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Circular hole in an infinite plate for elastic stress, out-of-plane bending (simple bending, $M_2=0$)

Circular hole in an infinite plate d r t
Circular hole in an infinite plate
Elastic stress, out-of-plane bending σ b σ a σ b M 1 M 1 M 2 M 2
Elastic stress, out-of-plane bending

Values for calculation

$r$ $\mathrm{mm}$
$t$ $\mathrm{mm}$
$M_1$ $\mathrm{Nmm}$
$M_2$ $\mathrm{Nmm}$

Calculation

The elastic stress concentration factor

$$K_t=1.79+\cfrac{0.25}{0.39+\left(2\cdot r/t\right)}+\cfrac{0.81}{1+\left(2\cdot r/t\right)^2}-\cfrac{0.26}{1+\left(2\cdot r/t\right)^3}$$
$K_t=1.79+\cfrac{0.25}{0.39+\left(2\cdot r/t\right)}+\cfrac{0.81}{1+\left(2\cdot r/t\right)^2}-\cfrac{0.26}{1+\left(2\cdot r/t\right)^3}$
Equations in LaTeX code
K_t=1.79+\cfrac{0.25}{0.39+\left(2\cdot r/t\right)}+\cfrac{0.81}{1+\left(2\cdot r/t\right)^2}-\cfrac{0.26}{1+\left(2\cdot r/t\right)^3}

Normal stress at point $ A $

$$σ_A=K_t\cdot\cfrac{6\cdot M_1}{t^2}$$
$σ_A=K_t\cdot\cfrac{6\cdot M_1}{t^2}$
Equations in LaTeX code
σ_A=K_t\cdot\cfrac{6\cdot M_1}{t^2}
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