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p751_ch2
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James Robert Harris, P.E., PhD
Contents	2.1	2.2	EARTHQUAKE PHENOMENA ........................................................................ 3	STRUCTURAL RESPONSE TO GROUND SHAKING ................................... 5	Response Spectra .......................................................................................... 5	Inelastic Response....................................................................................... 11	Building Materials ...................................................................................... 14	Building Systems ........................................................................................ 16	Supplementary Elements Added to Improve Structural Performance ........ 17	2.2.1	2.2.2	2.2.3	2.2.4	2.2.5	2.3	2.4	2.5	2.6	ENGINEERING PHILOSOPHY ....................................................................... 18	STRUCTURAL ANALYSIS ............................................................................. 19	NONSTRUCTURAL ELEMENTS OF BUILDINGS ...................................... 22	QUALITY ASSURANCE ................................................................................. 23	FEMA P-751, NEHRP Recommended Provisions: Design Examples
In introducing their classic text, Fundamentals of Earthquake Engineering, Newmark and Rosenblueth (1971) comment: In dealing with earthquakes, we must contend with appreciable probabilities that failure will occur in the near future. Otherwise, all the wealth of the world would prove insufficient to fill our needs: the most modest structures would be fortresses. We must also face uncertainty on a large scale, for it is our task to design engineering systems – about whose pertinent properties we know little – to resist future earthquakes and tidal waves – about whose characteristics we know even less. . . . In a way, earthquake engineering is a cartoon. . . . Earthquake effects on structures systematically bring out the mistakes made in design and construction, even the minutest mistakes. Several points essential to an understanding of the theories and practices of earthquakeresistant design bear restating: 1. Ordinarily, a large earthquake produces the most severe loading that a building is expected to survive. The probability that failure will occur is very real and is greater than for other loading phenomena. Also, in the case of earthquakes, the definition of failure is altered to permit certain types of behavior and damage that are considered unacceptable in relation to the effects of other phenomena. 2. The levels of uncertainty are much greater than those encountered in the design of structures to resist other phenomena. This is in spite of the tremendous strides made since the Federal government began strongly supporting research in earthquake engineering and seismology following the 1964 Prince William Sound and 1971 San Fernando earthquakes. The high uncertainty applies both to knowledge of the loading function and to the resistance properties of the materials, members and systems. 3. The details of construction are very important because flaws of no apparent consequence often will cause systematic and unacceptable damage simply because the earthquake loading is so severe and an extended range of behavior is permitted. The remainder of this chapter is devoted to a very abbreviated discussion of fundamentals that reflect the concepts on which earthquake-resistant design are based. When appropriate, important aspects of the NEHRP Recommended Seismic Provisions for New Buildings and Other Structures are mentioned and reference is made to particularly relevant portions of that document or the standards that are incorporated by reference. The 2009 Provisions is composed of three parts: 1) “Provisions”, 2) “Commentary on ASCE/SEI 7-2005” and 3) “Resource Papers on Special Topics in Seismic Design”. Part 1 states the intent and then cites ASCE/SEI 7-2005 Minimum Design Loads for Buildings and Other Structures as the primary reference. The remainder of Part 1 contains recommended changes to update ASCE/SEI 7-2005; the recommended changes include
Resource Paper 12 (“Evaluation of Geologic Hazards and Determination of Seismic Lateral Earth Pressures”) in Part 3 of the Provisions includes a description of current procedures for prediction of seismic-induced slope instability. but where pertinent the specific part is referenced and ASCE/SEI 7-2005 is referred to as the Standard. large portions of a few metropolitan areas with the potential for significant ground shaking are susceptible to liquefaction. These waves cause the surface of the ground to shake violently.1 EARTHQUAKE	PHENOMENA	According to the most widely held scientific belief. Modification of soil properties to protect against liquefaction is one important exception. Long-period sloshing of the liquid contents of tanks is addressed by the Provisions. they do not provide for ground failure. liquefaction and gross settlement are the result of ground shaking on susceptible soil formations. and it is common to locate structures so that mass soil failures and fault breakage are of no major consequence to their performance. design for such events is specialized. and virtually all such earthquakes occur at or near the boundaries of these plates. Abrupt ground displacements occur where a fault intersects the ground surface. Once again. that they should not be considered during site exploration and analysis.) Mass soil failures such as landslides. liquefaction and surface fault rupture. and it is this ground shaking that is the principal concern of structural engineering to resist earthquakes. The sudden movement releases strain energy and causes seismic waves to propagate through the crust surrounding the fault. Lifelines that cross faults require special design beyond the scope of the Provisions. and it is common to avoid constructing buildings and similar structures where such phenomena are likely to occur. ASCE/SEI 7-2005 itself refers to several other standards for the seismic design of structures composed of specific materials and those standards are essential elements to achieve the intent of the Provisions. Earthquakes have many effects in addition to ground shaking. called plates. Missouri. All three parts are referred to herein as the Provisions. and seiches (long-period sloshing) in lakes and inland seas can have similar effects along shorelines. seismic sea waves or tsunamis can cause very forceful flood waves in coastal regions. earthquake or the very large New Madrid.Chapter 2: Fundamentals
commentary on each specific recommendation. The surface along which movement occurs is known as a fault. For example. The structural loads specified in the Provisions are based solely on ground shaking. most earthquakes occur when two segments of the earth’s crust suddenly move in relation to one another. (This commonly occurs in California earthquakes but apparently did not occur in the historic Charleston.
