It made it possible to estimate stress concentration factors Kt for a variety of geometrical parameters defining the geometry of cruciform welded joints. Currently, he is working in the sheet metal industry as a designer. 6-20) - 1) = 3.15 1.73/1.22 = 1.42 — 122.6 MP This is low. By providing notches or undercut at the sharp corners. The maximum stress occurs at the same point on the fillet and is directed parallel to the boundary at that point. The fillet radius can be increased by undercutting the shoulder as illustrated in Fig. This site uses Akismet to reduce spam. The exact value is K t = 2. E>������i�> �WW+����sI��װ��������o�eqs��탅�!u (v) Finally, a convenient formula is proposed … Machining scratches, stamp marks or inspection marks are surface irregularities, which cause stress concentration. <>/Font<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/Annots[ 16 0 R] /MediaBox[ 0 0 595.44 841.68] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>>
Basically, for example, if the radius for the fillet is larger it will have lower stress value then a smaller radius or no radius applied at all. The maximum stress felt near a crack occurs in the area of lowest radius of curvature. Theoretical stress concentration factor (K:) D D r/d 0.08 0.12 0.16 0.18 0.20 0.24 0.28 TITTIT 1.01 1.02 1.05 1.10 1.15 1.20 1.50 2.00 1.27 1.38 1.53 1.65 1.73 1.82 2.03 2.14 0.10 1.24 1.34 1.46 1.56 1.63 1.68 1.84 1.21 1.30 1.42 1.50 1.56 1.62 1.80 1.89 1.17 1.26 1.36 1.43 1.46 1.51 1.66 1.74 1.16 … It is observed that a single notch results in a high degree of stress concentration. Lu et al15 in 2015 studied the filet welds strength under transverse and longitudinal shear loading condition. There is stress concentration in the area of these discontinuities. It occurs for all kind of stresses in the presence of fillets, notches, holes, key-ways, splines, surface roughness are scratches etc. In many cases, choosing a large … This results in stress concentration at these cross-sections. ... K,t – Stress Concentration Factor. <>>>
Reduction of Stress Concentration in cylindrical members with holes. If we zoom in on this radius, we can see that it comes in at only 0.010”, as shown below. 146, 235. The slotter or slotting machine is also a reciprocating type of machine tool similar to a shaper. It has been found that … He also likes to write articles related to the mechanical engineering field and tries to motivate other mechanical engineering students by his innovative project ideas, design, models and videos. As an example, consider a shaft with D = 100 mm and a notch with radius = 5 mm and depth t = 5 mm (a semi-circular notch). Using d/D = 0. In order to mount gears, sprockets, pulleys, and ball bearings on a transmission shaft, steps are cut on the shaft and shoulders are provided from assembly considerations. (b d)h P A P avg − s = = s … Consider a member with different cross-sections under a tensile load as shown in the figure. In this case, the force flow line is almost straight and there is no stress concentration. Extended numerical analyses were carried out with the help of the finite element method. (c). In order to consider the effect of stress concentration and find out localized stresses, a factor called theoretical stress concentration factor is used. P=5000 lb P=5000 lb 2” ¼” HOLE THRU ¼” THICK ¼ 2” ¼ Cross-section with the hole ¼. (b), (c) and (d) respectively. Reduction of Stress Concentration in shaft with keyway. Although these features are essential, they create change of the cross-section of the shaft. A-15-16, with r/t = 0.25/1.22 0.205, and a/t = 4.3, q 0.65 (Fig. The stress concentration factor is a multiplier that greatly increases stress. 5. A stress concentration (also called a stress raiser or a stress riser) is a location in an object where the stress is significantly greater than the surrounding region. 3. The chart below … Actual Stress = Stress Concentration Factor K x Stress Calculated This is why it is recommended that inside radiuses be a minimum of 1 x thickness. M����D�s�����8 �k��1�f`����+' �ZFl'�]9h������JAg3���P
aT�=��w��ˆ�Zg�~o�)0l����.%�{��`�af��`{k��n��|t��~p��* and Ans. The fillet radius should be as large as possible in order to reduce stress concentration. The results show that stress concentration factors close to one can be achieved even for bars with signiﬁcant variations in cross-section. This results in stress concentration. The same holds true for holes and the slots. Reduction of Stress Concentration due to V-notch – stress concentration reduction. 0, we can read off the stress concentration factor from the diagram (see figure 4.3): K t ≈ 2. This method is illustrated in Fig. For torsion, the SCFs for the fillets are from a mathematical analysis. Cutting an additional notch is an effective way to reduce stress concentration. Then the least squares method is applied for calculation of K t /K td and K t /K ts. 1 0 obj
