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Tension of a tube with a transverse hole

Tension of a tube with a transverse hole D P P d σ max d i
Tension of a tube with a transverse hole

Values for calculation

$P$ $\mathrm{N}$
$d$ $\mathrm{mm}$
$D$ $\mathrm{mm}$
$d_i$ $\mathrm{mm}$

Calculation

Coefficient $ C_1 $

$$C_1=3$$
$C_1=3$
Equations in LaTeX code
C_1=3

Coefficient $ C_2 $

$$C_2=0.427-6.770\cdot\left(\cfrac{d_i}{D}\right)+22.698\cdot\left(\cfrac{d_i}{D}\right)^2-16.670\cdot\left(\cfrac{d_i}{D}\right)^3$$
$C_2=0.427-6.770\cdot\left(\cfrac{d_i}{D}\right)+22.698\cdot\left(\cfrac{d_i}{D}\right)^2-16.670\cdot\left(\cfrac{d_i}{D}\right)^3$
Equations in LaTeX code
C_2=0.427-6.770\cdot\left(\cfrac{d_i}{D}\right)+22.698\cdot\left(\cfrac{d_i}{D}\right)^2-16.670\cdot\left(\cfrac{d_i}{D}\right)^3

Coefficient $ C_3 $

$$C_3=11.357+15.665\cdot\left(\cfrac{d_i}{D}\right)-60.929\cdot\left(\cfrac{d_i}{D}\right)^2+41.501\cdot\left(\cfrac{d_i}{D}\right)^3$$
$C_3=11.357+15.665\cdot\left(\cfrac{d_i}{D}\right)-60.929\cdot\left(\cfrac{d_i}{D}\right)^2+41.501\cdot\left(\cfrac{d_i}{D}\right)^3$
Equations in LaTeX code
C_3=11.357+15.665\cdot\left(\cfrac{d_i}{D}\right)-60.929\cdot\left(\cfrac{d_i}{D}\right)^2+41.501\cdot\left(\cfrac{d_i}{D}\right)^3

Stress concentration factor with the nominal stress based on gross area

$$K_{tg}=C_1+C_2\cdot\left(\cfrac{d}{D}\right)+C_3\cdot\left(\cfrac{d}{D}\right)^2$$
$K_{tg}=C_1+C_2\cdot\left(\cfrac{d}{D}\right)+C_3\cdot\left(\cfrac{d}{D}\right)^2$
Equations in LaTeX code
K_{tg}=C_1+C_2\cdot\left(\cfrac{d}{D}\right)+C_3\cdot\left(\cfrac{d}{D}\right)^2

Maximum normal stress

$$σ_{max}=\cfrac{K_{tg}\cdot P}{\left(π/4\right)\cdot\left(D^2-d_i^2\right)}$$
$σ_{max}=\cfrac{K_{tg}\cdot P}{\left(π/4\right)\cdot\left(D^2-d_i^2\right)}$
Equations in LaTeX code
σ_{max}=\cfrac{K_{tg}\cdot P}{\left(π/4\right)\cdot\left(D^2-d_i^2\right)}
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