Introduction to Building Types

In this chapter we will explore the nature of deformations and forces in buildings during earthquake shaking. Of course, buildings are complex connections of columns, beams, and walls, the study of which deserves and entire course in structural engineering. However, for the purposes of this class, with limited time to devote to the topic of building response, it is instructive to investigate the nature of forces and deformations that would occur in a solid body whose properties are similar to the average properties of a building. We begin with a simple description of different types of buildings and their characteristics. In general we will characterise buildings with the following parameters (refer to Figure 9.1).

Density

Important because it is used to calculate inertial momentum.

The density of buildings ranges about 100 kg/m³ (tall flexible frame buildings) to 200 kg/m³ (stiff heavy shear wall buildings). Earthquake loads in buildings generally increase with the density of the building.

Yield strength

- the maximum horizontal load that can be applied to a building.

It is expressed in units of acceleration if the yield force is normalized by the weight of the building. While increasing yield strength is generally desirable, it usually comes with the penalty of increasing stiffness.

Stiffness

- the horizontal force distributed throughout a building divided by resulting lateral shear strain in the building (usually called drift).

Maximum stresses in a building generally increases with stiffness, so making a building stiff can lead to high stresses. While low stiffness has advantages, decreasing stiffness usually comes with the penalties of increasing shear strains and decreasing yield strength.

· Ductility

- the ratio of the horizontal shear strain at which a building collapses divided by the strain at which a building begins to strain inelastically.

Increasing ductility is always desirable, but it usually comes with the penalty of increasing cost.

Figure 9.1 Idealized building response.

The following examples give some idea of different classes of buildings.

Concrete Shear-Wall Buildings

This is a common class of buildings that generally have at least some walls that consist of continuous slabs of concrete. These concrete walls are very resistant to in-plane shearing forces. Perpendicular shear walls are generally connected with each other through 1) the strong floor slabs, and 2) sometimes they are connected at corners of rooms. When a building consists of a rectangular concrete box with interior columns supporting the floor slab, then this is generally referred to box/shear-wall construction. This type of construction is very common. It has the advantage of very high yield strength. Furthermore, if the walls are properly reinforced, the ductility is also high. This type of construction has the disadvantage that it tends to lead to very stiff buildings. As we see later in this Topic, this can lead to high stresses in a building. It also has the disadvantage that the architecture of the building is fixed. That is walls cannot be reconfigured once the building is constructed. Furthermore, because of their stiffness, it is impractical to build shear wall buildings taller than about 10 stories that also adequately resist earthquake loading.

Figure 9.2 shows two versions of the Olive View Hospital in the San Fernando Valley. The first version was a non-ductile concrete frame building that was completed just prior to its collapse in the 1971 San Fernando earthquake. The hospital was rebuilt as a shear wall structure (some of the shear walls were solid steel) and it experienced heavy shaking in the 1994 Northridge earthquake. In this case, though there was no structural damage because of the very high yield strength of the building.

Figure 9.3 shows an example of a Japanese concrete shear-wall apartment building after the 1964 M 7.5 Niigata earthquake (see the figure caption).

Moment Resisting Frame (MRF) Buildings

This is a very common class of buildings, whose structural system generally consists of a rectangular lattice-work of columns and beams (the frame), together with the relatively rigid floor slabs. The columns and beams can be either mild steel (SMRF) or reinforced concrete. Figure 9.4 shows an example of a SMRF. These buildings are currently popular with many architects since they are inexpensive, office space can be easily reconfigured, they are light, and they can be quite tall (the Library Towers in downtown Los Angeles is 80 stories high).

Figure 9.2 Two versions of the Olive View Hospital in the San Fernando Valley. The top picture shows the heavy damage that occurred to the first hospital (non-ductile concrete) in the 1971 M 6.7 San Fernando earthquake. The bottom picture shows the shear-wall structure that replaced the first one. This strong building had no structural damage as the result of the violent shaking in the 1994 M 6.7 Northridge earthquake.

Figure 9.3. Japanese concrete shear-wall apartment buildings after the 1964 M 7.2 Niigata earthquake. Despite the fact that the foundations of the buildings failed due to liquefaction, the building structures were undamaged and the buildings were later jacked back to an upright position and they were reoccupied.

Figure 9.4. Example of a steel moment resisting frame. The connections between the beams and columns are typically welded (called a moment-resisting connection) to keep the elements perpendicular. Many of these critical connections were observed to fracture in the 1994 Northridge earthquake.

