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Flat tension bar with opposite U-shaped notches

Flat bar with opposite U-shaped notches H r P P h t t
Flat bar with opposite U-shaped notches

Values for calculation

$P$ $\mathrm{N}$
$r$ $\mathrm{mm}$
$t$ $\mathrm{mm}$
$H$ $\mathrm{mm}$
$h$ $\mathrm{mm}$

Calculation

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
$$C_1=0.955+2.169\cdot\sqrt{t/r}-0.081\cdot t/r$$
$C_1=0.955+2.169\cdot\sqrt{t/r}-0.081\cdot t/r$
Equations in LaTeX code
C_1=0.955+2.169\cdot\sqrt{t/r}-0.081\cdot t/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_1=1.037+1.991\cdot\sqrt{t/r}+0.002\cdot t/r$$
$C_1=1.037+1.991\cdot\sqrt{t/r}+0.002\cdot t/r$
Equations in LaTeX code
C_1=1.037+1.991\cdot\sqrt{t/r}+0.002\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
$$C_2=-1.557-4.046\cdot\sqrt{t/r}+1.032\cdot t/r$$
$C_2=-1.557-4.046\cdot\sqrt{t/r}+1.032\cdot t/r$
Equations in LaTeX code
C_2=-1.557-4.046\cdot\sqrt{t/r}+1.032\cdot t/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_2=-1.886-2.181\cdot\sqrt{t/r}-0.048\cdot t/r$$
$C_2=-1.886-2.181\cdot\sqrt{t/r}-0.048\cdot t/r$
Equations in LaTeX code
C_2=-1.886-2.181\cdot\sqrt{t/r}-0.048\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
$$C_3=4.013+0.424\cdot\sqrt{t/r}-0.748\cdot t/r$$
$C_3=4.013+0.424\cdot\sqrt{t/r}-0.748\cdot t/r$
Equations in LaTeX code
C_3=4.013+0.424\cdot\sqrt{t/r}-0.748\cdot t/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_3=0.649+1.086\cdot\sqrt{t/r}+0.142\cdot t/r$$
$C_3=0.649+1.086\cdot\sqrt{t/r}+0.142\cdot t/r$
Equations in LaTeX code
C_3=0.649+1.086\cdot\sqrt{t/r}+0.142\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
$$C_4=-2.461+1.538\cdot\sqrt{t/r}-0.236\cdot t/r$$
$C_4=-2.461+1.538\cdot\sqrt{t/r}-0.236\cdot t/r$
Equations in LaTeX code
C_4=-2.461+1.538\cdot\sqrt{t/r}-0.236\cdot t/r
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$C_4=1.218-0.922\cdot\sqrt{t/r}-0.086\cdot t/r$$
$C_4=1.218-0.922\cdot\sqrt{t/r}-0.086\cdot t/r$
Equations in LaTeX code
C_4=1.218-0.922\cdot\sqrt{t/r}-0.086\cdot t/r

Stress concentration factor with the nominal stress based on net area

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

$$σ_{nom}=\cfrac{P}{h\cdot\left(H-2\cdot t\right)}$$
$σ_{nom}=\cfrac{P}{h\cdot\left(H-2\cdot t\right)}$
Equations in LaTeX code
σ_{nom}=\cfrac{P}{h\cdot\left(H-2\cdot t\right)}

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

$$σ=\cfrac{P}{h\cdot H}$$
$σ=\cfrac{P}{h\cdot H}$
Equations in LaTeX code
σ=\cfrac{P}{h\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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