2. Nearly all large earthquakes are tectonic in origin – that is. however. For various reasons. the other effects generally are not major considerations in the design of buildings and similar structures. earthquakes of the nineteenth century. Designing structures to resist such hydrodynamic forces is a very specialized topic. South Carolina. they are associated with movements of and strains in large segments of the earth’s crust. This is the
. This is not to say. These are outside the scope of the Provisions.
it is not based upon as robust an analysis as the other two parameters. the geological record is essential. As of the 1997 edition. and their causes are not as completely understood. The third value. there is no place in the United States where the historical record is long enough to be used as a reliable basis for earthquake prediction – certainly not as reliable as with other phenomena such as wind and snow. NEHRP Recommended Provisions: Design Examples
case with earthquakes in the far western portion of the United States where two very large plates. defines an important transition point for long period (low frequency) behavior.” which is defined as having a 2 percent probability of being exceeded in a 50year reference period. In the 2009 edition of the Provisions the design basis has been refined to target a 1% probability of structural collapse for ordinary buildings in a 50 year period. the historical record is too short to justify sole reliance on the historical record. combined with the smaller amount of data about central and eastern earthquakes (because of their infrequency). at a given location. This effect is captured. come together. there is more geological data available for the far western United States than for other regions of the country. Such data require very careful interpretation. The amplitude of earthquake ground shaking diminishes with distance from the source.FEMA P-751. Two are based on statistical analysis of the database of seismological information: the SS values are pertinent for higher frequency motion. On the whole. the necessarily crude lumping of parameters and other related issues. and the rate of attenuation is less for lower frequencies of motion than for higher frequencies. TL. In the central and eastern United States. Given the infrequency of major earthquakes. but they are used widely to improve knowledge of seismicity. This new
. their probabilistic basis. or seismicity.” which was defined as having a 10 percent probability of being exceeded in a 50-year reference period. however. the basis became to “avoid structural collapse at the maximum considered earthquake (MCE) ground motion. to an extent. The MCE ground motion has been adjusted to deliver this level of risk combined with a 10% probability of collapse should the MCE ground motion occur. Prior to its 1997 edition. Geological data have been developed for many locations as part of the nuclear power plant design process. This factor. earthquakes are not associated with such a plate boundary. Two basic data sources are used in establishing the likelihood of earthquake ground shaking. Even in the West. The Commentary provides a more thorough discussion of the development of the maps. the basis of the Provisions was to “provide life safety at the design earthquake motion. Thus. means that the uncertainty associated with earthquake loadings is higher in the central and eastern portions of the nation than in the West. the uncertainty (when considered as a fraction of the predicted level) about the hazard level is probably greater in areas where the mapped hazard is low than in areas where the mapped hazard is high. by the fact that the Provisions use three parameters to define the hazard of seismic ground shaking for structures. the North American continent and the Pacific basin. and the S1 values are pertinent for other middle frequencies. The first is the historical record of earthquake effects and the second is the geological record of earthquake effects. Even on the eastern seaboard. Both sets of data have been taken into account in the Provisions seismic ground shaking maps.
which were tied to a single level of probability of ground shaking occurrence. records of the acceleration at one point along one axis. 2. Even though the most used design procedure resorts to the use of a concept called the equivalent static force for actual calculations. Forces within the structure are due almost entirely to the pressure loading rather than the acceleration of the mass of the structure.
. The stresses and strains within the superstructure are created entirely by its dynamic response to the movement of its base. not static. The increasing power and declining cost of computational aids are making such analyses more common but. however. Precise analysis of the elastic response of an ideal structure to such a pattern of ground motion is possible. it is not commonly done for ordinary structures. the aboveground portion of a structure is not subjected to any applied force. are analyzed for specific response to a specific ground motion. at this time. But with earthquake ground shaking. some knowledge of the theory of vibrations of structures is essential. the ground.1 Response	Spectra	Figure 2.2 STRUCTURAL	RESPONSE	TO	GROUND	SHAKING	The first important difference between structural response to an earthquake and response to most other loadings is that the earthquake response is dynamic.2.
2.2-1 shows accelerograms. Note the erratic nature of the ground shaking and the different characteristics of the different accelerograms. for several representative earthquakes. For most structures.Chapter 2: Fundamentals
approach incorporates a fuller consideration of the nature of the seismic hazard at a location than was possible with the earlier definitions of ground shaking hazard. only a small minority of structures designed across the country. even the response to wind is essentially static.
) 1971 Landers (Joshua Tree) 1992
North Palm Springs 1986
Figure 2. Great earthquakes extend for much longer periods of time.2-1 Earthquake Ground Acceleration in Epicentral Regions (all accelerograms are plotted to the same scale for time and acceleration – the vertical axis is % gravity).2-2 shows further detail developed from an accelerogram. velocity and displacement for the same event at
. Part (a) shows the ground acceleration along with the ground velocity and ground displacement derived from it. Part (b) shows the acceleration.FEMA P-751.
Figure 2. NEHRP Recommended Provisions: Design Examples
Northridge (Sylmar 360°) 1994 San Fernando (Pacoima Dam) 1971 Tabas 1978
Kern Taft 1952
El Centro 1940
Morgan Hill (Gilroy) 1984
Imperial 6 (Hudson) 1979
Northridge (Sylmar 90°) 1994 Loma Prieta (Oakland Wharf) 1989
San Fernando (Orion Blvd.
the response of a specific structure to an earthquake is ordinarily estimated from a design response spectrum such as is specified in the Provisions. The first step in creating a design response spectrum is to determine the maximum response of a given structure to a specific ground motion (see Figure 2. It depends very much on the vibrational characteristics of the structure and the characteristic frequencies of the ground shaking at the site. velocity and displacement and (b) north-south roof acceleration. reinforced concrete frame building. velocity and displacement (Housner and Jennings. The Holiday Inn.4 1971 San Fernando Earthquake: (a) north-south ground acceleration. a 7-story. was approximately 5 miles from the closest portion of the causative fault. The vibrational characteristics of
In design.2-2(b) (the vertical scales are essentially the same).Chapter 2: Fundamentals
the roof of the building located where the ground motion was recorded. The recorded building motions enabled an analysis to be made of the stresses and strains in the structure during the earthquake. This increase in response of the structure at the roof level over the motion of the ground itself is known as dynamic amplification.2-2). Note that the peak values are larger in the diagrams of Figure 2.
