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Filleted bars in bending

Filleted bars in bending H r h d t L M M
Filleted bars in bending

Values for calculation

M \mathrm{Nm}
H \mathrm{mm}
h \mathrm{mm}
d \mathrm{mm}
r \mathrm{mm}
L \mathrm{mm}

Calculation

Depth of groove, notch

t=\cfrac{H-d}{2}

0.1\le t/r\le 20

Coefficient C_1

\text{if }\ 0.1\le t/r\le 2.0
C_1=1.006+0.967\cdot\sqrt{t/r}+0.013\cdot t/r
\text{else}
C_1=1.058+1.002\cdot\sqrt{t/r}-0.038\cdot t/r

Coefficient C_2

\text{if }\ 0.1\le t/r\le 2.0
C_2=-0.270-2.372\cdot\sqrt{t/r}+0.708\cdot t/r
\text{else}
C_2=-3.652+1.639\cdot\sqrt{t/r}-0.436\cdot t/r

Coefficient C_3

\text{if }\ 0.1\le t/r\le 2.0
C_3=0.662+1.157\cdot\sqrt{t/r}-0.908\cdot t/r
\text{else}
C_3=6.170-5.687\cdot\sqrt{t/r}+1.175\cdot t/r

Coefficient C_4

\text{if }\ 0.1\le t/r\le 2.0
C_4=-0.405+0.249\cdot\sqrt{t/r}-0.200\cdot t/r
\text{else}
C_4=-2.558+3.046\cdot\sqrt{t/r}-0.701\cdot t/r

Stress concentration factor

K_t=C_1+C_2\cdot\left(\cfrac{2\cdot t}{H}\right)+C_3\cdot\left(\cfrac{2\cdot t}{H}\right)^2+C_4\cdot\left(\cfrac{2\cdot t}{H}\right)^3

Nominal or reference normal stress

σ_{nom}=\cfrac{6\cdot M\cdot 10^3}{h\cdot d^2}

Maximum normal stress

σ_{max}=K_t\cdot σ_{nom}