nisee National Information Service for Earthquake Engineering University of California, Berkeley

### The Nature of Ground Motion and Its Effect on Buildings

#### By Christopher Arnold, A.I.A.

Note: This presentation, which draws on materials from the author's book "Building Configuration and Seismic Design," by Christopher Arnold and Robert Reitherman, published by John Wiley (New York, 1982), is based on a paper given at an architects' workshop in Seattle, Washington in 1985 sponsored by the National Science Foundation and FEMA called "Designing for Earthquakes in the Pacific Coast States." It is used here in a slightly shorter format by permission of the author.

### I. Ground Motion

#### A. The Nature of Ground Motion

If one could hover motionless during an earthquake over a marked spot on the earth it might be seen to move erratically, tracing out a random path resembling that of the wandering of an insect. "Ground motion" is a literal description; the ground moves, to a maximum distance of about a foot, relative to its stationary starting point.:

In 1887 Prof. Sekiya of Japan modeled in a three-dimensional wire diagram, the motion of a point in the earth during the first 20 seconds of an earthquake (Figure 1). This was based on the seismogram of the Japanese earth-quake on January 15, 1887. The model is made to scale about twelve and a half times greater than the actual earth movement. The actual amount of motion was about 0.29 inch. It is important to consider the small size of characteristic earth motion, and to realize that it is the building reaction to this movement that causes the large structural displacements that ultimately lead to damage and failure.

Occasionally, the ground motion is predominantly back and forth in one general direction (such as in the 1978 Sendai or 1963 Skopje earthquakes) or is composed of a single shock, (as in the 1960 Agadir event) but this cannot be predicted.

The fact that ground motion is commonly more emphatic along some axes rather than others, was understood very early in history. John Milne, one of the European scientists in Japan in the last half of the 1800s who helped lay the groundwork for Japan's subsequent prominence in seismic research, found a contemporary account of an ancient (136 A.D.) Chinese seismoscope, which elegantly illustrates the point that inertial forces may be exerted in any direction.

"When an earthquake occurs, and the bottle is shaken, the dragon instantly drops the ball ... With this arrangement, although one dragon may drop the ball, it is not necessary for the other seven dragons to drop their balls unless the movement has been in all directions; thus we can easily tell the direction of an earthquake."

Earthquakes are the result of slippage along a fault plane, often well below the surface of the earth. Geologists have various methods of determining the presence of fault planes and their characteristics. The presence of a fault indicates the possibility of an earthquake, though determination of its likelihood and size is still a very uncertain science.

Slippage along a fault line deep in the earth's surface may eventually result in "surface faulting," the crack or split on the earth's surface that provides the layman's vision of earthquakes. Surface faulting may result in large earth movements - perhaps several yards - and a building located across a surface fault is almost certain to suffer very severe damage however well it is designed. However, the probability of a building location straddling a line of surface rupture is relatively low compared to the probability of a building location that will be affected by ground motion caused by fault slippage.

The epicenter is the point on the earth's surface directly above where the faulting and energy release first begins. Since the faulting plane is not necessarily exactly vertical, and since the fault may rupture along a considerable distance, shaking at the epicenter may not be the most intense, although it will almost certainly be among the more heavily shaken areas in a given earthquake.

The ground motion that is transmitted through the base of a building, then, has a random form, but sometimes an emphatic direction. The motion originates in four clearly defined types of waves created by a fault rupture (Figure 4). These are the primary, or P wave, which is the fastest, traveling at about 8km. per second, or 18,000 mph., and arrives first. It has the form of a sound wave that, as it spreads out, alternately pushes and pulls at the ground material. The second type of wave is the secondary or S wave; this shears the rock sideways at right angles to the direction of travel. The third type is a surface wave called the Love wave, that is similar to a secondary (S) wave with no vertical displacement; it moves the ground from side to side horizontally parallel to the earth's surface, at right angles to the direction of propagation, and produces horizontal shaking. The fourth type of wave, also a surface wave, is known as the Rayleigh wave; in this the disturbed material moves both vertically and horizontally in a vertical plane pointing in the direction in which the waves are traveling. Of the two surface waves, Love waves generally travel faster than Rayleigh.

The nature of the ground motion that affects the building can be summarized in a conceptual way as follows. The waves that create motion emanate from the line of fault rupture, and so approach the building from a given direction. The nature of the waves and their interactions is such that actual movement at the ground will be random: predominantly horizontal, often with some directional emphasis, and sometimes with a considerable vertical component. The actual horizontal ground displacement is small, generally measured in fractions of an inch, except in the immediate area of the fault rupture where displacements of several feet may occur.

The other threatening type of movement of the ground is the family of geologic hazards. Liquefaction is a condition in which the soil changes temporarily from a solid to a liquid state. This effect is related to loose granular soils and sand and the presence of water, and hence tends to apply to sites located adjoining rivers, lakes, and bays. Engineering to mitigate the effects of liquefaction involves foundation design, or stabilization of the soil itself. Because of the uncertainties and costs of such measures, avoidance of sites with a potential for liquefaction represents the best design approach.

Landslides, or ground disturbance, can be triggered by earthquake ground motion. Tsunami ("tidal waves") are earthquake-caused wave movements in the ocean, and seiches are similar sloshing in closed lakes or bays.

