Risk Management Series Designing for Earthquakes
A Manual for Architects
FEMA 454 / December 2006

EARTHQUAKE EFFECTS ON BUILDINGS BY CHRISTOPHER ARNOLD
4.1 Introduction
This chapter explains how various aspects of earthquake ground motion affect 
structures and also how certain building attributes modify the ways in which the 
building responds to the ground motion. The interaction of these characteristics 
determines the overall seismic performance of the building: whether it is 
undamaged; suffers minor damage; becomes unusable for days, weeks, or months; or 
collapses with great loss of life.   
Explanations of some characteristics of ground motion are followed by 
descriptions of several material, structural, and building attributes that, by 
interacting with ground motion, determine the buildings seismic performancethe 
extent and nature of its damage.
This chapter uses the information on the nature of ground motion in Chapters 2 
and 3, and applies it to structures and buildings. Chapter 5, on seismic issues 
in architectural design, continues the exploration of design and construction 
issues that, in a seismic environment, determine building performance.
4.2 Inertial Forces and Acceleration
The seismic body and surface waves create inertial forces within the building. 
Inertial forces are created within an object when an outside force tries to make 
it move if it is at rest or changes its rate or direction of motion if it is 
moving. Inertial force takes us back to high school physics and to Newton's 
Second Law of Motion, for when a building shakes it is subject to inertial 
forces and must obey this law just as if it were a plane, a ship, or an athlete. 
Newton's Second Law of Motion states that an inertial force, F, equals mass, M, 
multiplied by the acceleration, A. (Figure 4-1)
Mass can be assumed as equivalent (at ground level) to the weight of the 
building, and so this part of the law explains why light buildings, such as wood 
frame houses, tend to perform better in earthquakes than large heavy ones - the 
forces on the building are less.  
The acceleration, or the rate of change of the velocity of the waves setting the 
building in motion, determines the percentage of the building mass or weight 
that must be dealt with as a horizontal force. 
Acceleration is measured in terms of the acceleration due to gravity or g 
(Figure 4-2). One g is the rate of change of velocity of a free falling body in 
space.  This is an additive velocity of 32 feet per second per second.  Thus, at 
the end of the first second, the velocity is 32 feet per second; a second later 
it is 64 feet per second, and so on.  When parachutists or bungee jumpers are in 
free fall, they are experiencing an acceleration of 1g.  A building in an 
earthquake experiences a fraction of a second of g forces in one direction 
before they abruptly change direction. 
Engineering creations (planes, ships, cars, etc.) that are designed for a 
dynamic or moving environment can accommodate very large accelerations.  
Military jet planes, for example, are designed for accelerations of up to 9g.  
At this acceleration, the pilot experiences 9 times the body weight pressing 
down on the organs and blacks out.  
A commercial airliner in fairly severe turbulence may experience about 20 
percent g (or 0.2g), although unbuckled passengers and attendants have been 
known to hit the ceiling as a result of an acceleration drop of over 1g. A 
fast moving train on a rough track may also experience up to about 0.2g.
Poorly constructed buildings begin to suffer damage at about 10 percent g (or 
0.1g).  In a moderate earthquake, the waves of vibration may last for a few 
seconds, and accelerations may be approximately 0.2g. For people on the ground 
or at the bottom of a building, the sensations will be very similar to those of 
the occupants of the plane in turbulence or passengers standing in the fast 
moving train: they feel unsteady and may need to grab onto something to help 
them remain standing.  Earthquakes cause additional alarm because when the 
shaking starts, those experiencing it do not know whether it will quickly end or 
is the beginning of a damaging and dangerous quake.  Short accelerations may, 
for a fraction of a second, exceed 1.0g.  In the Northridge earthquake in 1994, 
a recording station in Tarzana, five miles (8 km) from the epicenter, recorded 
1.92g. 
4.3	Duration, Velocity, and Displacement
Because of the inertial force formula, acceleration is a key factor in 
determining the forces on a building, but a more significant measure is that of 
acceleration combined with duration, which takes into account the impact of 
earthquake forces over time. In general, a number of cycles of moderate 
acceleration, sustained over time, can be much more difficult for a building to 
withstand than a single much larger peak. Continued shaking weakens a building 
structure and reduces its resistance to earthquake damage.  
A useful measure of strong-motion duration is termed the bracketed duration.  
