STRESS CONCENTRATION FACTOR FORMULAS


Stress concentration factor formulas for

- Central Single Circular Hole in Finite Width Plate

- Eccentric Single Circular Hole in Finite Width Plate

- Large Circumferential Groove in Circular Shaft

- Opposite Shoulder Fillets in Stepped Flat Bar

- Rectangular Hole with Round Corners in Infinite Plate

- Round Pin Joint with Closely Fitting Pin in Finite Width Plate

- Single Circular Hole in Infinite Plate

- Single Elliptical Hole in Finite Width Plate

- Shoulder Fillet in a Stepped Circular Shaft

- Transverse Circular Hole in Round Bar

- Two Circular Holes in an Infinite Plate


Central Single Circular Hole in Finite Width Plate

Stress concentration factors for central single circular hole in finite-width plate
Tension
Stress concentration factors for central single circular hole in finite-width plate under tension
For $$0\le \frac { d }{ D } \le 1$$
$$3.000-3.140\frac { d }{ D } +3.667{ \left( \frac { d }{ D } \right) }^{ 2 }-1.527{ \left( \frac { d }{ D } \right) }^{ 3 }$$
$${ \sigma }_{ nom }=P/[(D-d)t]$$
$${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$
In-Plane Bending
Stress concentration factors for central single circular hole in finite-width plate under bending
At the edge of hole
Kta = 2 (independent of d/D)
$${ \sigma }_{ nom }=6Md/[({ D }^{ 3 }-{ d }^{ 3 })t]$$
σmax@A = Ktσnom
At the edge of plate
$${ K }_{ tb }=\frac { 2d }{ D } (\alpha ={ 30 }^{ \circ })$$
$${ \sigma }_{ nom }=6MD/[({ D }^{ 3 }-{ d }^{ 3 })t]$$
σmax@B = Ktσnom
Simple Transverse  Bending
Stress concentration factors for central single circular hole in finite-width plate under simple transverse bending
For $$0\le \cfrac { d }{ D } \le 0.3$$ and $$1\le d/t\le 7$$
$${ K }_{ t }=\left[ 1.793+\frac { 0.131 }{ d/t } +\frac { 2.052 }{ { \left( d/t \right) }^{ 2 } } -\frac { 1.019 }{ { \left( d/t \right) }^{ 3 } } \right] \times \left[ 1-1.04(d/D)+1.22{ (d/D) }^{ 2 } \right]$$
$${ \sigma }_{ nom }=6{ M }_{ 1 }/[(D-d){ t }^{ 2 }]$$
σmax@A = Ktσnom

Eccentric Single Circular Hole in Finite Width Plate

Stress concentration factors for central single circular hole in finite-width plate
Tension
Stress concentration factors for central single circular hole in finite-width plate under tension
$${ K }_{ t }=3.000-3.140\frac { d }{ 2c } +3.667{ \left( \frac { d }{ 2c } \right) }^{ 2 }-1.527{ \left( \frac { d }{ 2c } \right) }^{ 3 }$$
$${ \sigma }_{ nom }=\frac { P\sqrt { 1-{ \left( d/2c \right) }^{ 2 } } }{ Dt(1-d/2c) } \frac { 1-c/D }{ 1-(c/d)\left[ 2-\sqrt { 1-{ (d/2c) }^{ 2 } } \right] } $$
$${ \sigma }_{ max }={ \sigma }_{ B }={ K }_{ t }{ \sigma }_{ nom }$$
Bending
Stress concentration factors for central single circular hole in finite-width plate under bending
For Point B $$0\le d/2c\le 0.5,\quad 0\le c/e\le 1.0$$
$${ C }_{ 1 }=3.000-0.631(d/2c)+4.007{ \left( d/2c \right) }^{ 2 }$$
$${ C }_{ 2 }=-5.083+4.067(d/2c)-2.795{ \left( d/2c \right) }^{ 2 }$$
$${ C }_{ 3 }=2.114-1.682(d/2c)-0.273{ \left( d/2c \right) }^{ 2 }$$
$${ K }_{ tB }={ C }_{ 1 }+{ C }_{ 2 }\frac { c }{ e } +{ C }_{ 3 }{ (\frac { c }{ e } ) }^{ 2 }$$
$${ \sigma }_{ nom }={ 6M }/{ t{ D }^{ 2 } }$$
$${ \sigma }_{ B }={ K }_{ tB }{ \sigma }_{ nom }$$
For Point A
$${ C' }_{ 1 }=1.0286-0.1638(d/2c)+2.702{ \left( d/2c \right) }^{ 2 }$$
$${ C' }_{ 2 }=-0.05863-0.1335(d/2c)-1.8747{ \left( d/2c \right) }^{ 2 }$$
$${ C' }_{ 3 }=0.18883-0.89219(d/2c)+1.5189{ \left( d/2c \right) }^{ 2 }$$
$${ K }_{ tA }={ C' }_{ 1 }+{ C' }_{ 2 }\frac { c }{ e } +{ C' }_{ 3 }{ (\frac { c }{ e } ) }^{ 2 }$$
$${ \sigma }_{ nom }={ 6M }/{ t{ D }^{ 2 } }$$
$${ \sigma }_{ A }={ K }_{ tA }{ \sigma }_{ nom }$$

