Rozciąganie i ściskanie prętów płaskich

$\frac{P}{A} = \sigma$ , $\ l = \frac{P \bullet l}{E \bullet A}$ , lc = l1 + l2 , d’ = d₁(1- ϑ$\frac{l}{l}$ )

Ścinanie techniczne:

$\frac{T}{n \bullet i\ \bullet \frac{\pi d^{2}}{4}} \leq \text{kt}$ , $\frac{P}{\text{idt}} \leq Pdop,\ \ $ $\frac{P}{n \bullet d \bullet g_{1}} \leq \text{Pdop}$

$\sigma_{A - A} = \frac{P}{(b - d) \bullet g_{1}} \leq \text{kr}\ ,\ \ \ \ \ \ \ \ \ \ \ \ \frac{P}{g_{1 \bullet \text{kr}}} \leq b \bullet d\ ,\ \ \ \ \ \ \ \ \ \ b \geq \frac{P}{g1 \bullet \text{kr}} + d$

$\frac{P}{b \bullet w} \leq \text{kt} = > b \geq \frac{P}{w \bullet \text{kt}}$

Ms-9550$\frac{N}{n} = w\left\lbrack \text{Nm} \right\rbrack\ \ ,\ \ \ \ \ \ \ \ \frac{T}{b \bullet l} \leq \text{kt},\ \ \ \ \ \ \ \ \ \ \mathrm{\tau}\mathrm{=}\frac{F}{\sum a \bullet l}$

Skręcanie prętów prostych o przekroju kołowym:1)tuleja2)wał

$\mathbf{1)}\text{τmax} = \frac{\text{Ms}}{\text{Wo}}$ , $\text{Wo} = \frac{pd^{3}}{16}$

$I_{0} = \text{Ix} + \text{Iy} = \frac{\pi d^{4}}{32}\text{\ \ }\text{Io} = \frac{\pi d^{4}}{32} - \ \frac{\text{πd}w^{4}}{32} = \ \frac{\pi}{32}(\text{dz}w^{4} - dw^{4}$)

$\text{τw} = \frac{\text{Ms}}{\text{Io}}\ \bullet \frac{\text{dw}}{2}$ , $\varphi = \frac{\text{Ms} \bullet l}{G \bullet \text{Io}}\left\lbrack \text{rad} \right\rbrack\ \ ,\ \ \ \varphi^{o} = \frac{180}{\pi} \bullet \varphi$

2)$\ \varphi = \frac{\text{Ms} \bullet l}{G \bullet \text{Io}} \leq \varphi\text{dop}$, Ms-9550$\frac{N}{n} = w\left\lbrack \text{Nm} \right\rbrack,\ \ $Io=$\frac{\pi d^{4}}{32}$, $\varphi = \frac{\pi}{180} \bullet \varphi\ \lbrack rad\rbrack$, Wo=$\frac{\pi d^{3}}{16}$,  $\text{τmax} = \frac{\text{Ms}}{\text{Wo}}$,

Zginianie prętów prostych:

$\frac{\begin{matrix} \\ \text{dMg}(x - \text{mysl},\text{przek}) \\ \end{matrix}}{\text{dx}1} = T\left( m.p \right) = 0,\ \ \ \ P - \text{qx}\left( \text{mp}* \right) = 0,\ \ \ \ \ \ x*\ = \ \frac{P}{q},\ Mg(x*)$

$\frac{\text{Mgmax}}{\text{Wy}} \leq kg$

$Wy = \frac{\text{Ix}}{\text{ymax}} = \frac{a^{3}}{6}$ , $\odot \text{Wg} = \frac{\pi d^{3}}{\begin{matrix} 32 \\ \\ \end{matrix}}\text{\ \ }$ , $\parallel Wg = \frac{2b^{3}}{3}$