This is the shaking duration above a certain threshold acceleration value, 
commonly taken as 0.05g, and is defined as the time between the first and last 
peaks of motion that exceeds this threshold value. In the San Fernando 
earthquake of 1971, the bracketed duration was only about 6 seconds. In both the 
Loma Prieta and the Northridge earthquakes, the strong motion lasted a little 
over ten seconds, yet caused much destruction. In the 1906 San Francisco 
earthquake, the severe shaking lasted 45 seconds, while in Alaska, in 1964, the 
severe motion lasted for over three minutes.   
Two other measures of wave motion are directly related to acceleration and can 
be mathematically derived from it.  Velocity, which is measured in inches or 
centimeters per second, refers to the rate of motion of the seismic waves as 
they travel through the earth. This is very fast.  Typically, the P wave travels 
at between 3 km/sec and 8 km/sec or 7,000 to 18,000 mph.  The S wave is slower, 
traveling at between 2 km/sec and 5 km/sec, or 4,500 mph to 11,000 mph. 
Displacement refers to the distance that points on the ground are moved from 
their initial locations by the seismic waves. These distances, except 
immediately adjacent to or over the fault rupture, are quite small and are 
measured in inches or centimeters. For example, in the Northridge earthquake, a 
parking structure at Burbank, about 18 miles (29 km) from the epicenter recorded 
displacements at the roof of 1.6 inches (4.0 cm) at an acceleration of 0.47g.  
In the same earthquake, the Olive View hospital in Sylmar, about 7.5 miles (12 
km) from the epicenter, recorded a roof displacement of 13.5 inches (34 cm) at 
an acceleration of 1.50g. 
The velocity of motion on the ground caused by seismic waves is quite slowhuge 
quantities of earth and rock are being moved. The velocity varies from about 2 
cm/sec in a small earthquake to about 60 cm/sec in a major shake. Thus, typical 
building motion is slow and the distances are small, but thousands of tons of 
steel and concrete are wrenched in all directions several times a second.
In earthquakes, the values of ground acceleration, velocity, and displacement 
vary a great deal in relation to the frequency of the wave motion. High
frequency waves (higher than 10 hertz) tend to have high amplitudes of 
acceleration but small amplitudes of displacement, compared to low-frequency 
waves, which have small accelerations and relatively large velocities and 
displacements.
4.4	Ground Amplification
Earthquake shaking is initiated by a fault slippage in the underlying rock. As 
the shaking propagates to the surface, it may be amplified, depending on the 
intensity of shaking, the nature of the rock and, above all, the surface soil 
type and depth.  
A layer of soft soil, measuring from a few feet to a hundred feet or so, may 
result in an amplification factor of from 1.5 to 6 over the rock shaking. This 
amplification is most pronounced at longer periods, and may not be so 
significant at short periods. (Periods are defined and explained in the next 
section, 4.5.1.) The amplification also tends to decrease as the level of 
shaking increases.  
As a result, earthquake damage tends to be more severe in areas of soft ground.  
This characteristic became very clear when the 1906 San Francisco earthquake was 
studied, and maps were drawn that showed building damage in relation to the 
ground conditions. Inspection of records from soft clay sites during the 1989 
Loma Prieta earthquake indicated a maximum amplification of long-period shaking 
of three to six times. Extensive damage was caused to buildings in San 
Francisco's Marina district, which was largely built on filled ground, some of 
it rubble deposited after the 1906 earthquake.
Because of the possibility of considerable shaking amplification related to the 
nature of the ground, seismic codes have some very specific requirements that 
relate to the characteristics of the site. These require the structure to be 
designed for higher force levels if it is located on poor soil. Specially 
designed foundations may also be necessary.
4.5 Period and Resonance
4.5.1 Natural Periods
Another very important characteristic of earthquake waves is their period or 
frequency; that is, whether the waves are quick and abrupt or slow and rolling. 
This phenomenon is particularly important for determining building seismic 
forces.
All objects have a natural or fundamental period; this is the rate at which they 
will move back and forth if they are given a horizontal push (Figure 4-3). In 
fact, without pulling and pushing it back and forth, it is not possible to make 
an object vibrate at anything other than its natural period.  When a child in a 
swing is started with a push, to be effective this shove must be as close as 
possible to the natural period of the swing.  If correctly gauged, a very small 
push will set the swing going nicely.  Similarly, when earthquake motion starts 
a building vibrating, it will tend to sway back and forth at its natural period. 
Period is the time in seconds (or fractions of a second) that is needed to 
complete one cycle of a seismic wave.  Frequency is the inverse of thisthe 
number of cycles that will occur in a secondand is measured in Hertz.  One 
Hertz is one cycle per second. 