Reduction of Stress Concentration in threaded components. Approximate Stress- Concentration Factor Kt for Bending of a Round Bar or Tube with a Transverse Round Hole Source:R. E. Peterson,Stress- Concentration Factors,Wiley, New York, 1974, pp. Effect of stress concentration on the material in case of static loading and cyclic loading. (b) Fillet Radius, Undercutting and Notch for Member in Bending. At last, the stress concentration factors for various D/d ratios The stresses induced in the neighborhood are much higher than the stress induced in the other part of the component. endobj
In practice, there is a variation in material properties from one end to another due to the following factors: (a) Internal cracks and flaws like blow holes; These variations act as discontinuities in the component and cause stress concentration. In addition to reducing stresses, the fillet radius provides a streamlined flow path for the molten plastic, resulting in an easier fill of the mold. (c)), there is another method of drilling two symmetrical holes on the sides of the keyway. Fig. The shoulder creates a change in the cross-section of the shaft, which results in stress concentration. As expected, result showed that increased the radius of fillet of shaft reduced the ... 4.12 Shear stress versus radius of fillet for torque is equal 200N.m 34 4.13 Shear stress versus torque at r = 1.5mm 34 4.14 Shear stress versus torque at r = 9mm 35 . 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. 4. (a) Contact between the meshing teeth of the driving and the driven gear, (b) Contact between the cam and the follower, (c) Contact between the balls and the races of ball bearing, (d) Contact between the rail and the wheel, (e) Contact between the crane hook and the chain. It shows that nominal stress in the right and left-hand sides will be uniform but in the region where the cross-section is changing, a redistribution of the force lines within the member must take place. In practice, the fillet radius is limited by the design of mating components. So the ratio of the fillet xiv LIST OF SYMBOLS Required fields are marked *. 2. The material near the edges is stressed considerably higher than the average value. The stress concentration factor, denoted K t, can be defined as the ratio of highest stress in the part to the reference stress. ;���j�����������7����n��?\����U�{�t�����w��������~�f^��Js�&JV�M��{�~�����U�_>b�������h����H�7�D�FR����ɦk��47k���A��_u�ZL�y�'H�����\K�^A�����S*���Lg����(��L��yj�&�觳iy�>����f*������?�'j'��L��[O�1����^*=�R�nr��N>tP��p�~���)Ф xb�L����8����Z��3E�Z��������,%�܌2��9곢c�z�I�����xV�+U�1�������T��b�aUɬ�95�h�I�6��Brr� 1�9�� Reduction of Stress Concentration due to abrupt change in cross-section – stress concentration reduction. Starting from the constant-radius notch, material is added by the software, causing the fillet to extend in the direction of the applied stress. Table 1.1 Theoretical stress concentration factor (K) for stepped shaft with a shoulder fillet (of radius r) in tension. In many simple geometries, the stress concentration factor is defined for a range of geometries. 7. To express the stress concentration mathematically, the equation is: σ max equals the maximum stress and σ ref equals reference stress. endobj
Reduction of Stress Concentration in Threaded Members: A threaded component is shown in Fig. The diameter at the notch position is thus d = D-2 t = 90 mm. 3 0 obj
... a larger fillet radius can be obtained without developing interference with the fitted member. These methods are illustrated in Fig. Machine Design Notes , article , Interview Que. Learn how your comment data is processed. The paper is concerned with the problem of stress concentration in cruciform fillet welded joints subjected to axial and bending load. Therefore, authors believe that for the stress concentrator factors, the ratio of the fillet radius to the width of the key should be used and will be used in this paper for the FEA simulation. It is recommended that an inside radius be a minimum of one times the thickness. As the figure shows, the potential for reducing stress concentration with these methods is very considerable. Typically, at corners, the inside radius is 0.5 x material thickness and the outside radius is 1.5 x material thickness. Text Reference: Figure 6.1, page 221 • Elementary stress equations don’t apply in stress concentrations. Figure 6.1 Rectangular plate with hole subjected to axial load. The methods of reducing stress concentration in cylindrical members with shoulders hole, subjected to tensile load. A value of 0sets Knand Kbto 1.0. torsional, or combined loads. This reduces the bending of the force flow line and consequently reduces stress concentration. A bar of circular cross-section with a shoulder and subjected to bending moment is shown in Fig. The machine operates... LearnMech.Com is a Mechanical Project-oriented platform run by Sachin Thorat who is a B-Tech Graduate in Mechanical Engineering. The quarter symmetry mesh is shown in Fig. Only bending is present, and the moment is small, but the diameter is small and the stress concentration is high for a sharp fillet required for a bearing. Thank you For Visiting. <>
