding probability of occurrence.
The guidelines for loads and their combinations for application to bridge structures in the USA follow those published by the American Association of State Highway and Transportation Ofﬁcials (AASHTO). In general, AASHTO has adopted the reference design stresses and adjustment factors of the American Wood Council’s National Design Speciﬁcation for Wood Construction.
The stress/strain response of timber is substantially affected by the rate of loading in the test machine. It can absorb relatively large sudden loads without permanent distress, but will gradually creep under long-term load. This phenomenon is accounted for in timber evaluation and design by the load duration factor, which is incorporated in the stress evaluation process according to the duration of the speciﬁc group of loads being considered. Examples include:
Dead only – assumed to be permanent throughout the life of the structure – AASHTO assumes the load duration factor, CD, to be 0.9. This reduces the allowable to account for long-term creep.
Dead + Vehicular Live – AASHTO assigns a value of the load duration factor equivalent to a total of 10 years of accumulated design loading over the life of the structure. CD is 1.0, since the reference values are given for an assumed load duration of 10 years.
Dead + Wind – AASHTO assigns a value of the load duration factor equivalent to a total of 10 minutes of full design wind force over the life of the structure with a corresponding CD of 1.6. This recognises the ability of wood to absorb relatively short bursts of loading.
Proceeding through the various combinations of loads with application of corresponding CD, one arrives at the highest predicted stress to compare against the allowable stress selected from the tables, with appropriate adjustments.
The problem here is that predicted stresses of extant covered bridges routinely indicate overstress – lack of sufﬁcient capacity of the bridge – when compared to the NDS/AASHTO allowables. But in many cases, structure performance demonstrates more capacity than indicated by the standard allowables. This leads to conﬂict with respect to the need for element replacement/reinforcement.
So what is wrong with the evaluation? It is important to recognise that the dead load of covered bridges is much higher as a proportion to total load than is typical of modern steel or concrete bridges. The unit weight of timber elements varies depending on species, moisture content and preservative treatment. Bridge design is performed in accordance with AASHTO, which speciﬁes a density of 50pcf (0.8tcm) for design of new timber bridges, based on timber elements with high moisture content and creosote preservative. In-service weight of extant covered bridges is usually much lower – often less than 30pcf (0.5tcm). This makes a big difference to the reserve capacity for live loading. Use of site-speciﬁc unit weights for extant covered bridges is accepted by AASHTO.
The determination of capacity of an existing bridge begins with the basics – what tree species is involved. Then the grade of wood involved must be considered. This is not as easy, but is tackled by a visual examination of elements (a certiﬁed lumber grader is the best person to conduct this activity) to identify size and distribution of knots, the slope of grain and so on. When examining elements within an extant structure, usual practice is to identify the highest grade that can be assigned to the element based on what is visible, because the unseen material could be better or worse. Recognising that each element has its own defects and, therefore, its own grade, it is important to be practical in this exercise and not assign different grades for each element. A Town lattice is much more difﬁcult to evaluate than any other truss conﬁguration due to the signiﬁcant proportion of mating surfaces. It is then up to the engineer to choose a grade that is appropriate – a daunting decision and one that may or may not be made conservatively, depending on conﬁdence and circumstances.
Given species and grade for the given type of element, the next step is to consider the NDS tabulation and ﬁnd the reference design stresses. Identifying all appropriate adjustment factors via NDS, with AASHTO overrides as appropriate, the engineer comes up with the allowable stress to compare to the predicted actual stress for the various group loading combinations.
Based on the results of the above assessment, it is unlikely that the bridge has the anticipated live load capacity. However, there are other factors related to loads and stresses that can be tweaked for covered bridges with hope of gaining the capacity that seems hidden. For covered bridges, it is possible to calculate a revised value of this load ampliﬁcation factor based on actual, estimated or hypothetical trafﬁc information, or at least seemingly more rational values than the generic value of 10 years used by AASHTO.
The following equation from Forest Products Laboratory Research Paper RP-487 was used to develop duration of load factors for various types of load. The formula is in the shape of a hyperbolic curve.
108.4 ÷ (60X)0.04635 + 18.3 where X is the total number of minutes for which the given load has been applied over the life of the structure. For the 10-year CD values in the tables, the formula yields:
108.4 ÷ (60 x 10yrs x 365days x 24hr x 60mins) ^0.04635 + 18.3 = 62.1
So, suppose that our extant bridge was built in 1880 and has been crossed by heavy loads equivalent to our intended design vehicle on average 10 times per day since it was ﬁrst built, with an average duration to the loaded element of one second during the passage of the vehicle. That yields a total duration of loading of:
133yrs x 365days x 10 passages per day x 1sec per passage ÷ 60secs = 8,090mins
That is only six days, not 10 years as AASHTO would suggest. Then the formula yields a value of:
108.4 ÷ (60 x 8,090mins)^0.04635 + 18.3 = 77.4 compared to the normal loading value of 62.1 – indicating a load duration factor of 77.4 ÷ 62.1 = 1.24 which is 24% less live load than when using AASHTO’s generic value of 1.0.