Figure 2. 1982).2-2 Holiday Inn Ground and Building Roof Motion During the M6. The underlying theory is based entirely on the response of a single-degree-of-freedom oscillator such as a simple onestory frame with the mass concentrated at the roof.
will lead to a smoother set of spectra. Mathematically it is often convenient to use the angular frequency expressed as radians per second rather than Hz. computing response spectra for several different ground motions and then averaging them. NEHRP Recommended Provisions: Design Examples
such a simple oscillator may be reduced to two: the natural period1 and the amount of damping. The word frequency is often used with no modifier. the family of response spectra for one ground motion may be determined. Figure 2.2-3 shows such a result for the ground motion of Figure 2. be careful with the units. Such smoothed spectra are an important step in developing a design spectrum. The figure also illustrates the significance of damping. The cyclic frequency (cycles per second.
Much of the literature on dynamic response is written in terms of frequency rather than period. By recalculating the record of response versus time to a specific ground motion for a wide range of natural periods and for each of a set of common amounts of damping. Thus. f for cyclic frequency (Hz) and ω for angular frequency (radians per second). based on some normalization for different amplitudes of shaking.2-2(a) and illustrates that the erratic nature of ground shaking leads to a response that is very erratic in that a slight change in the natural period of vibration brings about a very large change in response. The conventional symbols used in earthquake engineering for these quantities are T for period (seconds per cycle).
. It is simply the plot of the maximum value of response for each combination of period and damping.FEMA P-751. Different earthquake ground motions lead to response spectra with peaks and valleys at different points with respect to the natural period. or Hz) is the inverse of period.
0. or displacement may be obtained from Figure 2. T (s)
Figure 2. Note that acceleration. 2%.2-4 for a structure with known period and damping.2-3 or 1.5
Spectral Acceleration.Chapter 2: Fundamentals
Figure 2. 20% of critical damping) recorded at the Holiday Inn.2-4 is an example of an averaged spectrum.
.2-3 Response spectrum of north-south ground acceleration (0%.5
2% 5% 20% 10%
3 Period. 5%. velocity. approximately 5 miles from the causative fault in the 1971 San Fernando earthquake. 10%.
0. The soil at a site has a significant effect on the characteristics of the ground motion and.2 and 1. soft soils amplify the motion at the surface with respect to
. NEHRP Recommended Provisions: Design Examples
mean plus one standard deviation
Acceleration. T. such as a multistory building. and the design response spectrum is computed more directly. modeling each mode as an equivalent singledegree-of-freedom oscillator. = 0). T (s)
Figure 2. determining the maximum response for each mode from a single-degree-of-freedom response spectrum and then estimating the maximum total response by statistically summing the responses of the individual modes. the maps that characterized the ground shaking hazard were plotted in terms of peak ground acceleration (at period. This has removed a portion of the uncertainty in predicting response accelerations. on the structure’s response. allow a reasonable approximation of the maximum response of a multi-degree-of-freedom oscillator. With the introduction of the new maps in the 1997 edition. this procedure changed. Now the maps present spectral response accelerations at two periods of vibration. Especially at low amplitudes of motion and at longer periods of vibration. The procedure involves dividing the total response into a number of natural modes. therefore.)
Prior to the 1997 edition of the Provisions.2-4. and design response spectra were created using expressions that amplified (or de-amplified) the ground acceleration as a function of period and damping.FEMA P-751. however. The Provisions does not require consideration of all possible modes of vibration for most buildings because the contribution of the higher modes (lower periods) to the total response is relatively minor. The principles of dynamic modal analysis. Few structures are so simple as to actually vibrate as a single-degree-of-freedom system. if many specific conditions are met.2-4 Averaged Spectrum(In this case. as implied by the smooth line in Figure 2.0 second. the statistics are for seven ground motions representative of the de-aggregated hazard at a particular site. Sa (g)
smoothed elastic spectrum
which in turn produces a displacement. 2.2 and 1.2 Inelastic	Response	The preceding discussion assumes elastic behavior of the structure.0 second spectral accelerations for various classes of soils. which in turn produces an internal force. Note that the ultimate resistance (Hu) in a force-controlled system is marginally larger than the yield resistance (Hy). The Provisions accounts for this effect by providing amplifiers that are to be applied to the 0. Two graphs are plotted with the independent variables on the horizontal axis and the dependent response on the vertical axis. and the force is the dependent result. The dynamic nature of earthquake ground shaking means that a large portion of the shaking energy can be dissipated by inelastic deformations if the structure is ductile and some damage to the structure is accepted. while part (c) is characteristic of induced displacements such as earthquake ground shaking (or foundation settlement). The principal extension beyond ordinary behavior referenced at the beginning of this chapter is that structures are permitted to strain beyond the elastic limit in responding to earthquake ground shaking. Thus. due to yielding in the soil. Response spectra may be calculated for oscillators with different levels of ductility. very different design response spectra are specified depending on the type of soil(s) beneath the structure. At the risk of gross oversimplification. The degree to which a member or structure may deform beyond the elastic limit is referred to as ductility. Figure 2. The Commentary (Part 2) contains a thorough explanation of this feature. Different materials and different arrangements of structural members lead to different ductilities. This amplification is diminished somewhat. Earthquake ground motion creates displacement between the base and the mass.2-5(1) would represent a cantilever beam if the load W were small and a column if W were large. Figure 2.0 g (the acceleration due to gravity) for a structure with moderately low damping – for only a moderately large earthquake! Even structures that resist lateral forces well will have a static lateral strength of only 20 to 40 percent of gravity.2-5 will be used to illustrate the significant difference between wind and seismic effects.2. The point being made with the figures is that ductile structures have the ability to resist displacements much larger than those that first cause yield. while the ultimate displacement (Δu) in a displacementcontrolled system is much larger than the yield displacement (Δy). This is dramatically different from the case of design for other types of loads in which stresses and therefore strains. (The ground motion maps in the Provisions are drawn for sites on rock. The reason is economic.) Thus. especially at shorter periods as the amplitude of basic ground motion increases. The displacement is the independent variable. the following conclusions may be drawn:
. are not permitted to approach the elastic limit.2-3 shows a peak acceleration response of about 1.Chapter 2: Fundamentals
bedrock motions. Wind pressures create a force on the structure. The force is the independent variable and the displacement is the dependent result. Figure 2. part (b) of the figure is characteristic of the response to forces such as wind pressure (or gravity weight).
