In the aftermath of Harvey, a great deal of attention is being paid to flood-prone areas of the country – specifically, the FEMA maps that show a location’s annual flood risk. These maps are important – beyond showing flooding risk, they determine whether federally-funded mortgages will require flood insurance or not.
It’s also useful to know if you’re building a chemical plant that might explode if it gets flooded.
(Spoiler alert: pretty much anywhere near a river or the coast is at significant risk of flooding.)
If you’re interested in knowing whether your house is in a flood zone (and you should be), FEMA has an online tool for viewing the flood map of an address here. You can also download a layer for viewing on google earth here.
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).
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.
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).
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.
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.
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.
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.
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.
Recently, there’s been a flurry of news surrounding a new paper which examined the mineral structure of concrete samples taken from a 2000 year-old Roman breakwater. The articles range from measuredly pointing out it’s carbon efficiency, to extolling it’s near-mystical properties. The fact that these structures are still intact after millennia, while ours often decay to the point of uselessness after less than 50 years, obviously raises some questions. Namely, was Roman concrete better than ours? Why does ours fail so quickly?
On June 1st, new design values for southern pine lumber came into effect. These results are based on full-scale testing of various lumber sizes, and supersede the interim results that went into effect last year, which only affected 2″-4″ sized lumber. The kick in the teeth is that the new values show a sizable decrease in capacity for compression, bending, and tension, with reductions ranging from 10-30%. More information can be found at the SPIB site.
The changes are the result of the large-scale destructive testing of thousands of pieces of southern pine lumber. Wood is a highly variable material, and so requires a large number of samples to reliably establish safe design values. This sort of testing first began in the late 1800’s, and is conducted every so often by lumber testing organizations. Testing standards have changed over the years, but currently must follow ASTM D 1990. Testing organizations must be certified by the American Lumber Standards Committee. There are currently seven organizations, which are responsible for various regions and wood varieties. Southern pine lumber is covered by the Southern Pine Inspection Bureau.
Engineering is a game of optimization under constraints. Problems are never just “design a beam that can span a hundred feet“, but “design a beam that can span a hundred feet, is made of concrete, weighs less than 40 tons, and is less than five feet tall.” Or, more likely, “design a beam that can span a hundred feet as cheaply as possible”. Problems with only one requirement are easy to solve – it’s the ones with multiple, sometimes conflicting requirements that require clever solutions.
One of the most important of these requirements is “…and design it using only these tools“. This isn’t something that shows up in the design contract, but it’s a necessary reality. The tools humans have invented so far, be they wrenches or word-processors, are a limited subset of what’s theoretically possible to accomplish. And the tools any given engineer will have available are a limited subset of that. Much like MacGyver, we can’t solve engineering problems any way we’d like. We have to use whatever junk happens to be lying around.
As I’m so fond of mentioning, engineering design required the use of a number of creative methods before the invention of calculators and computers. Some of the most important and widespread of these were graphic methods of analysis. Graphic methods essentially translate problems of algebra into geometric representations, allowing solutions to be reached using geometric construction (ie: drawing pictures) instead of tedious and error-prone arithmetic.
Unfortunately, these methods are slowly being forgotten. It’s extremely rare to ever see them used, outside of a select few occasionally taught in structural analysis courses. But understanding how, and more importantly why, they work unquestionably makes for a better engineer.
To remedy this, this post will lay out some of the basics of graphic statics. If there’s interest, more posts on more advanced methods will follow.