Maybe that would be too conservative and we are unwilling to go this far. Let’s assume twice the occurrences – 20 times per day. That leads to a value of 75.5 for the equation or a CD value of 1.21 – still 21% less than the generic value. While this may not represent a lot of savings, it is fair to explore this concept in a real life evaluation. A younger covered bridge would probably have a larger CD due to many fewer passages of vehicles, which indicates more capacity. But the weight of individual vehicles crossing the bridge varies with the vehicle. Evaluating the effect of a speciﬁc weight of vehicle over a speciﬁc period of time and attempting to identify the total number of minutes of those passages is a sticky issue. We could be evaluating the results of a vehicle weighing less, but with more passages per day, for comparison. There simply is no easy way to consolidate this topic into something that is both black and white as well as widely accepted.
To muddy the waters even more, since covered bridges can have snow on top of the roof while vehicles pass through the bridge, we have to also consider a group load combination of dead plus live plus snow at its own load duration factor as well as its own probability of occurrence group loading factor. Snow loads are not contained in AASHTO for modern design, as we use snow plows to push snow off bridges.
Let us assume that our reﬁned predicted actual stresses are still indicative of problems.
What about load testing?
Strain gauge measurements are commonly used on metal elements and sometimes on concrete. Can we use strain gauges on timber?
I postulate that the hidden defects of larger bridge elements mean reliance on strain measurements as indicators of actual stress is not advisable. How can an engineer be sure they are measuring a legitimate average stress in an element, or even a realistic maximum stress? And what about the connections? If we measure strains in an element and predict a capacity, it seems difﬁcult to say with any certainty that the joints have a similar or higher factor of safety. However, it is possible to compare the relative load sharing by strain measurements. For instance, the distribution of forces around a termination of a chord element of a Town lattice truss can be evaluated by strains with some degree of conﬁdence. But what about deﬂection measurements? Flexural elements can be tested with some degree of conﬁdence based on deﬂection, but it is the timber truss that is the focus of this article. Deﬂections of timber trusses are extremely small and the accuracy of measurement makes reliance on it very suspect too.
Regardless of whether we use a simpliﬁed hand analysis based on pinned joint representation of truss behaviour, a computer programme based on frame behaviour or a more advanced ﬁnite element representation, it is traditional that the analysis of the trusses be performed on a ﬁrstorder 2D basis representing a single truss. Does this adequately account for the behaviour of the structure as a whole? Should we attempt to expand this into a full 3D representation of the structure, complete with ﬂoor system, bottom lateral bracing system (if one exists), overhead bracing system, and maybe even the rafters, rooﬁng and siding? Clearly, these structures move and shift forces among the various available load paths, especially at joints, in ways we cannot model or even fathom.
It remains vital that we always strive for weight limitations on covered bridges. They were not built for modern trafﬁc and should not be expected to support it. Allowing heavier vehicles to use these precious structures only hastens their demise. We should not be looking for hidden capacity to support unnecessarily heavy loads.
Let us think about that 95% exclusion value again. It was selected for the purpose of sizing structures or elements and it has proven to yield structures that stand up to loads quite well. But is it too conservative for evaluation of covered bridges? Further reﬂection seems necessary.
If an existing element was one of those with a lower initial capacity due to some defect or poorer overall quality, there is a good chance that it has already failed and been replaced with one with a much higher capacity than that indicated by our 95% exclusion allowable. On the other hand, if we believe that the element is one with higher capacity, how do we justify increasing the exclusion value?
It is possible to develop a tabulation to compare the increased basic reference stress from an increase in exclusion. If we consider this effect alone, and limit ourselves to coastal douglas ﬁr as an example, we ﬁnd that for a 20% exclusion (or alternatively at 86% of the mean), we gain about 23% in strength. At a 30% exclusion (or 91% of the mean), we gain about 32%. Similar ﬁndings can be shown for any other species, based on their test data.
So what is an appropriate value for this exclusion value to account for within-species variability? Should it be a function of age? Beyond the discussion of related issues that follow, consideration of age seems like a stretch for justiﬁcation of modiﬁcation of the exclusion value. Or should it be a function of element location within the bridge? A bridge with a lower design stress level may have been subjected to a few instances of high overstress, hence worthy of less caution and perhaps allowing a higher exclusion value. If it is one with a higher design stress, it has probably had many more instances of even higher overstress, thereby dipping into that reserve capacity more frequently – and thereby being more prone to failure sooner rather than later – we should be more careful in this situation and a lower exclusion limit is probably appropriate. Perhaps it should be a function of bridge location? A bridge that has survived on a more heavily travelled road might have more inherent capacity than one on a lightly travelled road, thereby potentially justifying a higher exclusion. Or it may be on the verge of its capacity, while a bridge on a lightly travelled road may not have seen many heavy loads and it could have ample, or little, reserve. It is very hard to judge how to modify the exclusion value in the case of location, hence it would seem inadvisable to advocate this as a viable parameter for consideration.
I am not advocating for a speciﬁc answer or value, but I am advocating for thoughtful consideration of this factor when faced with the implied need to replace elements. It may be that accepting a slightly higher exclusion rule would support retention of elements that appear to be serving well, regardless of numerical implications of weakness.
Not with a deﬁnitive answer, but hopefully offering food for thought and a hunger to continue this exercise, I remain convinced that the 95% exclusion rule is the one aspect of evaluation of existing bridges that is most suspect.
For more information or to discuss the topic further, contact Phillip Pierce, Senior Principal Engineer at CHA, email@example.com