Amplitude Strong Ground Motion and Concept of Response Spectrum March 2013 Sudhir K Jain, IIT Gandhinagar Sudhir K. Jain March 2013 1 EQ Ground Motions Low Amplitude Vibrations Long distance events Usually displacements Earth Scientists Teleseismic Earthquake Recording P PP S Surface Waves 0 200 400 600 800 1000 1200 Time (s) Sudhir K. Jain March 2013 Slide 2 1
Accn. (g) EQ Ground Motions Strong Ground Motions Near-field ground motions Usually accelerations Engineers 0.3 0.2 PGA=0.32g 0.1 0-0.1-0.2-0.3 0 10 20 30 40 50 60 70 80 Time (seconds) Sudhir K. Jain March 2013 Slide 3 Peak Ground Parameters Acceleration (PGA) Velocity (PGV) Displacement (PGD) Sudhir K. Jain March 2013 Slide 4 2
Maximum Recorded Motion Sudhir K. Jain March 2013 (Martinez-Pereira, Slide 1999) 5 Characteristics Parameters Duration of Significant Shaking Frequency Content 1985 Mexico Earthquake (SCT 1A; N90E) 0.5g 1940 Imperial Valley Earthquake (El Centro; S00E) 1971 San Fernando Earthquake (Pacoima Dam; N76W) 0 10 20 30 40 50 60 Time (sec) 1991 Uttarkashi Earthquake (Uttarkashi, N75E) Sudhir K. Jain March 2013 Slide 6 3
Characteristics Influence of Magnitude of EQ Source mechanism Type of faulting Fault Distance from source Fault Soil/rock medium along travel path Local soil site, geology, topology, etc.,. Attenuation with Distance Sudhir K. Jain March 2013 Slide 7 Accelerogram During ground shaking, one can measure ground acceleration versus time (accelerogram) using an accelerograph Accelerograph is the instrument Accelerogram is the record obtained from it Accelerogram is the variation of ground acceleration with time (also called time history of ground motion) Sudhir K. Jain March 2013 Slide 8 4
Typical Accelerograph This is a typical analog instrument. These days, digital instruments are becoming popular (photo from Earthquakes by Bolt) Sudhir K. Jain March 2013 Slide 9 Typical Accelerograms From Dynamics of Structures by A K Chopra, Prentice Hall Time, sec Sudhir K. Jain March 2013 Slide 10 5
Response Spectrum (contd ) If the ground moves as per the given accelerogram, what is the maximum response of a single degree of freedom (SDOF) system (of given natural period and damping)? Response may mean any quantity of interest, e.g., deformation, acceleration T=2 sec, a(t)/g Damping =2% Ground motion time history Time, sec Sudhir K. Jain March 2013 Slide 11 Response Spectrum (contd ) Using a computer, one can calculate the response of SDOF system with time (time history of response) Can pick maximum response of this SDOF system (of given T and damping) from this response time history See next slide Sudhir K. Jain March 2013 Slide 12 6
Response Spectrum (contd ) Maximum response = 7.47 in. d(t) Time, sec Time History of Deformation (relative displacement of mass with respect to base) response T=2 sec, Damping =2% a(t)/g Ground motion time history Time, sec Sudhir K. Jain March 2013 Slide 13 Response Spectrum (contd ) Repeat this exercise for different values of natural period. For design, we usually need only the maximum response. Hence, for future use, plot maximum response versus natural period (for a given value of damping). Such a plot of maximum response versus natural period for a given accelerogram is called response spectrum. Sudhir K. Jain March 2013 Slide 14 7
Response Spectrum (contd ) T=0.5 sec =2% a g (t)/g d(t)/g Time, sec Displacement Response Spectrum for the above time history T=1.0 sec =2% d(t)/g T=2.0 sec =2% d(t)/g d max Time, sec Figure After Chopra, 2001 T, sec Sudhir K. Jain March 2013 Slide 15 Response Spectrum (contd ) Response Spectrum is useful to obtain maximum response of any SDOF system for that accelerogram and for that value of damping. See example on next slide Sudhir K. Jain March 2013 Slide 16 8
Maximum Velocity, in/sec Maximum Acceleration, g Acceleration, g Example 3m Mass = 10,000kg Natural Period T=1 sec Damping =5% of critical Time (sec) Ground Acceleration Time History From Response Spectrum: Spectral Acceleration (for T=1sec) = 0.48 g Max. Base Shear = Mass x Spectral Accln. =(10,000kg) x (0.48x9.81m/sec 2 ) = 47,000 N = 47 kn Max. Base Moment =(47kN) x (3m) = 141 kn-m Undamped Natural Period T (sec) Acceleration Response Spectrum for the above accelerogram for 5% damping (Fig. from Seed and Idriss, 1982) Sudhir K. Jain March 2013 Slide 17 Response Spectrum (contd ) May repeat the entire process for different values of damping Velocity response spectra for N-S component of 1940 El Centro record (damping values of 0, 2, 5 and 10%) Fig From Housner, 1970 Natural Period T (sec) Sudhir K. Jain March 2013 Slide 18 9
