《建筑结构抗震设计》课程教学资源（参考资料）Seismic Design of Building Structures.doc_P11-P15

Damage considerable in specially designed structures:well-designed frame at in substantial 、Buildingss Some well-built wooden structures destroyed:most masonry and frame structures with foundations destroved Rails bent Few,if any masonry structures remain standing.Bridges destroyed. Rails bent greatly Damage t total.Lines of sight and level are distorted.Objects thrown into a 2-2 Isoseismal maps(等展线图) It is possible to compile a map of earthquake intensity over a region.Data for such an isoseismal map can be obtained by observation in some cases,by questions by resid 23 Richter ade Scale里民震级 In 1935,Charles F.Richter of the California Institute of Technology developed the Richter magnitude scale to measure earthquake strength.The magnitude,M,of an earthquake is determined from the logarithm to base ten of the amplitude recorded by a seismomete ee Secs.2-4 and 2-5.)Adjustment reincluded in the magnitude compensate for the variation in the distar nce between eters and th epicenter.Because the Richter magnitude is a logarithmic scale,each whole number ncrease in magnitude represents a ten-fold increase in measured amplitude. Richter magnitude is expressed in whole numbers and decimal fractions.For example,a mag nitde moderate earthquake.Astrong earthqu ke might be rated at73.Great earthquakes have magnitude above75 Earthquakes with magnitudes of 2.0 or less are known as micro earthquakes.While recorded on seismometers,micro earthquakes are rarely felt by people. The magnitude of an earthquake depends on the length and breadth of the fault slip, as well as on the amount of slin The largest examples of fault slip recorded in nied the earthauakes of 1857 1872 and 1906- -all of which had estimated magnitudes over 8.0 on the Richter scale Although the Richter scale has no lower or upper limit (i.e,it is"open ended").the largest known shocks have had magnitudes in the 8.7 to 8.9 range.The actual factor limiting energy release-and hence Richter magnitude-is the strength of the rocks in the Earth's crust Because of the physical limitations of the faults and crust in the area,earthquakes larger than insouthern Californiaare considered to be highly improbable 2-4 Richter Magnitude Calculation The Richer magnitude,M,is calculated from the maximum amplitude,A,of the seismometer trace,as illustrated in Fig.2.2.A.is the seismometer reading produced by an earthquake of standard size (i.e.,a calibration earthquake).Generally,is 3.94×10-5n0.001)

Ⅸ Damage considerable in specially designed structures；well-designed frame structures thrown out of plumb。Damage great in substantial buildings，with partial collapse。Buildings shifted off foundations . Ⅹ Some well-built wooden structures destroyed；most masonry and frame structures with foundations destroyed。Rails bent。 Ⅺ Few，if any ，masonry structures remain standing. Bridges destroyed. Rails bent greatly。 Ⅻ Damage total. Lines of sight and level are distorted。Objects thrown into air. 2-2 Isoseismal maps（等震线图） It is possible to compile a map of earthquake intensity over a region. Data for such an isoseismal map can be obtained by observation or, in some cases, by questions answered by residents after an earthquake . 2-3 Richter Magnitude Scale（里氏震级） In 1935, Charles F.Richter of the California Institute of Technology developed the Richter magnitude scale to measure earthquake strength. The magnitude, M, of an earthquake is determined from the logarithm to base ten of the amplitude recorded by a seismometer. (See Secs.2-4 and 2-5.) Adjustments are included in the magnitude to compensate for the variation in the distance between the various seismometers and the epicenter. Because the Richter magnitude is a logarithmic scale, each whole number increase in magnitude represents a ten-fold increase in measured amplitude. Richter magnitude is expressed in whole numbers and decimal fractions. For example, a magnitude of 5.3 might correspond to a moderate earthquake. A strong earthquake might be rated at 7.3. Great earthquakes have magnitude above 7.5 . Earthquakes with magnitudes of 2.0 or less are known as micro earthquakes. While recorded on seismometers, micro earthquakes are rarely felt by people. The magnitude of an earthquake depends on the length and breadth of the fault slip, as well as on the amount of slip. The largest examples of fault slip recorded in California accompanied the earthquakes of 1857, 1872 and 1906—all of which had estimated magnitudes over 8.0 on the Richter scale . Although the Richter scale has no lower or upper limit (i.e, it is “open ended”). the largest known shocks have had magnitudes in the 8.7 to 8.9 range. The actual factor limiting energy release –and hence Richter magnitude –is the strength of the rocks in the Earth’s crust. Because of the physical limitations of the faults and crust in the area, earthquakes larger than 8.5 in southern California are considered to be highly improbable. 2-4 Richter Magnitude Calculation The Richer magnitude, M, is calculated from the maximum amplitude, A, of the seismometer trace, as illustrated in Fig.2.2. A. is the seismometer reading produced by an earthquake of standard size (i.e., a calibration earthquake). Generally, A0 is 5 3.94 10−  in (0.001)

