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The goal of this article is to translate the stiffness of a vertical elements (column, wall, surface support) to a spring constant $k$ which can be applied in the Y-direction in Diamonds.

For a column

With Hooke’s Law $F=k \cdot \Delta x$ and the formula for stress $\sigma=\frac{F}{A}$ , a formula for the spring constant can be deducted. This formula assumes that the element is supported at the buttom.

$k=\frac{F}{\Delta x} = \frac{\sigma A}{\Delta x} = \frac{E \varepsilon A}{\Delta x} = \frac{E (\Delta x /l) A}{\Delta x} = \frac{E A}{l}$

with

$E$ the modulus of elasticity of the column
$A$ the cross-section area of the column
$l$ the length of the column

Input

Young’s modulus E [N/mm²]

Width b [mm]

Length h [mm]

Level height H [mm]

$k = \dfrac{E \times b \times h}{H} = \dfrac{30\,000 \times 300 \times 300}{3\,000} =$

900 000kN/m

Note: E is in N/mm², b, h and H are in mm; the result is converted to kN/m.