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Question 13.8: Plot the peak deformations in a SDOF bilinear system for dif...

Plot the peak deformations in a SDOF bilinear system for different ductility ratios equal to 1, 1.5, 2, 4 and 6 when subjected to the same ground motion of Example 13.5.

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The values of maximum deformations in an inelastic SDOF system were shown in Table 13.5. The same data is plotted in Figure 13.35(a) on semi log scale. The portion up to T =T_{C} is enlarged in Figure 13.35(b) for clarity. Beyond T_{C} , inelastic and elastic displacements are equal, therefore, all curves for different ductility merge.

Table 13.5 Relation between Maximum Elastic and Inelastic Displacements with Period T for Different Ductility μ

µ = 1 µ = 1.5 µ = 2
S_{a}/g S_{de}(cm} S_{d}/S_{de} R S_{a}/g S_{d} S_{d}/S_{de} R S_{a}/g S_{d} S_{d}/S_{de}
1 0.01 0.0025 1 1 1 0.0037 1.5 1 1 0.0050 2
1 0.02 0.0099 1 1 1 0.0149 1.5 1 1 0.0199 2
1 0.03 0.0224 1 1 1 0.0336 1.5 1 1 0.0448 2
1.3 0.04 0.0517 1 1.0724 1.2123 0.0724 1.3988 1.1171 1.1637 0.0926 1.7904
1.5 0.05 0.0933 1 1.1321 1.3250 0.1236 1.325 1.2173 1.2323 0.1533 1.643
1.8 0.06 0.1612 1 1.1833 1.5211 0.2043 1.2676 1.3058 1.3785 0.2469 1.5317
1.9 0.07 0.2316 1 1.2285 1.5466 0.2828 1.221 1.3856 1.3713 0.3343 1.4434
2 0.08 0.3184 1 1.269 1.5761 0.3764 1.1821 1.4587 1.3711 0.4365 1.3711
2.2 0.09 0.4433 1 1.3058 1.6848 0.5092 1.1487 1.5263 1.4414 0.5808 1.3103
2.4 0.1 0.597 1 1.3396 1.7916 0.6685 1.1197 1.5895 1.5099 0.7512 1.2583
2.6 0.11 0.7825 1 1.371 1.8964 0.8562 1.0941 1.6489 1.5768 0.9492 1.2129
2.71 0.125 1.0533 1 1.4142 1.9163 1.1172 1.0607 1.7321 1.5646 1.2162 1.1547
2.71 0.13 1.1392 1 1.4142 1.9163 1.2083 1.0607 1.7321 1.5646 1.3155 1.1547
2.71 0.14 1.3212 1 1.4142 1.9163 1.4014 1.0607 1.7321 1.5646 1.5256 1.1547
2.71 0.15 1.5167 1 1.4142 1.9163 1.6087 1.0607 1.7321 1.5646 1.7513 1.1547
2.71 0.16 1.7257 1 1.4142 1.9163 1.8304 1.0607 1.7321 1.5646 1.9926 1.1547
2.71 0.17 1.9481 1 1.4142 1.9163 2.0663 1.0607 1.7321 1.5646 2.2495 1.1547
2.71 0.18 2.1841 1 1.4142 1.9163 2.3165 1.0607 1.7321 1.5646 2.5219 1.1547
2.71 0.19 2.4335 1 1.4142 1.9163 2.5811 1.0607 1.7321 1.5646 2.8099 1.1547
2.71 0.2 2.6964 1 1.4142 1.9163 2.8599 1.0607 1.7321 1.5646 3.1135 1.1547
2.71 0.22 3.2626 1 1.4142 1.9163 3.4605 1.0607 1.7321 1.5646 3.7673 1.1547
2.71 0.24 3.8828 1 1.4142 1.9163 4.1183 1.0607 1.7321 1.5646 4.4834 1.1547
2.71 0.26 4.5569 1 1.4142 1.9163 4.8333 1.0607 1.7321 1.5646 5.2618 1.1547
2.71 0.28 5.2849 1 1.4142 1.9163 5.6055 1.0607 1.7321 1.5646 6.1025 1.1547
2.71 0.3 6.0668 1 1.4142 1.9163 6.4348 1.0607 1.7321 1.5646 7.0054 1.1547