Large Circumferential Groove in Circular Shaft

Stress concentration factors for large circumferential groove
Tension
Stress concentration factors for large circumferential groove under tension
$$ 0.3\quad \le \quad \frac { r }{ d } \le \quad 1.0 $$ , $$ 1.005\quad \le \quad \frac { D }{ d } \le \quad 1.10 $$
$${ C }_{ 1 }=-81.39+153.10(D/d)-70.49{ (D/d) }^{ 2 }$$
$${ C }_{ 2 }=119.64-221.81(D/d)+101.93{ (D/d) }^{ 2 }$$
$${ C }_{ 3 }=-57.88+107.33(D/d)-49.34{ (D/d) }^{ 2 }$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { r }{ d } +{ C }_{ 3 }{ (\frac { r }{ d } ) }^{ 2 }$$
$${ \sigma }_{ nom }=4P/\pi { d }^{ 2 }$$
$${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ t }{ \sigma }_{ nom }$$
Bending
Stress concentration factors for large circumferential groove under bending
$$ 0.3\quad \le \quad \frac { r }{ d } \le \quad 1.0 $$ , $$ 1.005\quad \le \quad \frac { D }{ d } \le \quad 1.10 $$
$${ C }_{ 1 }=-39.58+73.22(D/d)-32.46{ (D/d) }^{ 2 }$$
$${ C }_{ 2 }=-9.477+29.41(D/d)-20.13{ (D/d) }^{ 2 }$$
$${ C }_{ 3 }=82.46-166.96(D/d)+84.58{ (D/d) }^{ 2 }$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { r }{ d } +{ C }_{ 3 }{ (\frac { r }{ d } ) }^{ 2 }$$
$${ \sigma }_{ nom }=32M/\pi { d }^{ 3 }$$
$${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ t }{ \sigma }_{ nom }$$
Torsion
Stress concentration factors for large circumferential groove under torsion
$$ 0.3\quad \le \quad \frac { r }{ d } \le \quad 1.0 $$ , $$ 1.005\quad \le \quad \frac { D }{ d } \le \quad 1.10 $$
$${ C }_{ 1 }=-35.16+67.57(D/d)-31.28{ (D/d) }^{ 2 }$$
$${ C }_{ 2 }=79.13-148.37(D/d)+69.09{ (D/d) }^{ 2 }$$
$${ C }_{ 3 }=-50.34+94.67(D/d)-44.26{ (D/d) }^{ 2 }$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { r }{ d } +{ C }_{ 3 }{ (\frac { r }{ d } ) }^{ 2 }$$
$${ \tau }_{ nom }=16T/\pi { d }^{ 3 }$$
$${ \tau }_{ max }=\tau _{ A }={ K }_{ t }{ \tau }_{ nom }$$

