# Bending of a thin beam with a circular hole displaced from the center line

## Values for calculation

$M$ $\mathrm{Nm}$
$H$ $\mathrm{mm}$
$h$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$c$ $\mathrm{mm}$

## Calculation

### Dimension $e$

$$e=H-c$$

$$0\le c/e\le 1$$

### Coefficient $C_1$

$$C_1=3-0.631\cdot\left(\cfrac{d}{2\cdot c}\right)+4.007\cdot\left(\cfrac{d}{2\cdot c}\right)^2$$

### Coefficient $C_2$

$$C_2=-5.083+4.067\cdot\left(\cfrac{d}{2\cdot c}\right)-2.795\cdot\left(\cfrac{d}{2\cdot c}\right)^2$$

### Coefficient $C_3$

$$C_3=2.114-1.682\cdot\left(\cfrac{d}{2\cdot c}\right)-0.273\cdot\left(\cfrac{d}{2\cdot c}\right)^2$$

### Coefficient $C'_1$

$$C'_1=1.0286-0.1638\cdot\left(\cfrac{d}{2\cdot c}\right)+2.702\cdot\left(\cfrac{d}{2\cdot c}\right)^2$$

### Coefficient $C'_2$

$$C'_2=-0.05863-0.1335\cdot\left(\cfrac{d}{2\cdot c}\right)-1.8747\cdot\left(\cfrac{d}{2\cdot c}\right)^2$$

### Coefficient $C'_3$

$$C'_3=0.18883-0.89219\cdot\left(\cfrac{d}{2\cdot c}\right)+1.5189\cdot\left(\cfrac{d}{2\cdot c}\right)^2$$

### Stress concentration factor with the nominal stress based on gross area at point $B$

$$K_{tgB}=C_1+C_2\cdot\left(\cfrac{c}{e}\right)+C_3\cdot\left(\cfrac{c}{e}\right)^2$$

### Stress concentration factor with the nominal stress based on gross area at point $A$

$$K_{tgA}=C'_1+C'_2\cdot\left(\cfrac{c}{e}\right)+C'_3\cdot\left(\cfrac{c}{e}\right)^2$$

### Maximum normal stress $σ_{maxB}$

$$σ_{maxB}=\cfrac{K_{tgB}\cdot6\cdot M\cdot10^3}{H^2\cdot h}$$

### Maximum normal stress $σ_{maxA}$

$$σ_{maxA}=\cfrac{K_{tgA}\cdot6\cdot M\cdot10^3}{H^2\cdot h}$$