Menu

Elliptical hole in a finite-width thin element in uniaxial tension

Elliptical hole in a finite-width thin element in uniaxial tension H σ max 2a 2 b c σ σ
Elliptical hole in a finite-width thin element in uniaxial tension

Values for calculation

$σ$ $\mathrm{MPa}$
$H$ $\mathrm{mm}$
$a$ $\mathrm{mm}$
$b$ $\mathrm{mm}$
$c$ $\mathrm{mm}$

Calculation

Coefficient $ C_1 $

$$C_1=1.109-0.188\cdot\sqrt{a/b}+2.068\cdot a/b$$
$C_1=1.109-0.188\cdot\sqrt{a/b}+2.068\cdot a/b$
Equations in LaTeX code
C_1=1.109-0.188\cdot\sqrt{a/b}+2.068\cdot a/b

Coefficient $ C_2 $

$$C_2=-0.486+0.213\cdot\sqrt{a/b}-2.588\cdot a/b$$
$C_2=-0.486+0.213\cdot\sqrt{a/b}-2.588\cdot a/b$
Equations in LaTeX code
C_2=-0.486+0.213\cdot\sqrt{a/b}-2.588\cdot a/b

Coefficient $ C_3 $

$$C_3=3.816-5.510\cdot\sqrt{a/b}+4.638\cdot a/b$$
$C_3=3.816-5.510\cdot\sqrt{a/b}+4.638\cdot a/b$
Equations in LaTeX code
C_3=3.816-5.510\cdot\sqrt{a/b}+4.638\cdot a/b

Coefficient $ C_4 $

$$C_4=-2.438+5.485\cdot\sqrt{a/b}-4.126\cdot a/b$$
$C_4=-2.438+5.485\cdot\sqrt{a/b}-4.126\cdot a/b$
Equations in LaTeX code
C_4=-2.438+5.485\cdot\sqrt{a/b}-4.126\cdot a/b

Stress concentration factor with the nominal stress based on net area

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

Nominal or reference normal stress

$\text{if }\ \cfrac{H}{c}=2$
$\text{if }\ \cfrac{H}{c}=2$
Equations in LaTeX code
\text{if }\ \cfrac{H}{c}=2
$$σ_{nom}=\cfrac{σ}{1-2\cdot a/H}$$
$σ_{nom}=\cfrac{σ}{1-2\cdot a/H}$
Equations in LaTeX code
σ_{nom}=\cfrac{σ}{1-2\cdot a/H}
$\text{else}$
$\text{else}$
Equations in LaTeX code
\text{else}
$$σ_{nom}=\cfrac{\sqrt{1-\left(a/c\right)^2}}{1-a/c}\cdot\cfrac{\left(1-c/H\right)\cdot σ}{1-\left(c/H\right)\cdot\left[2-\sqrt{1-\left(a/c\right)^2}\right]}$$
$σ_{nom}=\cfrac{\sqrt{1-\left(a/c\right)^2}}{1-a/c}\cdot\cfrac{\left(1-c/H\right)\cdot σ}{1-\left(c/H\right)\cdot\left[2-\sqrt{1-\left(a/c\right)^2}\right]}$
Equations in LaTeX code
σ_{nom}=\cfrac{\sqrt{1-\left(a/c\right)^2}}{1-a/c}\cdot\cfrac{\left(1-c/H\right)\cdot σ}{1-\left(c/H\right)\cdot\left[2-\sqrt{1-\left(a/c\right)^2}\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}

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}
On this page