M=log) A (2.1) Equation 2.1 assumes that a distance of 62 mi(100km)separates the seismometer and the epicenter.For other distances,the nomograph of Fig.2.3 and the following procedure can be used to calculate the magnitude.Due to the lack of reliable information on the nature of the Earth between the observation point and the earthquake epicenter,an error of 5to 20 mi(10 to 40km)in locating the epicenter is not unrealistic. Step 1:Determine the time between the arrival of the P-and S-waves. Step2:Determine the maximum amplitude of oscillation. Step 3:Connect the arrival time difference on the left scale and the amplitude on Step4: Read the Richter magnitude on the center scale Step 5:Read the distance separating the seismometer and the epicenter from the left scale Whereas one seismometer can determine the approximate distance to the epicenter. momet Once the Richter magnitude.M,is known,an approximate relationship can be used to calculate the energy,E,radiated.Most of the relationships are of the form of Eq.2.2. logo E=logoE。+aM 2.21 In 956.Gutenberg and Richter determined the approximate correlation to be as given in Eq.23.E is the energy in ergs(See app.A for conversions to other unites)Although there have been other relationships developed Eg.2.3 has been verified against data from underground explosions and is the primary correlation cited. 1ogoE=11.8+1.5M [2.3 The radiated energy is less than the total energy released by the earthquake.The difference goes into heat generation and other nonelastic effects,which are not included in Eq.2.3.little is known about the amount of total energy release The fact that a fault zone has xperienced an earthquake offers noassurance that enough stress has been relieved to noth rthquake.As indicated by the loga lat a small earthquak (of magnitude 5,for example)would radiate approximately only 1/32 of the energy of an earthquake just one magnitude larger (of magnitude 6.for example).Thus it would take 32 small earthquakes to release the same energy as an earthquake one magnitude larger 2.6 ength of active fault(活动断层的长度) the Richter magnitude.Mwith the total kilometers,involved in an earthquake.Such comrelations are very site dependent,and even ther there is considerable scatter in such data Equation 2.4 should be considered only representative of the general (approximate)form of the correlation. 1og1oL=1.90M-5.77 [2.4

10 0 log A M A   =     ( 2.1) Equation 2.1 assumes that a distance of 62 mi (100km) separates the seismometer and the epicenter. For other distances, the nomograph of Fig.2.3 and the following procedure can be used to calculate the magnitude. Due to the lack of reliable information on the nature of the Earth between the observation point and the earthquake epicenter, an error of 5to 20 mi (10 to 40km) in locating the epicenter is not unrealistic. Step 1: Determine the time between the arrival of the P-and S-waves. Step 2：Determine the maximum amplitude of oscillation. Step 3：Connect the arrival time difference on the left scale and the amplitude on the right scale with a straight line. Step 4；Read the Richter magnitude on the center scale. Step 5 : Read the distance separating the seismometer and the epicenter from the left scale. Whereas one seismometer can determine the approximate distance to the epicenter, it takes three seismometers to determine and verify the location of the epicenter. 2.5energy release and magnitude correlation（释放能量和震级的关系） Once the Richter magnitude,M, is known,an approximate relationship can be used to calculate the energy,E,radiated. Most of the relationships are of the form of Eq.2.2. 10 10 0 log log E E aM = + [2.2] In 1956,Gutenberg and Richter determined the approximate correlation to be as given in Eq.2.3. E is the energy in ergs.(See app.A for conversions to other unites ) Although there have been other relationships developed ,Eq.2.3 has been verified against data from underground explosions and is the primary correlation cited. 10 log 11.8 1.5 E M = + [2.3] The radiated energy is less than the total energy released by the earthquake. The difference goes into heat generation and other nonelastic effects ,which are not included in Eq.2.3. little is known about the amount of total energy release. The fact that a fault zone has experienced an earthquake offers no assurance that enough stress has been relieved to prevent another earthquake. As indicated by the logarithmic relationship between seismic energy and Richter magnitude, a small earthquake (of magnitude 5,for example) would radiate approximately only 1/32 of the energy of an earthquake just one magnitude larger (of magnitude 6,for example). Thus it would take 32 small earthquakes to release the same energy as an earthquake one magnitude larger. 2.6length of active fault（活动断层的长度） Equation 2.4correlates the Richter magnitude, M,with the approximate total fault length, L in kilometers, involved in an earthquake. Such correlations are very site dependent,and even then there is considerable scatter in such data. Equation 2.4 should be considered only representative of the general (approximate) form of the correlation. 10 log 1.90 5.77 L M = − [2.4]

