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Question 14.3: Draw the response spectrum curves of IS:1893 code on hard so...

Draw the response spectrum curves of IS:1893 code on hard soil for 2% and 5% damping in ADRS format.

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The response spectra of IS:1893-Part 1 was presented in Chapter 8. It can be
converted in ADRS format by the procedure outlined earlier using Equation (14.26) for
a given damping.

S_{di}=\frac{T_{I}^{2}}{4\pi ^{2}} S_{ai}g          (14.26)

Typical calculations are shown in Table 14.7. In the last five columns, spectral displacement has been computed for different periods (T = 0.5, 1, 1.5, 2 and 4 sec) corresponding to spectral accelerations for 2% damping. This data is used to plot constant period lines.

Table 14.7 Calculations for ADRS for IS:1893 Spectra

5% damping 2% damping T = 0.5 T = 1 T = 1.5 T = 2 T = 4
Period (T) Acceleration (S_{a}/g) Displacement (S_{d}) Acceleration (S_{a}/g) Displacement (S_{d}) Displacement (S_{d}) Displacement (S_{d}) Displacement (S_{d}) Displacement (S_{d}) Displacement (S_{d})
0 0.000 0.000 0.000 0.000 0 0 0 0 0
0.1 2.500 0.0062 3.500 0.0087 0.1555 0.6219 1.3992 2.4874 9.9497
0.2 2.500 0.0249 3.500 0.0348 0.1555 0.6219 1.3992 2.4874 9.9497
0.3 2.500 0.056 3.500 0.078 0.1555 0.6219 1.3992 2.4874 9.9497
0.4 2.500 0.099 3.500 0.139 0.1555 0.6219 1.3992 2.4874 9.9497
0.5 2.000 0.124 2.800 0.174 0.1244 0.4975 1.1193 1.9899 7.9598
0.6 1.667 0.149 2.333 0.209 0.1036 0.4146 0.9328 1.6583 6.6331
0.7 1.429 0.174 2.000 0.244 0.0888 0.3553 0.7995 1.4214 5.6855
0.8 1.25 0.199 1.750 0.279 0.0777 0.3109 0.6996 1.2437 4.9748
0.9 1.111 0.224 1.556 0.313 0.0691 0.2764 0.6219 1.1055 4.4221
1 1.000 0.249 1.400 0.348 0.0622 0.2487 0.5597 0.995 3.9799
1.1 0.909 0.274 1.273 0.383 0.0565 0.2261 0.5088 0.9045 3.6181
1.2 0.833 0.298 1.167 0.418 0.0518 0.2073 0.4664 0.8291 3.3166
1.3 0.769 0.323 1.077 0.453 0.0478 0.1913 0.4305 0.7654 3.0614
1.4 0.714 0.348 1.000 0.488 0.0444 0.1777 0.3998 0.7107 2.8428
1.5 0.667 0.373 0.933 0.522 0.0415 0.1658 0.3731 0.6633 2.6533
1.6 0.625 0.398 0.875 0.557 0.0389 0.1555 0.3498 0.6219 2.4874
1.7 0.588 0.423 0.824 0.592 0.0366 0.1463 0.3292 0.5853 2.3411
1.8 0.556 0.448 0.778 0.627 0.0345 0.1382 0.3109 0.5528 2.211
1.9 0.556 0.473 0.737 0.662 0.0327 0.1309 0.2946 0.5237 2.0947
2 0.500 0.497 0.700 0.696 0.0311 0.1244 0.2798 0.4975 1.9899
2.1 0.476 0.522 0.667 0.731 0.0296 0.1184 0.2665 0.4738 1.8952
2.2 0.455 0.547 0.636 0.766 0.0283 0.1131 0.2544 0.4523 1.809
2.3 0.435 0.572 0.609 0.801 0.027 0.1081 0.2433 0.4326 1.7304
2.4 0.417 0.597 0.583 0.836 0.0259 0.1036 0.2332 0.4146 1.6583
2.5 0.400 0.622 0.560 0.871 0.0249 0.0995 0.2239 0.398 1.592
2.6 0.385 0.647 0.538 0.905 0.0239 0.0957 0.2153 0.3827 1.5307
2.7 0.370 0.672 0.519 0.94 0.023 0.0921 0.2073 0.3685 1.474
2.8 0.357 0.696 0.500 0.975 0.0222 0.0888 0.1999 0.3553 1.4214
2.9 0.345 0.721 0.483 1.01 0.0214 0.0858 0.193 0.3431 1.3724
3 0.333 0.746 0.467 1.045 0.0207 0.0829 0.1866 0.3317 1.3266
3.1 0.323 0.771 0.452 1.08 0.0201 0.0802 0.1805 0.321 1.2838
3.2 0.313 0.796 0.438 1.114 0.0194 0.0777 0.1749 0.3109 1.2437
3.3 0.303 0.821 0.424 1.149 0.0188 0.0754 0.1696 0.3015 1.206
3.4 0.294 0.846 0.412 1.184 0.0183 0.0732 0.1646 0.2926 1.1706
3.5 0.286 0.871 0.400 1.219 0.0178 0.0711 0.1599 0.2843 1.1371
3.6 0.278 0.895 0.389 1.254 0.0173 0.0691 0.1555 0.2764 1.1055
3.7 0.270 0.920 0.378 1.288 0.0168 0.0672 0.1513 0.2689 1.0756
3.8 0.263 0.945 0.368 1.323 0.0164 0.0655 0.1473 0.2618 1.0473
3.9 0.256 0.970 0.359 1.358 0.0159 0.0638 0.1435 0.2551 1.0205
4 0.250 0.995 0.350 1.393 0.0155 0.0622 0.1399 0.2487 0.995

The ADRS spectrum curves for 2% and 5% damping are shown in Figure 14.21.
The radial lines are constant period lines.

Annotation 2022-10-20 122616

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