Why Buildings Shouldn’t Last 1000 Years

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One of the many criticisms leveled (badum-psh) against modern buildings is that they’re shoddy, lasting only a handful of years before they need to be torn down or replaced. Modern buildings are generally designed to have a 50 year lifespan, and many are torn down before they even reach that. Compare this to ancient buildings, some of which have lasted for hundreds or thousands of years, and continue to impress even today.

But it’s actually a good thing that our buildings don’t last that long. The reason is something called Net Present Value, which is how organizations decide the value of projects they’re considering funding. Net Present value is essentially the current value of all future cash flows, minus the initial cost. The higher the number, the more valuable the project is. The formula is below:

NPV

Where C0 is initial investment, Ct is annual cash-flow, r is the discount rate, and t is the number of years. Let’s plug in some numbers and compare a typical, 50 year life building with a theoretical building designed to last 1000 years.

First, the initial investment. We’ll say our typical building will cost 1,000,000 dollars. This might cover, say, a small (7-8000 square foot) commercial building like a store or a warehouse. It’s hard to say how much a hypothetical thousand year building would cost, but it would be FAR more expensive. NONE of our modern materials – steel, concrete, wood etc, would suffice, as they’re all subject to corrosion and decay. The only buildings that have lasted for a thousand years are ones constructed of stone. But let’s be conservative and say it costs three times as much – 3,000,000 dollars.

Next, the annual cash flow. For our typical building, we’ll assume a gross rent multiplier of 8 (which might make this a fairly lucrative building), which gives an annual rent of 125,000 dollars. We’ll give the same annual rent to the 1000 year building, because nothing about a 1000 year building would make it better for tenants (if anything, it’d be worse, as increasing durability tends to decrease usability).

But, our cashflow won’t be constant. Rents increase over time, even above inflation. This suggest an average increase of around 1.3% a year over inflation. This suggests a commercial rent increase of around 2-3% a year, though that isn’t inflation adjusted. We’ll assume an annual rent increase of 1.5% over inflation (though it’s unclear how realistic this is long-term – towards the end of a thousand years an initial 1000 dollar per month rent would turn into just over a billion, which seems…unlikely).

The discount rate is the theoretical rate of return you could get if you just held on to your money. For our discount rate, well, the 10-year treasury bond rate averages around 2% or so. The corporate bond rate has been steadily marching downward over the years, but is currently at 3.5%. The average return from the S&P 500 since it’s inception is 7% (inflation adjusted). This page suggest that 4-5% is a good number to use for a discount rate. We’ll go with 4%

Plugging these values in to a net present value calculator yields $2,571,612 for the typical building, and $2,075,000 for the 1000 year building.

In other words, the typical building is much more valuable, to the tune of ~25%, than the 1000 year building. And let’s be clear: I HEAVILY stacked the deck in favor of the 1000 year building by only making it 3 times more expensive, and assuming a perpetual rent increase of 1.5%.

It doesn’t matter that our 1000 year building lasts 50 times as long. Building it to last is so much more expensive that the “cheap” building comes out ahead. And keep in mind, assuming a building would actually last 1000 years, even if we designed it to, is a bold prediction. Vanishingly few buildings, even ones designed for longevity, have done so – the majority of them are rubble.

These numbers shouldn’t be that surprising. A building is just not that great of an investment. Buildings are nicer than they were 100 or 200 years ago, but they fulfill the same fundamental purpose they did then. They haven’t fundamentally changed the way we live our lives or the structure of civilization like the car or the computer or the plane or the cell phone have. In a dynamic, growing economy we should expect there to be much better places – more useful places – to put your money than a building. You don’t see the Vatican financing too many massive churches designed to last the ages these days, despite having a few billion dollars to invest. In some ways, ancient people’s predilections for long-lasting buildings reflects the fact that their economies were stagnant, with little innovation or growth.

How A Flying Buttress Works

buttress1

The flying buttress is an iconic architectural element, used most famously on Notre Dame and other large, historic churches. But what exactly does a flying buttress do?

Ancient buildings, the sort that were designed to last anyway, were almost always built out of masonry: solid blocks of clay or stone fitted together. Masonry has high strength in compression, but almost no strength in tension. To get around this limitation, builders had basically one engineering trick: the arch.

OLYMPUS DIGITAL CAMERA

So how does an arch work? Well, the easiest way of spanning between two points is with a simple beam. A beam works by having the top portion in compression in and the bottom portion in tension. An arch cheats this by switching out internal tensile forces for external compressive forces: instead of bending like a beam does, an arch pushes on its supports. This makes it perfect for using with materials with low tensile strength. The drawback is that using them requires a strong, stable surface that the arch can push against.

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Being the only play in the playbook, arches tended to get a lot of use – lots of ancient architectural elements are variations on it. A dome is essentially an arch wrapped around 360 degrees*. If a flat surface was needed, a flat arch could be used. And the “flying” part of a flying buttress is just an arch tilted on its side.