Natural periods vary from about 0.05 seconds for a piece of equipment, such as a 
filing cabinet, to about 0.1 seconds for a one-story building.  Period is the 
inverse of frequency, so the cabinet will vibrate at 1 divided by 0.05 = 20 
cycles a second or 20 Hertz.  
A four-story building will sway at about a 0.5 second period, and taller 
buildings between about 10 and 20 stories will swing at periods of about 1 to 2 
seconds.  A large suspension bridge may have a period of around 6 seconds. A 
rule of thumb is that the building period equals the number of stories divided 
by 10; therefore, period is primarily a function of building height.  The 60-
story Citicorp office building in New York has a measured period of 7 seconds; 
give it a push, and it will sway slowly back and forth completing a cycle every 
7 seconds.  Other factors, such as the building's structural system, its 
construction materials, its contents, and its geometric proportions, also affect 
the period, but height is the most important consideration (Figure 4-4).  
The buildings period may also be changed by earthquake damage.  When a 
reinforced concrete structure experiences severe ground shaking, it begins to 
crack: this has the effect of increasing the structures period of vibration: 
the structure is softening.  This may result in the structures period 
approaching that of the ground and experiencing resonance, which may prove fatal 
to an already weakened structure.  The opposite effect may also occur: a steel 
structure may stiffen with repeated cycles of movement until the steel yields 
and deforms.
4.5.2 Ground Motion, Building Resonance, and Response Spectrum
When a vibrating or swinging object is given further pushes that are also at its 
natural period, its vibrations increase dramatically in response to even rather 
small pushes and, in fact, its accelerations may increase as much as four or 
five times.  This phenomenon is called resonance. 
The ground obeys the same physical law and also vibrates at its natural period, 
if set in motion by an earthquake.  The natural period of ground varies from 
about 0.4 seconds to 2 seconds, depending on the nature of the ground. Hard 
ground or rock will experience short period vibration. Very soft ground may have 
a period of up to 2 seconds but, unlike a structure, it cannot sustain longer 
period motions except under certain unusual conditions.  Since this range is 
well within the range of common building periods, it is quite possible that the 
pushes that earthquake ground motion imparts to the building will be at the 
natural period of the building.  This may create resonance, causing the 
structure to encounter accelerations of perhaps 1g when the ground is only 
vibrating with accelerations of 0.2g.  Because of this, buildings suffer the 
greatest damage from ground motion at a frequency close or equal to their own 
natural frequency.
The terrible destruction in Mexico City in the earthquake of 1985 was primarily 
the result of response amplification caused by coincidence of building and 
ground motion periods (Figure 4-5). Mexico City was some 250 miles from the 
earthquake focus, and the earthquake caused the soft ground in margins of the 
old lake bed under the downtown buildings to vibrate for over 90 seconds at its 
long natural period of around 2 seconds. This caused buildings that were between 
about 6 and 20 stories in height to resonate at a similar period, greatly 
increasing the accelerations within them. Taller buildings suffered little 
damage. This amplification in building vibration is very undesirable. The 
possibility of it happening can be reduced by trying to ensure that the building 
period will not coincide with that of the ground. Thus, on soft (long-period) 
ground, it would be best to design a short, stiff (short-period) building.
Taller buildings also will undergo several modes of vibration so that the 
building will wiggle back and forth like a snake (Figure 4-6).
However, later modes of vibration are generally less critical than the natural 
period, although they may be significant in a high-rise building. For low-rise 
buildings, the natural period (which, for common structures, will always be 
relatively short) is the most significant. Note, however, that the low-period, 
low- to mid-rise building is more likely to experience resonance from the more 
common short-period ground motion.  
4.5.3	Site Response Spectrum
From the above, it can be seen that buildings with different periods (or 
frequency responses) will respond in widely differing ways to the same 
earthquake ground motion. Conversely, any building will act differently during 
different earthquakes, so for design purposes it is necessary to represent the 
buildings range of responses to ground motion of different frequency content.  
Such a representation is termed a site response spectrum. A site response 
spectrum is a graph that plots the maximum response values of acceleration, 
velocity, and displacement against period (and frequency). Response spectra are 
very important tools in earthquake engineering.
Figure 4-7 shows a simplified version of a response spectrum. These spectra 
show, on the vertical ordinate, the accelerations, velocities and displacements 
that may be expected at varying periods (the horizontal ordinate). Thus, the 
response spectrum illustrated shows a maximum acceleration response at a period 
of about 0.3 secondsthe fundamental period of a midrise building. This shows 
how building response varies with building period: as the period lengthens, 
accelerations decrease and displacement increases. On the other hand, one- or 
two-story buildings with short periods undergo higher accelerations but smaller 
displacements. 