#### B. The Measurement of Ground Motion

Ground motion is recorded by a seismograph, an instrument only in existence since the late nineteenth century. The Chinese seismoscope mentioned earlier showed only the principal direction of the earthquake, and did not record its history. The seismograph records the movement over time of a freely supported pendulum within a frame that is attached to the ground.

In modern seismographs, pendulum movement is converted into electronic signals on tape. Strong-motion seismographs, called accelerographs, are designed to record nearby rather than distant ground movement directly, and produce a record called an accelerogram (or seismogram). Instruments are normally placed so as to measure movements along the two horizontal axes and the one vertical. Three measures are of major interest: acceleration, velocity, and displacement. Acceleration is the rate of change of velocity: when multiplied by mass it results in the inertial force which the building must resist. Acceleration is commonly measured in g - the acceleration of a free falling body due to earth's gravity (approx. 32 ft/sec/sec., or 980 cm/sec/sec., or 980 gals, or 1.0g).

Velocity, measured in inches or centimeters per second, refers to the rate of ground motion. Displacement, measured in inches or centimeters, refers to the distance a particle is removed from its at rest position.

The accelerogram provides a picture of the ground shaking; accurate interpretation of this picture requires skill and experience. In the accelerogram the arrival of the P wave begins the motion. This is followed by the S wave: the time interval between the two enables the distance from the instrument to the earthquake focus to be calculated. The duration of strong motion shows clearly, and the maximum wave amplitude can be measured directly. The ground acceleration can be calculated by relating amplitude to time. Velocity and displacement are obtained mathematically by integrating the acceleration record once and twice respectively.

The level of acceleration generally taken as sufficient to produce some damage to weak construction is 0.1g. The lower limit of acceleration perceptible to people is set by observation and experiment at approximately 0.00lg or l cm/sec. squared at between 0.1g and 0.2g most people will have difficulty keeping their footing and sickness symptoms may be induced.

An acceleration approaching 0.50g on the ground is very high. On upper floors of buildings, maximum accelerations will be higher, depending on the degree to which the mass and form of the building acts to damp the vibratory effects. A figure of 1.00g may be reached, or 100% of gravity; diagrammatically equivalent, in a static sense, to trying to design a building that projects horizontally from a vertical surface (Figure 6). (When the behavior of real buildings is observed, it is seen that several factors modify this diagrammatic equivalence, and structures which could never cantilever from a vertical surface, can briefly withstand 1.0g earthquake shaking).

The measure of acceleration is commonly used to indicate the possible destructive power of an earthquake in relation to a building. A more significant measure is that of acceleration combined with duration. This is not hard to visualize intuitively, and it is important to understand that a number of cycles of moderate acceleration may be much more difficult to withstand than a single peak of much higher value. As will be discussed later, frequency is another major parameter of ground motion for design purposes. The instrumentation will also provide a measure of the duration of the strong motion.

The duration is thought to relate to the length of the fault break, and typically will occupy only a few seconds. The 1971 San Fernando earthquake only lasted a little over ten seconds, yet created much destruction. In 1906, San Francisco, the severe shaking lasted about 45 seconds; in Alaska in 1964 the earthquake was over 3 minutes. The record of the 1940 El Centro, California earthquake, for many years the best record available, showed strong motion continuing for approximately 25 seconds, with the major accelerations occurring for approximately 5 seconds. This earthquake recorded a maximum acceleration of 0.32g, a maximum ground velocity of 13.7 in./sec/ and a maximum ground displacement of 9.3 inches.

For building design, we are interested in a number of aspects of the measurement of earthquakes. We need a way of comparing one historic earthquake to another. We need to be able to estimate the characteristics of probable ground shaking of a future earthquake, and to be able to relate it to a known historic event so that, by analogy, we can estimate forces and damage. Two earthquake measurement systems are in common use: neither, for various reasons, is really satisfactory to us from the building-design viewpoint.

Earthquake magnitude is the first measure: it is expressed as a Richter Magnitude based on the scale devised by Prof. Charles Richter of California Institute of Technology in 1935. Richter selected the term magnitude by analogy with the corresponding astronomical usage for an absolute scale of star brightness independent of the location of the recording station. Richter's scale is based on the maximum amplitude of certain seismic waves recorded on a standard seismograph at a distance of 100 kilometers from the earthquake epicenter. Note that the scale tells us nothing about duration or frequency, which may be of great significance in causing damage.

Because, of course, the instrument will seldom be exactly 100km from the source, Richter developed a method for allowing for the diminishing of the wave amplitude record with increase of distance (just as the light of a star appears dimmer with distance). This method is shown graphically in Figure 8.

Because the size of earthquakes varies enormously, the graphic range of wave amplitude measured on seismograms is compressed by using as a scale the logarithm to base ten of the recorded wave amplitude. Hence each unit of magnitude indicates a 10 times increase in wave amplitude. But the energy increase represented by each unit is estimated by seismologists as approximately 31 times. Thus the amplitude of an 8.3 magnitude earthquake is 10,000 times that of an 4.3 shock, but its energy release is approximately 1,000,000 times.

The actual energy released by an earthquake is not a significant measure in relation to building reaction. It is of parenthetical interest to realize, however, that the energy release of earthquakes is very large indeed. It is estimated that the total energy released by earthquakes each year throughout the world is between 10 superscript 25 and 10 superscript 26 ergs. This is approximately equivalent to the present total yearly consumption of energy for all purposes in the United States.