Figure 9.5 shows the basic physics of how an MRF resists lateral motion. All connections on the 1st cartoon are moment resisting. In the 2^nd cartoon, as the frame is deflected horizontally, the beams and columns in the middle exterior must bend if their connections remain perpendicular. Note that only the middle exterior connections are moment resisting, while the interior connection and the edges are a simple connections, which act structurally more like a hinge. These beam-column connections are critical elements of a MRF since that is where the bending moment originates on a beam or column. It is critical that the MRF failure strength exceeds the flexural yield strength of the beams, since a building’s ductility (high ductility is good) derives from the inelastic bending of beams (it’s not good practice to allow inelastic bend or deformation of the columns since they carry gravitational loads).

In the case of Steel MRF’s, the moment resisting column-beam connections typically consists of welds between the flanges of the beams and columns (see Figure 9.4). These welded connections became popular in the 1960’s since they are inexpensive to use, and they were thought to have high strength. However, many of these welded connections fractured during the 1994 M 6.7 Northridge earthquake, so many of the existing steel MRF’s are not as ductile as designers thought when buildings were constructed.

Figure 9.5. 2 cartoons showing how the flexural bending of beams and columns provides a resistance to lateral deformation for a moment-resisting frame structure. In the 1^st cartoon, all connections are moment resisting. In the 2nd, only the 3 middle connections on the exterior are moment frame connections, whereas the interior and corner connections are “simple” connections (unwelded) that acts more like a structural hinge.

While steel MRF’s have the advantage that they are very flexible, that comes with the penalty that they have very low lateral strength. Figure 9.6 shows a pushover analysis (finite-element analysis by John Hall) of 20-story SMRF building that meets the 1992 UBC code for California. This analysis included numerous nonlinear effects on the deformation of the steel, as well as also explicitly including the effect of how gravitational forces act on the building for large finite displacements. That is, when the drift of the building becomes large, then every increasing lateral loads are put on the building by gravity (kind of like the Tower of Pisa). This is known as the effect and it is an important collapse mechanism for buildings.

Figure 9.6 (from John Hall). Finite-element pushover analysis of a 20-story building that meets the 1992 US code standards for zone 4. P refers to the assumption that the moment frame connections do not fracture, B assumes that weld fractures occur randomly at stresses compatible with what was observe in the Northridge earthquake, and T assumes that the welds had even less fracture resistance.

Figure 9.7. (from John Hall) Same as Figure 9.6., except for a 20 story steel fram building that meets Japanese codes in place in the 1990’s. Notice the higher yield strength compared to the US building.

The curves U20P refer to a 20 story building that meets US 1992 zone 4 codes, and for which the welded moment resisting connections behave perfectly (no failures). The curve that is designated as B refers to allowing failure of the moment resisting connections assuming weld behavior consistent with observations in the 1994 Northridge earthquake. T refers to the assumption of terrible performance of the welds. Notice that weld failure significantly decreases both the yield strength and the ductility of the structure. Also notice that a horizontal force of only 7% of the weight of the building is necessary to push over a typical 20-story building in high seismic risk areas of the US.

Figure 9.7 shows a similar analysis, but it assumes that the building meets the building code in force in Japan in the 1990’s. Japanese construction tends to put more emphasis on the yield strength of a structure, and it is common that all connections in a Japanese structure are moment-resisting connection (more costly than the US).

As it turns out, the code required yield strength tends to increase as building height both increases and decreases from 20 stories. This is because design forces for wind loads increase as the building becomes taller, whereas design forces for earthquakes decrease as the building becomes taller (we’ll visit this later). So buildings shorter than 20 stories are designed for earthquake loads and buildings taller than 20 stories are designed for wind loads.

Figures 9.8 and 9.9 show the pushover analyses of 6-story steel moment resisting frame buildings for 1990’s US and Japanese codes, respectively. Notice that the 6-story buildings are required to have a greater yield strength than the 20 story buildings.

Moment resisting frame buildings can also be constructed with reinforced concrete beams and columns. Concrete mrf’s have similar flexibility to steel mrf’s and the code requirement for pushover yield strength is also similar. Both types of mrf’s are required to have high ductility (approximately a factor of 10), but this is achieved in different ways with concrete. While steel is naturally ductile in tensional strain, unreinforced concrete is naturally brittle in tension (it is very strong in compression however). Steel reinforcing bars (rebar) are run longitudinally in concrete beams in order to greatly increase the tensional strength and ductility. While longitudinal rebar is very important, it is not sufficient to make a beam adequately ductile. This was discovered through the inspection of elements that failed in shear deformation in the 1971 San Fernando earthquake. An example of this type of failure is seen in Figure 9.10, which shows the failure of a freeway bridge column during the 1994 Northridge earthquake. Notice that the column originally fractured because of horizontal shear loads on the column. Once the concrete in the column cracked, the concrete fell away from the column and the remaining rebar buckled into a mushroom shape. This is an example of non-ductile concrete behavior. This deficiency was rectified by requiring spiral reinforcing bars that serves to confine the concrete to the beam, even if it is fractured. Figure 9.11 shows how a concrete column can continue to carry significant loads even though it has been strained well beyond its yield point. Unfortunately, this parking garage suffered significant collapse because the elements of the building were insufficiently connected to each other. That is, the reinforcing bars must adequately tie the different elements together.