For intermediate periods (which applies to nearly all buildings). the displacement increases until the yield point stress is reached. although in highly redundant structures the increase is more than illustrated for this very simple structure.2-5 Force Controlled Resistance Versus Displacement Controlled Resistance (after Housner and Jennings 1982). For a highly ductile element. the force producing the yield point stress is close to the force producing collapse. As the displacement is increased. the acceleration response of the ductile structure is essentially the same as that of the elastic structure. The ductility does not produce a large increase in load capacity. but the displacement is increased. the oscillator is excited into vibrations by the ground motion and it behaves essentially as a displacement-controlled system and can survive displacements much beyond the yield point. (As W increases. observation of the inelastic
. For this kind of system. As the displacement increases still more. Earthquake ground motions involve a significant number of reversals and repetitions of the strains.FEMA P-751. If H is given an additional increment (about 15 percent) a plastic hinge forms. giving large displacements. but the displacement response is generally about the same for the ductile structure as for the elastic structure strong enough to respond without yielding. In part (b) the force H is the independent variable. 3.) During an earthquake. NEHRP Recommended Provisions: Design Examples
1. Therefore. this ductility is decreased dramatically. As H is increased. the resistance (H) increases only a small amount. the displacement can be increased 10 to 20 times the yield point displacement before the system collapses under the weight W. For structures with very short natural periods. For structures with very long natural periods.
Inelastic response is quite complex. the acceleration response is reduced. 2. In part (c) the displacement is the independent variable.
HY HU HU /H Y = 1 (a) (b)
ΔU Δ U /Δ Y >> 1
Figure 2. the acceleration response is reduced by a factor equivalent to the ductility ratio (the ratio of maximum usable displacement to effective yield displacement – note that this is displacement and not strain). This explains why ductile structures can survive ground shaking that produces displacements much greater than yield point displacement. the base moment increases until the yield point is reached.
or at least approximates. Most structures are designed for seismic response using a linear elastic analysis with the strength of the structure limited by the strength at its critical location.5 2 2. stability of resistance under repeated reversals of inelastic deformation and overstrength. toughness and overstrength depend primarily on the type of building system. the redistributions allowed therein are minor compared to what occurs in response to strong ground motion. Most structures possess enough complexity so that the peak strength of a ductile structure is not accurately captured by such an analysis. Cycling the deformation can cause degradation of strength. Yield must develop at four locations before the peak resistance is achieved. The natural frequency is dependent on the mass and stiffness of the building. Note that a few key design standards (for example.2-6 shows the load versus displacement relation for a simple frame. Three coefficients – R.δ curve
Figure 2. Damping. member. but not the building’s size or shape. stiffness.)
To summarize. Systems that have a proven capacity to maintain a stable resistance to a large number of cycles of inelastic deformation are allowed to exercise a greater portion of their ultimate ductility in designing for earthquake resistance. Cd and Ω0 – are
. or both. The margin from the first yield to the peak strength is referred to as overstrength.
0 0 0. the characteristics important in determining a building’s seismic response are natural period.2-6 Initial Yield Load and Failure for a Ductile Portal Frame (The margin from initial yield to failure (mechanism in this case) is known as overstrength. and it plays a significant role in resisting strong ground motion. Using the Provisions the designer calculates. American Concrete Institute (ACI) 318 for the design of concrete structures) do allow for some redistribution of internal forces from the critical locations based upon ductility. however.Chapter 2: Fundamentals
properties of a material. ductility.5 1 1. or system under a monotonically increasing load until failure can be very misleading. the natural period of vibration (the inverse of natural frequency). but this is not the same as the classic definition used in mechanics of materials. damping. ductility.5 5
(b) H .5 4 4.5 3 3. This property is often referred to as toughness. Figure 2.