Churches tended to have ceilings made of large, ornate masonry vaults. A vault is, once again, just a slightly different flavor of arch, and these would create outward thrusts at the top of the wall. Handling these forces is a difficult task for a comparatively thin wall – something larger is needed to resist them.

 

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One way is just a regular old buttress – a thick heavy section that is big enough to contain the outward thrust (i.e.: keep the member entirely in compression).

goachurch

You could also move the buttress outside and connect them back to the support walls. This is perhaps a more elegant architectural choice, but it doesn’t improve your  actual design much – you’ll need just as large of a buttress wall as you did before.

But if you slope your arch downward, the outside wall will be at a lower elevation. This lowers the overturning moment (force wanting to topple the wall over), and allows for a smaller buttress, and a lighter, more airy church design.

So, to sum up: a flying buttress was an arch that transferred lateral thrust from the roof vault. Transferring the force like this allowed the use of smaller, shorter buttresses on the outside and produced a lighter, more elegant design.

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The flying buttress, like every other flavor of arch, isn’t used much anymore. With the development of steel it became economical to design structures that could carry large tensile forces, making the arch unnecessary. In some ways this is the main difference between ancient and modern (post 1850 or so) construction – the former are designed to only be in compression, while the latter can handle both tension and compression with ease. For this reason, it’s unlikely we’ll see a revival of the flying buttress any time soon.

US vs Japanese Building Codes


Japan has sort of famously strict building codes (to the extent that any building codes can be ‘famous’, anyway). During the 2011 earthquake, Japanese buildings suffered relatively little damage, a fact credited to diligent enforcement of very strict building codes.

But how strict are these codes, anyway? How would a typical Japanese building compare to a typical US one?

Let’s look at a sort of “typical” building that might be built, and see how it’ll differ under US and Japanese seismic design. For this example we’ll use a 4 story steel building, with composite deck flooring and concentric braced frames to resist lateral forces. This could be an apartment complex, or a hotel, or a classroom, or something else — it’s an extremely common method of construction. Since earthquake forces are a function of a buildings’ weight, we’ll assume it weighs 100,000 pounds (100 kips).

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Our building might look something like this before the architects get a hold of it.er a caption

In both codes, the seismic design procedure is relatively similar. First, calculate the amount of force an earthquake is likely to inflict on a building. Scale this value using various factors based on construction type, building height, type of lateral system, etc. Design the lateral system to withstand this much force. Finally, perform checks to make sure the building doesn’t sway too much, and that, should it fail, it fails slowly and safely, allowing people time to get out.

For the US codes I’ll be using ASCE 7–10 and AISC 341–10. For the Japanese code I’ll be using the design method from the 1981 Building Standard Law Enforcement Order.

(If you don’t feel like following along with these calculations, go ahead and skip to the TLDR at the end).


We’ll start with the Japanese code. Here’s the Japanese formula for lateral seismic forces:

To get the seismic force Q, we multiply the building weight W by a shear coefficient Ci, which is a function of the following factors:

  • Z is the seismic zone factor, which comes from the map below. (I believe the numbers represent the ground acceleration, as a fraction of gravity, that would be experienced in a 500-year earthquake. Most countries use similar criteria, but the Japanese code is somewhat unusual and I couldn’t find good information on this). The lowest number on the map is 0.7, or 70% of g, which is an extremely high seismic force. We’ll use a value of 1.0.
  • R is the vibration characteristics factor. We’ll conservatively set this to 1.
  • A is a factor for evaluating the force at different levels. For this example we’ll just consider the force at the ground (called the ‘base shear’), so we’ll use 1. (Japanese and US codes use similar methods for evaluating force as a function of building height).
  • C is the standard shear coefficient. For a building less than 31 meters tall and without any major irregularities, we can use a shear coefficient of 0.2.
Map for finding seismic zone factor.

The Japanese code also has some provisions for steel buildings specifically, the most relevant being one that requires multiplying the calculated seismic force by up to 1.5. (The other provisions are about member size/strength and building shape, and seem to have similar analogues in the US code).

Factor for increasing seismic forces in steel buildings.

This gives us a base shear of 100 kips x 1.0 x 1.0 x 0.2 x 1.5 = 30 kips. Our lateral-resisting system has to be designed to withstand 30,000 pounds of force.


