As a Montreal resident, I sometimes wonder if the roads are as bad in other major cities.  It seems as though the roads within the province of Quebec suffer from a contagious disease constrained within its borders.  The disease transforms an otherwise developed nation into Colombia with snow.

The moment you cross the border into the United States, the crater-sized potholes vanish and the uneven surfaces become smooth.  If you listen closely, you can hear the suspension system of your car breathe a sigh of relief as you leave Quebec.  If you happen upon a road imperfection while driving in the states, it will be most certainly preceded by one or two warning signs.  If every hole in Montreal's roads were well-marked, there would be no space left for the speed limit signs (which we don't follow anyway, but that's another story).

In truth, dodging potholes and bouncing around in one's car is part of the quebecois experience; the locals have grown accustomed to it.  What the public will never come to accept, however, are falling overpasses and tunnels.  Over the past five years, several such incidents have occurred in the city of Montreal.  In the summer of 2011, reports of a major structure crumbling in some way seemed to become a weekly tradition.  Due to the local media coverage of these incidences, the average Montrealer now knows what a gusset is, and could probably submit a decent draft for our next bridge's design.

Let's first examine why structures fail, and then look at why so many are failing these days in particular.

An overpass or bridge is designed to support its own weight plus that of the cars and trucks that travel across it.  In addition, these spans must contend with high wind loads.  These external loads can be amplified if they are cyclical in nature, particularly if they happen to cycle at a similar rate as any of the natural frequencies of the structure itself.  At a minimum, the structure is designed to support all of these loads if they were to occur simultaneously.

The bridge is then sized with an additional safety factor.  A safety factor of two would imply that the external loading would have to be twice the worst-case-scenario that was assumed in order for the material limits to be exceeded.  This kind of failure is known as an ultimate failure.  It is very rare to find a structure that fails due to weight or wind loads, although the 1940 Tacoma Narrows bridge is one such exception.  A more common reason for why a structure's maximum strength might be exacerbated is due to surface vibrations, or earthquakes.  If all structures were designed to withstand a 9.0 earthquake, their cost would increase significantly.  In certain places of the world, such costs are necessary to undertake.

There is one other major form of stress that structures face: enforced displacement due to thermal expansion.  The amount of extension or compression experienced by a material is proportional to the change in temperature.  In Montreal, the temperature can change a lot over the course of a day.  Over the course of the year, the typical range of temperature is about 75 degrees Celsius.  It is even greater for dark substances, which absorb so much radiation from the sun.  Temperature gradients across structures cause them to deform, and crack.  When a crack is introduced into a material, its maximum load-carrying capacity drops dramatically.

Fortunately, structures are designed with such temperature fluctuations in mind.  Cracks are expected to occur, and corresponding decreases in material strength are anticipated and planned for.

Beyond these external loads placed on the structure as a whole, Montreal structures must survive the elements of the local environment.  While water, air, sun, ice and salt do not damage the insides of a bridge directly, they do affect the exposed surfaces.  Here, the alterations to the material are chemical in nature, rather than mechanical.  Still, a gradual chemical change can have serious effects on a material's functionality.  If the exposed surfaces are not maintained (painted every so often, for example), outer defects can propagate internally.  Scanning through the long list of defects for the Mercier bridge, one notices that every second word is "corrosion".

There is clearly a long list of threats to a structure's integrity, and they add up over time.  Time is in fact the key parameter for a well-designed structure.

The reason that a failure will eventually occur in every structure is due to the failure mode known as fatigue.  Like a person, when a material is pushed every which way enough times, it eventually loses it and cracks.  After enough back and forth expansion and contraction, not to mention vibration, a structure will fail at a much lower value than it would have when it was brand new.  Of course, engineers know a great deal about fatigue failure, and consider it very carefully when designing a bridge, tunnel, or overpass.

Fatigue failure is the reason why a city's infrastructure will one day fall to pieces unless it is carefully monitored.  Like food, all structures come with a "best-before date".  Once a bridge's life is extended beyond this period of time, the likelihood of it failing increases significantly. 

So, why is Montreal now experiencing so much failure at one time?  It is actually not so surprising.

Large supporting structures designed for a fairly extreme climate have a life expectancy in the area of fifty years with regular maintenance, while some can last up to one hundred years (it depends on the load-bearing material...Steel bridges outlast concrete ones).  That is not to say that such structures will immediately collapse on their fiftieth birthday, but around this time they will become statistically more likely to fail.

It turns out that a large quantity of the structures in Montreal are around five decades old.  This makes sense, as the city saw major infrastructure expansions in preparation for major events like Expo 67 and the Olympics in 1976.  In those days, these major investments were seen in a positive light, as they placed Montreal on the world stage, increased tourism, and allowed for the local population to grow.

Today, investments similar to those made half a century ago must be made again.  Unfortunately, these investments, made today, will not correspond to any economic growth; they will merely prevent the city from falling to pieces any more than it already has.

In summary, Montreal's many bridges, overpasses and tunnels are not poorly designed.  The soup we currently find ourselves in is the result of a big infrastructure boom many decades ago.  A large spike such as that will always call for a similar spike in the future; it is one consequence of rapid expansion.  If a city finds itself unprepared for an infrastructure overhaul, it amounts to a failure in city planning, not engineering.

As local defects within these structures are repaired - and certain bridges beyond saving are replaced altogether - the city must continue to function.  Its citizens should not drive around in a panic.  I have heard many people in this city express their fear of driving under or over their bridges to go to work.  Such fears are the result of much media attention, but they are statistically irrational.

