Torsion formula for Thin walled tubes
where,
=maximum shearing stress, Pa
=Shearing stress at any point a distance x from the centre of a section
r=radius of the section, m
d=diameter of a solid circular shaft, m
=polar moment of inertia of a cross-sectional area, m4
T=resisting torque, N-m
N= rpm of shaft
P=power, kW
=angle of twist, radian
L=length of shaft, m
G=shear modulus, Pa
do=outer diameter of hollow shaft, m
di=inner diameter of hollow shaft, m
and
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Torsion formula for Circular Shafts
where,
=Ip, polar moment of inertia for thin-walled tubes
r=mean radius
t=wall thickness
Modulus of Rigidity or G, (shear modulus) is a materials constant. For example: @ room temp
[tr] [td]Material[/td] [td]Shear Modulus[/td] [/tr] [tr] [td]---[/td][td](10^6 psi)[/td] [td](GPa)[/td] [/tr] [tr] [td]Aluminum Alloys[/td] [td]3.9[/td] [td]27[/td] [/tr] [tr] [td]Aluminum, 6061-T6[/td] [td]3.8[/td] [td]24[/td] [/tr] [tr] [td]Aluminum, 2024-T4[/td] [td]4.0[/td] [td]28[/td] [/tr] [tr] [td]Beryllium Copper[/td] [td]6.9[/td] [td]48[/td] [/tr] [tr] [td]Brass[/td] [td]5.8[/td] [td]40[/td] [/tr] [tr] [td]Bronze[/td] [td]6.5[/td] [td]44.8[/td] [/tr] [tr] [td]Carbon Steel[/td] [td]11.2[/td] [td]77[/td] [/tr] [tr] [td]Cast Iron[/td] [td]5.9[/td] [td]41[/td] [/tr] [tr] [td]Concrete[/td] [td]3.0[/td] [td]21[/td] [/tr] [tr] [td]Copper[/td] [td]6.5[/td] [td]45[/td] [/tr] [tr] [td]Glass, 96% silica[/td] [td]2.8[/td] [td]19[/td] [/tr] [tr] [td]Inconel[/td] [td]11.5[/td] [td]79[/td] [/tr] [tr] [td]Iron, Ductile[/td] [td]9.1 - 9.6[/td] [td]63 - 66[/td] [/tr] [tr] [td]Iron, Malleable[/td] [td]9.3[/td] [td]64[/td] [/tr] [tr] [td]Kevlar[/td] [td]2.8[/td] [td]19[/td] [/tr] [tr] [td]Lead[/td] [td]1.9[/td] [td]13.1[/td] [/tr] [tr] [td]Magnesium[/td] [td]2.4[/td] [td]16.5[/td] [/tr] [tr] [td]Molybdenum[/td] [td]17.1[/td] [td]118[/td] [/tr] [tr] [td]Monel metal[/td] [td]9.6[/td] [td]66[/td] [/tr] [tr] [td]Nickel Silver[/td] [td]6.9[/td] [td]48[/td] [/tr] [tr] [td]Nickel Steel[/td] [td]11.0[/td] [td]76[/td] [/tr] [tr] [td]Nylon[/td] [td]0.59[/td] [td]4.1[/td] [/tr] [tr] [td]Phosphor Bronze[/td] [td]5.9[/td] [td]41[/td] [/tr] [tr] [td]Plywood[/td] [td]0.09[/td] [td]0.62[/td] [/tr] [tr] [td]Polycarbonate[/td] [td]0.33[/td] [td]2.3[/td] [/tr] [tr] [td]Structural Steel[/td] [td]11.5[/td] [td]79.3[/td] [/tr] [tr] [td]Stainless Steel[/td] [td]11.2[/td] [td]77.2[/td] [/tr] [tr] [td]Steel, Cast[/td] [td]11.3[/td] [td]78[/td] [/tr] [tr] [td]Steel, Cold-rolled[/td] [td]10.9[/td] [td]75[/td] [/tr] [tr] [td]Titanium, Grade 2[/td] [td]5.9[/td] [td]41[/td] [/tr] [tr] [td]Titanium, Grade 5[/td] [td]5.9[/td] [td]41[/td] [/tr] [tr] [td]Titanium, 10% Vanadium[/td] [td]6.1[/td] [td]42[/td] [/tr] [tr] [td]Wood, Douglas Fir[/td] [td]1.9[/td] [td]13[/td] [/tr] [tr] [td]Z-nickel[/td] [td]11[/td] [td]76[/td] [/tr]