2 Steel	Steel is the most ductile of the common building materials. The moderate-to-large reduction from elastic response to design response allowed for steel structures is primarily a reflection of this ductility and the stability of the resistance of steel. Cd is intended to be a reasonable mean for the amplification necessary to convert the elastic displacement response computed for the reduced ground motion to actual displacements.2. It is used to compute a required strength. or board sheathing on wood framing) possess much more ductility than the basic material primarily because the nails. These structures also possess a much higher degree of damping than the damping that is assumed in developing the basic design spectrum. such as earthquake. stability of resistance and overstrength. and its strength increases significantly for brief loadings. ductility. Ω0 is intended to deliver a reasonably high estimate of the peak force that would develop in the structure. 2. Cd and Ω0 are specified in the Provisions for the most common structural materials and systems.3. 2. Capacities and design and detailing rules for wood elements of seismic force-resisting systems are now found in the Special Design Provisions for Wind and Seismic supplement to the National Design Specification for Wood Construction. even though wood is a brittle material as far as tension and flexure are concerned. It has some ductility in compression (generally monotonic). oriented strand board.3 Building	Materials	The following brief comments about building materials and systems are included as general guidelines only. This is confirmed by their generally good performance in earthquakes.2. Members subject to buckling (such as bracing) and connections subject to brittle fracture (such as
. and high damping combine to give timber structures a large reduction from elastic response to design level. Conventional timber structures (plywood. The increased strength. The large reduction in acceleration combined with the light weight timber structures make them very efficient with regard to earthquake ground shaking when they are properly connected.1 Wood	Timber structures nearly always resist earthquakes very well. connection ductility.2. R is intended to be a conservatively low estimate of the reduction of acceleration response in a ductile system from that for an elastic oscillator with a certain level of damping. not for specific application.3. 2. NEHRP Recommended Provisions: Design Examples
provided to encompass damping.FEMA P-751. This large reduction should not be used if the strength of the structure is actually controlled by bending or tension of the gross timber cross sections. Sets of R. and other steel connection devices yield. and the wood compresses against the connector. Computations of displacement based upon ground motion reduced by the factor R will underestimate the actual displacements. Much of this damping is caused by slip at the connections.
the response reduction factors for design of reinforced masonry are not quite as large as those for reinforced concrete. however. which can lead to large reductions from the elastic response.
. buckling of compression bars. to take some of the steps (e. also affect earthquake resistance as demonstrated in the Northridge earthquake. The nature of masonry construction. Unreinforced masonry possesses little ductility or stability. requires special detailing.Chapter 2: Fundamentals
partial penetration welds under tension) are much less ductile and are addressed in the Provisions in various ways.3.3 Reinforced	Concrete	Reinforced concrete achieves ductility through careful limits on steel in tension and concrete in compression. 2. Reinforced concrete beams with common proportions can possess ductility under monotonic loading even greater than common steel beams. reinforced masonry behaves in a fashion similar to reinforced concrete. 2. Thus. grout and the masonry unit create additional failure phenomena. Further. Providing stability of the resistance to reversed inelastic strains. the sequence of plastification and other factors. For certain types of members (such as pure cantilever shear walls).3. confinement of compression members) used with reinforced concrete to increase ductility.2. however. makes it difficult. such as stress concentrations and flaws in welds. in which local buckling is usually a limiting factor. the discrete differences between mortar. Capacities and design and detailing rules for seismic design of hot-rolled structural steel are found in the Seismic Provisions for Structural Steel Buildings (American Institute of Steel Construction (AISC) Standard 341) and similar provisions for cold-formed steel are found in the “Lateral Design” supplement to the North American Specification for the Design of Cold-Formed Steel Structures published by AISI (American Iron and Steel Institute).g. The basic and applied research program that grew out of that experience has greatly increased knowledge of how to avoid low ductility details in steel construction. Thus. and stability.. except for rocking of masonry piers on a firm base and very little reduction from the elastic response is permitted.4 Masonry	Masonry is a more complex material than those mentioned above and less is known about its inelastic response characteristics. The Commentary and the commentary with the ACI 318 standard Building Code Requirements for Structural Concrete explain how to design to control premature shear failures in members and joints. concrete compression failures (through confinement with transverse reinforcement). there is a wide range of reduction factors from elastic response to design response depending on the detailing for stable and assured resistance. Defects. if not impossible.2. Capacities and design and detailing rules for seismic design of masonry elements are contained within The Masonry Society (TMS) 402 standard Building Code Requirements for Masonry Structures.
Successful performance of such systems requires that the connections perform in a ductile manner. are penalized: the R factors permit less reduction from elastic response. These structures generally are an attempt to combine the most beneficial aspects of each material. Clever arrangements of connections can create systems in which yielding under earthquake motions occurs away from the connections. 2.2.3. The connections between pieces of precast concrete commonly are not as strong as the members being connected.4 Building	Systems	Three basic lateral-load-resisting elements – walls. This requires some extra effort in design but it can deliver successful performance.2. however. Capacities and design and detailing rules are found in the Seismic Provisions for Structural Steel Buildings (AISC Standard 341). for seismic design of precast structures. in which case the similarity to reinforced concrete is very real. Connection details often make development of ductility difficult in braced frames. this is because frames are more redundant.FEMA P-751.3. having several different locations with approximately the same stress levels and common beam-column joints frequently exhibit an ability to maintain a stable response through many cycles of reversed inelastic deformations. The Provisions includes guidance. The actual failure of steel bracing often occurs because local buckling associated with overall member
. will not do so. Unbraced frames generally are allowed greater reductions from elastic response than walls and braced frames. braced frames and unbraced frames (moment resisting frames) – are used to build a classification of structural types in the Provisions. and there are also supplemental ACI standards for specialized seismic force-resisting systems of precast concrete. In the context of the Provisions. the most common wood seismic resisting systems perform well yet have connections (nails) that are significantly weaker than the connected elements (structural wood panels). some only for trial use and comment (Part 3). As a point of reference.6 Composite	Steel	and	Concrete	Reinforced concrete is a composite material. ACI 318 also includes provisions for precast concrete elements resisting seismic forces. 2. composite is a term reserved for structures with elements consisting of structural steel and reinforced concrete acting in a composite manner. Many common connection schemes.2. and buckling of compression members also limits their inelastic response.5 Precast	Concrete	Precast concrete obviously can behave quite similarly to reinforced concrete but it also can behave quite differently. NEHRP Recommended Provisions: Design Examples
2. such as unconfined concrete and the welded steel joint used before the Northridge earthquake. Some carefully detailed connections also can mimic the behavior of reinforced concrete. In part. Systems using connection details that have not exhibited good ductility and toughness.