2.7length of fault slip（断层滑动长度） Equation 2.5(as derived by King and Knopoff in 1968) correlates the richter magnitude,M, and the fault length,L (in meters), with the approximate length of vertical or horizontal fault slip,D(for displacement ) in meters. As with Eq.2.4, this correlation should be considered representative of the general relationship. 2 6 10 log ( 10 ) 1.90 2.65 LD M  = − [2.5] 2-8 PEAK GROUND ACCELERATION Peak Ground Acceleration（地震峰值加速度） The peak (maximum) ground acceleration , PGA, is easily measured by a seismometer (see sec. 2-14) or accelerometer (see sec.2-15) and is one of the most important characteristics of an earthquake. The PGA can be given in various units, including ft/sec2 , in/sec2 ,or m/s2 . however ,it is most common to specify the PGA in gs(i.e.,as a fraction or percent of gravitational acceleration). Significant ground accelerations in California include 1.25 g (1971 san Fernando earthquake, Pacoima damsite), 0.50 g (1966 parkfield earthquake),0.65 g (1989 loma prieta earthquake ), and 1.85 g (1992 cape Mendocino earthquake); Equation 2.7 (as determined by Gutenberg and Richter in 1956) is one of many approximate relationships between the richter magnitude, m, and the PGA at the epicenter. Of course, the ground acceleration (in rock) will decrease as the distance from the epicenter increases, and for this reason, relationships called attenuation equations have been developed. (see sec. 2-13) blume’s 1965 equation (eq. 2.7) for California earthquakes depends on the epicentral distance (r’ in kilometers), the local depth (h in kilometers), and a specific site factor (b). Attenuation equations are very site dependent. Since eq.2.7 was developed, newer studies have resulted in better correlations in different formats and for many different locations, but they are all based on limited data. Such studies regularly result in revisions of the seismic provisions of building codes. Table 2.2 is a commonly cited correlation between magnitude, PGA, and duration of strong-phase shaking (see sec. 2-14) in the vicinity of the epicenter of california earthquakes. The values of acceleration in the table are somewhat on the high side. Ground acceleration in observed earthquakes usually has been lower. Table 2.2 Approximate peak ground acceleration and Duration of strong-phase shaking (California earthquakes) maximum magnitude Acceleration(g) Duration(sec) 5.0 0.09 2 5.5 0.15 6 6.0 0.22 12 6.5 0.29 18 7.0 0.37 24 7,5 0.45 30 8.0 0.50 34 8.5 0.50 37 2.9correlation of intensity , magnitude ,and acceleration with damage

Although there are some empirical relationship.no exact correlations of intensity magnitude and acceleration with damage are possible since many factors contribut to seismic behavior and structural performance.For example,seismic damage depends on the care that was taken at the time of building design and construction. Building in villages in undeveloped countries fare much worse than high-rise buildings in develoned countries in earthauakes of equal magnitudes this damage causes a coresponding lack of comrelation between intensity and magnitude. However,within a geographical region with consistent design and construction methods,fairly good correlation exists between structural performance and ground acceleration,because the Mercalli intensity scale is based specifically on observed damage Table 2.3 Approximate Relationship Between Mercalli Intensity and Peak Ground Acceleration Mercalli Intensity Peak Ground Acceleration 0.03 andbelow 0.03-0.08 VI 0.08-0.15 分 0.15-0.25 0.25-0.45 0.45-0.60 X 0.60-080 XⅪ 0.80-0.90 XⅫ 0.90 and above 2-I0 VERTICALACCELERATION(垂直加速度) The shear waves are at right angles to the compression waves.since there is nothing comstraining the shear waves to a horizontal direction,it is not surprising that the shear wave can be broken down into horizontal and vertical shear waves,respectively. Vertical ground acceleration is known to occur in almost all earthquankes the peak vertical acceeration is usually approximately one-third of the peak horizontal often reaches a ratio of two-thirds.combined with resonance site effects,vertical forces an become substantial.furthermore.forces from all three coordinate directions combine into a resultant force that can easily exceed the yield strength of a member The current UBC-97 seismic design code is generally based on horizontal acceleration alone.This practice is justified by assuming that structures with horizontal seismic resistance will automatically have adequate vertical resistance.Oe of the reasons this sassumption has been accepted is that factors of safety should have been applied during the building design to ensure that a member is able to withstand a force equal to one gravity downward. Experience has shown,however,that disregarding details to resist vertical forces can be a serious

