Official Journal of the Japan Wood Research Society
Table 1 Resisting compression stress distributions
From: Theoretical model and finite element analysis for restoring moment at column foot during rocking
Sub-states | \(w_{i}^{+}(x)\) |
|---|---|
\(S_{2}^{{\text{+}}}\) | Â |
 Elastic | \(w_{{2{\text{e}}}}^{+}(x)=\frac{{\tan \theta {E_{\text{t}}}}}{h}(x - r)+q_{{{\text{ar}}}}^{+}\qquad (34)\) |
 Elasto-plastic | \(w_{{2{p_{\rm I}}}}^{+}(x)=\frac{{q_{{{\text{al}}}}^{+} - {\sigma _{{\text{pc}}}}}}{{ - {L_{{\theta _{\text{e}}}}}}}\left( {x - {L_{{\theta _{\text{e}}}}}+r} \right)+{\sigma _{{\text{pc}}}}, - r \leqslant x \leqslant {L_{{\theta _{\text{e}}}}} - r\qquad (35)\) \(w_{{2{p_\Pi }}}^{+}(x)={\sigma _{\text{pc}}},\quad {L_{{\theta _e}}} - r < x \leqslant r\qquad (36)\) |
\(S_{3}^{{\text{+}}}\) | Â |
 Elastic | \(w_{{3{\text{e}}}}^{+}(x)=\frac{{\tan \theta {E_{\text{t}}}}}{h}(x+r)\qquad (37)\) |
 Elasto-plastic | \(w_{{3{p_{\rm I}}}}^{+}(x)=\frac{{{\sigma _{{\text{pc}}}}}}{{{L_{{\theta _{\text{e}}}}}}}(x+r),\quad - r \leqslant x \leqslant {L_{{\theta _{\text{e}}}}} - r\qquad (38)\) \(w_{{3{p_\Pi }}}^{+}(x)={\sigma _{{\text{pc}}}},\quad {L_{{\theta _{\text{e}}}}} - r < x \leqslant r\qquad (39)\) |
\(S_{4}^{{\text{+}}}\) | Â |
 Elastic | \(w_{{4{\text{e}}}}^{+}(x)=\frac{{\tan \theta {E_{\text{t}}}}}{h}(x - r+{L_\theta })\qquad (40)\) |
 Elasto-plastic | \(w_{{4{p_{\rm I}}}}^{+}(x)=\frac{{{\sigma _{{\text{pc}}}}}}{x}(x - r+{L_\theta }),\quad r - {L_\theta } \leqslant x \leqslant r - {L_{{\theta _{\text{y}}}}}\qquad (41)\) \(w_{{4{p_\Pi }}}^{+}(x)={\sigma _{{\text{pc}}}},\quad r - {L_{{\theta _{\text{y}}}}} < x \leqslant r\qquad (42)\) |
\(S_{5}^{{\text{+}}}\) | Â |
 Elastic | \(w_{{5{\text{e}}}}^{+}(x)=\frac{{\tan \theta {E_{\text{t}}}}}{h}x\qquad (43)\) |
 Elasto-plastic | \(w_{{5{p_{\rm I}}}}^{+}(x)=\frac{{{\sigma _{{\text{pc}}}}}}{{{L_{{\theta _{\text{e}}}}}}}x,\quad 0 \leqslant x \leqslant {L_{{\theta _{\text{e}}}}}\qquad (44)\) \(w_{{5{p_\Pi }}}^{+}(x)={\sigma _{{\text{pc}}}},\quad {L_{{\theta _{\text{e}}}}} < x \leqslant r\qquad (45)\) |
\(S_{6}^{{\text{+}}}\) | Â |
 Elastic | \(w_{{6{\text{e}}}}^{+}(x)=\frac{{\tan \theta {E_{\text{t}}}}}{h}\left( {x - r+{L_\theta }} \right)\qquad (46)\) |
 Elasto-plastic | \(w_{{6{p_{\rm I}}}}^{+}(x)=\frac{{{\sigma _{{\text{pc}}}}}}{{{L_{{\theta _{\text{e}}}}}}}(x - r+{L_\theta }),\quad r - {L_\theta } \leqslant x \leqslant r - {L_{{\theta _{\text{y}}}}}\qquad (47)\) \(w_{{6{p_\Pi } }}^{ + } (x) = \sigma _{{{\text{pc}}}} ,\quad r - L_{{\theta _{{\text{y}}} }} < x \leqslant r \qquad (48)\) |