Columns + Kinematics and Stresses

$SR=\frac{L_e}{k}$
effective length / radius of gyration

$k=\sqrt{\frac{I}{A}}

$L_e=KL

$S=\frac{F}{A}

$FS=\frac{S_{ultimate}}{S_{design}}

$S=\frac{F}{\frac{π}{4}(D^2-d^2)}

$t=\frac{D-d}{2}$
$t=r_o-r_i

$S=\frac{F}{πDt}

$S_{bolt}=\frac{\frac{PA_{cylinder}}{N_{bolts}}}{A_{bolt}}

$E_{steel}=30x10^6 psi

$E_{Al}=\frac{1}{3}E_{steel}

$G=12x10^6psi

$v=-\frac{Ɛ_{lateral}}{Ɛ_{longitudinal}}$

$E=2(v+1)G

$δ=\frac{FL}{AE}

$Ɛ=\frac{δ}{L}

$δ=\frac{ρgL^2}{2E}

$e=Ɛ_x+Ɛ_y+Ɛ_z$

$e=\frac{F}{AE}(1-2v)

$δ=αL∆T$

$S=Eα∆T$

$\alpha=6.51x10^{-6}°

$S_b=\frac{Mc}{I_x}

$S_b=\frac{6M}{bh²}

$S_b=\frac{32M}{πD³}

$S_b=\frac{3V}{2bh}

$M_{max}=\frac{ωL^2}{8}$

$M_{max}=\frac{PL}{4}

$S=\frac{Et}{D}

$SR=\frac{L_e}{k}

$L_e=KL$
$C=\frac{1}{K^2}

$M_{max}=\frac{PL}{4}$

$M_{max}=\frac{\omega L^2}{8}

$I_x=\frac{bh^3}{12}

$I_x=\frac{bh^3}{36}

$I_x=\frac{\pi r^4}{4}$
$I_x=\frac{\pi D^4}{64}

$k=\sqrt{\frac{I}{A}}

$F_c=\frac{π^2EI}{L_e^2}

$F_c=S_yA\left[1-\frac{S_y(L_e/k)^2}{4π^2E}\right]

$Ss_{max}=\sqrt{\left(\frac{S_x-S_y}{2}\right)^2+S_s^2}

$S_{max}=\frac{S_x+S_y}{2}+Ss_{max}

$S_{min}=\frac{S_x+S_y}{2}-Ss_{max}

$DOF=3(N-1)-2L_{pair}-H_{pair}$

$DOF=3(N-1)-2L_{pair}

$S_a=\frac{S_x-S_y}{2}

$S_m=\frac{S_x+S_y}{2}

$FS=\frac{S_y}{S_m}$

$FS=\frac{S_u}{S_m}

$v=r\omega$

$\omega=\frac{v_A}{r_A}=\frac{v_B}{r_B}