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material, then the shaft will fail by a crack initiating at the surface and propagating through to the core of the shaft, fracturing in a 45-degree angle helical shape. This is often demonstrated by twisting a piece of blackboard chalk between one's fingers.
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881:. If the shaft is loaded only in torsion, then one of the principal stresses will be in tension and the other in compression. These stresses are oriented at a 45-degree helical angle around the shaft. If the shaft is made of
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Fakouri
Hasanabadi, M.; Kokabi, A.H.; Faghihi-Sani, M.A.; Groß-Barsnick, S.M.; Malzbender, J. (October 2018). "Room- and high-temperature torsional shear strength of solid oxide fuel/electrolysis cell sealing material".
92:
In non-circular cross-sections, twisting is accompanied by a distortion called warping, in which transverse sections do not remain plane. For shafts of uniform cross-section unrestrained against warping, the torsion is:
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for the section. For circular rods, and tubes with constant wall thickness, it is equal to the polar moment of inertia of the section, but for other shapes, or split sections, it can be much less. For more accuracy,
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such as rough spots. Thus, shafts for use in high torsion are polished to a fine surface finish to reduce the maximum stress in the shaft and increase their service life.
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In the case of thin hollow shafts, a twisting buckling mode can result from excessive torsional load, with wrinkles forming at 45° to the shaft axis.
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Note that the highest shear stress occurs on the surface of the shaft, where the radius is maximum. High stresses at the surface may be compounded by
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is the perpendicular distance between the rotational axis and the farthest point in the section (at the outer surface).
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763:, the result is a diameter of 69 cm, the approximate size of a turboset shaft in a nuclear power plant.
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490:; this is the typical frequency in Europe. In North America, the frequency is 60 Hz.
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158:{\displaystyle T={\frac {J_{\text{T}}}{r}}\tau ={\frac {J_{\text{T}}}{\ell }}G\varphi }
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741:{\displaystyle D=\left({\frac {16T_{\max }}{\pi {\tau }_{\max }}}\right)^{1/3}}
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is the length of the object to or over which the torque is being applied.
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of 5 and re-calculates the radius with the maximum stress equal to the
85:(ft·lbf). In sections perpendicular to the torque axis, the resultant
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647:{\displaystyle T_{\max }={\frac {{\tau }_{\max }J_{\text{zz}}}{r}}}
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355:{\displaystyle \tau _{\varphi _{z}}(r)={Tr \over J_{\text{T}}}}
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425:{\displaystyle \varphi _{}={\frac {T\ell }{GJ_{\text{T}}}}.}
215:(FEA) is the best method. Other calculation methods include
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Case and
Chilver "Strength of Materials and Structures
197:(tau) is the maximum shear stress at the outer surface
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873:The shear stress in the shaft may be resolved into
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536:The torque carried by the shaft is related to the
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175:is the applied torque or moment of torsion in Nm.
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89:in this section is perpendicular to the radius.
291:The shear stress at a point within a shaft is:
61:is the twisting of an object due to an applied
955:Torsional Analysis of Structural Steel Members
498:can be calculated with the following formula:
34:Twisting of an object due to an applied torque
8:
575:The angular frequency is therefore 314.16
372:The angle of twist can be found by using:
861:Learn how and when to remove this message
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73:unit for newtons per square metre, or in
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953:Seaburg, Paul; Carter, Charles (1997).
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259:(psi), or lbf/ft or in ISO units N/mm.
247:is the shear modulus, also called the
476:of the steel used to make the shaft (
65:. Torsion is expressed in either the
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799:adding citations to reliable sources
462:Power carried by the shaft is 1000
77:(psi) while torque is expressed in
486:Electricity has a frequency of 50
27:For other notions of torsion, see
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899:List of area moments of inertia
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237:(phi) is the angle of twist in
41:Torsion of a square section bar
996:10.1016/j.ceramint.2018.10.134
526:{\displaystyle \omega =2\pi f}
466:; this is typical for a large
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1032:The dictionary definition of
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455:shaft radius for a turboset:
219:and shear flow approximation.
49:Example of torsion mechanics
583:and the torque 3.1831 × 10
540:by the following equation:
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657:After substitution of the
565:{\displaystyle P=T\omega }
251:, and is usually given in
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810:"Torsion" mechanics
29:Torsion (disambiguation)
590:The maximal torque is:
213:finite element analysis
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904:Saint-Venant's theorem
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190:{\displaystyle \tau }
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851:December 2014
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793:Please help
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253:gigapascals
1057:Categories
941:References
821:newspapers
287:Properties
1063:Mechanics
1012:139371841
1004:0272-8842
708:τ
703:π
619:τ
560:ω
518:π
509:ω
399:ℓ
384:φ
308:φ
303:τ
185:τ
153:φ
145:ℓ
127:τ
81:(N·m) or
69:(Pa), an
893:See also
753:diameter
18:Torquing
1035:torsion
931:or -bar
883:brittle
835:scholar
255:(GPa),
239:radians
206:is the
168:where:
59:torsion
1068:Torque
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470:plant.
257:lbf/in
67:pascal
63:torque
1008:S2CID
842:JSTOR
828:books
538:power
481:yield
1000:ISSN
877:via
814:news
751:The
494:The
992:doi
797:by
713:max
696:max
624:max
606:max
585:N·m
577:rad
1059::
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988:45
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634:zz
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488:Hz
464:MW
71:SI
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692:T
682:(
677:=
674:D
640:r
630:J
611:=
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554:=
551:P
521:f
515:2
512:=
478:τ
420:.
412:T
408:J
404:G
396:T
390:=
346:T
342:J
337:r
334:T
328:=
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322:r
319:(
312:z
282:.
280:T
277:w
270:G
267:T
264:J
245:G
241:.
235:φ
229:ℓ
223:r
204:T
201:J
173:T
150:G
140:T
136:J
130:=
122:r
117:T
113:J
107:=
104:T
31:.
20:)
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