In general, a more flexible longer period design may be expected to experience 
proportionately lesser accelerations than a stiffer building.A glance at a 
response spectrum will show why this is so: as the period of the building 
lengthens (moving towards the right of the horizontal axis of the spectrum), the 
accelerations reduce. Currently our codes recognize the beneficial aspect of 
flexibility (long period) by permitting lower design coefficients. However, 
there is an exchange, in that the lower accelerations in the more flexible 
design come at the expense of more motion. This increased motion may be such 
that the building may suffer considerable damage to its nonstructural 
components, such as ceilings and partitions, in even a modest earthquake.
Seismic codes provide a very simple standardized response spectrum that is 
suitable for small buildings (Figure 4-8). The code also provides a procedure 
for the engineer to construct a more accurate response spectrum for the 
building, based on various assumptions. For larger buildings in which a 
geotechnical consultant provides information on the site characteristics and an 
estimate of ground motions, detailed response spectra will also be provided to 
assist the engineer in the calculation of forces that the building will 
encounter. 
The response spectrum enables the engineer to identify the resonant frequencies 
at which the building will undergo peak accelerations. Based on this knowledge, 
the building design might be adjusted to ensure that the building period does 
not coincide with the site period of maximum response. For the site 
characteristics shown, with a maximum response at about 0.3 seconds, it would be 
appropriate to design a building with a longer period of 1 second or more. Of 
course, it is not always possible to do this, but the response spectrum shows 
clearly what the possible accelerations at different periods are likely to be, 
and the forces can be estimated more accurately. Information gained from a 
response spectrum is of most value in the design of large and high structures. 
How does one "tune" a building, or change its period, if it is necessary to do 
so? One could change the natural period of a simple structure such as a flag 
pole by any or all combinations of the methods shown in Figure 4-9:
  Changing the position of the weight to a lower height
  Changing the height of the pole
  Changing the sectional area or shape of the pole
  Changing the material
  Altering the fixity of the base anchorage 

There are analogous possibilities for buildings, though the building is much 
more complex than the simple monolithic flagpole:   

	Tune the building by ensuring that the structural characteristics of a 
design are compatible with those of the site as the preliminary design is 
developed. 
	Incorporate devices in the structure that dissipate energy and change the 
response characteristics. These devices are discussed in Chapter 7. 
	After the Mexico City earthquake of 1985, a number of damaged buildings 
had their upper floors removed to lower their period and reduce their mass, thus 
reducing the likelihood and consequences of resonance.  
4.6 Damping 
If a structure is made to vibrate, the amplitude of the vibration will decay 
over time and eventually cease. Damping is a measure of this decay in amplitude, 
and it is due to internal friction and absorbed energy. The nature of the 
structure and its connections affects the damping; a heavy concrete structure 
will provide more damping than a light steel frame.  Architectural features such 
as partitions and exterior faade construction contribute to the damping.  
Damping is measured by reference to a theoretical damping level termed critical 
damping. This is the least amount of damping that will allow the structure to 
return to its original position without any continued vibration. For most 
structures, the amount of damping in the system will vary from between 3 percent 
and 10 percent of critical. The higher values would apply to older buildings 
(such as offices and government buildings) that employed a structure of steel 
columns and beams encased in concrete together with some structural walls, which 
also had many heavy fixed partitions (often concrete block or hollow tile), and 
would have high damping values. The lower values would apply to a modern office 
building with a steel-moment frame, a light metal and glass exterior envelope, 
and open office layouts with a minimum of fixed partitions.  
The main significance of damping is that accelerations created by ground motion 
increase rapidly as the damping value decreases. The response spectra shown in 
Figure 4-10 show that the peak acceleration is about 3.2g for a damping value of 
0 %, 0.8g for a damping value of 2 % and a value of about  0.65g for a value of 
10 %.  
Tables are available that indicate recommended damping values, and the damping 
characteristics of a structure can be fairly easily estimated.  Response spectra 
generally show acceleration values for 0, 2, 5, and 10 % damping. A damping 
value of zero might be used in the design of an simple vibrator, such as a flag 
pole or a water tank supported on a single cantilever column. For typical 
structures, engineers generally use a value of 5 % critical.
Damping used to be regarded as a fixed attribute of buildings, but in recent 
years a number of devices have been produced that enable the engineer to 
increase the damping and reduce the building response.  This greatly increases 
the designers ability to provide a tuned response to the ground motion.  