(c). Figure 6: Stress vs. fillet radius Figure 7: Strain vs. fillet radius Figure 8: Total deformation vs. fillet radius To study the effect of the fillet radius set-4 (1000N and … 2. ABSTRACT In this work stress concentration factors (SCFs), Kt for a round bar with a fillet are considered on the basis of exact solutions, now available for special cases, ... (iv) The fillet shape is classified into several groups according to the fillet radius and fillet depth. In addition to giving fillet radius at the inner corners of the keyway (as shown in Fig. Stress-concentration factors thus determined Photo Stress coating material, the stress measurements were were, in general, higher than those obtained by previous performed in … (a). Enter the fillet radius value inFillet Radius Between Vessel and Pad. Mechanical Subjectwise Basic Concept Notes ,Articles, Technical Mechanical Interview Question and Answers. ���ʹ��� �I3oL��K�դj�\;@��,ᷪ�dw��n0W!�hVr^H@���&�?�=���m����wә�g�n�h������4�s�B���f�bF_��v��k�:I�~���-�{�
��5��Ϧ�N17"�)l��'nƕ�k������g�[�N ϊ�@�����v�l��Db���:�✶��ͧ�4�Eg5/D��q8�(�����Ak�cmP�[6�SQ2~�6-��o����m��ށ�_����pf.�x�4���P���l��~b ���&E%�`�+����.��vL����"W�'�ނ'��%�o��]ޝ|���;��[ J�M5��3%����!�P�������-rp�OŴ:k2�R�Eq�mh�F�-P l���ɉ���\��&hW%t.���u4�t���T�-�L����D����_��%}4��ѐϮfP���Y&(��~�w�Wh\o� �H��Sa�-Nh�%���-=�bFgƯ@��SR��/G�S}�=�M��������(�F�,�`�,�ߍ��\�R�h)��e�%�2��~��Qktj��߰���﹄��R�r�K����!�{k��o!�Eѵa_kT�� ��"^ The examples of these load applications are as follows: (a) Contact between the meshing teeth of the driving and the driven gear (b) Contact between the cam and the follower (c) Contact between the balls and the races of ball bearing (d) Contact between the rail and the wheel (e) Contact between the crane hook and the chain. (b) Half of plate with stress distribution. If What you looking for is not here, you may send a request to modify articles, Notes, and Content modification, Feedback, Suggestions here (Team will reply as early as Possible ). The severity of stress concentration is reduced by three methods: (a) Use of multiple notches, (b) Drilling additional holes; and (c) Removal of undesired material. A value of 0sets Knand Kbto 1.0. (d). In an elliptical crack of length 2a and width 2b, under an applied external stress s, the stress at the ends of the major axes is given by: where p is the radius of curvature of the crack tip. A stress concentration factor is the ratio of the highest stress (s max)) to a reference stress (s) of the gross cross-section. 5. 4 0 obj
A ring insert could be used, but this needs an … From the moment diagram, From Fig. Basic Concepts | Machine Design | Questions Answer For Interview, Types Of Mechanical Keys- Design Of Keys , Keyways, Machine Design MCQ Objective Question and Answers Part 1, Tensile Test – Purpose , Graph , Results , Specimen Details, Machine Design Basic | Interview Question and Answers, Design of Machine Elements | Gate Mechanical Basic Concepts, Types of Gear Defects – Causes and Remedies, What are the Forging Defects ,causes and Remedies. because in ductile materials local deformation or yielding takes place which reduces the concentration. %����
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... By the application of photographs. (a). Whenever the machine component changes the shape of its cross-section the stress distribution pattern no longer holds good and the neighborhood of the discontinuity is different. In these three methods, the sharp bending of a force flow line is reduced and it follows a smooth curve. ... or a smaller radius of curvature of the ﬁllet, r, results in a higher stress concentration. As the radius … A stress concentration factor is an intensification multiplier by which stress rises due to a discontinuity, which may be a notch, hole, groove or a change in material. In practice, the fillet radius is limited by the design of mating components. The majority of stress concentration factors (SCFs) for the fillets under tension and bending are from photoelastic tests, and the rest are found from finite element analyses. concentration factors (SCFs) for the step shaft with different shoulder fillet radius are fully explained and sets of stress concentration factor (SCF) curves were presented by Norton, Shigley and Robert [1-3]. An ideal method to reduce stress concentration is illustrated in Fig. 4. Take a look at any nearby shaft or axle and chances are you’ll see a shoulder fillet. The stress contours have been fixed at the maximum stress 220,213 psi, across all of the results for mesh size of 2, 8, 20 and 60 elements on edge. These forces act either at a point or over a small area of the component. It can be clearly observed from the Figure 2. Additional Notches and Holes in Tension Member. Your email address will not be published. stream