Now let’s consider the same building built in the US. Here’s the equation for lateral seismic forces (from ASCE 7–10):

  • Sds is roughly the equivalent of the Z factor in the Japanese code, the ground acceleration felt under a 500 year earthquake. We’ll use the same value as 1 (100% of g), the sort of acceleration which could be experienced along the west coast, or in places like Charleston or Missouri.
  • This isn’t in the above formula, but an acceleration this high will put our building into seismic design category ‘D’. This is a category for buildings which are likely to experience extremely high seismic forces. It will, among other things, force us to multiply our seismic forces by an overstrength factor of 2.0. (Courtesy of AISC 341–10).
  • R here is the response modification factor, which lets us reduce the design forces for systems which are highly ductile. Because we’re in seismic design category D and taller than 35 feet, our frames will have to be “Special Concentric Braced Frames”, which have an R value of 6. (The Japanese code also uses a ductility factor, but it’s values are generally lower, and it’s only used in a design procedure we’re able to skip).
  • I is importance factor, which is higher for buildings which meet certain importance criteria. We’ll assume our building is unimportant and use a value of 1.

This gives us a base shear for the US codes of 100 kips x 2.0 x 1.0 / (6 / 1) = 33.33 kips.

This is in fact slightly more than the force required under the Japanese code. We have being in seismic design category D and being taller than 35 feet to thank for that — those facts combined mean some extremely burdensome design requirements.


Besides lateral force, the other major component of seismic design codes are drift limits, which dictate how much the building can shake back and forth. Limiting drift prevents damage to drywall, windows, face brick, and other non-structural portions of the building that might be damaged during an earthquake even if the structure itself remains standing.

For this sort of building, the Japanese code limits story drift to 1/200th of the story height. For a story height of 12 feet, this is about 3/4 of an inch.

The US code limits deflection for this category of building to 2% of the story height. However, it also requires multiplying the calculated deflection by a “deflection factor”, which in this case is 5. This results in an allowable drift of 5/8 of an inch. Once again, the US code is slightly more strict than the Japanese code.

Formula for calculating deflection in ASCE 7–10.

So, to sum up: The US building code requires designing for a slightly higher lateral force, and slightly lower story drift. The Japanese code is less strict than the US one, though the requirements for each are very close.

A few caveats to this surprising conclusion:

  • We’d get slightly different results with different types of construction, and different building heights. Buildings taller than 31 meters in Japan require an additional, stricter design procedure. And buildings taller than 60 meters require special approval from the government, so it’s hard to tell how restrictive the design for them has to be (though US buildings of this height also have very restrictive provisions). But in both countries the majority of construction is going to be short buildings similar to our example.
  • I am not an expert on either the Japanese building code, or designing US buildings in high seismic areas. It’s very common for building codes to have a single, obscure line that completely changes the design requirements. It would have been very easy for me to miss something in the code that substantially alters the above calculations.
  • Building codes in the US vary from state to state. The calculations above were done with the latest versions of the code, and states that still use older versions would have less strict requirements.

However, for a building of moderate height in a seismically active area, the most recent US code provisions seem to be just as strict, if not stricter, than the Japanese ones.

The San Francisco Earthquake and Reinforced Concrete

Concrete has been used as a material for thousands of years. But reinforced concrete – concrete with steel embedded in it – is a much more recent invention. It didn’t start to be used until the mid 1800’s (it’s first use is usually traced to some reinforced garden tubs built in France), and it was years after that before people started using it effectively.

One of the first “modern” systems of reinforced concrete was the Ransome system, invented by Ernest Ransome in 1884. This system was distinguished by using twisted steel bars to improve their bond with the concrete.

ransome

Engineers are sort of skeptical of new technology by nature (and by incentive), and reinforced concrete (including the Ransome system) wasn’t any different. Up through the end of the 19th century it remained unpopular to use as a building material, being used for foundations but not much else. Most building codes didn’t even recognize it.

One of the few buildings made of reinforced concrete during this period was a museum on the Stanford campus, built in 1891 using the Ransome system. Reinforced concrete was chosen for it’s speed – it could be put up much quicker than a traditional masonry building. It was later enlarged with wings on either side, but these were built of conventional masonry construction and built to match the appearance of the original building.

stanford

In 1906, a 7.8 magnitude earthquake struck the San Francisco bay area. Thousands of buildings were damaged or destroyed by the shaking and the subsequent fires. The wings of the Stanford museum, built out of masonry, were reduced to rubble. But the original reinforced concrete structure suffered no damage at all.

Unreinforced masonry (masonry with no steel embedded in it) is perhaps the worst possible material to use if you want your building to survive an earthquake. As the building shakes back and forth, parts of it are put in tension which normally only see compression. Masonry is exceptionally weak in tension, but reinforced concrete, with it’s steel skeleton, is far more resilient. Engineers inspecting the Stanford Museum, built using the Ransome system, were impressed with how little damage it suffered.

Buildings are designed to survive worst-case loading that, in all likelihood, they’ll never see. Because of this, engineering practice tends to proceed one disaster at a time. The success of the Stanford Museum (and other reinforced concrete buildings in the bay area) helped popularize reinforced concrete as a building material. And modern steel reinforcing is specifically designed and shaped to grip the concrete, like Ransome’s bars were.