S-shape stiffness
$C_x=\frac{Ebt^3}{L^3} $
$C_y=\frac{Etb^3}{L^3} $ if $R_x$ is fixed, $C_y=\frac{Etb^3}{4L^3} $ if $R_x$ is free
$C_z=\frac{EA}{L}$ only if $u_x=0 $
$C_z=\frac{700EAI_y}{L(700I_y+{u_x}^2A)}$ for $u_x\neq0$
$K_x=\frac{Etb^3}{12L}$ for $u_x=0$
$K_y=\frac{Ebt^3}{12L}$ for $u_x=0$
$K_z=\frac{Gbt^3}{3L}=\frac{Ebt^3}{6\left(1+\nu\right)L}$ for $u_x=0$
S-shape motion characteristics
$u_x=\frac{F_x}{C_x}$
$u_{xmax}=\frac{1}{3}\frac{L^2}{Et}\sigma_{max}$
$u_z=\frac{3}{5}\frac{u_x^2}{L}$
S-shape force limits
$\sigma_{max}=\frac{M_{max}}{I}\frac{1}{2}t=\frac{\frac{F_xL}{2}}{I}\frac{1}{2}t=\frac{F_xLt}{4I}$
dynamic movements: $\sigma_{max}<$ fatigue stress limit
static deformation: $\sigma_{max}<$ yield stress limit $(\sigma_{0.2})$
See Beam Theory: Buckling for equations to calculate the maximum buckling load.
C-shape stiffness
$C_x=\frac{Ebt^3}{{4L}^3} $
$C_y=\frac{Etb^3}{4L^3} $
$C_z=\frac{EA}{L}$ only if $u_x=0$
$K_x=\frac{Etb^3}{12L}$ for $u_x=0$
$K_y=\frac{Ebt^3}{12L}$ for $u_x=0$
$K_z=\frac{Gbt^3}{3L}=\frac{Ebt^3}{6\left(1+\nu\right)L}$ for $u_x=0$
C-shape motion characteristics
$u_x=\frac{F_x}{C_x}$
$u_{xmax}=\frac{2}{3}\frac{L^2}{Et}\sigma_{max}$
$u_z=\frac{3}{5}\frac{u_x^2}{L}$
C-shape force limits
$\sigma_{max}=\frac{M_{max}}{I}\frac{1}{2}t=\frac{F_xL}{I}\frac{1}{2}t=\frac{F_xLt}{2I}$
dynamic movements: $\sigma_{max}<$ fatigue stress limit
static deformation: $\sigma_{max}<$ yield stress limit $(\sigma_{0.2})$
See Beam Theory: Buckling for equations to calculate the maximum buckling load.