2.71 0.32 6.9027 1 1.4142 1.9163 7.3214 1.0607 1.7321 1.5646 7.9706 1.1547
2.71 0.33 7.3409 1 1.4142 1.9163 7.7862 1.0607 1.7321 1.5646 8.4765 1.1547
2.71 0.35 8.2576 1 1.4142 1.9163 8.7585 1.0607 1.7321 1.5646 9.5351 1.1547
2.71 0.38 9.7339 1 1.4142 1.9163 10.3243 1.0607 1.7321 1.5646 11.2397 1.1547
2.71 0.4 10.7855 1 1.4142 1.9163 11.4397 1.0607 1.7321 1.5646 12.454 1.1547
2.71 0.43 12.464 1 1.4142 1.9163 13.22 1.0607 1.7321 1.5646 14.3921 1.1547
2.71 0.47 14.8907 1 1.4142 1.9163 15.794 1.0607 1.8800 1.4415 15.8412 1.0638
2.71 0.49 16.1849 1 1.4700 1.8435 16.5152 1.0204 1.9600 1.3827 16.5152 1.0204
2.71 0.5 16.8523 1 1.5000 1.8067 16.8523 1.0000 2.0000 1.3550 16.8523 1.0000
2.3 0.6 20.5959 1 1.5000 1.5333 20.5959 1.0000 2.0000 1.1500 20.5959 1.0000
1.95 0.7 23.7673 1 1.5000 1.3 23.7673 1.0000 2.0000 0.9750 23.7673 1.0000
1.77 0.8 28.1775 1 1.5000 1.18 28.1775 1.0000 2.0000 0.8850 28.1775 1.0000
1.6 0.9 32.237 1 1.5000 1.0667 32.237 1.0000 2.0000 0.8000 32.237 1.0000
1.5 1 37.3114 1 1.5000 1 37.3114 1.0000 2.0000 0.7500 37.3114 1.0000
1 1.5 55.967 1 1.5000 0.6667 55.967 1.0000 2.0000 0.5000 55.967 1.0000
0.7 2 69.6479 1 1.5000 0.4667 69.6479 1.0000 2.0000 0.3500 69.6479 1.0000
0.55 2.5 85.5052 1 1.5000 0.3667 85.5052 1.0000 2.0000 0.2750 85.5052 1.0000
0.45 3 100.7406 1 1.5000 0.3 100.7406 1.0000 2.0000 0.2250 100.7406 1.0000
0.313 4 124.5702 1 1.5000 0.2087 124.5702 1.0000 2.0000 0.1565 124.5702 1.0000
0.2 5 124.3712 1 1.5000 0.1333 124.3712 1.0000 2.0000 0.1000 124.3712 1.0000
0.139 6 124.4707 1 1.5000 0.0927 124.4707 1.0000 2.0000 0.0695 124.4707 1.0000
0.102 7 124.3214 1 1.5000 0.068 124.3214 1.0000 2.0000 0.051 124.3214 1.0000
0.078 8 124.1722 1 1.5000 0.052 124.1722 1.0000 2.0000 0.039 124.1722 1.0000
0.062 9 124.9184 1 1.5000 0.0413 124.9184 1.0000 2.0000 0.0310 124.9184 1.0000
0.05 10 124.3712 1 1.5000 0.0333 124.3712 1.0000 2.0000 0.0250 124.3712 1.0000
0.0084 20 83.5774 1 1.5000 0.0056 83.5774 1.0000 2.0000 0.0042 83.5774 1.0000
0.0029 30 64.9218 1 1.5000 0.0019 64.9218 1.0000 2.0000 0.0015 64.9218 1.0000
0.00156 40 62.0861 1 1.5000 0.001 62.0861 1.0000 2.0000 0.0008 62.0861 1.0000
0.001 50 62.1856 1 1.5000 0.0007 62.1856 1.0000 2.0000 0.0005 62.1856 1.0000
0.0007 60 62.6831 1 1.5000 0.0005 62.6831 1.0000 2.0000 0.0004 62.6831 1.0000
0.00052 70 62.7701 1 1.5000 0.0003 62.7701 1.0000 2.0000 0.0003 62.7701 1.0000
0.00039 80 62.0861 1 1.5000 0.0003 62.0861 1.0000 2.0000 0.0002 62.0861 1.0000
0.00031 90 62.4592 1 1.5000 0.0002 62.4592 1.0000 2.0000 0.0002 62.4592 1.0000
0.00025 100 62.1856 1 1.5000 0.0002 62.1856 1.0000 2.0000 0.0001 62.1856 1.0000
Annotation 2022-10-18 221404
Annotation 2022-10-18 221419

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