Figure 9.8 from John Hall. Same as Figure 9.6, but for US code 6-story steel frame building.

Figure 9.9 from John Hall. Same as Figure 9.6, but for Japanese code 6-story steel frame building

Figure 9.10. Example of a nonductile concrete column failure on a freeway bridge during the 1994 Northridge earthquake. The column was fractured by horizontal shear, the concrete fell away, and then the weight of the bridge deck caused the rebar to buckle. This failure could have been avoided by adding more spiral reinforcing loops radially around the column to make it more ductile.

Figure 9.11. Example of ductile deformation of concrete columns from the 1994 Northridge earthquake. Adequate spiral reinforcing resulted in more ductile behavior than was shown in Figure 9.10. Unfortunately the structure had other inadequacies that led to collapse as is shown in Figure 9.12.

Figure 9.12. Despite the ductile behavior of the concrete columns, this parking structure collapsed because the floor slabs were not adequately connected to the rest of the structure. That is, the beams and columns were ductile, but the connections between these elements were not.

Non-ductile concrete frame buildings are recognized as a class of particularly dangerous structures. They have the particularly bad combination of having a low yield stress combined with a low ductility (they’re brittle). The tremendous loss of life in the 1999 Izmet Turkey earthquake was an example on non-ductile concrete frame failure. These failures are often very disastrous since the building often pancakes into a pile of floor slabs (very nasty). Figure 9.13 shows an example of the remains of an 8-story non-ductile concrete frame building that collapse in Mexico City in the 1957 Acapulco earthquake. Many concrete moment resisting frame buildings that were constructed in the United States prior to 1975 can also be classified as non-ductile concrete frames. Failures in the 1971 San Fernando earthquake resulted in a building code change in 1975 that significantly enhanced the ductility of buildings built after 1975. Unfortunately, there are no ordinances that force a building owner to strengthen these buildings. Furthermore, most of the occupants of these buildings are not aware of the potential deficiencies of their building.

Unfortunately, very many buildings in Puerto Rico, including the majority of single and double story dwellings, are constructed of under-strength concrete with insufficient re-inforceing details, and so are non-ductile. School buildings have been damaged even in moderately weak ground motions, such as the 1987 Ml4.7 Boqueron Earthquake (Peak MMI: VI). In addition, the thin gravity load columns popular for hillside homes are at particular risk of brittle catastrophic failure in future earthquakes.

Figure 9.13. Collapse of an 8-story non-ductile concrete moment resisting frame building in Mexico City from the 1957 Acapulco earthquake. (NISEE/Caltech)

Braced Frame Structures

The lateral yield strength of a building can be increased by adding diagonal braces to a structure, as is shown in Figure 9.13. While diagonal braces increase the yield strength, they also increase the stiffness of a building. That is, there is a trade-off between the desired trait of high strength and the undesired trait of high stiffness. Furthermore, it can be difficult to make a braced frame that has high ductility. This is because the use of large bracing elements tends to result in very stiff braces that apply very large loads to their connections with the structure, thereby concentrating damage at these connections. However, the use of small diameter bracing elements can end up with braces that tend to have ductile extension, but they buckle in compression. As a building undergoes cyclic loading, small braces become ineffectual, since they permanently extend and buckle (see Figure 9.14). Caltech’s Broad Center is one of the first buildings in the United States to use new style of brace called an unbonded brace. This consists of a small diameter steel brace that is jacketed in a concrete liner. There is a lubricating element between the concrete and the steel. The concrete jacket prevents the brace from buckling in compression and hence this brace is ductile in both extension and compression. Figure 9.15 shows an example of Broad Center’s unbonded brace.

Figure 9.13. Example of a braced steel-frame.

Figure 9.14 Large braces are stiff and they put large loads into a frame, but small braces can buckle in compression.

Figure 9.15. Broad Center unbonded brace. The steel is ductile in tension and compression since it is jacketed by concrete (yellow) to prevent buckling in compression.