The vast majority of car accidents would be averted if drivers were attentive, careful, and of course, sober.  The number of car accidents involving falling structures is tiny when compared to those involving reckless driving.  So, whether you are driving over a new bridge or an old one, the greatest threat to your safety remains the cars around you.

Still, given the state of Montreal's roads and bridges, no one can be faulted for muttering a small prayer upon entering a motor vehicle.

The more puzzling question than "Why are our bridges falling apart," is "Why do they cost more to tend to and replace in Montreal than anywhere else?"  The answer to that is likely attributed to our needlessly high number of bureaucratic jobs, but perhaps even more so to the troubling presence of organized crime in this city.  Sadly, efforts to repair these issues require more than duct tape and epoxy.

Nearly all engineering designs serve a purpose.  When they fail to serve the purpose for which they were designed, they are considered to have failed.  Failure is an expectation, as nothing has an infinite lifetime.  As such, all engineering designs have an expected or intended lifetime after they are built and delivered, which may be thought of as a best-before date. 

Things with moving parts, like cars, may have a lifetime of fifteen years and 200,000 km.  That is because a very popular mode of failure is fatigue.  The strength of a material actually decreases when it is stressed, even at low values.  On the other hand, static objects, like chairs, tend to survive longer than is required – typically, the paint will fade long before a leg breaks.  A chair tends to go out of style before it falls apart.  This is not surprising: whenever it is possible, engineers apply a high safety factor to their designs.

A safety factor is a number that represents the extent to which a product is over-designed.  If a chair is designed to hold a 250 lb individual before yielding or buckling, a safety factor of five (typical when human life is at stake) may be applied when determining the thickness of the wooden legs.  As a result, a failure would occur if a 1,250 lb individual were to sit in the chair.  The weight and material cost associated with thickening the legs of the chair is very small.  In fact, a chair is first designed for aesthetics and ergonomics alone.  The last step of the design process is to check the extent to which the design is structurally sound.  It is so easy to design a chair that its factor of safety becomes an after-thought.

It is not as trivial to design an airplane, for example.  Here, aesthetics do matter, but are of lesser importance than proper function.  Safety is of the highest importance for many products, and the first order of business for these is to assign minimum allowable safety factors for the various failure modes of the various parts.  If an airplane is intended to take 2,000 flights in its designed lifetime, the wings may be sized so that they ought to survive 10,000 flights without a failure.  Still, the plane will be grounded after 2,000 flights so that its safety factor remains at five.

When human life is not at stake, the safety factor may be reduced to 1.4, or when necessary, 1.25.  These figures may seem arbitrary, but they are chosen based on statistics, and insurance companies that ensure the parts require minimum values.  Creating aggressive designs of this type is the closest most engineers get to living on the edge.

An example of an engineering design with a very low safety factor is a satellite.  It is merely a hunk of metal with some wires, and carries no life as it orbits the Earth.  Insurance companies still charge huge sums to ensure satellites, but far less than space missions, which transport living people.  The trade-off for the engineering firm goes as follows: which is cheaper, to pay launch fees for extra mass (more mass will allow for a higher safety factor) or extra insurance costs for a design that is tight on safety?  In all cases, a tight design with careful engineering is chosen, simply because the cost to place a satellite in Geo orbit is around $20,000 US per kilogram payload.

Although safety factors are associated with engineering, we all make use of them when we make decisions in our day to day lives.  The best example of this is when we buy a home.

In choosing a reasonable mortgage to undertake, those looking to purchase a home are often advised (and even encouraged) by bank employees to undertake the maximum mortgage their current incomes can support.  This is ridiculous, as it corresponds to a safety factor of 1.0, and an engineer would never place themselves in such a situation with regards to any design, even one that does not place one personally at risk.  A mortgage does place the home owner in financial risk, and as such, should be taken very seriously.

The recent economic crisis has really hurt first-time home buyers.  Many of them have lost their jobs, and their unsubstantial safety factor associated with their mortgages has left them in big trouble.  So many Americans have declared bankruptcy, and a sad number of suburban streets have a very low occupancy rate.  We need to learn from this.

It is prudent, and very smart, when undertaking a mortgage, to apply a safety factor of two.  How can one do this?  Pretend that one of the two people involved in paying for the mortgage were to lose his or her job.  Choose the maximum mortgage that would still be affordable in this case.

This sort of conservative approach would of course delay many people from buying their first home, but it would allow them to sleep easier at night once they do invest.  Risk is among the top concerns for a program manager at an engineering firm, and ought to be considered when it applies to major life decisions.

The decisions we make have a corresponding safety factor.  In the name of pragmatism, we must all apply reasonable safety factors to our lives.  How would you feel if you travelled in a car with a safety factor of 1.25?  It could fail if the temperature were to be lower than had been designed for by just a few degrees, or if the engine were revved at just a slightly higher rate than the automaker had predicted. 

On the other hand, there is a balance that we must strike.  It would be prohibitively expensive to apply a safety factor of ten (if not impossible) to all facets of an airplane.  We must realize that there is some inherent risk associated with everything that we do, and make decisions that we are comfortable with.  As in life, there is an important balance to strive for as an engineer, whose holy grail is an optimal design.

It’s like the old joke.  The pessimist says the cup is half empty.  The optimist says it is half full.  The engineer points out that the cup is twice as large as it needs to be.

A safety factor of two, as it turns out.