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Bending of a flat beam with semicircular edge notches

Bending of a flat beam with semicircular edge notches H r h M M
Bending of a flat beam with semicircular edge notches

Values for calculation

$M$ $\mathrm{Nm}$
$r$ $\mathrm{mm}$
$H$ $\mathrm{mm}$
$h$ $\mathrm{mm}$

Calculation

Stress concentration factor with the nominal stress based on net area

$$K_{tn}=3.065-6.637\cdot\left(\cfrac{2\cdot r}{H}\right)+8.229\cdot\left(\cfrac{2\cdot r}{H}\right)^2-3.636\cdot\left(\cfrac{2\cdot r}{H}\right)^3$$
$K_{tn}=3.065-6.637\cdot\left(\cfrac{2\cdot r}{H}\right)+8.229\cdot\left(\cfrac{2\cdot r}{H}\right)^2-3.636\cdot\left(\cfrac{2\cdot r}{H}\right)^3$
Equations in LaTeX code
K_{tn}=3.065-6.637\cdot\left(\cfrac{2\cdot r}{H}\right)+8.229\cdot\left(\cfrac{2\cdot r}{H}\right)^2-3.636\cdot\left(\cfrac{2\cdot r}{H}\right)^3

Nominal or reference normal stress

$$σ_{nom}=\cfrac{6\cdot M\cdot 10^3}{\left(H-2\cdot r\right)^2\cdot h}$$
$σ_{nom}=\cfrac{6\cdot M\cdot 10^3}{\left(H-2\cdot r\right)^2\cdot h}$
Equations in LaTeX code
σ_{nom}=\cfrac{6\cdot M\cdot 10^3}{\left(H-2\cdot r\right)^2\cdot h}

Maximum normal stress

$$σ_{max}=K_{tn}\cdot σ_{nom}$$
$σ_{max}=K_{tn}\cdot σ_{nom}$
Equations in LaTeX code
σ_{max}=K_{tn}\cdot σ_{nom}

Normal stress

$$σ=\cfrac{6\cdot M\cdot 10^3}{H^2\cdot h}$$
$σ=\cfrac{6\cdot M\cdot 10^3}{H^2\cdot h}$
Equations in LaTeX code
σ=\cfrac{6\cdot M\cdot 10^3}{H^2\cdot h}

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=\cfrac{σ_{max}}{σ}$$
$K_{tg}=\cfrac{σ_{max}}{σ}$
Equations in LaTeX code
K_{tg}=\cfrac{σ_{max}}{σ}
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