Opposite Shoulder Fillets in Stepped Flat Bar

Stress concentration factors for opposite shoulder fillets in stepped bar
Tension
Stress concentration factors for opposite shoulder fillets in stepped bar under tension
$$0.1\le \frac { h }{ r } \le 2.0$$ $$2\le \frac { h }{ r } \le 20$$
$${ C }_{ 1 }=1.006+1.008\sqrt { h/r } -0.044h/r$$ $${ C }_{ 1 }=1.020+1.009\sqrt { h/r } -0.048h/r$$
$${ C }_{ 2 }=-0.115-0.584\sqrt { h/r } +0.315h/r$$ $${ C }_{ 2 }=-0.065-0.165\sqrt { h/r } -0.007h/r$$
$${ C }_{ 3 }=0.245-1.006\sqrt { h/r } -0.257h/r$$ $${ C }_{ 3 }=-3.459+1.266\sqrt { h/r } -0.016h/r$$
$${ C }_{ 4 }=-0.135+0.582\sqrt { h/r } -0.017h/r$$ $${ C }_{ 4 }=3.505-2.109\sqrt { h/r } +0.069h/r$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2h }{ D } +{ C }_{ 3 }{ (\frac { 2h }{ D } ) }^{ 2 }+{ C }_{ 4 }{ (\frac { 2h }{ D } ) }^{ 3 }$$
where
$$\frac { L }{ D } >-1.89(\frac { r }{ d } -0.15)+5.5$$
$${ \sigma }_{ nom }=P/td$$
$${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$
Bending
Stress concentration factors for opposite shoulder fillets in stepped bar under bending
$$0.1\le \frac { h }{ r } \le 2.0$$ $$2\le \frac { h }{ r } \le 20$$
$${ C }_{ 1 }=1.006+0.967\sqrt { h/r } +0.013h/r$$ $${ C }_{ 1 }=1.058+1.002\sqrt { h/r } -0.038h/r$$
$${ C }_{ 2 }=-0.270-2.372\sqrt { h/r } +0.708h/r$$ $${ C }_{ 2 }=-3.652+1.639\sqrt { h/r } -0.436h/r$$
$${ C }_{ 3 }=0.662+1.157\sqrt { h/r } -0.908h/r$$ $${ C }_{ 3 }=6.170-5.687\sqrt { h/r } +1.175h/r$$
$${ C }_{ 4 }=-0.405+0.249\sqrt { h/r } -0.200h/r$$ $${ C }_{ 4 }=-2.558+3.046\sqrt { h/r } -0.701h/r$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2h }{ D } +{ C }_{ 3 }{ (\frac { 2h }{ D } ) }^{ 2 }+{ C }_{ 4 }{ (\frac { 2h }{ D } ) }^{ 3 }$$
where
$$\frac { L }{ D } >-2.05(\frac { r }{ d } -0.025)+2$$
$${ \sigma }_{ nom }={ 6M }/{ t{ d }^{ 2 } }$$
$${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$

Rectangular Hole with Round Corners in Infinite Plate

Stress concentration factors for rectangular hole in infinite plate
Tension
Stress concentration factors for rectangular hole in infinite plate under axial tension load
$$0.2\le r/b\le 1.0$$ and $$0.3\le b/a\le 1.0$$
$${ C }_{ 1 }=14.815-15.774\sqrt { r/b } +8.149r/b$$
$${ C }_{ 2 }=-11.201-9.750\sqrt { r/b } +9.600r/b$$
$${ C }_{ 3 }=0.202+38.662\sqrt { r/b } -27.374r/b$$
$${ C }_{ 4 }=3.232-23.002\sqrt { r/b } +15.482r/b$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { b }{ a } +{ C }_{ 3 }{ (\frac { b }{ a } ) }^{ 2 }+{ C }_{ 4 }{ (\frac { b }{ a } ) }^{ 3 }$$
$${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ 1 }$$

