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28-602: [REDACTED] Look up torsion in Wiktionary, the free dictionary. Torsion may refer to: Science [ edit ] Torsion (mechanics) , the twisting of an object due to an applied torque Torsion of spacetime, the field used in Einstein–Cartan theory and Alternatives to general relativity Torsion angle , in chemistry Biology and medicine [ edit ] Torsion fracture or spiral fracture,

56-561: A stress concentration (also called a stress raiser or a stress riser or notch sensitivity ) is a location in an object where the stress is significantly greater than the surrounding region. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress. This arises from such details as holes , grooves , notches and fillets . Stress concentrations may also occur from accidental damage such as nicks and scratches. The degree of concentration of

84-432: A bone fracture when torque is applied Organ torsion, twisting that interrupts the blood supply to that organ: Splenic torsion, causing splenic infarction Ovarian torsion Testicular torsion Penile torsion , a congenital condition Torsion of the digestive tract in some domestic animals: Torsion, a type of horse colic Gastric torsion , or gastric dilatation volvulus Torsion (gastropod) ,

112-523: A developmental feature of all gastropods Mathematics [ edit ] Torsion of a curve Torsion tensor , in differential geometry Torsion (algebra) , in ring theory Torsion group , in group theory and arithmetic geometry Tor functor , the derived functors of the tensor product of modules over a ring Torsion-free module , in algebra See also Torsion-free (disambiguation) Analytic torsion (Reidemeister torsion, R-torsion, Franz torsion, de Rham torsion, Ray-Singer torsion),

140-432: A discontinuity under typically tensile loads can be expressed as a non-dimensional stress concentration factor K t {\displaystyle K_{t}} , which is the ratio of the highest stress to the nominal far field stress. For a circular hole in an infinite plate, K t = 3 {\displaystyle K_{t}=3} . The stress concentration factor should not be confused with

168-404: A fine surface finish to reduce the maximum stress in the shaft and increase their service life. The angle of twist can be found by using: Calculation of the steam turbine shaft radius for a turboset: Assumptions: The angular frequency can be calculated with the following formula: The torque carried by the shaft is related to the power by the following equation: The angular frequency

196-410: A nuclear power plant. The shear stress in the shaft may be resolved into principal stresses via Mohr's circle . 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 brittle material, then the shaft will fail by a crack initiating at

224-441: A topological invariant of manifolds Whitehead torsion , in geometric topology Other uses [ edit ] Torsion field (pseudoscience) , a field alleged to make faster-than-light communication and paranormal phenomena possible Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Torsion . If an internal link led you here, you may wish to change

252-487: 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: where: The shear stress at a point within a shaft is: 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 stress concentrations such as rough spots. Thus, shafts for use in high torsion are polished to

280-399: Is adding a fillet to internal corners. Another example is in a threaded component, where the force flow line is bent as it passes from shank portion to threaded portion; as a result, stress concentration takes place. To reduce this, a small undercut is made between the shank and threaded portions Functionally Graded Materials : Using materials with properties that vary gradually can reduce

308-705: Is generally presumed that the material used is consistent and homogeneous throughout. In practice, however, material inconsistencies such as internal cracks, blowholes, cavities in welds, air holes in metal parts, and non-metallic or foreign inclusions can occur. These defects act as discontinuities within the component, disrupting the uniform distribution of stress and thereby leading to stress concentration. Contact Stress : Mechanical components are frequently subjected to forces that are concentrated at specific points or small areas. This localized application of force can result in disproportionately high pressures at these points, causing stress concentration. Typical instances include

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336-486: Is the ratio of the highest stress σ max {\displaystyle \sigma _{\max }} to a nominal stress σ nom {\displaystyle \sigma _{\text{nom}}} of the gross cross-section and defined as Note that the dimensionless stress concentration factor is a function of the geometry shape and independent of its size. These factors can be found in typical engineering reference materials. E. Kirsch derived

364-415: Is therefore 314.16 rad / s and the torque 3.1831 × 10 N·m . The maximal torque is: After substitution of the torsion constant , the following expression is obtained: The diameter is 40 cm. If one adds a factor of safety of 5 and re-calculates the radius with the maximum stress equal to the yield stress/5 , the result is a diameter of 69 cm, the approximate size of a turboset shaft in

392-415: The stress intensity factor , which is used to define the effect of a crack on the stresses in the region around a crack tip. For ductile materials, large loads can cause localised plastic deformation or yielding that will typically occur first at a stress concentration allowing a redistribution of stress and enabling the component to continue to carry load. Brittle materials will typically fail at

