
Tension 

$$0.1\le h/r\le 2.0$$ 
$$2.0\le h/r\le 20.0$$ 
$${ C }_{ 1 }=0.926+1.157\sqrt { h/r } 0.099h/r$$ 
$${ C }_{ 1 }=1.200+0.860\sqrt { h/r } 0.022h/r$$ 
$${ C }_{ 2 }=0.0123.036\sqrt { h/r } +0.961h/r$$ 
$${ C }_{ 2 }=1.8050.346\sqrt { h/r } 0.038h/r$$ 
$${ C }_{ 3 }=0.302+3.977\sqrt { h/r } 1.744h/r$$ 
$${ C }_{ 3 }=2.1980.486\sqrt { h/r } +0.165h/r$$ 
$${ C }_{ 4 }=0.3652.098\sqrt { h/r } +0.878h/r$$ 
$${ C }_{ 4 }=0.5930.028\sqrt { h/r } 0.106h/r$$ 
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C
}_{ 4 }(2h/D) }^{ 3 }$$ 
$${ \sigma }_{ nom }={ 4P }/{ \pi { d }^{ 2 } }$$ 
$${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$ 
Bending 

$$0.1\le h/r\le 2.0$$ 
$$2.0\le h/r\le 20.0$$ 
$${ C }_{ 1 }=0.947+1.206\sqrt { h/r } 0.131h/r$$ 
$${ C }_{ 1 }=1.232+0.832\sqrt { h/r } 0.008h/r$$ 
$${ C }_{ 2 }=0.0223.405\sqrt { h/r } +0.915h/r$$ 
$${ C }_{ 2 }=3.813+0.968\sqrt { h/r } 0.260h/r$$ 
$${ C }_{ 3 }=0.869+1.777\sqrt { h/r } 0.555h/r$$ 
$${ C }_{ 3 }=7.4234.868\sqrt { h/r } +0.869h/r$$ 
$${ C }_{ 4 }=0.810+0.422\sqrt { h/r } 0.260h/r$$ 
$${ C }_{ 4 }=3.839+3.070\sqrt { h/r } 0.600h/r$$ 
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C
}_{ 4 }(2h/D) }^{ 3 }$$ 
$${ \sigma }_{ nom }={ 32M }/{ \pi { d }^{ 3 } }$$ 
$${ \sigma }_{ max }={ K }_{ t }{ \sigma }_{ nom }$$ 
Torsion 

$$0.25\le h/r\le 4.0$$ 
$${ C }_{ 1 }=0.905+0.783\sqrt { h/r } 0.075h/r$$ 
$${ C }_{ 2 }=0.4371.969\sqrt { h/r } +0.553h/r$$ 
$${ C }_{ 3 }=1.557+1.073\sqrt { h/r } 0.578h/r$$ 
$${ C }_{ 4 }=1.061+0.171\sqrt { h/r } +0.086h/r$$ 
$${ K }_{ t }={ C }_{ 1 }+{ C }_{ 2 }(2h/D)+{ { C }_{ 3 }(2h/D) }^{ 2 }+{ { C
}_{ 4 }(2h/D) }^{ 3 }$$ 
$${ \tau }_{ nom }={ 16T }/{ \pi { d }^{ 3 } }$$ 
$${ \tau }_{ max }={ K }_{ t }{ \tau }_{ nom }$$ 