Redundancy is one reason. Both have specialized rules for response analysis and design detailing. Shear walls that do not bear gravity load are allowed a greater reduction than walls that are load bearing.3. The early provisions for
. The design of such systems requires a conservative estimate of the likely deformation of the isolator. The penalty factor of 1. Only two values of the redundancy factor. Systems that combine different types of elements are generally allowed greater reductions from elastic response because of redundancy. such as major hospitals and emergency response centers. A simple. the acceleration response beyond a threshold period is roughly proportional to the inverse of the period). Seismic isolation involves placement of specialized bearings with low lateral stiffness and large lateral displacement capacity between the foundation and the superstructure.Chapter 2: Fundamentals
buckling frequently leads to locally high strains that then lead to brittle fracture when the member subsequently approaches yield in tension.2. are defined: 1. deemed-to-comply exception is provided for certain structures.2-4. The 2010 earthquake in Chile is expected to lead to improvements in understanding and design of reinforced concrete shear wall systems because of the large number of significant concrete shear wall buildings subjected to strong shaking in that earthquake. Redundancy is frequently cited as a desirable attribute for seismic resistance. But the newer and potentially more popular bracing system is the buckling-restrained braced frame. such as masonry and concrete). Seismic isolation is becoming increasingly common for structures in which superior performance is necessary. but with performance that is superior as brace buckling is controlled to preserve ductility.3 is placed upon systems that do not possess some elementary measures of redundancy based on explicit consideration of the consequence of failure of a single element of the seismic force-resisting system. Eccentrically braced steel frames and new proportioning and detailing rules for concentrically braced frames have been developed to overcome these shortcomings. Design provisions appear in the Seismic Provisions for Structural Steel Buildings (AISC Standard 341).5 Supplementary	Elements	Added	to	Improve	Structural	Performance	The Standard includes provisions for the design of two systems to significantly alter the response of the structure to ground shaking. 2. and isolation makes it feasible to design such structures for lower total lateral force. ρ. This new system has the advantages of a special steel concentrically braced frame. It is used to substantially increase the natural period of vibration and thereby decrease the acceleration response of the structures. A quantitative measure of redundancy is included in the Provisions in an attempt to prevent use of large reductions from elastic response in structures that actually possess very little redundancy.0 and 1. Such structures are frequently designed with a stiff superstructure to control story drift. (Recall the shape of the response spectrum in Figure 2. another is that axial compression generally reduces the flexural ductility of concrete and masonry elements (although small amounts of axial compression usually improve the performance of materials weak in tension.
and falling ceilings. It is possible to reach effective damping levels of 20 to 30 percent of critical damping. pipes. and the effectiveness of increased damping can be seen in Figure 2. as-built details and overall quality of design. Added damping involves placement of specialized energy dissipation devices within stories of the structure. The devices can be similar to a large shock absorber.” At this point it is worth recalling the criteria mentioned earlier in describing the risktargeted ground motions used for design. large uncertainties as to the intensity and duration of shaking and the possibility of unfavorable response of a small subset of buildings or other structures may prevent full realization of the intent.
2. One percent in 50 years is actually a higher failure rate than is currently considered acceptable for buildings subject to other natural loads. equipment and other nonstructural components also cause deaths and injuries. building configuration. NEHRP Recommended Provisions: Design Examples
that factor were a precursor of the changes in ground motion mapping implemented in the 1997 Provisions.2-3. materials. Both also require considerations beyond common building construction to assure quality and durability. In addition. but other technologies are also available.FEMA P-751. (The “design earthquake” is currently taken as two-thirds of the MCE ground motion). Thus. Most earthquake injuries and deaths are caused by structural collapse. Added damping is used to reduce the structural response. Some collapse
. light fixtures. in fact. termed the maximum considered earthquake (MCE) motion…Falling exterior walls and cladding. the main thrust of the Provisions is to prevent collapse for very rare and intense ground motion.” states: ”The primary intent of the NEHRP Recommended Seismic Provisions for normal buildings and structures is to prevent serious injury and life loss caused by damage from earthquake ground shaking. under “Intent.” The Provisions states: “The degree to which these goals can be achieved depends on a number of factors including structural framing type. The probability of structural collapse due to ground shaking is not zero.3 ENGINEERING	PHILOSOPHY	The Commentary. The reason is as stated in the quote at the beginning of this chapter “…all the wealth of the world would prove insufficient…” Damage is to be expected when an earthquake equivalent to the design earthquake occurs. it is common to add damping at the isolator level of seismically isolated buildings. such as wind and snow. The damping does not have to be added in all stories. Isolation and damping elements require extra procedures for analysis of seismic response. which can reduce response by factors of 2 or 3.