Although there are some empirical relationship, no exact correlations of intensity, magnitude, and acceleration with damage are possible since many factors contribute to seismic behavior and structural performance. For example, seismic damage depends on the care that was taken at the time of building design and construction. Building in villages in undeveloped countries fare much worse than high-rise buildings in developed countries in earthquakes of equal magnitudes. This damage causes a corresponding lack of correlation between intensity and magnitude. However, within a geographical region with consistent design and construction methods, fairly good correlation exists between structural performance and ground acceleration, because the Mercalli intensity scale is based specifically on observed damage. Table 2.3 Approximate Relationship Between Mercalli Intensity and Peak Ground Acceleration Mercalli Intensity Peak Ground Acceleration Ⅳ 0.03 andbelow Ⅴ 0.03-0.08 Ⅵ 0.08-0.15 Ⅶ 0.15-0.25 Ⅷ 0.25-0.45 Ⅸ 0.45-0.60 Ⅹ 0.60-0.80 Ⅺ 0.80-0.90 Ⅻ 0.90 and above 2-10 VERTICAL ACCELERATION（垂直加速度） The shear waves are at right angles to the compression waves.since there is nothing comstraining the shear waves to a horizontal direction,it is not surprising that the shear wave can be broken down into horizontal and vertical shear waves,respectively. Vertical ground acceleration is known to occur in almost all earthquankes.the peak vertical acceleration is usually approximately one-third of the peak horizontal acceleration,but often reaches a ratio of two-thirds.combined with resonance site effects,vertical forces can become substantial.furthermore.forces from all three coordinate directions combine into a resultant force that can easily exceed the yield strength of a member. The current UBC-97 seismic design code is generally based on horizontal acceleration alone.This practice is justified by assuming that structures with horizontal seismic resistance will automatically have adequate vertical seismic resistance.One of the reasons this assumption has been accepted is that factors of safety should have been applied during the building design to ensure that a member is able to withstand a force equal to one gravity downward. Experience has shown, however, that disregarding details to resist vertical forces can be a serious

problem. Columns and walls in compression, cantilever beams, overhangs,and prestressed concrete structures that have not been designed according to specific seismic provisions are particularly susceptible to damage by vertical accelerations because they have little factor of safety against upward vertical acceleration. Transfer girders, horizontal members that support exterior perimeter columns in tube buildings, are definitely sensitive to vertical acceleration. The UBC-97covers these special cases in Sec1630.11 and ,for dynamic analysis, in Secs.1631.2,Item 5,and1631.5.5. 2.11Probability of occurrence The probability that an earthquake of magnitude M or greater will occur in a specify region in any given year is given approximately by Eq.2.8 B is a seismic parameter that has been approximately determined as 2.1 for the entire state of California and 0.48 for 1000,000 mi(26ooooKm) of southern California .While Eq2.8 does not palace any upper bound on M,the probability of exceeding 8.5 is effectively zero. The expected number of earthquakes having magnitude greater than M during R years is given by Eq .2.9. Earthquakes 2.9 is known as a recurrence formula .For northern California ,C=76.7 yr and B=0.847,approximately. For the San Francisco area, C=19.700 yr and B=0.463, approximately. 2.12FREQUENCY OF OCCURRENCE For a specific area , an equation for expected number , N ,of earthquakes of a given magnitude , M ,per year will be of the form Log10N = a - bM .(2.10) For the south-central segment of the San Andreas fault , a and b have values of 3.3 and 0.88 , respectively . Taking the entire world as a whole , the approximate relationship ( up to approximately M = 8.2) is log10 = 7.7 -0.9M.(2.11) Table 2.4 gives the expected number of earthquakes of any given magnitude per 100 years in California .(The table does not give the frequency over any particular location in the state . ) Table 2.4 cannot be derived exactly from Eq. 2.11 because adjustments have been made to account for California' s increased seismicity