Response Spectrum (contd ) Unless otherwise mentioned, response spectrum is based on a linear elastic system Sudhir K. Jain March 2013 Slide 19 Response Spectrum (contd ) By response we may mean any response quantity of interest to us, for example: Absolute acceleration of the mass Termed as Acceleration Response Spectrum Relative velocity of the mass with respect to base Termed as Velocity Response Spectrum Relative displacement of the mass with respect to base Termed as Displacement Response Spectrum Word Spectra is used to denote plural of Spectrum. Sudhir K. Jain March 2013 Slide 20 10
Velocity, ft/sec Response Spectrum (contd ) Since SDOF system responds maximum to the waves of frequency near its own natural frequency, Response spectrum is also a very good way to characterize the strong ground motion from engineering view point. For instance, relative strength of low frequency versus high frequency waves See example on next slide Sudhir K. Jain March 2013 Slide 21 Example: Velocity spectra from two accelerograms Natural Period T (sec) Note that the two response spectra above show very different frequency content. Ground motion B has more energy at low periods. An expert may be able to make out from these spectra that B is recorded at a short distance (say 15km) from a small earthquake, while A is recorded from a large earthquake at a large distance (say 100km) (Fig. edited from Housner, 1970) Sudhir K. Jain March 2013 Slide 22 11
Response Spectrum (contd ) Response spectrum is a very powerful tool. Uses of response spectrum: To obtain maximum response of a SDOF system (to the original accelerogram using which response spectrum was obtained) To obtain maximum response in a particular mode of vibration of a multi degree of freedom (MDOF) system It tells about the characteristics of the ground motion (accelerogram) Sudhir K. Jain March 2013 Slide 23 Response Spectrum (contd ) Different terms used in IS:1893 Design Acceleration Spectrum (clause 3.5) Response Spectrum (clause 3.27) Acceleration Response Spectrum (used in cl. 3.30) Design Spectrum (title of cl. 6.4) Structural Response Factor Average response acceleration coefficient (see terminology of Sa/g on p. 11) Title of Fig. 2: Response Spectra for. It is better if the code uses the term consistently. Sudhir K. Jain March 2013 Slide 24 12
Smooth Response Spectrum Real spectrum has somewhat irregular shape with local peaks and valleys For design purpose, local peaks and valleys should be ignored Since natural period cannot be calculated with that much accuracy. Hence, smooth response spectrum used for design purposes For developing design spectra, one also needs to consider other issues We will discuss this later. Sudhir K. Jain March 2013 Slide 25 Smooth Response Spectrum (contd ) Period (sec) Period (sec) Period (sec) Acceleration Spectra Velocity Spectra Displacement Spectra Shown here are typical smooth spectra used in design for different values of damping (Fig. from Housner, 1970) Sudhir K. Jain March 2013 Slide 26 13
Ground Acceleration (contd...) Note the term Peak Ground Acceleration (PGA) is max acceleration of ground. Because of deformation in the structure, the motion of its base and the superstructure will be different Max acceleration experienced by mass of the structure will be different from the PGA (except if the structure is rigid) Sudhir K. Jain March 2013 Slide 27 Ground Acceleration ZPA stands for Zero Period Acceleration. Implies max acceleration experienced by a structure having zero natural period (T=0). Sudhir K. Jain March 2013 Slide 28 14
Zero Period Acceleration An infinitely rigid structure Has zero natural period (T=0) Does not deform: No relative motion between its mass and its base Mass has same acceleration as of the ground Hence, ZPA is same as Peak Ground Acceleration For very low values of period, acceleration spectrum tends to be equal to PGA. We should be able to read the value of PGA from an acceleration spectrum. Sudhir K. Jain March 2013 Slide 29 Peak Ground Acceleration (contd ) Average shape of acceleration response spectrum for 5% damping (Fig. on next slide) Ordinate at 0.1 to 0.3 sec ~ 2.5 times the PGA There can be a stray peak in the ground motion; i.e., unusually large peak. Such a peak does not affect most of the response spectrum and needs to be ignored. Effective Peak Ground Acceleration (EPGA) defined as 0.40 times the spectral acceleration in 0.1 to 0.3 sec range (cl. 3.11) There are also other definitions of EPGA, but we will not concern ourselves with those. Sudhir K. Jain March 2013 Slide 30 15