The basic structural criteria are strength. Thus. and compatible with the basis of the design spectrum.4 STRUCTURAL	ANALYSIS	The Provisions sets forth several procedures for determining the force effect of ground shaking. a full history of dynamic response (previously referred to as a time-history analysis. These
. The most common design standards for timber and masonry are based on allowable stress concepts that are not consistent with the basis of the reduced design spectrum. the engineering profession has not yet embraced these new methods. of the building. The flow charts in Chapter 2 illustrate how these classifications are used to control application of various portions of the Provisions. other methods have been introduced into model building codes. Yield-level strengths for steel and concrete structures are easily obtained from common design standards. With the deletion of these methods from the Provisions. and the ASCE standard Minimum Design Loads for Buildings and Other Structures to factor downward the seismic load effects based on the Provisions for use with allowable stress design methods. which is achieved by applying the Ω0 amplifier to the design spectral response. Most of these adjustments were simple factors to be applied to conventional allowable stresses. due to any cause. The Provisions recognizes that the risk presented by a particular building is a combination of the seismic hazard at the site and the consequence of failure. This classification is called the Occupancy Category (Risk Category in the Standard). A third linear method. The two most fully constrained and frequently used are both linear methods: an equivalent static force procedure and a dynamic modal response spectrum analysis procedure. The yield-level strength provided must be at least that required by the design spectrum (which is reduced from the elastic spectrum as described previously).
2. Although strength-based standards for both materials have been introduced in recent years. Analytical procedures are classified by two facets: linear versus nonlinear and dynamic versus equivalent static. subject to certain limitations. The distortion criterion is a limit on story drift and is calculated by amplifying the linear response to the (reduced) design spectrum by the factor Cd to account for inelastic behavior. In the past. now referred to as a response-history analysis).Chapter 2: Fundamentals
is to be expected when and where ground motion equivalent to the MCE ground motion occurs. and a nonlinear method are also permitted. A combined classification called the Seismic Design Category (SDC) incorporates both the seismic hazard and the Occupancy Category. Structural elements that cannot be expected to perform in a ductile manner are to have greater strength. the Provisions stipulated adjustments to common reference standards for timber and masonry to arrive at a strength level equivalent to yield. stability and distortion. a classification system is established based on the use and size of the building. The stability criterion is imposed by amplifying the effects of lateral forces for the destabilizing effect of lateral translation of the gravity weight (the P-delta effect). The SDC is used throughout the Provisions for decisions regarding the application of various specific requirements.
The response to vertical ground motion is roughly estimated as a factor (positive or negative) on the dead load force effect. The specified elastic spectrum is based on a damping level at 5 percent of critical damping. Once the total lateral force is determined. With the equivalent static force procedure.) Calculation of a period based on an analytical model of the structure is encouraged. The particular acceleration for the building is determined from this spectrum by selecting a value for the natural period of vibration. but it is not included in the Standard. which ranges from 1-1/4 to 8. which is generally the total permanent load. Because the design computations are carried out with a design spectrum that is two-thirds the MCE spectrum that means the full reduction from elastic response ranges from 1. This set of forces will produce. The reduction from the elastic spectrum to design spectrum is accomplished by dividing the elastic spectrum by the coefficient R. The two most common linear methods make use of the same design spectrum. Ductility and overstrength make up the larger part of the reduction. also known as a pushover analysis. an envelope of gross overturning moment that is larger than many dynamic studies indicate is necessary. the base shear is obtained by multiplying it by the total effective mass of the building. A nonlinear static method. reduced by a resistance factor. and a peer review is required. These limits prevent the use of a very flexible model in order to obtain a large period and correspondingly low acceleration. Seismic Rehabilitation of Existing Buildings. and a part of the R factor accomplishes adjustments in the damping level. but limits are placed on the results of such calculations. but not by a factor of safety. The method is instructive for understanding the development of mechanisms but there is professional disagreement over its utility for validating a structural design. the equivalent static force procedure specifies how this force is to be distributed along the height of the building. The Provisions define the total effect of earthquake actions as a combination of the response to horizontal motions (or forces for the equivalent static force method) with response to vertical ground acceleration. the level of the design spectrum is set by determining the appropriate values of basic seismic acceleration. particularly in tall buildings. is described in Part 3 of the Provisions. The Provisions also reference ASCE 41. NEHRP Recommended Provisions: Design Examples
methods use real or synthetic ground motions as input but require them to be scaled to the basic response spectrum at the site for the range of periods of interest for the structure in question. the appropriate soil profile type and the value for R. Nonlinear analyses are very sensitive to assumptions about structural behavior made in the analysis and to the ground motions used as input. and the modal procedure is required for structures with large periods (essentially this means tall structures) in the higher seismic design categories.
.FEMA P-751. Once the overall response acceleration is found. Equations that require only the height and type of structural system are given to approximate the natural period for various building types. This distribution is based on the results of dynamic studies of relatively uniform buildings and is intended to give an envelope of shear force at each level that is consistent with these studies. Dynamic analysis is encouraged.9 to 12. for the pushover method. The resulting internal forces are combined with the effects of gravity loads and then compared to the full strength of the members. (The area and length of shear walls come into play with an optional set of equations.
