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31x

000711

2024-01-16

Formula 14

M_{cr} = 1.127 \cdot \frac{π^{2} \cdot 21, 000 \frac{kN}{{cm}^{2}} \cdot 10, 140 {cm}^{4}}{{(1 \cdot 650 cm)}^{2}} \cdot (\sqrt{(\frac{1}{1}) \cdot \frac{2, 883, 000 {cm}^{6}}{10, 140 {cm}^{4}} \frac{{(1.0 \cdot 650 cm)}^{2} \cdot 8, 076.92 \frac{kN}{{cm}^{2}} \cdot 292.5 {cm}^{4}}{π^{2} \cdot 21, 000 \frac{kN}{{cm}^{2}} \cdot 10, 140 {cm}^{4}} {(0.454 \cdot 18 cm)}^{2}} - 0.454 \cdot 18 cm)

M_{cr} = 115, 310 kNcm = 1, 153.10 kNm

{\bar{λ}}_{LT} = \sqrt{\frac{W_{pl, y} \cdot f_{y}}{M_{cr}}} = \sqrt{\frac{2, 683 {cm}^{3} \cdot 23.5 \frac{kN}{{cm}^{2}}}{115, 310 kNcm}} = 0.739

ϕ_{LT} = 0.5 \cdot [1 0.34 \cdot (0.739 - 0.4) 0.75 \cdot 0 . 739^{2}] = 0.762

χ_{LT} = \frac{1}{0.762 \sqrt{0 . 762^{2} - 0.75 \cdot 0 . 739^{2}}} = 0.85 < 1

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