The Richter scale has no fixed maximum, but about 9 is the greatest ever recorded. An earthquake of magnitude 2 on the scale is the smallest normally felt by humans; an event with a magnitude of 7 or more is commonly considered to be major. While the Richter scale accomplishes the goal of enabling us to make an objective comparison between earthquakes, it tells little about the local effects. It can also be an inadequate measure of the size of large earthquakes, in terms of the extent of geographical area affected.

To provide information directly related to local shaking and building damage, several intensity scales are in use. In the United States the commonly used scale is the Modified Mercalli (MM), originally proposed in Europe in 1902, modified in 1931 by Wood and Neuman, to fit construction conditions then prevalent in California and the United States. The MM Scale is based on subjective observation of the effects of the earthquake on buildings, ground, and people. Because these effects will be different depending on distance from the epicenter, nature of the ground etc., one earthquake will have many MM values. An abridged version of the MM Scale, developed by Richter in 1956, is shown below:

 The Abridged Modified Mercalli (MM) Intensity Scale (1956 version) Not felt. Marginal and long-period effects of large earthquakes. Felt by persons at rest, an upper floors, or favorably placed. Felt indoors. Hanging objects swing. Vibration like passing of light trucks. Duration estimated. May not be recognized as an earthquake. Hanging objects swing. Vibration like passing of heavy trucks; or sensation of a jolt like a heavy ball striking the walls. Standing cars rock. Windows, dishes, doors rattle. Glasses clink. Crockery clashes. In the upper range of IV, wooden walls and frames creak. Felt outdoors; direction estimated. Sleepers wakened. Liquids disturbed, some spilled. Small unstable objects displaced or upset. Doors swing, close, open. Shutters, pictures move. Pendulum clocks stop, start, change rate. Felt by all. Many frightened and run outdoors. Persons walk unsteadily. Windows, dishes, glassware broken. Knicknacks, books, etc. off shelves. Pictures off walls. Furniture moved or overturned. Weak plaster and masonry D cracked. Small bells ring (church, school). Trees, bushes shaken visibly, or heard to rustle. Difficult to stand. Noticed by drivers. Hanging objects quiver. Furniture broken. Damage to masonry D, including cracks. Weak chimneys broken at roof line. Fall of plaster, loose bricks, stones, tiles, cornices, also unbraced parapets and architectural ornaments. Some cracks in masonry C. Waves on ponds, water turbid with mud. Small slides and caving in along sand or gravel banks. Large bells ring. Concrete irrigation ditches damaged. Steering of cars affected. Damage to masonry C; partial collapse. Some damage to masonry B; none to masonry A. Fall of stucco and some masonry walls. Twisting. fall of chimneys, factory stacks, monuments, towers, elevated tanks. Frame houses moved on foundations if not bolted down; loose panel walls thrown out. Decayed piling broken off. Branches broken from trees. Changes in flow or temperature of springs or wells. Cracks in wet ground and on steep slopes. General panic. Masonry D destroyed; masonry C heavily damaged, sometimes with complete collapse; masonry B seriously damaged. General damage to foundations. Frame structures, if not bolted. shifted off foundations. Frames racked. Serious damage to reservoirs. Underground pipes broken. Conspicuous cracks in ground. In alluviated areas sand and mud ejected, earthquake fountains, sand craters. Most masonry and frame structures destroyed with their foundations. Some well-built wooden structures and bridges destroyed. Serious damage to dams, dikes, embankments. Large landslides. Water thrown on banks of canals, rivers, lakes, etc. Sand and mud shifted horizontally on beaches and flat land. Rails bent slightly. Rails bent greatly. Underground pipelines completely out of service. Damage nearly total. Large rock masses displaced. Lines of sight and level dis-torted. Objects thrown into the air. Masonry A. Good workmanship, mortar, and design; reinforced especially laterally, and bound together by using steel, concrete, etc.; designed to resist lateral forces. Masonry B. Good workmanship and mortar; reinforced. but not designed in detail to resist lateral forces. Masonry C. Ordinary workmanship and mortar, no extreme weaknesses like failing to tie at corners, but neither reinforced nor designed against horizontal forces. Masonry D. Weak materials, such as adobe; poor mortar; low standards of workmanship; weak horizontally.

Charles Richter has explained that:

"Magnitude can be compared to the power output in kilowatts of broadcasting station. Local intensity on the Mercalli scale is then comparable to the signal strength on a receiver at a given locality; in effect the quality of the signal. Intensity like signal strength will generally fall off with distance from the source, although it also depends on the local conditions and the pathway from the source to the point."

The MM Scale has been roughly correlated with ground acceleration, for example MM VII corresponds to a peak acceleration of between approximately 0.1g and 0.29g; MM IX corresponds to peak acceleration exceeding 0.50g. Similar twelve point scales are in use in China and Russia and Japan uses a comparable seven point damage intesity scale called the JMA Scale.

### II. Building Reaction to Ground Motion

#### A. Inertial Forces

Ground motion does not damage a building by impact similar to that of the wrecker's ball, or by externally applied pressure as by wind, but rather by internally generated inertial forces caused by vibration of the building's mass. The building's mass, size, and shape - its configuration - partially determine these forces and also partially determine how well they will be resisted.

Inertial forces are the product of mass and acceleration (Newton's F = m x a). Acceleration is the change of velocity (or speed in a certain direction) over time and is a function of the nature of the earthquake; mass is an attribute of the building. Since the forces are inertial, an increase in the mass generally results in an increase in the force. Hence the immediate virtue of the use of lightweight construction as a seismic design approach.