Round Pin Joint with Closely Fitting Pin in Finite Width Plate

Stress concentration factor for round pin joint with closely fitting pin in finite-width plate
Tension
Stress concentration factor for round pin joint with closely fitting pin in finite-width plate under tension
For $$0.15\le \frac { d }{ D } \le 0.75,\quad \frac { L }{ D } \ge 1$$
$${ K }_{ ta }=12.882-52.714\frac { d }{ D } +89.762{ (\frac { d }{ D } ) }^{ 2 }-51.667{ (\frac { d }{ D } ) }^{ 3 }$$
$${ K }_{ tb }=0.2880+8.820\frac { d }{ D } -23.196{ (\frac { d }{ D } ) }^{ 2 }+29.167{ (\frac { d }{ D } ) }^{ 3 }$$
Nominal stress based on net section: 
$${ \sigma }_{ na }=P/(D-d)h$$
Nominal stress based on bearing area:
$${ \sigma }_{ nb }=P/dh$$
$${ \sigma }_{ max\_ a }={ K }_{ t }{ \sigma }_{ na }$$
$${ \sigma }_{ max\_ b }={ K }_{ t }{ \sigma }_{ nb }$$

Single Circular Hole in Infinite Plate

Stress concentration factors for single circular hole in infinite plate
Tension
Stress concentration factors for single circular hole in infinite plate under tension
Uniaxial tension (σ2=0)
σmax = Ktσ1
σA = 3σ1 (Kt=3)
σB = -σ1 (Kt=-1)
Biaxial Tension
For σ2 = σ1 , σA = σB = 2σ1 (Kt=2)
For σ2 = -σ1(pure shear stress), σA = -σB = 4σ1 (Kt=4)
Transverse Bending
Stress concentration factors for single circular hole in infinite plate under bending
σmax = Ktσ, σ = 6M/t 2
Simple bending (M1=M, M 2=0)
For 0 ≤ d/t ≤ 7.0 , σmax = σA
$${ K }_{ t }=3.000-0.947\sqrt { d/t } +0.192d/t$$
Isotropic bending (M1 = M 2 = M)
σmax = σA
Kt=2 (independent of d/t)

Single Elliptical Hole in Finite Width Plate

Single elliptical hole in finite-width plate
Tension
Stress concentration factor for single elliptical hole in finite-width plate under tension
For 0.5 ≤ a/b ≤ 10.0
$${ C }_{ 1 }=1.000-0.000\sqrt { a/b } +2.000a/b$$
$${ C }_{ 2 }=-0.351-0.021\sqrt { a/b } -2.483a/b$$
$${ C }_{ 3 }=3.621-5.183\sqrt { a/b } +4.494a/b$$
$${ C }_{ 4 }=-2.270+5.204\sqrt { a/b } -4.011a/b$$
$${ K }_{ tA }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2a }{ D } +{ C }_{ 3 }{ (\frac { 2a }{ D } ) }^{ 2 }+{ C }_{ 4 }{ (\frac { 2a }{ D } ) }^{ 3 }$$
$${ \sigma }_{ nom }=P/[(D-2a)t]$$
$${ \sigma }_{ A }={ K }_{ tA }{ \sigma }_{ nom }$$
In-Plane Bending
Stress concentration factor for single elliptical hole in finite-width plate under in-plane bending
 0.4 ≤ 2a/D ≤ 1.0,  1.0 ≤ a/b ≤ 2.0
$${ C }_{ 1 }=3.465-3.739\sqrt { a/b } +2.274a/b$$
$${ C }_{ 2 }=-3.841+5.582\sqrt { a/b } -1.741a/b$$
$${ C }_{ 3 }=2.376-1.843\sqrt { a/b } -0.534a/b$$
$${ K }_{ tA }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2a }{ D } +{ C }_{ 3 }{ (\frac { 2a }{ D } ) }^{ 2 }$$
$${ \sigma }_{ nom }=12Ma/([{ D }^{ 3 }-8{ a }^{ 3 }]t)$$
$${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ tA }{ \sigma }_{ nom }$$


