Wytrzymałość materiałów Ściąga 2

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$
l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$	l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l $\mathbf{\sigma} = \frac{\|N\|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{\|My\|}{\text{Wy}} + \frac{\|Mz\|}{\text{Wz}} \leq f_{m,d}$ $\mathbf{\sigma} = \frac{\|My\|z}{\text{Jy}} + \frac{\|Mz\|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$ $\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$ $\mathbf{\sigma} = \frac{\|N\|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$ $\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$ 1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc) 2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop $\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$ $rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$ $\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{\|N\|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$ M_y(q_z) M_z(q_y) Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2 G=81GPa=0,8110^8 kN/m2 Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{}}{\text{EJ}}$ Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$ $\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\mathbf{\sigma} = \frac{N}{A}(1 + \frac{e_{y} \bullet y}{i_{z}^{2}} + \frac{e_{z} \bullet z}{i_{y}^{2}}) \leq f_{m,d}$ $\mathbf{i}_{\mathbf{y}}^{\mathbf{2}} = \frac{\text{Jy}}{A}$ $\mathbf{i}_{\mathbf{z}}^{\mathbf{2}} = \frac{\text{Jz}}{A}$

$\mathbf{\sigma} = \frac{|N|}{A \bullet \chi}$ $\mathbf{\lambda} = \frac{\text{Lcr}}{i_{\min}}$ $\mathbf{i}_{\mathbf{\min}} = \sqrt{\frac{\text{Jmin}}{A}}$ $\overset{\overline{}}{\mathbf{\lambda}} = \frac{\lambda}{\text{λp}}$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

$\mathbf{\text{Wy}} = \frac{b \bullet h^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{h \bullet b^{2}}{6}$ $\mathbf{\text{Wz}} = \frac{\text{Jz}}{y_{\max}}$ $\mathbf{\text{Wy}} = \frac{\text{Jy}}{z_{\max}}$ $\mathbf{A} \geq \frac{|N|}{\text{fy}}$ $\mathbf{\tau} = \frac{T \bullet Sy}{Jy \bullet b}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

l = l_p + l_t + l_m = δ $\mathbf{}\mathbf{l}_{\mathbf{p}} = \frac{P \bullet l}{\text{EA}}$ l_t = α • t • l

$\mathbf{\sigma} = \frac{|N|}{A} \leq f_{y}$ $\mathbf{\sigma} = \frac{M}{\text{Wy}} = \frac{M \bullet z}{\text{Jy}}$ $\mathbf{\sigma} = \frac{|My|}{\text{Wy}} + \frac{|Mz|}{\text{Wz}} \leq f_{m,d}$

$\mathbf{\sigma} = \frac{|My|z}{\text{Jy}} + \frac{|Mz|y}{\text{Jz}} \leq f_{y}$ $\mathbf{\sigma} = \frac{N}{A} + \frac{N \bullet e_{y}}{\text{Jz}}y + \frac{N \bullet e_{z}}{\text{Jy}}z$

$\frac{e_{y}}{\frac{{- i}_{z}^{2}}{y}} + \frac{e_{z}}{\frac{{- i}_{y}^{2}}{z}} = 1$ $\mathbf{\theta} = \sum_{}^{}\frac{Ms \bullet l}{GJ_{0}}$

1.war.wytrz: τ_max ≤ f_dr(skrecanie),$\frac{\text{Mmax}}{\text{Wx}} \leq fy$ (scisk,rozc)

2.war.sztyw: θ_dop ≥ θ_max(skrecanie),Wmax ≤ Wdop

$\mathbf{\tau}_{\mathbf{\max}} = \frac{\text{Msmax}}{\text{Ws}}$ $\mathbf{\text{Ws}} = \frac{J0}{0,5D}$ $kolo:\ \mathbf{J}_{\mathbf{0}} = \frac{\pi D^{4}}{32}$

$rura:\ J_{0} = \frac{\pi}{32}(D^{4} - d^{4}$

M_y(q_z) M_z(q_y)

Fy=235MPa=23,5kN/cm2 E=210GPa=21000kN/cm2

G=81GPa=0,81*10^8 kN/m2

Ugięcie w punkcie K: $w_{k} = \frac{M_{K}^{*}}{\text{EJ}}$

Kąt obrotu w punkcie K: $\varphi_{k} = \frac{T_{K}^{*}}{\text{EJ}}$

$\sigma_{z} = \sqrt{\sigma^{2} + 3\tau^{2}}$

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