The other detrimental aspect of mass, besides its role in increasing the lateral loads, is that failure of vertical elements such as columns and walls can occur by buckling when the mass pushing down due to gravity exerts its force on a member bent or moved out of plumb by the lateral forces. This phenomenon is known as the P-e, or P-Delta effect (Figure 11). The greater the vertical force, the greater the moment due to the product of the force, P, and the eccentricity, e (or Delta).

Although buildings generally have large vertical load carrying reserves due to code gravity load requirements, this safety factor does not necessarily mitigate the P-e problem, which can induce bending in columns

Earthquakes shake the ground in a variety of directions - including up and down components. Historically, codes generally treated these vertical earthquake forces lightly, although they may be two-thirds as great as the lateral earthquake forces, and "seismic design" and "design for lateral forces" are not really synonymous terms.

It is vertical loads that almost always cause buildings to collapse in earthquakes; however, in earthquakes buildings generally fall down, not over. The lateral forces use up the strength of the structure by bending and shearing columns, beams, and walls, and then gravity pulls the weakened and distorted structure down.

#### B. Period and Resonance

If one shook a flag pole with a heavy weight on top in the attempt to break it, one would quickly learn to synchronize one's pushes and pulls with the pole's natural tendency to vibrate back and forth at a certain rate - its fundamental period. If it tends to swing back and forth one complete cycle once a second when "plucked" and allowed to vibrate, it has a fundamental period of one second. If we can predict approximately the rate at which the ground will shake, which is similar to controlling the rate at which one shakes the base of the pole by hand, we could adjust the rate at which the pole will naturally vibrate so that the two either will or will not coincide. If they coincide, then the dimensions of the swing will start to increase, the pole will be said to resonate, and the loads on it will increase.

Ground motion will impart vibrations to a building of a similar nature to our shaking of the flag pole. The fundamental periods of structures may range from about 0.05 second for a well anchored piece of equipment, 0.1 for a one story simple bent or frame, 0.5 for a low structure up to about 4 stories, and between 1-2 seconds for a tall building from 10-20 stories. A water tank on an offshore drilling rig will be between 2.5 - 6, and a large suspension bridge may have a period of about 6 seconds.

Natural periods of soil are usually in the range of 0.5 - 1 second, so that it is possible for the building and ground to have the same fundamental period and therefore there is a high probability for the building to approach a state of partial resonance (quasi-resonance). Hence in developing a design strategy for a building, it is desirable to estimate the fundamental periods both of the building and of the site so that a comparison can be made to see if the probability of quasi-resonance exists. If the initial study shows this to be the case, then it would be advisable to change the resonance characteristics of the building (for the site characteristics are fixed) by methods that will be discussed later.

The natural periods of different types of ground are estimated by methods calling for a great deal of judgment, based on experience in previously recorded earthquakes on sites of like-or supposedly like-ground characteristics. These estimates are expressed by use of a response spectrum, which provides a useful illustration of the expected behavior of the site.

The principle of the response spectrum can be visualized as follows. Figure 13 shows a series of cantilever pendulums (similar to our flag pole) whose periods lengthen towards the right hand side. If these are imagined as attached to a movable base, and the base is agitated to represent the strong motion of an earthquake as recorded on a seismograph, the maximum response of each pendulum can be recorded - that is, the time and particular frequency during the earthquake at which each pendulum will tend to resonate, with vibration of maximum amplitude. These maximum responses can be plotted against the periods of the pendulum, and will provide a curve, or response spectrum, that relates the nature of the ground motion to a range of natural periods. Note that every site will also show a different response spectrum for each earthquake-in terms of magnitude, type of ground motion, and distance of the fault slippage from the site-that is plotted. A typical curve will appear as in Figure 14; the horizontal ordinate represents T, or periods, and the vertical ordinate generally represents equivalent acceleration.

In relating the estimated period of a new building to that of a site, curves will be drawn for the site that represent a range of responses; these will show the periods at which a maximum response is likely: part of the seismic design problem, then, is to "tune" the building in such a way that its own period is outside the range of probable site periods, and the possibility of forced amplification by resonance is reduced or eliminated.

How does one "tune" the building in this way? In the case of the simple flag pole paradigm, the pole's period might be altered by any or all combinations of the following: changing the position of the weight to some lower height; changing the height of the pole; changing the sectional area or shape of the pole; changing its 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 flag pole. A structure can have more than one period, even if all factors remain constant. There are higher modes of vibration in which the structure will experience increasingly snake-like deflections, rather than just bending back and forth. Though the first mode, simple to and fro motion, is generally the significant period of structural interest, higher modes can be important for tall slender buildings.

In general, a more flexible, longer period design may be expected to experience lesser forces, proportionately, than a stiffer building if the site is composed of bedrock which will efficiently transmit short period vibrations while filtering out longer-period motions. By contrast, since it is difficult for a layer of soft alluvium several hundred feet deep to vibrate rapidly, even though the input motion from the bedrock beneath it may be high frequency, a stiffer building may have much less response than one with a longer period.

It is generally true that locations closer to the fault from where the energy is released will experience higher frequencies of ground motion, and at large distances the motions will probably be of lower frequency type which eye witnesses will call rolling, slowly rocking, swaying, etc.

