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Stepped flat tension bar with shoulder fillets

Stepped flat tension bar with shoulder fillets H r P P h d t L
Stepped flat tension bar with shoulder fillets

Values for calculation

$P$ $\mathrm{N}$
$H$ $\mathrm{mm}$
$h$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$r$ $\mathrm{mm}$
$L$ $\mathrm{mm}$

Calculation

Depth of groove, notch

$$t=\cfrac{H-d}{2}$$
$t=\cfrac{H-d}{2}$
Equations in LaTeX code
t=\cfrac{H-d}{2}
$$0.1\le t/r\le 20$$
$0.1\le t/r\le 20$
Equations in LaTeX code
0.1\le t/r\le 20

Coefficient $ C_1 $

$\text{if }\ 0.1\le t/r\le 2.0$
$\text{if }\ 0.1\le t/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.1\le t/r\le 2.0
$$C_1=1.006+1.008\cdot\sqrt{t/r}-0.044\cdot t/r$$
$C_1=1.006+1.008\cdot\sqrt{t/r}-0.044\cdot t/r$
Equations in LaTeX code
C_1=1.006+1.008\cdot\sqrt{t/r}-0.044\cdot t/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_1=1.020+1.009\cdot\sqrt{t/r}-0.048\cdot t/r$$
$C_1=1.020+1.009\cdot\sqrt{t/r}-0.048\cdot t/r$
Equations in LaTeX code
C_1=1.020+1.009\cdot\sqrt{t/r}-0.048\cdot t/r

Coefficient $ C_2 $

$\text{if }\ 0.1\le t/r\le 2.0$
$\text{if }\ 0.1\le t/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.1\le t/r\le 2.0
$$C_2=-0.115-0.584\cdot\sqrt{t/r}+0.315\cdot t/r$$
$C_2=-0.115-0.584\cdot\sqrt{t/r}+0.315\cdot t/r$
Equations in LaTeX code
C_2=-0.115-0.584\cdot\sqrt{t/r}+0.315\cdot t/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_2=-0.065-0.165\cdot\sqrt{t/r}-0.007\cdot t/r$$
$C_2=-0.065-0.165\cdot\sqrt{t/r}-0.007\cdot t/r$
Equations in LaTeX code
C_2=-0.065-0.165\cdot\sqrt{t/r}-0.007\cdot t/r

Coefficient $ C_3 $

$\text{if }\ 0.1\le t/r\le 2.0$
$\text{if }\ 0.1\le t/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.1\le t/r\le 2.0
$$C_3=0.245-1.006\cdot\sqrt{t/r}-0.257\cdot t/r$$
$C_3=0.245-1.006\cdot\sqrt{t/r}-0.257\cdot t/r$
Equations in LaTeX code
C_3=0.245-1.006\cdot\sqrt{t/r}-0.257\cdot t/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_3=-3.459+1.266\cdot\sqrt{t/r}-0.016\cdot t/r$$
$C_3=-3.459+1.266\cdot\sqrt{t/r}-0.016\cdot t/r$
Equations in LaTeX code
C_3=-3.459+1.266\cdot\sqrt{t/r}-0.016\cdot t/r

Coefficient $ C_4 $

$\text{if }\ 0.1\le t/r\le 2.0$
$\text{if }\ 0.1\le t/r\le 2.0$
Equations in LaTeX code
\text{if }\ 0.1\le t/r\le 2.0
$$C_4=-0.135+0.582\cdot\sqrt{t/r}-0.017\cdot t/r$$
$C_4=-0.135+0.582\cdot\sqrt{t/r}-0.017\cdot t/r$
Equations in LaTeX code
C_4=-0.135+0.582\cdot\sqrt{t/r}-0.017\cdot t/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_4=3.505-2.109\cdot\sqrt{t/r}+0.069\cdot t/r$$
$C_4=3.505-2.109\cdot\sqrt{t/r}+0.069\cdot t/r$
Equations in LaTeX code
C_4=3.505-2.109\cdot\sqrt{t/r}+0.069\cdot t/r

Stress concentration factor

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

$$σ_{nom}=\cfrac{P}{h\cdot d}$$
$σ_{nom}=\cfrac{P}{h\cdot d}$
Equations in LaTeX code
σ_{nom}=\cfrac{P}{h\cdot d}

Maximum normal stress

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