Shoulder Fillet in a Stepped Circular Shaft

Stress concentration factors for shoulder fillet in stepped circular shaft
Tension
Stress concentration factors for shoulder fillet in stepped circular shaft under tension
$$0.1\le h/r\le 2.0$$ $$2.0\le h/r\le 20.0$$
$${ C }_{ 1 }=0.926+1.157\sqrt { h/r } -0.099h/r$$ $${ C }_{ 1 }=1.200+0.860\sqrt { h/r } -0.022h/r$$
$${ C }_{ 2 }=0.012-3.036\sqrt { h/r } +0.961h/r$$ $${ C }_{ 2 }=-1.805-0.346\sqrt { h/r } -0.038h/r$$
$${ C }_{ 3 }=-0.302+3.977\sqrt { h/r } -1.744h/r$$ $${ C }_{ 3 }=2.198-0.486\sqrt { h/r } +0.165h/r$$
$${ C }_{ 4 }=0.365-2.098\sqrt { h/r } +0.878h/r$$ $${ C }_{ 4 }=-0.593-0.028\sqrt { h/r } -0.106h/r$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C }_{ 4 }(2h/D) }^{ 3 }$$
$${ \sigma }_{ nom }={ 4P }/{ \pi { d }^{ 2 } }$$
$${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$
Bending
Stress concentration factors for shoulder fillet in stepped circular shaft under bending
$$0.1\le h/r\le 2.0$$ $$2.0\le h/r\le 20.0$$
$${ C }_{ 1 }=0.947+1.206\sqrt { h/r } -0.131h/r$$ $${ C }_{ 1 }=1.232+0.832\sqrt { h/r } -0.008h/r$$
$${ C }_{ 2 }=0.022-3.405\sqrt { h/r } +0.915h/r$$ $${ C }_{ 2 }=-3.813+0.968\sqrt { h/r } -0.260h/r$$
$${ C }_{ 3 }=0.869+1.777\sqrt { h/r } -0.555h/r$$ $${ C }_{ 3 }=7.423-4.868\sqrt { h/r } +0.869h/r$$
$${ C }_{ 4 }=-0.810+0.422\sqrt { h/r } -0.260h/r$$ $${ C }_{ 4 }=-3.839+3.070\sqrt { h/r } -0.600h/r$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C }_{ 4 }(2h/D) }^{ 3 }$$
$${ \sigma }_{ nom }={ 32M }/{ \pi { d }^{ 3 } }$$
$${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$
Torsion
Stress concentration factors for shoulder fillet in stepped circular shaft under torsion
$$0.25\le h/r\le 4.0$$
$${ C }_{ 1 }=0.905+0.783\sqrt { h/r } -0.075h/r$$
$${ C }_{ 2 }=-0.437-1.969\sqrt { h/r } +0.553h/r$$
$${ C }_{ 3 }=1.557+1.073\sqrt { h/r } -0.578h/r$$
$${ C }_{ 4 }=-1.061+0.171\sqrt { h/r } +0.086h/r$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C }_{ 4 }(2h/D) }^{ 3 }$$
$${ \tau }_{ nom }={ 16T }/{ \pi { d }^{ 3 } }$$
$${ \tau }_{ max }={ K }_{ t }{ \tau }_{ nom }$$