Another related concept needs to be understood: this is the characteristic of damping, which affects the dynamic behavior of the building, and modifies its response to ground motion.

#### C. Damping

If a building resonates in response to ground motion, its acceleration is amplified - just as the response of certain types of soils may amplify the ground motion. This amplification can be very great: for a pendulum the amplification might be fifty fold, an increase which, for a building, would result in disastrously large forces. However, buildings are prevented from resonating with the purity of a pendulum, because they are damped: that is, they are rather inefficient in their vibration, and when set in motion tend to return to their starting position quickly. The extent of damping in a building depends on its connections, nonstructural elements and construction materials, and we make assumptions about our designs based on knowledge of previous structures.

Critical damping refers to the amount of damping which will prevent oscillation from taking place-i.e. a pendulum will simply return to the center when plucked-and damping is measured as a percentage of critical damping. This is an arbitrary assumption because we have no rational approach to the theory of damping, and even the empirical data are less than quantitatively consistent. It is thus useful to modify the ground response spectrum by assuming percentages of damping that represent reasonable figures for buildings - generally of the order of 2% to 15% of critical, with figures at the low end of this scale most commonly used in design.

When damping is introduced, the general shape of the response curve remains the same, but the magnitudes are greatly reduced. Although damping is theoretically subject to alteration, in practice it is not generally regarded as a design variable.

Currently our codes recognize the beneficial aspect of flexibility (long period) by permitting lower design coefficients. However, the amount of motion experienced by these structures means that they may suffer much greater damage to their nonstructural components.

#### D. Ductility

Even if resonance is avoided, and the building is well damped, analysis will show that structures will be subject to forces that are much higher than those for which, under the building code, we will design. The code's equivalent static force formula method will produce a design lateral force of about 5 % to 20% of the building's mass in high seismic zones, or a theoretical design acceleration of 5% to 20% of gravity (.05 to .2g). Real earthquakes have produced accelerations considerably in excess of this amount but, the fact that, under these conditions, our structures are adequately safe can be partly explained by the material property called ductility. This is the property of certain materials - steel in particular - to fail only after considerable inelastic deformation has occurred. Inelastic deformation is that in which the material does not return to its original shape after distortion. Brittle materials, however, such as concrete can fail suddenly with a minimum of deformation. Note however, that the steel contained in reinforced concrete can give this material considerable ductility also. The act of deformation absorbs energy and defers absolute failure of the concrete.

Ductility and reserve capacity are closely related: past the elastic limit (the point at which loads cause permanent deformation), ductile materials can take further loading before completely rupturing. 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 not exceed elastic limits.

#### E. Torsion

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. Uniformly distributed mass results in the coincidence of a plan's geometric center with the center of mass. An eccentric distribution of mass locates the center of mass away from the geometric center. This means that since every particle of mass of an object is attracted by gravity toward the center of the earth's mass ("down"), the opposite force exerted upward to counteract this force or "weight" must be precisely located under the object's center of mass to make the object balance without any net moment: the tipping moments along all axes must cancel out.

When the particles of mass are accelerated horizontally due to earthquake inertia forces, the same balancing principles apply. Earthquakes create inertia forces which can be likened to a random, pulsating, horizontal equivalent of gravity: every particle of mass is accelerated laterally (and sometimes vertically as well). If the mass within a floor is uniformly distributed, then the resultant force of the horizontal acceleration of all of its particles of mass is exerted through the floor's center. If the resultant of the resistance (provided by walls or frames) pushes back through this point, and hence meets the resultant of the loads head on, translational dynamic balance is maintained. Otherwise, horizontal rotation, or torsion, would result. If the mass is eccentrically disposed, the earthquake load will be eccentric as well since the earthquake only generated a load because of the presence of mass, and the amount of load is directly proportional to the amount of mass. If the load is eccentric, then the resistance must also be eccentric so that the location of the center of mass and the center of horizontal resistance are at the same point, and torsion is avoided. Figure 22 shows the torsional effects created in a simple building configuration. Torsion is occurring because a uniformly distributed lateral force is not resisted by a uniformly distributed lateral resistance.

In a building in which the mass is approximately evenly distributed in plan -which would be typical of a symmetrical plan 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 what direction the floors are pushed, the structure pushes back with a balanced stiffness which prevents rotation from trying to occur. Hence the general rule is usually stated that symmetry is a valuable configuration characteristic; however, this admonition is a somewhat simplistic directive, as is discussed later.

#### F. Strength and Stiffness

Strength and stiffness are two of the most important characteristics of any structure. However, although these two concepts are present in structural design and analysis, the distinction between strength and stiffness is perhaps most critical and its study most highly developed in structural engineering as applied to the earthquake problem.

One measure of stiffness is deflection, and for vertical gravity loads is, in most cases, the only aspect of stiffness which is of concern. In the sizing of floor joists, deflection rather than strength often governs. The analogous lateral force condition is when limitation on drift, the horizontal story-to-story deflection, impose more severe requirements on members than the strength requirements (Figure 23). The strength problem is how to resist a given load without exceeding a certain stress; the stiffness or horizontal deflection problem is how to prevent the structure from moving out of alignment more than a given amount. In the design of a floor system, the joists may tolerate a certain deflection but the ceiling finish cannot; similarly drift must be limited, even if the structure can tolerate more, because of its effect on nonstructural components, particularly partition, skin and ceiling elements, and on the comfort of occupants. Excessive horizontal deflection can also cause loads to be applied eccentrically to their columns, discussed earlier as the P-e effect.