1.A₁=пr²/2, e=4r/3п, Iz₁=пd⁴/128=п16r⁴/128=пr⁴8, Iy₁=0,11r⁴, A₂=3r², Iz₂=bh³/12=3r*r³/12=r⁴/4, I_y2=r27r³/12=27r⁴/12, Z₀=A₁*e+A₂(-1,5r)/A₂+A₁=[пr²/2*4r/3п-3r²*1,5r]/[ пr²/2+3r²]=[2/3r³-4,5r³]/[( п/2+3)r²]=-3,833/4,57r=-0,84, I_zc=Iz₁+I_Z2=пr⁴/8+r⁴/4=2пr⁴/8, I_yc=I_Y1+A₁*(e+Z_o)²+I_yz+A₂(1,5-Z₀)²=0,11r⁴+пr²/2*(4r/3п-0,84)²+27/12r⁴+3r²(1,5r+0,84)^2. 2. Jx=bh³/12, P1=5a*a=5a² Jx₁=5a*a³/12, Jx₁=5a⁴/12, Jy₁=a*5a³/12=125a⁴/12, P₂=1/2*5a=2,5a², Jx₂=0,5a*5a³/12 = 0,5a*125a³/12=125a⁴/24, I₀=S_x/A=[P₁*5,5a+(P₂*2,5a)*2] / [5a²+2,5a²*2]= [5a²*5,5a+(2,5a²*2,5a)*2]/[5a²+2,5a²*2]=[27,5a³+12,5a³]/[10a²]= 4a, Iy₂=5a*(1/2a)³/12= 5a*a³/8*12=5a⁴/96, Iyc= Iy₁+( Iy₂+P₂*(2,25a)²*2=125a⁴/12 + (5a⁴/96+2,5a²*5,0625a²)= 125a⁴/12 + 5a⁴/96 + 12, 656 a⁴=23,125a⁴ $l = \frac{P \bullet l}{E \bullet A}$ $\frac{T}{n \bullet i\ \bullet \frac{\pi d^{2}}{4}} \leq \text{kt}$ , $\frac{P}{\text{idt}} \leq \text{Pdop},\ \ $ $\frac{P}{n \bullet d \bullet g_{1}} \leq \text{Pdop}$, $\text{Wo} = \frac{pd^{3}}{16}$ $\text{Io} = \frac{\pi d^{4}}{32}$ $\varphi = \frac{\text{Ms} \bullet l}{G \bullet \text{Io}}$ $\text{Wg} = \frac{\pi d^{3}}{\begin{matrix} 32 \\ \\ \end{matrix}}\text{\ \ }$ , $\text{Wg} = \frac{2b^{3}}{3}$

1.A₁=пr²/2, e=4r/3п, Iz₁=пd⁴/128=п16r⁴/128=пr⁴8, Iy₁=0,11r⁴, A₂=3r², Iz₂=bh³/12=3r*r³/12=r⁴/4, I_y2=r27r³/12=27r⁴/12, Z₀=A₁*e+A₂(-1,5r)/A₂+A₁=[пr²/2*4r/3п-3r²*1,5r]/[ пr²/2+3r²]=[2/3r³-4,5r³]/[( п/2+3)r²]=-3,833/4,57r=-0,84, I_zc=Iz₁+I_Z2=пr⁴/8+r⁴/4=2пr⁴/8, I_yc=I_Y1+A₁*(e+Z_o)²+I_yz+A₂(1,5-Z₀)²=0,11r⁴+пr²/2*(4r/3п-0,84)²+27/12r⁴+3r²(1,5r+0,84)^2. 2. Jx=bh³/12, P1=5a*a=5a² Jx₁=5a*a³/12, Jx₁=5a⁴/12, Jy₁=a*5a³/12=125a⁴/12, P₂=1/2*5a=2,5a², Jx₂=0,5a*5a³/12 = 0,5a*125a³/12=125a⁴/24, I₀=S_x/A=[P₁*5,5a+(P₂*2,5a)*2] / [5a²+2,5a²*2]= [5a²*5,5a+(2,5a²*2,5a)*2]/[5a²+2,5a²*2]=[27,5a³+12,5a³]/[10a²]= 4a, Iy₂=5a*(1/2a)³/12= 5a*a³/8*12=5a⁴/96, Iyc= Iy₁+( Iy₂+P₂*(2,25a)²*2=125a⁴/12 + (5a⁴/96+2,5a²*5,0625a²)= 125a⁴/12 + 5a⁴/96 + 12, 656 a⁴=23,125a⁴ $l = \frac{P \bullet l}{E \bullet A}$ $\frac{T}{n \bullet i\ \bullet \frac{\pi d^{2}}{4}} \leq \text{kt}$ , $\frac{P}{\text{idt}} \leq \text{Pdop},\ \ $ $\frac{P}{n \bullet d \bullet g_{1}} \leq \text{Pdop}$, $\text{Wo} = \frac{pd^{3}}{16}$ $\text{Io} = \frac{\pi d^{4}}{32}$ $\varphi = \frac{\text{Ms} \bullet l}{G \bullet \text{Io}}$ $\text{Wg} = \frac{\pi d^{3}}{\begin{matrix} 32 \\ \\ \end{matrix}}\text{\ \ }$ , $\text{Wg} = \frac{2b^{3}}{3}$