Transverse Circular Hole in Round Bar

Stress concentration factors of transverse circular hole in round bar
Tension
Stress concentration factors of transverse circular hole in round bar in tension
$$d/D\le 0.9\quad ,\quad 2r/D\le 0.45$$
$${ C }_{ 1 }=3.0$$
$${ C }_{ 2 }=0.427-6.770\frac { d }{ D } +22.698{ (\frac { d }{ D } ) }^{ 2 }-16.670{ (\frac { d }{ D } ) }^{ 3 }$$
$${ C }_{ 3 }=11.357+15.665\frac { d }{ D } -60.929{ (\frac { d }{ D } ) }^{ 2 }+41.501{ (\frac { d }{ D } ) }^{ 3 }$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2r }{ D } +{ C }_{ 3 }{ \left( \frac { 2r }{ D } \right) }^{ 2 }$$
$${ \sigma }_{ nom }=\frac { 4P }{ \pi ({ D }^{ 2 }-{ d }^{ 2 }) } $$
$${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ t }{ \sigma }_{ nom }$$
Bending
Stress concentration factors of transverse circular hole in round bar in bending
$$d/D\le 0.9\quad ,\quad 2r/D\le 0.4$$
$${ C }_{ 1 }=3.0$$
$${ C }_{ 2 }=-6.250-0.585\frac { d }{ D } +3.115{ (\frac { d }{ D } ) }^{ 2 }$$
$${ C }_{ 3 }=41.000-1.071\frac { d }{ D } -6.746{ (\frac { d }{ D } ) }^{ 2 }$$
$${ C }_{ 4 }=-45.000+1.389\frac { d }{ D } +13.889{ (\frac { d }{ D } ) }^{ 2 }$$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2r }{ D } +{ C }_{ 3 }{ \left( \frac { 2r }{ D } \right) }^{ 2 }+{ C }_{ 4 }{ \left( \frac { 2r }{ D } \right) }^{ 3 }$$
$${ \sigma }_{ nom }=\frac { 32MD }{ \pi ({ D }^{ 4 }-{ d }^{ 4 }) } $$
$${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ t }{ \sigma }_{ nom }$$
Torsion
Stress concentration factors of transverse circular hole in round bar in torsion
$$d/D\le 0.8\quad ,\quad 2r/D\le 0.4$$
$${ C }_{ 1 }=4.0$$
$${ C }_{ 2 }=-6.055+3.184\frac { d }{ D } -3.461{ (\frac { d }{ D } ) }^{ 2 }$$
$${ C }_{ 3 }=32.764-30.121\frac { d }{ D } +39.887{ (\frac { d }{ D } ) }^{ 2 }$$
$${ C }_{ 4 }=-38.330+51.542\sqrt { d/D } -27.483\frac { d }{ D } $$
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }\frac { 2r }{ D } +{ C }_{ 3 }{ \left( \frac { 2r }{ D } \right) }^{ 2 }+{ C }_{ 4 }{ \left( \frac { 2r }{ D } \right) }^{ 3 }$$
$${ \sigma }_{ max }={ \sigma }_{ A }={ K }_{ t }{ \tau }_{ nom }$$
$${ \tau }_{ nom }=\frac { 16TD }{ \pi ({ D }^{ 4 }-{ d }^{ 4 }) } $$
$${ \tau }_{ max }={ \tau }_{ A }={ 0.5K }_{ t }{ \tau }_{ nom }$$

Two Circular Holes in an Infinite Plate:

Stress concentration factors for two equal circular holes in infinite plate
Tension
Stress concentration factors for two equal circular holes in infinite plate under tension
for 0 ≤ d/L<1
$${ \sigma }_{ max }={ K }_{ t }\sigma $$
Uniaxial tension parallel to row of holes (σ1 = σ , σ2 = 0)
$${ K }_{ t }=3.000-0.712d/L+0.271{ (d/L) }^{ 2 }$$
Uniaxial tension normal to row of holes (σ2 = σ , σ1 = 0)
$${ \sigma }_{ max }={ \sigma }_{ B }={ K }_{ t }{ \sigma }_{ nom }\quad ,\quad { \sigma }_{ nom }\quad =\frac { \sigma \sqrt { 1-{ \left( d/L \right) }^{ 2 } } }{ 1-d/L } $$
$${ K }_{ t }=3.000-3.0018d/L+1.0099{ (d/L) }^{ 2 }$$
Biaxial tension (σ2 = σ, σ1 = σ)
$${ \sigma }_{ max }={ \sigma }_{ B }={ K }_{ t }{ \sigma }_{ nom }\quad ,\quad { \sigma }_{ nom }\quad =\frac { \sigma \sqrt { 1-{ \left( d/L \right) }^{ 2 } } }{ 1-d/L } $$
$${ K }_{ t }=2.000-2.119d/L+2.493{ (d/L) }^{ 2 }-1.372{ (d/L) }^{ 3 }$$

Supplements:

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