The Uniform Building Code prohibits drift from exceeding 1/2% (or .005) of the story height (under the design forces, with a multiplier to correct for safety factors). This would be 1" for a 16'-8" high story.

The relative rigidities of members is occasionally of concern for gravity loads, but it is 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 construction 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 problem.

#### G. Resistant Systems

In designing to resist seismic forces, the structural engineer uses a small vocabulary of components which are combined to form a complete resistance system.

In the vertical plane three kinds of components resist lateral forces: shear walls, braced frames, and moment resisting frames (sometimes called 'rigid frames'). In the horizontal plane diaphragms are used, generally formed by floor and roof plans of the building, or horizontal trusses (Figure 24). These elements are also basic architectural components. Their presence is the result of the schematic architectural design of the building.

It is useful for the architectural designer to acquire an understanding of the way these resistance systems work, in response to the forces that the earthquake generates: the detailed calculations can be left to the engineer. The architect may neither be able nor wish, to acquire the depth of theoretical understanding and experience which the engineer must have, but it is worth attempting to transfer a feeling for structural forces, because once acquired, this feeling can act as an almost automatic guide to the designer.

Most designers have acquired a sense of vertical static forces, if only through the experiences of their own bodies. A sense of dynamic forces is less easy to acquire naturally, but many athletes - skiers, high divers, skate boarders - also have a good sense of how movement modifies the effect of gravity. One way of attempting to transfer a feeling for the way in which lateral forces work is to imagine them as vertical forces, rotated 90 degrees. However, the reader should remember, as we have seen, that seismic forces are more complex than gravity forces and must always be visualized as dynamic-moving -and as multi-directional rather than operating in a single direction.

#### H. Diaphragms

The term 'diaphragm' is used to identify horizontal resistance elements, (generally floors and roofs) that act to transfer lateral forces between vertical resistance elements (shear walls or frames). The diaphragm acts as a horizontal beam: the diaphragm itself acts as the web of the beam, and its edges act as flanges (Figure 26).

Floors and roofs often have to be penetrated by staircases, elevator and duct shafts, skylights, or architectural features. The size and location of these penetrations is critical to the effectiveness of the diaphragms. The reason for this is not hard to see when the diaphragm is visualized as a beam: we can for example see that openings cut in the tension flange of this beam will seriously weaken its load carrying capability. In a vertical load system, a penetration through a beam flange would occur in either a tensile or compressive area; in a lateral load system, the hole will be in a region of both tension and compression, since the loading alternates direction.

When diaphragms form part of a resistant system, they may act either in a flexible or stiff manner. This is partly dependent on the size of the diaphragms - its area between enclosing resistance elements or stiffening beams and girders - and also a function of its material. The flexibility of the diaphragm, relative to the shear walls whose forces it is transmitting, also has a major influence on the nature and magnitude of those forces. This effect is shown by Figure 28.

Collectors, or drag struts, are diaphragm framing members which "collect" or "drag" diaphragm shear forces from laterally unsupported areas to vertical resisting elements. As the diaphragm attempts to move north (or south), walls 1, 2, and 3 resist via transfer of shear from diaphragm to top of wall (Figure 29). The forces shown in bold, which will be counteracted by a reaction supplied by Wall 2, cannot be directly transferred to the wall, and hence a collector (which may or may not be a beam for vertical loads) must drag these forces back to Wall 2. The diaphragm on either side of it delivers shears simultaneously, so they are additive. For the case shown, the collector would be in tension and through its anchorage it pulls on Wall 2. For the case when the diaphragm attempts to move south (northward ground movement) the collector would be in compression and would push Wall 2. The same situation occurs on the other axis, so an east-west collector would be used as well. The location of a hole (core, skylight, etc.) at the intersection of the component rectangles would interrupt the collector's load path, and hence should be avoided.

#### I. Shear Walls and Braced Frames

Vertical cantilever walls which are designed to receive lateral forces from diaphragms and transmit them to the ground are commonly termed shear walls. The forces in these walls are predominantly shear forces, though a slender wall will also incur significant bending. Figure 33 shows a simple building with shear walls at its ends. Ground motion enters the building and creates inertial forces which move the floor diaphragms. This movement is resisted by the shear walls, and the forces are transmitted back down to the foundation.

If the building is visualized as rotated so that it extends horizontally. It is clear that the shear walls are acting as cantilever girders which support beams represented by the floor diaphragms. However, unlike a normal cantilever supporting gravity forces, the shear wall must resist dynamic forces that are reversing their direction, for as long as the strong motion continues which is dependent on the characteristics of the earthquake.

The size and location of shear walls is extremely critical. Plans can be conceived of as collections of resistant elements with varying orientations to resist translational forces, and placed at varying distances from the center of rigidity to resist torsional forces. Braced frames act in the same manner as shear walls, though they may be of lower resistance depending on their detailed design. Bracing generally takes the form of steel rolled sections, circular bar sections, or tubes; vibrating forces may cause it to elongate or compress, in which case it loses its effectiveness and permits large deformations or collapse of the vertical structure (Figure 35). Inelastic behavior must be designed into the bracing to create a safe assembly.

