Design Spectra Page 1 Design Spectra Reading Assignment Course Information Lecture Notes Pp. 73-75 Kramer Appendix B7 Kramer Other Materials Responsespectra.pdf (Chopra) ASCE 7-05.pdf Sakaria time history Homework Assignment #1 Install Seismosignal software on your computer For the Sakaria acceleration time history do the following: Baseline correct the time history and plot the acceleration, velocity and displacement records. Use the quadratic function for the baseline correction. (5 points) Determine peak ground acceleration (pga) from the time history. (5 points) Develop and plot a pseudo acceleration response spectrum for this record at 5 percent damping using Seismosignal. (5 points) Determine the predominate period. (5 points) Scale the record by 1.5 (increase the acceleration values by 50 percent) and replot the pseudo acceleration response spectrum. (5 points) Install the ground motion hazards java program from the United States Geological Survey (USGS) on your computer http://earthquake.usgs.gov/hazards/designmaps/grdmotion.php Install Google Earth on your computer and find the latitude and longitude of the Meldrum Civil Engineering (MCEB). Use these coordinates and USGS java software to find the Ss and S1 values for the MCEB. (10 points) Use the Ss and S1 values above and ASCE 7-05 to develop a design spectrum for the MCEB. (20 points) Assume the MCEB is found on a site class C soil. Show all calculations and inputs to calculations. Check your solution against the design spectrum calculated by the USGS java calculator.
Design Spectra Page 2 Design Spectra (cont.) Monday, January 06, 2014 2:32 PM Definition - Plot of maximum response (acceleration, velocity displacement amplitude) of a single degree of freedom system (SDOF) for a particular input ground motion as a function of frequency or period and damping ratio of the SDOF. The equation that relate the response of the SDOF to the input ground motion for a linear elastic, damped system is Duhamel's integral (see Kramer p. 566) If a response spectrum has been developed, then the spectral displacement Sd, spectral velocity, Sv and spectral acceleration Sa for lightly damped systems can be approximated by: Steven F. Bartlett, 2014
Design Spectra Page 3 Stiffness and Damping Representation
Design Spectra Page 4
Acceleration [g] Response Acceleration [g] Design Spectra Page 5 Plotting Response Spectra for an Earthquake (cont.) 0.8 0.6 0.4 0.2 0-0.2-0.4 0 1 2 3 4 Time [sec] 5 6 7 8 Acceleration time history (ground surface) 1.8 1.7 1.6 Damp. 5.0% 1.5 1.4 1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 1 2 Period [sec] 3 Acceleration Response Spectrum for above time history from Seismosignal TM Important Concepts: An acceleration response spectrum, such as that above, is widely used in geotechnical and structural engineering. It expresses the maximum acceleration response of a single degree of freedom system (SDOF) as a function of period for a given level of structural damping (usually 5 percent, unless otherwise stated.) The above spectrum is not a design spectrum. It is jagged because it represents a spectrum for a given time history. An acceleration time history can be converted to an acceleration response spectrum which represents the response of the SDOF for the given input motion. Software is usually used to do this conversion. Seismosignal is recommended
Design Spectra Page 6 Representing Earthquake Motion in Design Methods of Developing Design Spectra and Design Strong Motion Empirical attenuation relations (CVEEN 6330) Building code design spectra (CVEEN 6330 and CVEEN 7330) Site-specific Ground Response Analyses (CVEEN 6330 and CVEEN 7330) Equivalent Linear Techniques (computer program SHAKE or DEEPSOIL) (CVEEN 7330) Nonlinear Techniques (CVEEN 6330 and CVEEN 7330) FEM (finite element methods) (computer program DEEPSOIL) (CVEEN 7330) FDM (finite difference methods) (computer program FLAC) (CVEEN 6330 and CVEEN 7330)
Design Spectra Page 7 Development of Design Spectra using ASCE 7-05 Ss and S1 are obtained from the United States Geological Survey National Strong Motion Program. The link for this computer program (Java Script) is given in the homework assignment.
Design Spectra Page 8 ASCE 7-05 (cont.)
Design Spectra Page 9 ASCE 7-05 (cont.)
Spectral acceleration (g) Design Spectra Page 10 ASCE 7-05 (cont.) Generic Design Spectrum from ASCE 7-05 2.10 2.00 1.90 1.80 1.70 1.60 1.50 1.40 1.30 1.20 1.10 1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 To Sa = SDS Sa =0.4 SDS a T = 0 Sa = pga Ts = SD1/SDS Sa = SD1/T ASCE 7-05 Spectrum - Site Class D 0.00 0 0.5 1 1.5 2 Period (s)
Design Spectra Page 11 ASCE 7-05 (cont.)
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