Erratum for “Nonlinear Inelastic Dynamic Analysis of I-Beams Curved In-Plan” by R. Emre Erkmen and Mark A. Bradford

$$“{\mathbf{\sigma }}_{t+\text{δ}t}^j={\mathbf{\sigma }}_t+{\mathbf{E}}^{\mathbf{e}}\mathrm{\Delta }{\mathbf{\epsilon }}_{t+\text{δ}t}^j-\frac{{\overline{\sigma }}_{ef}({\overline{\sigma }}_{ef}-{\sigma }_y)}{\left({\overline{\sigma }}^2+3{\overline{\tau }}^2\right)}{\overline{\mathbf{\sigma }}}_{t+\text{δ}t}^j+\frac{H\prime {\overline{\sigma }}_{ef}^3({\overline{\sigma }}_{ef}-{\sigma }_y)}{\left(H\prime {\overline{\sigma }}_{ef}^2+E{\overline{\sigma }}^2+9G{\overline{\tau }}^2\right)\left({\overline{\sigma }}^2+3{\overline{\tau }}^2\right)}{\overline{\mathbf{\sigma }}}_{t+\text{δ}t}^j$$

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where $\overline{\sigma }$ and $\overline{\tau }$ = components of ${\overline{\mathbf{\sigma }}}_{t+\delta t}^j$ and ${\overline{\sigma }}_{ef}=\sqrt{{\overline{\sigma }}^2+3{\overline{\tau }}^2}$. According to the third term in the preceding equation, the trial stresses are scaled onto the yield surface. It should be noted that the yield surface is not a circle, and the term radial is used loosely herein to indicate the direction toward the center of the yield surface. The last term considers the extension of the yield surface because of strain hardening.”