Powrót do: Siła krytyczna
Treść
Oblicz siłę krytyczną i sprawdź czy pręt ulegnie wyboczeniu.
Dane: 
Rozwiązanie
![\begin{aligned} &A=200 cm^2\\ &I_{y}=\frac{bh^3}{12}=6666,67 cm^4\\ &I_{z}=\frac{b^3h}{12}=1666,67 cm^4\\ &I_{min}=I_{z}\\ &i_{min}=\sqrt{\frac{I_{z}}{A}}=2,8867 cm\\ &\lambda_{gr}=pi \sqrt{\frac{E}{R_{h}}}=114,715 [-]\\ &\lambda=\frac{lw}{i_{min}}=\frac{\alpha l}{i_{min}}=69,28 [-]\\ &\lambda<\lambda_{gr}\\ &P_{TI}=A(R_{e}-\frac{R_{e}-R_{h}}{\lambda_{gr}}\lambda)\\ &P_{TI}=2000\cdot 10^{-4}(200-\frac{200-150}{114,715}69,28)\cdot 10^6=3,396 MN\ &P_{kr}>P\\ \end{aligned}](https://s0.wp.com/latex.php?latex=+%5Cbegin%7Baligned%7D+%26A%3D200+cm%5E2%5C%5C+%26I_%7By%7D%3D%5Cfrac%7Bbh%5E3%7D%7B12%7D%3D6666%2C67+cm%5E4%5C%5C+%26I_%7Bz%7D%3D%5Cfrac%7Bb%5E3h%7D%7B12%7D%3D1666%2C67+cm%5E4%5C%5C+%26I_%7Bmin%7D%3DI_%7Bz%7D%5C%5C+%26i_%7Bmin%7D%3D%5Csqrt%7B%5Cfrac%7BI_%7Bz%7D%7D%7BA%7D%7D%3D2%2C8867+cm%5C%5C+%26%5Clambda_%7Bgr%7D%3Dpi+%5Csqrt%7B%5Cfrac%7BE%7D%7BR_%7Bh%7D%7D%7D%3D114%2C715+%5B-%5D%5C%5C+%26%5Clambda%3D%5Cfrac%7Blw%7D%7Bi_%7Bmin%7D%7D%3D%5Cfrac%7B%5Calpha+l%7D%7Bi_%7Bmin%7D%7D%3D69%2C28+%5B-%5D%5C%5C+%26%5Clambda%3C%5Clambda_%7Bgr%7D%5C%5C+%26P_%7BTI%7D%3DA%28R_%7Be%7D-%5Cfrac%7BR_%7Be%7D-R_%7Bh%7D%7D%7B%5Clambda_%7Bgr%7D%7D%5Clambda%29%5C%5C+%26P_%7BTI%7D%3D2000%5Ccdot+10%5E%7B-4%7D%28200-%5Cfrac%7B200-150%7D%7B114%2C715%7D69%2C28%29%5Ccdot+10%5E6%3D3%2C396+MN%5C+%26P_%7Bkr%7D%3EP%5C%5C+%5Cend%7Baligned%7D&bg=ffffff&fg=000&s=0&c=20201002)
Pręt nie ulegnie wyboczeniu!
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