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Uniaxial tension of a finite-width thin element with an infinite row of circular holes stress parallel to the axis of the holes

Finite-width thin element with an infinite row of circular holes stress parallel to the axis of the holes H σ σ l d σ max
Finite-width thin element with an infinite row of circular holes stress parallel to the axis of the holes

Values for calculation

$σ$ $\mathrm{MPa}$
$H$ $\mathrm{mm}$
$d$ $\mathrm{mm}$
$l$ $\mathrm{mm}$

Calculation

Coefficient $ C_1 $

$$C_1=1.949+1.476\cdot\left(\cfrac{d}{H}\right)$$
$C_1=1.949+1.476\cdot\left(\cfrac{d}{H}\right)$
Equations in LaTeX code
C_1=1.949+1.476\cdot\left(\cfrac{d}{H}\right)

Coefficient $ C_2 $

$$C_2=0.916-2.845\cdot\left(\cfrac{d}{H}\right)$$
$C_2=0.916-2.845\cdot\left(\cfrac{d}{H}\right)$
Equations in LaTeX code
C_2=0.916-2.845\cdot\left(\cfrac{d}{H}\right)

Coefficient $ C_3 $

$$C_3=-1.926+1.069\cdot\left(\cfrac{d}{H}\right)$$
$C_3=-1.926+1.069\cdot\left(\cfrac{d}{H}\right)$
Equations in LaTeX code
C_3=-1.926+1.069\cdot\left(\cfrac{d}{H}\right)

Stress concentration factor with the nominal stress based on net area

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

Nominal or reference normal stress

$$σ_{nom}=\cfrac{σ}{1-d/H}$$
$σ_{nom}=\cfrac{σ}{1-d/H}$
Equations in LaTeX code
σ_{nom}=\cfrac{σ}{1-d/H}

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}
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