Wood-Frame Structures

Wood frame is the most common type of construction in many parts of the USA, including California; most residences and many commercial structures there are in this category. Since wood is thought of as a “flexible” material, you might think of a very flexible building when you think of a wood frame structure. This would be a mistake. In fact, most wood frame construction is extensively braced. Furthermore, continuous plywood panels, and sheetrock panels are typically fastened to either side of the wooden framing. Such walls may be best described as shear panels. These panels are geometrically connected into rectangular box shapes. In this sense, most wood frame construction might be better described as a shell type of structure. Another feature of wood frame construction is that the structure is relatively light (the dead load) compared with the weight of the contents (the live load). Since it is not feasible to allow the structure to deform significantly because of the live loads (the plaster would crack), wood frame structures tend to be extremely strong (and stiff) compared to their weight. They are also relatively ductile (the framing is redundant, and nails must be pulled out to disconnect elements). As a result of these features, wood frame structures tend to perform very well in earthquakes. Despite the fact that these structures have been located in areas of violent shaking in past earthquakes, collapse of these structures is exceedingly rare. Figure 9.15 shows the Turnagain Heights housing development (wood frame) following the 1964 Alaskan Earthquake. Despite the tremendous damage caused by a massive landslide beneath the development, the wood frame houses essentially remained intact.

Figure 9.15. Wood frame houses that rode through the massive landslide triggered by the 1964 Alaskan earthquake.

Unreinforced Masonry

In the earlier part of the 20^th Century, many buildings were constructed of unreinforced brick; that is the exterior walls are several courses of brick and mortar, whereas the inner walls, floors, and roof can be of alternate construction, such as wood frame. The structural exterior brick walls in this type of construction tend to be heavy and brittle. That is, the walls cannot sustain tension. URM’s have the undesirable characteristics that they are heavy, stiff, and quite brittle. The inadequacies of unreinforced masonry (URM) became obvious in the 1933 Long Beach, CA earthquake and many municipalities adopted building codes (between the mid 1930’s and 1950, depending on the city) that required that these masonry construction buildings should be reinforced with steel. However, several cities have numerous examples of these historic structures. Following serious damage to URM’s in the 1971 San Fernando earthquake, the cities of Los Angeles and Long Beach adopted controversial legislation that required that all URM should have some strengthening. At a minimum, this involved making stronger connections between the wooden floor trusses and the brick walls. This tends to decrease the bending moments on the base of the brick walls for out-of-plane shaking. Some buildings are also reinforced by building another structural system (often steel) within the building. A more expensive alternative for important buildings may be base isolation, where rubber sliders are placed between the foundation and building, which prevent transmission of damaging high frequency ground vibrations into the structure. Although strengthened URM are an improvement on the pre-existing structures, there is a widely held belief that they are still lacking in strength and ductility. Despite their obvious shortcoming, the interior walls of URM’s often prevent the catastrophic pancaking of the floors seen in non-ductile concrete frame buildings.

Figure 9.16. Example of an unreinforced masonry building (URM).

Table 9.1 Qualitative summary of the characteristics of different building types.

Building type stiffness density yield strength ductility

Shear wall high high high medium

MRF low low low high

Braced MRF medium low medium high/medium

Wooden house high low high high

Nonductile concrete medium medium low low

URM high high medium low

Building Models

Building as a Rigid Block

Buildings are not rigid blocks! However, it is still instructive to investigate the forces in a rigid block that is subject to ground acceleration. This example has some application if the lowest natural frequency of the structure is high compared to the predominant frequency of the ground acceleration.

If both the building and the ground are considered to by rigid (how do you have earthquakes in a rigid earth?), then there are no waves and the problem can be solved by balancing force as follows. Consider a rigid building of height h , length and width w, and average density be subjected to a horizontal acceleration as shown in Figure 9.17.

Figure 9.17. Forces acting on a rigid rectangular building that is sitting on a rigid earth. There are both shear stresses to horizontally accelerate the building, and also a moment that is applied to the base to keep the building from rotating.

The total momentum of the building can be considered to be the sum of the translation of the center of mass of the building and also the rotational momentum of the building about an axis running through the center of the building. Since the ground is considered as rigid, the building cannot rotate and the translational momentum of the building (translational momemtum, ) is just

where is the momentum in the direction (that’s all there is in this problem). The total horizontal force on the bottom of the building (force = rate of change of momentum) is

Therefore the shear stress on the bottom of the building is just the force divided by the cross sectional area, or

So the shear stress at the bottom of a rigid building on a rigid earth just depends on the ground acceleration and the height of the building (assuming that the density is constant). However, there is more to this simple problem. The shear stress at the bottom of the building would cause the building to rotate if there were no counteracting forces on the base of the building. That is the total moment applied to the base of the building must be zero, or

where we assumed that the normal force on the base of the building consists of the weight of the building plus a moment that keeps the building from rotating. If we assume that the normal stress consists of constant compressional stress from the weight of the building plus another stress that varies linearly with distance along the base then

where is now only a function of time. In this case

Substituting into and performing the integration yields