4.7 Dynamic Amplification
It was early observed and calculated that for most structures, the structural 
movement is greater than that of the ground motion.  The increase of the 
structural movement over that of the ground motion is commonly referred to as 
dynamic amplification.  This amplification is caused when energy is reflected 
from the P and S waves when they reach the earths surface, which is 
consequently affected almost simultaneously by upward and downward moving waves 
(See Chapter 2, Section 2.3.2). The extent of amplification also varies 
depending on the dynamic properties of the structure and the characteristics of 
the initial earthquake ground motion encountered.  The important engineering 
attributes of the structure are:
	The period of vibration of the structure
	The damping properties of the structure 
For typical earthquake motions and for structures having the common damping 
value of 5 percent damping and a period range of 0.5 seconds to 3.3 seconds, the 
dynamic amplification factor would be about 2.5, which is a significant 
increase. For higher damping values, the amplification factor is reduced.
4.8	Higher Forces and Uncalculated Resistance
Even if a building is well damped and is unlikely to resonate, it may be 
subjected to forces that are much higher than the computed forces for which it 
was designed. For those familiar with the assumptions of design for vertical 
loads and the large factors of safety that are added into the calculations, this 
may seem surprising. Why is this so?
The answer is that to design a building for the very rare maximum conceivable 
earthquake forces, and then to add a factor of safety of two or three times as 
is done for vertical loads, would result in a very expensive structure whose 
functional use would be greatly compromised by massive structural members and 
structural walls with very limited openings: the ordinary building would 
resemble a nuclear power plant or a military bunker. 
Experience has shown, however, that many buildings have encountered forces far 
higher than they were designed to resist and yet have survived, sometimes with 
little damage. This phenomenon can be explained by the fact that the analysis of 
forces is not precise and deliberately errs on the conservative side so that the 
building strength is, in reality, greater than the design strength. In addition, 
the building often gains additional strength from components, such as 
partitions, that are not considered in a structural analysis. Some structural 
members may be sized for adequate stiffness rather than for strength, and so 
have considerable reserve strength. Materials often are stronger in reality than 
the engineer assumes in his calculations. Finally, seismically engineered 
structures have an additional characteristic that acts to provide safety in the 
event of encountering forces well beyond the design threshold: this is the 
important property of ductility. Taken together, these characteristics, though 
not all explicit, provide a considerable safety factor or uncalculated 
additional resistance. 
4.9	Ductility
The gap between design capacity (the theoretical ability of a building to 
withstand calculated forces) and possible actual forces is, finally, largely 
dealt with by relying on the material property of ductility. This is the 
property of certain materials (steel in particular) to fail only after 
considerable inelastic deformation has taken place, meaning that the material 
does not return to its original shape after distortion. This deformation, or 
distortion, dissipates the energy of the earthquake.
This is why it is much more difficult to break a metal spoon by bending it than 
one made of plastic. The metal object will remain intact, though distorted, 
after successive bending to and fro while the plastic spoon will snap suddenly 
after a few bends. The metal is far more ductile than the plastic (Figure 4-11).
The deformation of the metal (even in the spoon) absorbs energy and defers 
absolute failure of the structure. The material bends but does not break and so 
continues to resist forces and support loads, although with diminished 
effectiveness. The effect of earthquake motion on a building is rather like that 
of bending a spoon rapidly back and forth: the heavy structure is pushed back 
and forth in a similar way several times a second (depending on its period of 
vibration).
Brittle materials, such as unreinforced masonry or inadequately reinforced 
concrete, fail suddenly, with a minimum of prior distortion. The steel bars 
embedded in reinforced concrete can give this material considerable ductility, 
but heavier and more closely spaced reinforcing bars and special detailing of 
their placement are necessary. 
 Ductility and reserve capacity are closely related: past the elastic limit (the 
point at which forces cause permanent deformation), ductile materials can take 
further loading before complete failure.  In addition, the member proportions, 
end conditions, and connection details will also affect ductility.  Reserve 
capacity is the ability of a complete structure to resist overload, and is 
dependent on the ductility of its individual members.  The only reason for not 
requiring ductility is to provide so much resistance that members would never 
exceed elastic limits.
Thus, buildings are designed in such a way that in the rare case when they are 
subjected to forces higher than those required by a code, the materials and 
connections will distort but not break.  In so doing, they will safely absorb 
the energy of the earthquake vibrations, and the building, although distorted 
and possibly unusable, is at least still standing. 