420-474: The design phase, there are multiple approaches to estimating stress concentration factors. Several catalogs of stress concentration factors have been published. Perhaps most famous is Stress Concentration Design Factors by Peterson, first published in 1953. Finite element methods are commonly used in design today. Other methods include the boundary element method and meshfree methods . Stress concentrations can be mitigated through techniques that smoothen

448-471: The effective crack tip radius and thus reduce the stress concentration. Hole Reinforcement : Adding higher strength material around the hole, usually in the form of bonded rings or doublers. Composite reinforcements can reduce the SCF. Shape Optimization : Adjusting the hole shape, often transitioning from circular to elliptical, to minimize stress gradients. This must be checked for feasibility. One example

476-416: The equations for the elastic stress distribution around a hole . The maximum stress felt near a hole or notch occurs in the area of lowest radius of curvature . In an elliptical hole of length 2 a {\displaystyle 2a} and width 2 b {\displaystyle 2b} , under a far-field stress σ 0 {\displaystyle \sigma _{0}} ,

504-464: The flow of stress around a discontinuity: Material Removal : Introducing auxiliary holes in the high stress region to create a more gradual transition. The size and position of these holes must be optimized. Known as crack tip blunting, a counter-intuitive example of reducing one of the worst types of stress concentrations, a crack , is to drill a large hole at the end of the crack. The drilled hole, with its relatively large size, serves to increase

532-417: The flow of stress. Geometric discontinuities cause an object to experience a localised increase in stress. Examples of shapes that cause stress concentrations are sharp internal corners, holes, and sudden changes in the cross-sectional area of the object as well as unintentional damage such as nicks, scratches and cracks. High local stresses can cause objects to fail more quickly, so engineers typically design

560-526: The geometry to minimize stress concentrations. Material discontinuities, such as inclusions in metals, may also concentrate the stress. Inclusions on the surface of a component may be broken from machining during manufacture leading to microcracks that grow in service from cyclic loading. Internally, the failure of the interfaces around inclusions during loading may lead to static failure by microvoid coalescence . The stress concentration factor , K t {\displaystyle K_{t}} ,

588-443: The interactions at the points of contact in meshing gear teeth, the interfaces between cams and followers , and the contact zones in ball bearings . Thermal Stress : Thermal stress occurs when different parts of a structure expand or contract at different rates due to variations in temperature. This differential in thermal expansion and contraction generates internal stresses, which can lead to areas of stress concentration within

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616-449: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Torsion&oldid=1197193594 " Categories : Disambiguation pages Mathematics disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Torsion (mechanics) In non-circular cross-sections, twisting

644-483: The radius of curvature approaches zero, such as at the tip of a sharp crack, the maximum stress approaches infinity and a stress concentration factor cannot therefore be used for a crack. Instead, the stress intensity factor which defines the scaling of the stress field around a crack tip, is used. Stress concentration can arise due to various factors. The following are the main causes of stress concentration: Material Defects : When designing mechanical components, it

672-410: The stress at the ends of the major axes is given by Inglis' equation: where ρ {\displaystyle \rho } is the radius of curvature of the elliptical hole. For circular holes in an infinite plate where a = b {\displaystyle a=b} , the stress concentration factor is K t = 3 {\displaystyle K_{t}=3} . As

700-443: The stress concentration. However, repeated low level loading may cause a fatigue crack to initiate and slowly grow at a stress concentration leading to the failure of even ductile materials. Fatigue cracks always start at stress raisers, so removing such defects increases the fatigue strength . Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to

728-624: The structure. Geometric Discontinuities : Features such as steps on a shaft, shoulders, and other abrupt changes in the cross-sectional area of components are often necessary for mounting elements like gears and bearings or for assembly considerations. While these features are essential for the functionality of the device, they introduce sharp transitions in geometry that become hotspots for stress concentration. Additionally, design elements like oil holes, grooves, keyways, splines, and screw threads also introduce discontinuities that further exacerbate stress concentration. Rough Surface : Imperfections on

756-406: 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. 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. Stress concentrations In solid mechanics ,

784-549: The surface of components, such as machining scratches, stamp marks, or inspection marks, can interrupt the smooth flow of stress across the surface, leading to localized increases in stress. These imperfections, although often small, can significantly impact the durability and performance of mechanical components by initiating stress concentration. There are experimental methods for measuring stress concentration factors including photoelastic stress analysis , thermoelastic stress analysis, brittle coatings or strain gauges . During

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