Rod Spring

Construction Fundamentals

S-shape stiffness

$C_x=C_y=\frac{12EI}{L^3}=\frac{3\pi E\ d^4}{16L^3}$
$C_z=\frac{EA}{L}$ only if $u_x=0$
$C_z=\frac{1}{\frac{L}{EA}+\frac{u_x^2L}{700EI}}$ for $u_x\neq0$

$K_x=K_y=\frac{EI}{L}=\frac{\pi E\ d^4}{64L}$
$K_z=\frac{G{\pi d}^4}{32L}=\frac{E{\pi d}^4}{64\left(1+\nu\right)L}$

S-shape motion characteristics

$u_x=\frac{F_x}{C_x}$
$u_{xmax}=\frac{1}{3}\frac{L^2}{Ed}\sigma_{max}$
$u_z=\frac{3}{5}\frac{u_x^2}{L}$

S-shape force limits

$\sigma_{max}=\frac{M_{max}}{I}\frac{1}{2}d=\frac{\frac{F_xL}{2}}{I}\frac{1}{2}d=\frac{F_xLd}{4I}$

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.

Rod Spring S-Shape Deformation
Rod spring in s-shape deformation: $I=\frac{\pi d^4}{64}$

C-shape stiffness

$C_x=C_y=\frac{3EI}{L^3} $
$C_z=\frac{EA}{L}$ only if $u_x=0$

$K_x=K_y=\frac{EI}{L}=\frac{\pi E\ d^4}{64L}$
$K_z=\frac{G{\pi d}^4}{32L}=\frac{E{\pi d}^4}{64\left(1+\nu\right)L}$

C-shape motion characteristics

$u_x=\frac{F_x}{C_x}$
$u_{xmax}=\frac{2}{3}\frac{L^2}{Ed}\sigma_{max}$
$u_z=\frac{3}{5}\frac{u_x^2}{L}$

C-shape force limits

$\sigma_{max}=\frac{M_{max}}{I}\frac{1}{2}d=\frac{F_xL}{I}\frac{1}{2}d=\frac{F_xLd}{2I}$

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.

Rod Spring C-Shape Deformation
Rod spring in c-shape deformation: $I=\frac{\pi d^4}{64}$

Tech Support

Please submit a message and we will come back to you on short notice.

Precision Point sheet download

Please fill in your details to receive the requested Precision Point sheet.

We use cookies to ensure to give you the best experience on our website. If you continue to use this site we will assume that you are okay with it.