## 3 Results  
Figure 3 displays a comparison of height-wise distribution for THMA error (error 1) and six relevant variables (\(u_{1}\), \(\Delta_{1}\), \(\
abla_{1}\), \(a_{1}\), \(V_{\mathrm{S1}}\), \(V_{\mathrm{D1}}\)) in two representative systems (B3-1, typical of frame behavior and B3-\(\infty\), representative of pure shear behavior for GMS B and 3% inherent damping). Every sub-plot displays the min, \(x^{10}\), \(x^{50}\), \(x^{90}\) and max error for each story, thus allowing quick identification of the error magnitude and vertical distribution. For brevity, similar plots for RSA-SRSS error (error 2) and RSA-CQC error (error 3) are included as Supplementary Materials, Figures S1 and S2. This information is supplemented by scatter plots providing a visual overview of THMA error (error 1) in Figures 4 and 5. In addition to sheer representation of the data points, useful analytical results are also provided in the last set of plots: (i) three markers have been included pointing the 10%, 50%, and 90% percentiles (\(x^{10}\), \(x^{50}\), \(x^{90}\)) of data in the set (triangular red, circular blue and triangular green markers, respectively), and the variable values corresponding to these percentiles are indicated in the left and bottom margins in the corresponding color; (ii) an Engineering Acceptability Range (EAR) [\(-0.15\); \(+0.25\)] has been marked with dashed lines (red and green) as a visual reference to allow quick comparison between plots; the percentage of data below, within and above this range is indicated at the right and top margins of the plot; (iii) the maximum and minimum value of each data set is presented at the bottom right corner (for data in y axis) and top left corner (for data in x axis); (iv) the Pearson correlation coefficient \(\rho\) between both sets of data is presented at the bottom left corner of the plot. To simplify interpretation, text regarding data for \(x\)-axis is oriented vertically, whereas text regarding data for \(y\)-axis is oriented horizontally; the correlation coefficient text is rotated diagonally. As an example,focusing on the left column of Figure 4b, presenting the plot for \(\Delta_{1,\text{error,average}}\), it can be seen that for the case B3-1 100% results are within EAR, with \(x^{50}=-0.01\), \(x^{10}=-0.05\) and \(x^{90}=+0.01\), and extreme values \(x_{\text{min}}=-0.16\), \(x_{\text{max}}=+0.20\); for case B3-\(\infty\), \(4.3\%\) of the results are too unconservative (below \(-0.15\)) and \(95.7\%\) of results are within range, with \(x^{50}=-0.01\), \(x^{10}=-0.10\), \(x^{90}=+0.02\) and extreme values \(x_{\text{min}}=-0.28\) and \(x_{\text{max}}=+0.26\). Between both sets the correlation is \(\rho=0.76\). The Engineering Acceptability Range (EAR) was introduced by [PERSON] and [PERSON] in the context of equivalent linearization to express the acceptable range of error when an engineering variable is obtained using an approximate method [44]. The asymmetry of the range follows from the fact that conservative errors are, engineeringly speaking, more acceptable than unconservative ones. The range adopted in this study is based on a survey among structural engineering professionals and is purely indicative; details can be found in [25]. Figure 3: Plots of THMA errors (error 1): (**a**) frame-type system B3-1; (**b**) shear-type system B3-\(\infty\).