*Bill Harvey is a world expert on masonry arch and tunnel behaviour and author of the Archie-M software package for analysis of masonry arch bridges. He is also a long serving member of the IABSE British Group Executive Committee. In this article, he challenges the technical and procedures behind arch bridge assessment.*

**All views expressed are those of the author and do not necessarily reflect those of IABSE or the IABSE British Group**.

I have just been listening to “in our time” about Hannah Arendt. She came up with the expression “the banality of evil” and there was some discussion of what she meant. The point seems to be that Eichman did evil things as a thoughtless bureaucrat. He had no internal conversation, no introspection.

That set me thinking about engineering being handled in a thoughtless bureaucratic way mixed with the seriousness of what we do. Do we acknowledge that all we can do is our best or do we fret that we can never be good enough? And if the latter, how can we then manage our lives in such a way that we can live with ourselves and sleep at night?

The bureaucratic way of thinking provides such escape but requires a hierarchy in which the member at the face of the danger can shelter behind instruction from someone who believes themselves in some way better, but is so far removed from the consequences of decisions that there is no proper link.

If I employ someone to write a set of rules of engineering, if I set up a committee to oversee that work, then am I absolved of responsibility for the outcomes? At the other end of that train, does working within the boundaries of a set of rules somehow absolve me of responsibility?

The process leads to a situation in which adherence to the rules is seen by all parties as both necessary and sufficient. If the rules are found to be unworkable they are somehow changed, but the concept of them being wrong is never considered.

Engineers work in a world in which the laws of physics are immutable but not understood, or worse, wrongly understood. Modern physics does not really impact on structural engineers. The refinements of Einstein are too fine grained to impact on the effects of Newtonian mechanics. Structural engineering is largely taught as a two-dimensional exercise, only extended into three dimensions in later stages. Even dynamics and fatigue, where time is an essential part of the problem, are often treated as two dimensional. The stress here changes with time and that change causes the “strength” to change in some way but then we are only looking at the two dimensions of stress and time.

I work in the narrow field of masonry bridges. Over my 40 years in the field I have become progressively aware of the dire results of attempts to simplify the problems. That simplification begins with conceptualising the arch as the structure and everything else as somehow “load”. Even a bare arch occupies three-dimensional space and defies attempts to narrow its behaviour to two dimensions.

That brings us to questions of conservatism. We are taught the need to make conservative (read safe) assumptions. To do that, it is necessary to understand behaviour well enough to know what is conservative. When the whole philosophy of design changes, as it did early in my career, mapping the outcomes of design may seem appropriate but all that really matters is the consequences. If your aim is that a beam should have a very similar apparent capacity, the fact that the capacity is arrived at through a different process can be masked but may have deep consequences, for people see rules as things to explore the boundaries of. The new rules may lead to a new way of formulating a solution but the formulation is driven by the codified rules not the underlying laws of physics.

This is all very hypothetical. Some concrete, tangible, examples are needed. To do that I need to set out the different design philosophies. In my youth, safety of structures was seen as an issue of setting a safe working load. In steel design, we began with a strength called the guaranteed yield stress. We could then design a beam such that the anticipated load never caused the stress anywhere to exceed that guaranteed yield. That concept was mapped into concrete, where the material is inherently more variable and providing a guaranteed strength is not really possible. In any case, the guarantee is masking a statistical situation in which what is being offered is a capacity from which it is extremely unlikely to fall short. The new philosophy recognised that variability and noted that there is always a chance of a load being exceeded. Either because of inherent variability (how much does a bed weigh?) or because of a fundamental change in design (can I put a water bed on this 18th century floor?).

My point here is that if the concept of analysis is built around a safe working load and not around basic physics, it becomes inherently dangerous to apply new fundamental rules of design without properly investigating the corresponding rules of analysis.

If the arch were the entire structure of a masonry bridge it would still be complicated by being wide and continuous. If we conceive the possibility of simplifying the problem to two dimensions by considering an effective strip to carry a particular load, we can then conceptually calibrate the strip on the basis of outcomes. We (the masonry bridge community) carried out tests and noted the point at which cracks first became apparent. We then juggled our distribution model so that a load that caused a crack would be deemed just unsafe. If our distribution model was fundamentally wrong, that rule is only safe for the particular bridges tested. It cannot be extrapolated safely. It is NOT a model.

So let’s get a little more concrete. During the first world war, Tanks proved damaging to masonry bridges. The army needed to be able to decide rationally whether to begin to take a squadron over a bridge. After the war AJS Pippard developed a simplistic rule that he (not unreasonably) believed would provide that rationale.

His analytical work needed assumptions. One of those was that the load could be considered to occupy an effective strip of arch. That is fundamentally untrue but the next step compounds the error. His distribution model to calculate the effective strip assumed that there was a major element of distribution through the fill and then another component from the arch, essentially working in transverse bending. He applied his load at the crown because that was where distribution was least and he believed that the distribution effect would outweigh the more onerous bending condition with the load at the quarter point. That gave him a two-dimensional structure.

