To begin, we should remember that one cannot build an “earthquake-proof” structure. There are no magical steps with which you can build a structure that will render it immune to earthquakes. Simply put, if the earthquake is big and/or close enough, the structure will fall. And there is no way to accurately predict the size, location, or maximum magnitude of future earthquakes.

Building earthquake resistant structures relies on the study and use of both real-life earthquake scenarios as well as that of laboratory experimentation. I covered some of the general methods used to make earthquake resistant structures in What Makes a Structure Strong or Resistant to an Earthquake, but in this article I’ll be going into some of the specifics in terms of exact building codes here in Japan.

Due to being one of the most seismic regions in the world, Japan – by necessity – leads the way in many key aspects of earthquake engineering. We all know that the taller a structure is, the more complicated it becomes to build it safely. With tall skyscrapers popping up here and there around the world, naturally, people question how safe they are in an earthquake.

But what about the short ones — say, your average 1 or 2 floor homes many of us go back home to? Skyscrapers obviously, but if our individual homes scattered across the country were built more earthquake resistant, we would be much better prepared in event of an earthquake and who knows how many lives might be saved as a result.

**Required Building Code in Japan for Wooden Houses**

Okay, on to the specific building code used here in Japan. This code is required by law for all wooden houses with a collective floor area of 50 square meters or more. Floor area is calculated by center to center measurement of the outer wall columns, not the outer perimeter. Also, bear in mind that this includes closets, toilets, etc as well.

An accurate floor area value is essential for the calculation of the structure so we’ll need to cover some additional details. There are some areas of a house that can be ambiguous as to whether they are included in the total floor area. These are:

**Lofts and attics** — Lofts and attics must by law, be no more than 1400 millimeters in height, otherwise they are considered “living quarters”. In terms of earthquake code, they are included in the area of a given floor (ie, first, second) if and only if they exceed one-eighth of that floor area, as well as remains under HALF of the same.

where *a* is the value you must add to the total floor area, *h* is the mean height of the loft, and *A* is the collective horizontal surface area of the loft.

**Balconies** — Multiply the balcony floor area by 0.4 and add to the total floor area of the first floor. Note here that this only applies in cases where the balcony in question is supported by the structure.

**Overhangs** — All overhangs are included in the floor area of their respective floors, and must be factored in when solving for the “one-fourth Division law” (explained further below).

**Introducing the Seismic Coefficients**

Now that we’ve defined what the floor area includes, let’s talk about the seismic coefficients used for this purpose. This value is different depending on the number of floors the structure in question has, the general weight of its roof (classified as either light or heavy), as well as on the floor itself. (Refer to the image below.) As far as single story houses are concerned, they go by the coefficients 11 and 15, light and heavy weight roofs respectively.

**Structural Wall Scale Factor**

*Note: The term “structural wall” used throughout this article is defined as a wall containing one of the 5 bracing combinations depicted in the Scale Factor image below. *

There are three standard ways in which you can brace your structure to resist lateral loads — either by a single diagonal brace, a double diagonal brace, or shear wall. And there are 2 standard cross-sectional dimensions that are commonly used for diagonal bracing here in Japan — 30 by 90 millimeters and 45 by 90 millimeters. Between these, there are 5 standard combinations (refer to image).

The image above displays the 5 combinations and their accompanying scale factors. As you can see, the scale factor increases with the strength of the structural bracing. Note that all diagonal bracing must be fastened with the certified steel hardware and fasteners for this purpose. Image below shows one of several kinds of certified steel bracing plates.

**So how do you Calculate the Requirements and what is the “One-fourth Division Law”?**

First, we must calculate the required number of structural walls a given structure must have to meet the earthquake code. This is done by the following equation:

where *RSW* is the required number of structural walls, *A* is the total floor area, *μ _{e}* is the earthquake coefficient,

*l*is the mean length of a single structural wall, and

_{sw}*K*is the scale factor.