4.10 Strength, Stiffness, Force Distribution and Stress Concentration	 

4.10.1 Strength and Stiffness	
Strength and stiffness are two of the most important characteristics of any 
structure.  Although these two concepts are present in non-seismic structural 
design and analysis, the distinction between strength and stiffness is perhaps 
most critical, and its study most highly developed, in structural engineering 
for lateral forces.
Sufficient strength is necessary to ensure that a structure can support imposed 
loads without exceeding certain stress values.  Stress refers to the internal 
forces within a material or member that are created as the structural member 
resists the applied load. Stress is expressed in force per unit area (for 
example, pounds per square inch).  
Stiffness is measured by deflection, the extent to which a structural member, 
such as a floor, roof, or wall structure, bends when loaded. Deflection is 
generally expressed as a fraction of length of the member or assembly. For 
gravity loads, this is usually the only aspect of stiffness that is of concern.  
When floor joists are designed for a house, for example, it is often deflection 
rather than strength that dictates the size of the joiststhat is, the depth of 
the joists is determined by how much they will bend under load rather than by 
whether they can safely support the floor loads. Typically, an unacceptable 
amount of bending (in the form of an uncomfortable springy feeling to 
occupants) will occur well before the joists are stressed to the point at which 
they may break because of overload.  
To ensure sufficient strength and stiffness, codes such as the International 
Building Code (IBC) provide stress and deflection limits that are not to be 
exceeded for commonly used materials and assemblies.  For example, interior 
partitions shall be designed to resist all loads to which they are subjected, 
but not less than a force of 5 pounds per square foot applied perpendicular to 
the walls. In addition, the deflection of such walls under a load of 5 pounds 
per square foot shall not exceed 1/240 of the span for walls with brittle 
finishes and 1/120 of the span for walls with flexible finishes.  
Most designers are familiar with deflection in this sense, and have an intuitive 
feel for this quality.  In seismic design, deflection of vertical structural 
members, such as columns and walls, is termed drift. Analogous to the deflection 
of horizontal members, limitations on drift may impose more severe requirements 
on members than the strength requirements. Story drift is expressed as the 
difference of the deflections at the top and bottom of the story under 
consideration: this is also often expressed as a ratio between the deflection 
and the story, or floor-to-floor height (Figure 4-12). Drift limits serve to 
prevent possible damage to interior or exterior walls that are attached to the 
structure and which might be cracked or distorted if the structure deflects too 
much laterally, creating racking forces in the member. Thus the IBC requires 
that drift be limited in typical buildings to between 0.02 and 0.01 times the 
building height, depending on the occupancy of the building. For a building that 
is 30 feet high, drift would be limited to between 3.6 inches and 7.2 inches 
depending on the building type.      
When the earthquake-induced drift is excessive, vertical members may become 
permanently deformed; excessive deformation can lead to structural and 
nonstructural damage and, ultimately, collapse.
  
Thus strength and stiffness are two important characteristics of any structural 
member. Two structural beams may have approximately equal material strengths and 
be of similar shape but will vary in their stiffness and strength, depending on 
how they are oriented relative to the load.This concept can be easily understood 
by visualizing the flexibility of a narrow, deep beam placed where it has to 
support a load: the extent of deflection will depend on whether the load is 
placed on the beams flat surface or on its edge (Figure 4-13).
4.10.2 Force Distribution and Stress Concentration
In seismic design, there is another very important characteristic of stiffness, 
besides that of deflection.  The simple solution of determining the overall 
lateral force on the building by multiplying the building weight by its 
acceleration has already been discussed.  But the engineer needs to know how 
this force is allocated to the various resisting structural elements that must 
be designed: each shares some proportion of this overall force. The answer is 
that the force is distributed in proportion to the relative stiffness of the 
resisting members.  In other terms, the applied forces are attracted to and 
concentrated at the stiffer elements of the building.  Thus the engineer must 
calculate the stiffness of the resisting elements to ascertain the forces that 
they must accommodate.
The relative rigidities of members are a major concern in seismic analysis.  As 
soon as a rigid horizontal element or diaphragm, such as a concrete slab, is 
tied to vertical resisting elements, it will force those elements to deflect the 
same amount.  If two elements (two frames, walls, braces, or any combination) 
are forced to deflect the same amount, and if one is stiffer, that one will take 
more of the load. Only if the stiffnesses are identical can it be assumed that 
they share the load equally.  Since concrete slab floors or roofs will generally 
fit into the "rigid diaphragm" classification, and since it is unusual for all 
walls, frames, or braced frames to be identical, the evaluation of relative 
rigidities is a necessary part of most seismic analysis problems in order to 
determine the relative distribution of the total horizontal force to the various 
resisting elements. 
