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<br />7.4 RESPONSE SPECTRA <br /> <br />Response spectra represent a graphical relationship of the maximum <br />response of asingle-degree-of-freedom elastic system to dynamic <br />motion. Such spectra account for the amplitude, frequency and <br />duration of the input ground motion and are plotted as curves on tripaz- <br />tite logarithmic graph paper showing variations of peak spectral accel- <br />eration, displacement, and velocity of the system with its correspond- <br />ing period of vibration. Several curves may be plotted representing <br />various damping factors (generally 0%, 2%, 5%, 7%, 10% and 20% of <br />critical) where critical damping is the minimum which will prevent <br />oscillation from taking place. <br />In general, damping factors depend on the type of structure to be <br />analyzed and foundation conditions at the site. Brady and others <br />EERL, 1972) indicate damping factors of 2% [0 8% of critical aze <br />appropriate for buildings and damping factors of 5% to 10% of critical <br />are suitable for earthwork. Hays and others (1975) relate damping <br />factors to foundation geologic materials and sheaz wave velocity (V,) <br />according to the following: <br />TABLE IV <br />DAMPING FACTORS <br />SITE CONDITION SI-IEAR WAVE <br />VELOCITY, V, <br />feeUsecond DAMPING <br />FACTOR <br />% OF CRITICAL <br />Bedrock site >6000 2 - 5% <br />Firm soil site >2000 to <6000 5 - 7% <br />Soft soil site <2000 7 - 10% <br />Shear wave velocity is generally about 0.6 of compressional wave <br />(P-wave) velocity which can be obtained directly from refraction <br />seismic investigations or other geophysical methods. Selection of a <br />critical damping factor for use in engineering analyses depends on the <br />type of structure, site conditions and judgment of the design engineers. <br />For Trout Creek dam, a range of critical damping values (5%, 7% and <br />10%) was selected for use in prepazing the response spectra. <br />35 <br />