Detailing to ensure complete load paths for the high forces is very important, and detailing which causes eccentricity may greatly reduce the effectiveness of bracing, although some sophisticated bracing schemes now coming into use incorporate offset joints. These are designed to ensure that non-linear behavior would occur first in beams rather than columns, and through failure control and the use of ductility, delay the onset of total collapse caused by column buckling.

#### J. Moment Resistant Frames

When seismic resistance is provided by moment resistant frames, lateral forces are resisted by bending and shearing of columns and beams, which are connected by moment connections. Joints become highly stressed, and the details of their construction are important. In addition, behavior of the frame in the inelastic, or plastic, range becomes an important feature in resistance strategy, by using the energy absorption obtained by permanent deformation of the structure prior to ultimate failure. For this reason moment resistant frames are generally conceived as steel structures with stiff welded joints, in which the natural ductility of the material is of advantage. Recently, however, properly reinforced concrete frames have also been accepted as ductile frames: that is, they will retain some resistance capacity in the inelastic range, prior to failure.

The use of moment resistant frames is of architectural significance in two ways. One is that their use may obviate the need for shear walls or braced frames, with the possible restricting planning implications of both. The other is that moment resisting frame structures tend to be much more flexible than shear wall type structures, with consequent implications for the design of accompanying architectural elements such as curtain walls, partitions, and ceilings.

### III. Building Configuration: The Architecture of Seismic Design

#### A. Introduction

In the United States the architect's role in seismic design has been overshadowed by that of the structural engineer. The causes of this are two: U.S. structural engineers have maintained strongly that seismic design is an engineering problem, and architects have, by default, been willing to accept this position. In consequence, seismic design tends to be delegated by the architect to his structural engineer, and U.S. architects are not well educated in seismic design issues. In recent years - particularly following the 1971 San Fernando earthquake - it has become clear that architectural configuration (the size and shape of the building) makes a major contribution to the success or failure of the building's seismic performance. Long recognized by engineers, this factor assumed additional importance through the use of new configurations in the 1950s, made possible by the widespread use of steel and concrete frame construction. At present this ability to construct almost any building configuration, combined with the determinants of urban building sites and planning requirements, characteristic planning solutions, and the efforts to provide interesting and unique architectural images, has resulted in a number of building typologies - building occupancy types combined with configurations - that have led to some serious problems.

While configuration alone is not likely to be the sole cause of building failure, it may be a major contributor. Historically, before the use of steel and reinforced concrete construction, good configuration was one of the major determinants of good seismic performance.

Building plans tended to be symmetrical, spans were short so that there was a high density of supporting walls, and the need for massive load bearing construction, although it increased earthquake forces in the building, tended to keep unit stresses in the materials to very low values. Load paths were direct, and much redundancy was provided.

The advent of the modern framed structure, and the use of quantitative engineering calculations rather than relying on intuition and experience, enabled much smaller amounts of structural material to be used. Figure 37 shows graphically the differences between historical and modern structures in the amount of structural material used to bring forces down to the ground. But since in the modern structure the material is highly stressed, and there is much less redundancy; irregularities of configuration will tend to result in dangerous stress concentrations and torsional forces that did not exist in more traditional configurations.

#### B. Configuration and the Code

Most countries have institutionalized the solution of building problems of life and safety in the form of a code that mandates safe standards for design and construction. How do our building codes deal with the configuration and seismic design issue?

In the United States, until the 1973 edition of the Uniform Building Code, configuration was not dealt with in a specific clause at all, and at present (1981) it treats the issue only with a general caveat.

"Structures having irregular shapes or framing systems: The distribution of the lateral forces in structures which have highly irregular shapes, large differences in lateral resistance or stiffness between adjacent stories or other unusual structural features shall be determined considering the dynamic characteristics of the structure."

If the subject is important, why does the code treat it in only a general and suggestive way? The problem seems to be that although engineers involved in the seismic field have long recognized that configuration is a key issue, it has been found too difficult to reduce to the relatively simple set of prescriptive rules that is our typical code format. This difficulty is explained in the commentary portion of the Structural Engineers Association of California (SEAOC) Recommended Lateral Force Requirements And Commentary (1975);

"Due to the infinite variation of irregularities (in configuration) that can exist, the impracticality of establishing definite parameters and rational rules for the application of this Section are readily apparent. These minimum standards have, in general, been written for uniform buildings and conditions. The subsequent application of these minimum standards to unusual buildings or conditions has, in many instances, led to an unrealistic evaluation."

SEAOC has produced updated editions of the Recommended Lateral Force Requirements And Commentary since 1959. The "Requirements" of these documents has been adopted almost verbatim into successive editions of the Uniform Building Code, but the Commentary section has not. In this section are listed over twenty specific types of "irregular structures or framing systems" as examples of designs which should involve extra analysis and dynamic consideration rather than use of the normal equivalent static force method. These are illustrated in Figure 38, which is a graphic interpretation of the SEAOC list.

Scrutiny of these conditions will show that the majority of irregularities are configuration issues within the terms of our definition. Further, inspections show that somewhere between 65-80% of buildings built in the last fifteen years in the United States fall into one or more of these irregular categories: the percentage range allows for relative judgments in subjectively allocating designs to a category.

It is safe to say that well over half the buildings that have been designed recently do not conform to the simple uniform building configuration upon which the code is based and hence, to a greater or lesser extent, the code forces are inapplicable. The simple equivalent static force method of the code must be augmented by engineering experience and judgment, perhaps combined with a full dynamic analysis. While major building projects will have careful engineering conception and analysis there remain many irregular buildings designed in bare adherence to the code in which, for reasons of cost or ignorance, the modification of seismic performance created by configuration irregularities may not have been carefully considered and accommodated in the design.

