Question 14.4: Construct an ADR spectrum for ductility ratio of 1, 1.5, 2, ...

The inelastic response spectra for this ground motion for ductility ratio of 1.5, 2, 4 and 6 were developed in Example 13.5. An alternative format was shown in Example 13.6. The same data was used to develop the ADRS. The reduction factor R depends upon the acceleration or velocity-sensitive regions given by Equation (14.31). The spectral displacements are computed using Equation (14.32). Typical calculations for generating inelastic ADRS are shown in Table 14.8. Similar calculations can be done for other ductility ratios. The double lines in the table show change in reduction factor region.
The inelastic ADRS is shown in Figure 14.22.

R = 1       for         T < T_{A}               (14.31a)

R=(2\mu -1)^{y/2}        for    T_{A}< T <T_{B}       (14.31b)

R=(2\mu-1)^{0.5}    \text{for}     T_B\lt T\lt T_C^{\prime}      (14.31c)

R=(T/T_C)\mu    \text{for}    T_C^{\prime}\lt T\lt T_C    (14.31d)

R=\mu    \text{for}    T\gt T_C            (14.31e)

\gamma =\frac{\log\left\lgroup\frac{T}{T_A} \right\rgroup }{\log \left\lgroup\frac{T_B}{T_A} \right\rgroup }         (14.31f)

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

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

Table 14.8 calculations for R, S_{a} and S_{d} coordinates