1.A₁=пr²/2, e=4r/3п, Iz₁=пd⁴/128=п16r⁴/128=пr⁴8, Iy₁=0,11r⁴, A₂=3r², Iz₂=bh³/12=3r*r³/12=r⁴/4, I_y2=r27r³/12=27r⁴/12, Z₀=A₁*e+A₂(-1,5r)/A₂+A₁=[пr²/2*4r/3п-3r²*1,5r]/[ пr²/2+3r²]=[2/3r³-4,5r³]/[( п/2+3)r²]=-3,833/4,57r=-0,84, I_zc=Iz₁+I_Z2=пr⁴/8+r⁴/4=2пr⁴/8, I_yc=I_Y1+A₁*(e+Z_o)²+I_yz+A₂(1,5-Z₀)²=0,11r⁴+пr²/2*(4r/3п-0,84)²+27/12r⁴+3r²(1,5r+0,84)^2. 2. Jx=bh³/12, P1=5a*a=5a² Jx₁=5a*a³/12, Jx₁=5a⁴/12, Jy₁=a*5a³/12=125a⁴/12, P₂=1/2*5a=2,5a², Jx₂=0,5a*5a³/12 = 0,5a*125a³/12=125a⁴/24, I₀=S_x/A=[P₁*5,5a+(P₂*2,5a)*2] / [5a²+2,5a²*2]= [5a²*5,5a+(2,5a²*2,5a)*2]/[5a²+2,5a²*2]=[27,5a³+12,5a³]/[10a²]= 4a, Iy₂=5a*(1/2a)³/12= 5a*a³/8*12=5a⁴/96, Iyc= Iy₁+( Iy₂+P₂*(2,25a)²*2=125a⁴/12 + (5a⁴/96+2,5a²*5,0625a²)= 125a⁴/12 + 5a⁴/96 + 12, 656 a⁴=23,125a⁴ $l = \frac{P \bullet l}{E \bullet A}$ $\frac{T}{n \bullet i\ \bullet \frac{\pi d^{2}}{4}} \leq \text{kt}$ , $\frac{P}{\text{idt}} \leq \text{Pdop},\ \ $ $\frac{P}{n \bullet d \bullet g_{1}} \leq \text{Pdop}$, $\text{Wo} = \frac{pd^{3}}{16}$ $\text{Io} = \frac{\pi d^{4}}{32}$ $\varphi = \frac{\text{Ms} \bullet l}{G \bullet \text{Io}}$ $\text{Wg} = \frac{\pi d^{3}}{\begin{matrix} 32 \\ \\ \end{matrix}}\text{\ \ }$ , $\text{Wg} = \frac{2b^{3}}{3}$