The above gives some indication of the difficulties experienced in the attempt to codify the influence of configuration. In work currently in progress to develop a sophisticated set of recommended provisions for seismic design, the NEHRP Provisions, these difficulties remain essentially unresolved. It is also clear that bare adherence to the code will not ensure that the influence of configuration has been addressed.

That a situation should prevail in which the basis upon which many buildings are designed is different from that upon which the seismic code is based, is a cause not for alarm but for understanding. Conceptual recognition of problems caused by configuration predates by many decades today's analytical study. Much of the information is empirical: early observers noted the behavior in earthquakes of buildings of certain types of materials, construction, and configuration. But this situation emphasizes the danger for the designer of relying exclusively on the code provisions, and not also developing a conceptual understanding of the nature of the dynamic environment and the way in which the building responds.

The configurations that cause concern are those illustrated in Figure 38. In general the most concern is with plan irregularities that will accentuate the development of torsional forces, and with vertical irregularities that tend to produce structural discontinuities and stress concentrations. In addition, variations of strength and stiffness, whether horizontal or vertical, tend to overstress the stiff elements and understress the more flexible, resulting in a structure in which a small number of elements may receive an undue proportion of the forces.

In plan, the most dangerous forms have proven to be those in which there is a wide variation of strength and stiffness between various building elevations. The performance of the Penney Department Store in the Alaska earthquake of 1964 was a notable example of the poor performance of these forms (Figure 39). In the area of vertical structural discontinuity the problem of the 'soft first story' and in particular a sub-class of this configuration, the discontinuous shear wall, have been revealed as the most vulnerable. The performance of Olive View Hospital in the San Fernando earthquake of 1971, and the Imperial County Services Building, in Imperial County, 1979, are text book examples of the problems associated with these configurations. Both these types of vertical configuration are characteristic of modern building style and are twentieth century inventions only made possible by modern steel and reinforced concrete structural technology.

#### C. Olive View Hospital, San Fernando, California

The general vertical configuration of the main building was a 'soft' two-story layer of rigid frames on which was supported a four story (five, counting penthouse) shear wall-plus-frame structure. The second floor extends out to form a large plaza: thus, in photographs, the main building appears to have a single soft story, rather than two. The severe damage occurred in the soft story portion, which is generally to be expected (Figure 41). The upper stories moved as a unit, and moved so much that the columns at ground level could not accommodate such a huge displacement between their bases and tops and hence failed. The largest amount by which a column was left permanently out of plumb was 2-1/2 feet.

A discontinuity in vertical stiffness and strength leads to a concentration of stresses and damage, and the story which must hold up all the rest of the stories in a building should be the last, rather than the first, component to sacrifice. Had the columns at Olive View been more strongly reinforced, their failures would have been postponed, but it is unrealistic to think that they would have escaped damage. Thus the significant problem lies in the configuration, and not, totally in the column reinforcement.

#### D. The Imperial County Services Building, El Centro, California

The Imperial County Services Building, El Centro, California, is a prototypical example of a common building configuration of the last few decades, that of a number of repetitive floors of rectangular plan, with blank, or nearly blank, end walls that stop at the second floor level to permit an open ground floor.

The behavior of this building in the Imperial Valley earthquake of 1979 provided a text book example of the effects of architectural characteristics on seismic resistance. The building was a six story reinforced concrete structure built in 1969. In the relatively mild earthquake, in which only a few of the poorest unreinforced masonry buildings suffered structural damage, this building suffered a major structural failure, resulting in column fracture and shortening - by compression - at one end (the East) of the building. The origin of this failure lies in the discontinuous shear wall at this end of the building. The building was subsequently demolished.

The fact that the failure originated in the configuration is made clear by the architectural difference between the East and West ends (Figure 44). The difference in location of the ground floor shear walls was sufficient to create a major behavioral difference in response to rotational, or overturning, forces on the large end shear walls.

The solution to the problem of the discontinuous shear wall is unequivocally to eliminate the condition. To do this may create architectural problems of planning or circulation or of image. If this is so, then it indicates that the decision to use shear walls as resistant elements was wrong from the inception of the design. Conversely, if the decision is made to use shear walls, then their presence must be recognized from the beginning of schematic design, and their size and location early made the subject of careful architectural and engineering coordination.

#### E. Conclusion

Since configuration is important, and since the architect devises and controls the configuration it follows that he is, even if ignorant, a major participant in the seismic design process. Too often the architect and engineer discuss configuration too late - when the design is already set - and in antagonistic terms. The engineer complains because the architect's configuration makes his design work difficult, expensive, and even unsafe, while the architect complains because the engineer places unreasonable restrictions on the programmatic and aesthetic requirements to which the design responds.

More knowledge and understanding on both sides is clearly required. One problem in the United States is the wide separation between the two professions which begins with their education, in separate schools with very different characters and objectives. The training of the architect is primarily conceptual: that of the engineer is analytical, and the result is each profession has difficulty communicating effectively with the other.

The configuration problem is a universal concern, affects all building types, all types of construction and buildings of all ages. To the extent that the architect is influencing seismic performance through his choice of configuration he has a professional responsibility to become better informed as to the consequences of his acts.

Updated June 17, 1998.
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