The reason why forces are related to the stiffness of the resisting elements can 
be understood by visualizing a heavy block supported away from a wall by two 
short beams. Clearly, the thick, stiff beam will carry much more load than the 
slender one, and the same is true if they are turned 90 degrees to simulate the 
lateral force situation (Figure 4-14).
An important aspect of this concept in relation to column lateral stiffness is 
illustrated in Figure 4-15. In this figure the columns have the same cross 
section, but the short column is half the length of the long one. 
Mathematically, the stiffness of a column varies approximately as the cube of 
its length. Therefore, the short column will be eight times stiffer instead of 
twice as stiff and will be subject to eight times the horizontal load of the 
long column. Stress is concentrated in the short column, while the long column 
is subject to nominal forces.  
In a building with members of varying stiffness, an undue proportion of the 
overall forces may be concentrated at a few points of the building, such as a 
particular set of beams, columns, or walls, as shown at the top of Figure 4-15. 
These few members may fail and, by a chain reaction, bring down the whole 
building. People who are in the building demolition business know that if they 
weaken a few key columns or connections in a building, they can bring it down. 
An earthquake also tends to "find" these weak links. 
This condition has serious implications for buildings with column or shear walls 
of different length.  In designing a structure, the engineer tries to equalize 
the stiffness of the resisting elements so that no one member or small group of 
members takes a disproportionate amount of the load.  If this cannot be done - 
if their size and stiffness vary for architectural reasons, for example -- then 
the designer must make sure that stiffer members are appropriately designed to 
carry their proportion of the load.
A special case of this problem is that sometimes a short-column condition is 
created inadvertently after the building is occupied.  For example, the space 
between columns may be filled in by a rigid wall, leaving a short space for a 
clerestory window. Such a simple act of remodeling may not seem to require 
engineering analysis, and a contractor may be hired to do the work: often such 
work is not subject to building department reviews and inspection.  Serious 
damage has occurred to buildings in earthquakes because of this oversight 
(Figure 4-16).
4.11 Torsional Forces
The center of mass, or center of gravity, of an object is the point at which it 
could be exactly balanced without any rotation resulting.  If the mass (or 
weight) of a building is uniformly distributed (in plan), the result is that the 
plan's geometric center will coincide with the center of mass.  In a building, 
the main lateral force is contributed by the weight of the floors, walls, and 
roof, and this force is exerted through the center of mass, usually the 
geometric center of the floor (in plan). If the mass within a floor is uniformly 
distributed, then the resultant force of the horizontal acceleration of all its 
particles is exerted through the floor's geometric center.  If the resultant 
force of the resistance (provided by shear walls, moment frames, or braced 
frames) pushes back through this point, dynamic balance is maintained. 
Torsional forces are created in a building by a lack of balance between the 
location of the resisting elements and the arrangement of the building mass.  
Engineers refer to this as eccentricity between the center of mass and the 
center of resistance, which makes a building subjected to ground motion rotate 
around its center of resistance, creating torsion - a twisting action in plan, 
which results in undesirable and possibly dangerous concentrations of stress  
(Figure 4-17).
In a building in which the mass is approximately evenly distributed in plan 
(typical of a symmetrical building with uniform floor, wall and column masses) 
the ideal arrangement is that the earthquake resistant elements should be 
symmetrically placed, in all directions, so that no matter in which direction 
the floors are pushed, the structure pushes back with a balanced stiffness that 
prevents rotation from trying to occur. This is the reason why it is recommended 
that buildings in areas of seismic risk be designed to be as symmetrical as 
possible. In practice, some degree of torsion is always present, and the 
building code makes provision for this.
4.12 Nonstructural Components
For many decades, seismic building codes focused exclusively on the structure of 
the buildingthat is, the system of columns, beams, walls, and diaphragms that 
provides resistance against earthquake forces.  Although this focus remains 
dominant for obvious reasons, experience in more recent earthquakes has shown 
that damage to nonstructural components is also of great concern. In most modern 
buildings, the nonstructural components account for 60 to 80 percent of the 
value of the building (Figure 4-18). Most nonstructural components are fragile 
(compared to the building structure), easily damaged, and costly to repair or 
replace (Figure 4-19).
The distinction between structural and nonstructural components and systems is, 
in many instances, artificial. The engineer labels as nonstructural all those 
components that are not designed as part of the seismic lateral force-resisting 
system. Nature, however, makes no such distinction, and tests the whole 
building. Many nonstructural components may be called upon to resist forces even 
though not designed to do so.
