Wzór Żurawskiego

$\sigma_{T} = \frac{T\left( x_{1} \right)}{I_{3}}\frac{S}{b\left( x_{2} \right)}$, $S = \frac{b}{2}\left( \frac{h}{2} - x_{2} \right)\left( \frac{h}{2} + x_{2} \right) =$

$$\frac{bh^{2}}{8}\left\lbrack 1 - 4\left( \frac{x_{2}}{h} \right)^{2} \right\rbrack,$$

$I_{3} = \frac{1}{12}bh^{3},\ b\left( x_{2} \right) = b$

$\sigma_{T} = \frac{3}{2}\frac{T}{\text{bh}}\left\lbrack 1 - 4\left( \frac{x_{2}}{h} \right)^{2} \right\rbrack,\ $

$\sigma_{\text{T\ max}} = \frac{3}{2}\frac{T}{\text{bh}} = \frac{3}{2}\sigma_{T\ sr},\ $

$$\text{\ σ}_{T\ sr} = \frac{T}{\text{bh}},$$

$\sigma = \begin{bmatrix} 300 & 0 \\ 0 & - 100 \\ \end{bmatrix}$ $\sigma = \begin{bmatrix} 300 & - 50 \\ - 50 & - 100 \\ \end{bmatrix}$

Hip. Hubera

A $\sigma_{\text{zred}} = \sqrt{\sigma_{11}^{2} + \sigma_{22}^{2} - \sigma_{11}\sigma_{22} + 3\sigma_{12}^{2}}$=

B $\sigma_{\text{zred}} = \sqrt{\sigma_{11}^{2} + \sigma_{22}^{2} - \sigma_{11}\sigma_{22} + 3\sigma_{12}^{2}}$=

Hip. Coulomba – Treski

A σ_zred = σ_max − σ_min,

σ₁₁ = σ₁ = max, σ₂₂ = σ₂ = min

B $\begin{matrix} \sigma_{1} \\ \sigma_{2} \\ \end{matrix}\} = \frac{1}{2}\left( \sigma_{11} + \sigma_{22} \right) \pm$

$\frac{1}{2}\sqrt{\left( \sigma_{11} - \sigma_{22} \right)^{2} + 4\sigma_{12}^{2}} = \left\{ \begin{matrix} \max \\ \min \\ \end{matrix} \right.\ \ $,

σ_zred = σ_max − σ_min

$\frac{E}{\rho}I_{3} = M_{g}$

$\frac{1}{\rho} = \frac{M_{g}}{EI_{3}} = x_{g},$

$\sigma_{g} = \frac{M_{g}}{I_{3}}x_{2},$

$\sigma_{\text{g\ max}}^{r} = \frac{M_{g}}{I_{3}}x_{2}^{r} = \frac{M_{g}}{W_{\text{gr}}},$

$\sigma_{\text{g\ max}}^{c} = \frac{M_{g}}{I_{3}}\left| x_{2}^{c} \right| = \frac{M_{g}}{W_{\text{gc}}},$

$\gamma\left( \rho \right) = \rho\frac{\text{dφ}}{\text{dx}} = \rho x_{s},$

$\gamma\left( \rho \right) = \frac{\sigma_{s}}{G},$

$\sigma_{s} = G\frac{\text{dφ}}{\text{dx}}\rho,$

M_s = ∫_Aρσ_sdA,

  $M_{s} = G\frac{\text{dφ}}{\text{dx}}\int_{A}^{}{\rho^{2}\text{dA}},$

$$I_{s} = \int_{A}^{}{\rho^{2}\text{dA}},\ \frac{\text{dφ}}{\text{dx}} =_{s} = \frac{M_{s}}{GI_{s}},\ \varphi = \frac{M_{s}l}{GI_{s}},$$

$$\sigma_{s} = \frac{M_{s}}{I_{s}}\rho,\ \sigma_{\text{s\ max}} = \frac{M_{s}}{I_{s}}\rho_{\max} = \frac{M_{s}}{W_{s}},$$

$W_{s} = \frac{I_{s}}{\rho_{\max}}$, $W_{s} = W_{0} = \frac{\pi}{16}\frac{D^{4} - d^{4}}{D} \cong$

$\cong 0,2\frac{D^{4} - d^{4}}{D}\left\lbrack m^{3} \right\rbrack$