Question 14.7: Construct an ADR spectrum for ductility ratio of 1, 2, 3, 4,...

Plot the elastic spectral acceleration-spectral displacement curve for 5% damping using Equation (14.26) along with radial lines for T = 0.5, 1, 1.5 and 2 sec as in previous examples. The reduction factors for spectral accelerations specified in Eurocode 8 are as follows:

R = (µ − 1)T/$T_{C}$ + 1     for      $T < T_{C}$    (14.33a)

R = µ      for     $T >T_{C}$      (14.33a)

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

The spectral displacements are obtained using Equation (14.32). Typical calculations for generating inelastic ADRS are shown in Table 14.11. The double lines in the table show change in reduction factor R region. Similar calculations can be done for other ductility ratios.
The constant ductility ADRS is shown in Figure 14.25.

$S_{\text{d inelastic}} =µ S_{\text{d inelastic}}/R$    for    $T < T_{C}$     (14.32a)

$S_{\text{d inelastic}} =S_{\text{d inelastic}}$      for    $T > T_{C}$        (14.32b)

Table 14.11 Calculations for r, $S_{a}$ and $S_{d}$ coordinates