The nonstructural components or systems may modify the structural response in 
ways detrimental to the safety of the building. Examples are the placing of 
heavy nonstructural partitions in locations that result in severe torsion and 
stress concentration, or the placement of nonstructural partitions between 
columns in such a way as to produce a short column condition, as described in 
Section 4.10 and illustrated in Figure 4-16. This can lead to column failure, 
distortion, and further nonstructural damage. Failure of the fire protection 
system, because of damage to the sprinkler system, may leave the building 
vulnerable to post-earthquake fires caused by electrical or gas system damage.
4.13 Construction Quality
One other characteristic that applies to any structure may be obvious, but must 
be emphasized:  the entire structural system must be correctly constructed if it 
is to perform well. Lateral forces are especially demanding because they 
actively attempt to tear the building apart, whereas vertical loads (with the 
exception of unusual live loads such as automobiles or large masses of people) 
sit still and quiet within the materials of the building. 
The materials of the seismically resistant structure must have the necessary 
basic strength and expected properties, but most importantly, all the structural 
components must be securely connected together so that as they push and pull 
against one another during the earthquake, the connections are strong enough to 
transfer the earthquake forces and thereby maintain the integrity of the 
structure.This means that detailed design and construction of connections are 
particularly important. 
The correct installation of reinforcing steel and anchors in concrete 
structures; the correct design, fabrication and installation of connection 
members in steel structures; and correct nailing, edge clearances and 
installation of hold-downs in wood framing are all critical. For nonstructural 
components, critical issues are the maintenance of correct clearances between 
precast concrete cladding panels, at seismic separation joints, and between 
glazing and window framing, and the correct design and installation of bracing 
of heavy acceleration-sensitive components such as tanks, chillers, heavy 
piping, electrical transformers and switch gear. 
Quality control procedures must be enforced at all phases of design and 
construction, including material testing and on-site inspection by qualified 
personnel. The earthquake is the ultimate testing laboratory of the construction 
quality of the building.
4.14 CONCLUSION	
This chapter has discussed a number of key characteristics of earthquake ground 
shaking that affect the seismic performance of buildings.  In addition, a number 
of building characteristics have been reviewed that, together with those of the 
ground, determine the buildings seismic performance: how much damage the 
building will suffer.  These characteristics are common to all buildings, both 
new and existing, and all locations.  
The building response to earthquake shaking occurs over the time of a few 
seconds. During this time, the several types of seismic waves are combining to 
shake the building in ways that are different in detail for each earthquake. In 
addition, as the result of variations in fault slippage, differing rock through 
which the waves pass, and the different geological nature of each site, the 
resultant shaking at each site is different.  The characteristics of each 
building are different, whether in size, configuration, material, structural 
system, method of analysis, age, or quality of construction: each of these 
characteristics affects the building response.  
In spite of the complexity of the interactions between the building and the 
ground during the few seconds of shaking there is broad understanding of how 
different building types will perform under different shaking conditions.  This 
understanding comes from extensive observation of buildings in earthquakes all 
over the world, together with analytical and experimental research at many 
universities and research centers. 
Understanding the ground and building characteristics discussed in this chapter 
is essential to give designers a feel for how their building will react to 
shaking, which is necessary to guide the conceptual design of their building.  
The next chapter continues this direction by focusing on certain architectural 
characteristics that influence seismic performance - either in a positive or 
negative way.  
4.15 References 
Building Seismic Safety Council, NEHRP Recommended Provisions for Seismic 
Regulations for New Buildings and Other Structures, Part 2 Commentary, FEMA 450,  
2003, Washington, DC.
International Code Council, International Building Code 2003 (IBC), Birmingham, 
AL.
Stratta, James, Manual of Seismic Design,1987, Prentice-Hall, Englewood Cliffs, 
NJ

4.16	to find out more
MCEER, Center for Earthquake Engineering Research.  mceer@buffalo.edu
Bolt, B. A., Earthquakes (4th edition) W. H. Freeman and Company New York N. Y. 
2002.
Gere J. M. and Shah, H.C.,1984 Terra non Firma, Stanford Alumni Association, 
Stanford CA. 
Levy M. and Salvadori M.,Why Buildings Stand Up, W. W. Norton and Company, New 
York, NY. 1990.
Levy M. and Salvadori M.,Why the Earth Quakes, W. W. Norton and Company, New 
York, NY. 1997.
Levy M. and Salvadori M.,Why Buildings Fall Down, W. W. Norton and Company, New 
York, NY 2002.

[End of Chapter 4]