the results are not statically compatible (that is. Yielding of one component leads to redistribution of the forces within the structural system. stiffnesses. and. The sum of the absolute values for each mode is always conservative. the accidental torsion must be amplified. The distribution of displacements and accelerations (forces) and the resulting story shears. The Provisions requires that the center of force be displaced from the calculated center of mass by an arbitrary amount in either direction (this torsion is referred to as accidental torsion). neither will give a particularly accurate picture of behavior in an earthquake approaching the design event. the two procedures give very similar results. Total values for subsequent analysis and design are determined by taking the square root of the sum of the squares for each mode. while this may be very significant. This summation gives a statistical estimate of maximum response when the participation of the various modes is random. the remainder of the equivalent static force analysis is basically a standard structural analysis. the moment calculated from the summed floor forces will not match the moment from the summation of moments). If two or more of the modes have very similar periods. the story shears and the overturning moments are separately obtained from the summing procedure. all results are scaled up in direct proportion. the modal analysis procedure is very similar to the equivalent static force procedure. and the approximate periods specified in the static procedure. These are calculated from a mathematical model of the structure. none of the linear methods can account for it. When this limit is violated. more advanced techniques for summing the values are required. which is common. these procedures must account for coupling in the response of close modes. That exception accounts for uncertainties in the location of the center of mass.Chapter 2: Fundamentals
With one exception. thus. The modal procedure is required for such structures in higher seismic design categories. Both methods are based on purely elastic behavior. overturning moments and story drifts are determined for each mode directly from the procedure. The base shear for each mode is determined from a design spectrum that is essentially the same as that for the static procedure. In many respects. Early recognition of this will avoid considerable problems in later analysis and checking. A lower limit to the base shear determined from the modal analysis procedure is specified based on the static procedure.
. uncertainties in the strength and stiffness of the structural elements and rotational components in the basic ground shaking. The procedure requires inclusion of enough modes so that the dynamic response of the analytical model captures at least 90 percent of the mass in the structure that can vibrate. The primary difference is that the natural period and corresponding deflected shape must be known for several of the natural modes of vibration. The twist produced by real and accidental torsion is then compared to a threshold and if the threshold is exceeded. This concept is referred to as horizontal torsion. For structures that are very uniform in a vertical sense. The modal analysis method is better for buildings having unequal story heights. Because the equivalent static forces applied at each floor. The consideration of horizontal torsion is the same as for the static procedure. or masses.
2. many of their nonstructural elements must remain undamaged. The technique is referred to as the P-delta analysis and is only an approximation of stability at inelastic response levels. such as hospitals and fire stations. and are useful in understanding the demands upon nonstructural components. The response of the component is often amplified above the response of the supporting structure. 2. Some buildings. Application of the response spectrum concept would indicate that the response history of motion of a building roof to which mechanical equipment is attached looks like a ground motion to the equipment. the relative height of the component within the structure and a crude approximation of the flexibility of the component or its anchorage. need to be functional immediately following an earthquake. and small dimensions often lead to fundamental periods of vibration that are very short). as in the case of heavy partitions or facades. as in the case of a fire suppression system. Damage to nonstructural elements can pose a hazard to life in and of itself. The technique is based on elastic amplification of horizontal displacements created by the action of gravity on the displaced masses. The Provisions treats damage to and from nonstructural elements in three ways. The component mass. or it can create a hazard if the nonstructural element ceases to function. More restrictive limits are placed upon those Occupancy Categories (Risk Categories in the Standard) for which better performance is desired given the occurrence of strong ground shaking. many components must be anchored for an equivalent static force. may not offer enough protection to brittle elements that are rigidly bound by the structure. Second. not just their anchorage) to accommodate specific structural deformations or seismic forces is required. An estimate of component acceleration that depends on the structural response acceleration for short period structures. however. the explicit design of some elements (the elements themselves. The Provisions simplifies the concept greatly.5 NONSTRUCTURAL	ELEMENTS	OF	BUILDINGS	Severe ground shaking often results in considerable damage to the nonstructural elements of buildings. Response spectra developed from the history of motion of a point on a structure undergoing ground shaking are called floor spectra.FEMA P-751. Some components are rigid with respect to the structure (light weights. NEHRP Recommended Provisions: Design Examples
Both of the common methods require consideration of the stability of the building as a whole. the limits specified. therefore. First. A simple factor is calculated and the amplification is provided for in designing member strengths when the amplification exceeds about 10 percent.
. The dynamic response of the structure provides the dynamic input to the nonstructural component. The force for which components are checked depends on: 1. indirect protection is provided by an overall limit on structural distortion. Third.
Tragically. The Provisions also requires that the contractor and building official be aware of the requirements specified by the designer. The function or importance of the component or the building.Chapter 2: Fundamentals
3. mistakes occasionally will pass this test only to cause failure later.6 QUALITY	ASSURANCE	Since strong ground shaking has tended to reveal hidden flaws or weak links in buildings.
. The quality assurance provisions require a systematic approach with an emphasis on documentation and communication. The actively implemented provisions for quality control are actually contained in the model building codes. and must communicate the results of their work to all concerned parties. In the final analysis. Furthermore. Loads experienced during construction provide a significant test of the likely performance of ordinary buildings under gravity loads. No comparable proof test exists for horizontal loads. which is not the case for response to other loads. there is no substitute for a sound design. and the material design standards. The designer who conceives the systems to resist the effects of earthquake forces must identify the elements that are critical for successful performance as well as specify the testing and inspection necessary to confirm that those elements are actually built to perform as intended. The inertial force demands tend to control the seismic design for isolated or heavy components whereas the imposed deformations are important for the seismic design for elements that are continuous through multiple levels of a structure or across expansion joints between adjacent structures. The available ductility of the component or its anchorage. such as the International Building Code. Also included in the Provisions is a quantitative measure for the deformation imposed upon nonstructural components. detailed requirements for assuring quality during construction are contained in the Provisions by reference to the Standard. This is coupled with the seismic design approach based on excursions into inelastic straining. and experience has shown that flaws in construction show up in a disappointingly large number of buildings as distress and failure due to earthquakes. those individuals who carry out the necessary inspection and testing must be technically qualified. such as Seismic Provisions for Structural Steel Buildings. Minimum levels of testing and inspection are specified in the Provisions for various types of systems and components. such as cladding or piping. and 4. but it is fairly rare. soundly executed.
2. where they are located in an appendix.
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