Spectral Acceleration (g) Typical shape of acceleration spectrum 1.80 1.60 1.40 1.20 1.00 0.80 0.60 PGA = 0.6g 0.40 0.20 0.00 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Period (sec) Typical shape of acceleration response spectrum Spectral acceleration at zero period (T=0) gives PGA Value at 0.1-0.3 sec is ~ 2.5 times PGA value (for 5% damping) Sudhir K. Jain March 2013 Slide 31 What is Design Spectrum Seismic Design Force can be specified in terms of Response Spectrum: Termed as Design Spectrum Sudhir K. Jain March 2013 Slide 32 16
Spectral Acceleration, g Response Spectrum versus Design Spectrum Consider the Acceleration Response Spectrum Notice the region of red circle marked: a slight change in natural period can lead to large variation in maximum acceleration Undamped Natural Period T (sec) Sudhir K. Jain March 2013 Slide 33 Response Spectrum versus Design Spectrum (contd ) Natural period of a civil engineering structure cannot be calculated precisely Design specification should not very sensitive to a small change in natural period. Hence, design spectrum is a smooth or average shape without local peaks and valleys you see in the response spectrum Sudhir K. Jain March 2013 Slide 34 17
Spectral Acceleration, g Design Spectrum Since some damage is expected and accepted in the structure during strong shaking, design spectrum is developed considering the overstrength, redundancy, and ductility in the structure. The site may be prone to shaking from large but distant earthquakes as well as from medium but nearby earthquakes: design spectrum may account for these as well. See Fig. next slide. Sudhir K. Jain March 2013 Slide 35 Design Spectrum (contd ) Natural vibration period T n, sec Fig. from Dynamics of Structures by Chopra, 2001 Sudhir K. Jain March 2013 Slide 36 18
Design Spectrum (contd ) Design Spectrum is a design specification It must take into account any issues that have bearing on seismic safety. Sudhir K. Jain March 2013 Slide 37 Design Spectrum (contd ) Design Spectrum must be accompanied by: Load factors or permissible stresses that must be used Different choice of load factors will give different seismic safety to the structure Damping to be used in design Variation in the value of damping used will affect the design force. Method of calculation of natural period Depending on modeling assumptions, one can get different values of natural period. Type of detailing for ductility Design force can be lowered if structure has higher ductility. Sudhir K. Jain March 2013 Slide 38 19
Spectral Acceleration Coefficient (S a /g) Soil Effect Recorded earthquake motions show that response spectrum shape differs for different type of soil profile at the site Fig. from Geotechnical Earthquake Engineering, by Kramer, 1996 Period (sec) Sudhir K. Jain March 2013 Slide 39 Soil Effect (contd ) This variation in ground motion characteristic for different sites is now accounted for through different shapes of response spectrum for three types of sites. Fig. from IS:1893-2002 Period(s) Sudhir K. Jain March 2013 Slide 40 20
Spectral acceleration Shape of Design Spectrum The three curves in Fig. 2 have been drawn based on general trends of average response spectra shapes. In recent years, the US codes (UBC, NEHRP and IBC) have provided more sophistication wherein the shape of design spectrum varies from area to area depending on the ground motion characteristics expected. Sudhir K. Jain March 2013 Slide 41 Design Spectrum for Stiff Structures For very stiff structures (T < 0.1sec), ductility is not helpful in reducing the design force. As a stiff structure gets damaged during the Design spectrum assumes peak shaking, its period extends to T=0 Actual shape of response spectrum elongates (may be used for higher modes only) i.e., during the same ground shaking, a very stiff structure may ride up the ascending part of the graph. Codes tend to disallow the reduction in force in the period range of T < 0.1sec T(seconds) Concept sometimes used by the codes for response spectrum in low period range. Sudhir K. Jain March 2013 Slide 42 21