Next, we note that there is a Japanese law (the One-fourth Division Law) that requires the more or less even distribution of such structural walls (read on to find out how it’s done). We will follow the image that shows a floor plan of the first and second floor with the accompanying math that explains what’s going on. As you can see however, it’s all in Japanese, but numbers are universal, so bear with me.

(Click on image to get larger view)

The image starts out with 4 diagrams, the first 2 being the first floor and the second 2 being the second floor. Note the second floor is smaller in area than the first, and covers only a portion of the first floor area from above. The diagram is graphed into 12 rows and columns, the distance between which symbolizes a single wall span of 910 millimeters, or 0.91 meters. This adds to a total of 10.92 meters.

**The one-fourth division law check system in simple English using the method and the floor plan in the diagram:**

In a typical house with 4 walls of more or less equal length, the south and north walls, and the east and west walls, must be balanced with each other in terms of their placement of shear or structural walls. To better illustrate this principle, here’s an analogy:

If 4 men were to lift a heavy object but 3 men picked up the front end and left the 1 man to lift the back, what do you think would happen? Well, a house with structural walls distributed with no regard as to their placement, when subject to heavy seismic activity, will behave in much the same way. In fact, the stress will be concentrated in the weakest sector, and can result in heavier damage than if fewer structural walls were used but evenly distributed.

By following what’s being done in the image as an example, we can see how to practically check a structure for balance. In this case the structural walls are already in place and we’ll simply be conducting a test to ensure they fall within the acceptable range. Okay, on to the math. I’ll be using the shaded area “1” with the corresponding upper, left hand table in the image below the diagram as an example.

(We are treating the example structure as a “heavy” structure. See seismic coefficients above.)

- Determine the local floor area (
*A*): Divide the total length of the outer wall by 4 (2.73m); Multiply this value by the adjacent wall length (10.92m) to get the local floor area (29.81m^{2}) “*A1*“. - Determine the wall length of the existing structural walls (
*Le*): take the length of a single wall, which in this case is 0.91 meters, multiply by the number of structural walls (6, in thick black), and multiply by the scaling factor (in this case 1.5; refer to scaling factor image and explanation further above). The result is Le, 8.19 meters. - Determine the required structural wall length (
*Lr*): Multiply the local floor area by the corresponding seismic coefficient — in the case of A1, it’s 15, as we are treating it as a single floor structure due to the placement of the second floor. The result is*Lr*, 4.47 meters. - We now divide
*Le*over*Lr*to get the ratio, 1.83.

We should note here that although it’s preferable that *Le* is greater than *Lr* even at this local level, because *Lr* is designed for the entire perimeter of the floor in question, as long as the collective *Le* is greater than the collective *Lr* **AND the balance is up to snuff**, your structure should be fine.

Following the table in the image, if we repeat this same approach with shaded area “2”, which is the opposite side of “1”, we get the resultant ratio for “2”. Note that because “2” bears part of the load of the second floor, **it has a seismic coefficient of 33, not 15**. We now divide the smaller of the two ratios by the larger to get the final result, 0.45.

According to the One-fourth Division Law, either the structural wall ratio between the 2 parallel walls is no less than 0.5, or the ratio of *Le* to *Lr* per side is greater than 1. This means that the current balance for walls 1 and 2, 0.45, is **unacceptable** by Japanese standards, as it fails both criteria. You may be able to deduce as much by the writing in red, indicating the failure to meet the criteria.

From here, the rest is probably decipherable. 3 and 4 meet the criteria, as their structural wall ratio exceeds 0.5; 5, 6, 7, and 8 all meet the criteria, as they each have an individual *Le* to *Lr* value greater than 1. Just remember that the seismic coefficient changes depending on the given floor and whether or not it bears the load from the second floor. Refer to the seismic coefficient image further above.

— Diagrams and images are courtesy of house-support.net and ads-network.

**Additional reading:**

— Earthquake Building Codes in Japan.

— The Value of Good Design: Earthquake-Resistance in Japan Since 1971.

— Earthquake Engineering — Wikipedia.

— Japan, a Leader in Earthquake Engineering

— 7 story wooden house on E-Defense Shake table

— How Earthquakes Affect Wood Buildings