He regarded the whole self-weight of the bridge as acting vertically and treated the arch as parabolic and the road as horizontal so the effect of that load could be treated by direct integration.

He recognised that there would also be longitudinal distribution but declared that there were already too many assumptions and treating the live load as a line would surely be conservative (as well as easy to calculate).

He also reduced the mathematical complexity by treating the arch as pinned at each end so there was only one degree of redundancy.

The arch was treated as an elastic rib which was centred at the intrados, though the span to rise ratio at the centre line is only slightly different and there might be a reasonable case for regarding the span on the centre line as being the same as that on the intrados.

In his first calculation he sought a no tension result (Thrust remains everywhere in the middle third) but found that to grossly underestimate the load at which the observed first crack developed. He (or rather his research assistant Leticia Chitty) then tried middle half. Eventually they found that if they used an arbitrary compressive stress limit at the crown the results for the bridges that had been tested produced a reasonable correlation.

Every one of those steps was rational within the environment in which he was required to work.

Finally, having produced a complex equation relating load to compressive stress, he plotted it and used a curve fit to reduce the complexity. I will not set out the terms in the original equation but will merely present it to demonstrate the complexity.

By plotting a curve of that result for arches of 4:1 span to rise ratio they were able to create a simpler curve where the result was everywhere less than the detailed one. That equation is more familiar:

Here, S is the span, h is the depth of fill at the crown and d is the ring thickness at the crown. That enabled him to produce a graphical slide rule for use in the field where no calculation would be possible.

The original approach was soon modified in practice. I guess the first relaxation was “not to be used if h>d” was re-interpreted as make h the measured value up to a maximum of d and down the years there have been further modifications.

When they did that on the railways in 1971 they used an influence line for crown moment and considered single axles and bogies, but the bogie axles were placed 2m apart which isn’t common even now. The load distribution was then wrongly distributed through the fill and the load approximated to a UDL over more than 2.5m, whereas in reality the axles do not interact until over a metre of depth.

If the load on the arch is distributed to a udl over 2.5m+, the most onerous place to put it is symmetrically across the crown. If the two axles are independent, no matter how little, the worst case will always be with one axle central.

By that time MEXE was nearly 50 years old and engineers had become blasé. How often have I been told “No arch has ever failed if it passed MEXE.” Well, this arch passes MEXE at a 40 tonne capacity and the damage was done by 22.5 tonne axles.

“But it hasn’t collapsed” isn’t an answer because MEXE was based on safe working load. Neither is it a valid answer to say “but the condition has changed”. This damage is undoubtedly caused by live loads.

Meanwhile, engineers were happy to modify MEXE to give higher capacities because they “knew” it was safe. One National Authority briefly inserted a proviso that the condition factor should be doubled before applying it. So if the engineer gave it a value of 0.4 which would mean that immediate repairs were needed, it would simply be changed to 0.8 because 0.4 is over conservative.

There is a sense in which we have left MEXE behind, but its legacy lingers on. The distribution model for transverse spread is still used in all more modern 2D analyses, so refinement is given with one hand and taken away with the other. There is good reason to suppose that distribution is more something that happens as the thrust flows through the arch not as the load spreads through the fill. That means an element of the distribution depends on arc length not on fill depth. Such a distribution alters the shape of the thrust line so that a mechanism failure can never happen. Instead we get the sort of local damage shown previously.

And we are still required to apply a condition factor based on photographs of typical damage with arbitrary (in the true sense, decided by an arbiter) numbers attached. If we are to have a hope of reasonable predictions of capacity we need (at least) both a new distribution model and a new criterion of failure.

**The banality of bridge assessment**

What has all this to do with Hannah Arendt? Begin with the bureaucracy of bridge assessment. Arch bridge assessment is easy. Put the required numbers into a program and out pops the answer. It can be done by junior engineers working as drones. I interact with many of them. When I say to them that the dimensions appear to be wrong, perhaps because they are just the wrong sort of number, they will usually reply that they must use the numbers they are given. If I get to speak to the bosses, I find myself arguing about how accurate it needs to be and “anyway, the client is not prepared to pay for a remeasure”.

Some of the senior engineers involved in drafting and redrafting the codes dislike the idea of engineers using judgement so they (without thought) make the judgement at one more step removed and write instructions not guidance. The various codes for arch assessment are very dubious things. They are built on sand and extended beyond defence. Even when built at the same time by the same people, no two bridges are alike.

The only real way to judge their response is to look at them, and perhaps to measure the response. Engineering, like medicine is an area where the juniors must speak truth to power. If the truth is hidden from them, they can never do that. With luck, the consequences will not be fatal.