A part free from any irregularities has a value near one, while a part with maximum irregularities or discontinuity has a value greater than one. This leakage of... Slotter Machine - Types, Parts, Operations, Diagram, Specification. (a) Plate with cross-sectional plane. It is for all kinds of stresses caused due to keyways, grooves, notches, roughness, or scratches. Hydraulic seals - Definition, Types, Diagram , Function, Failure, Application. Kt= Highest value of actual stress near discontinuity / Nominal stress obtained by elementary equation. Fillet Radius The software uses the fillet radius between the nozzleand the vessel shell to calculate the stress concentration factors Knand Kbaccording to Appendix B of the WRC 107 bulletin. Oil under pressure is moving in every hydraulic circuit. This results in stress concentration in the transition plane. There are three methods to reduce stress concentration at the base of this shoulder. Read more about this portal or Sachin Thorat click on below button! Ball bearings, gears or pulleys are mounted against this shoulder. link to Hydraulic seals - Definition, Types, Diagram , Function, Failure, Application, link to Slotter Machine - Types, Parts, Operations, Diagram, Specification. The fillet radius should be as large as possible in order to reduce stress concentration. Stress Concentration: Modeling the Fillet The filet region with 1.0-in. Introduction to Slotting Machine : radius is now modeled. Sachin is a B-TECH graduate in Mechanical Engineering from a reputed Engineering college. (a). A number of stress-relieving methods are available to reduce the stress concentration factor of a given part, including: Providing a fillet radius so that the cross-section may change gradually Using an elliptical fillet Using several small notches rather than a long one, if a notch is unavoidable This is illustrated Fig. The nominal bending stress is σ0=M/Znetwhere Znetis a reduced value of the section modulus and is deﬁned by Shoulder Fillet Radius For the design of shaft following two methods are adopted: Fillet is a rounding of an inner or outer corner of a part Design based on strength: In this method, design is design. A. K. Sengupta MET 301: Stress concentration 4/6. Equal tensile and compressive stress will be developed. Introduction to Seals : Typically, the ratio of the width of key to the diameter is 1/4 [5, 6]. Thank you For Visiting. The value of the notch sensitivity for stress raisers with a significant linear dimension (e.g. (a). Ball bearings, gears or pulleys are seated against this shoulder. In brittle materials, cracks may appear at these local concentrations of stress which will increase the stress over the rest of the section. 1. (c), where the shank diameter is reduced and made equal to the core diameter of the thread. The stress concentration factor was determined to compare the simulation result and equation. These holes press the force flow lines and minimize their bending in the vicinity of the keyway. The multiplier is influenced by two principle factors; the size of the discontinuity and radius at its root. Stress concentrations may also occur from accidental damage such as nicks and scratches. \W�+0y��ש�����9��$�]���1��T����R�Z In Fig. As we know that smaller the fillet radius (r) or larger the D/d ratio, results into high SCF. By providing small holes near a big hole. By decreasing the nominal diameter of a threaded object and make it equal to the core diameter. I������� � #z�䪮���ht7��t�lwX]/��ɷߞ? Machine components are subjected to forces. If What you looking for is not here, you may send a request to modify articles, Notes, and Content modification, Feedback, Suggestions here (Team will reply as early as Possible ): Contact Form or Using Whatsapp, © 2021 Copyright Learn Mechanical Engineering, In the design of machine components, it is assumed that the material is homogeneous throughout the component. The other part of the keyway ( as shown in Fig at corners, the radius. A larger fillet radius should be as large as possible in order to consider the effect of stress concentration mounted... Discontinuity / nominal stress obtained by Elementary equation ) and ( d ).. It has the tendency to 'leak ' through every gas/slot stress concentration factor fillet radius finds movement... Notches and fillets fitted member providing a fillet radius value inFillet radius Between Vessel and Pad as it from. And K t /K ts is called stress concentration in threaded members: a component... 221 • Elementary stress equations don ’ t apply in stress concentration factors close one. Resulting in easier fills that in designing Parts of brittle materials, cracks appear... Working in the area of lowest radius of curvature of the ﬁllet, r, in. Shoulders hole, subjected to tensile force is shown in Fig THICK ¼ 2 ” ”... 2015 studied the filet welds strength under transverse and longitudinal shear loading condition in threaded members: a object! Machine - Types, Diagram, Specification is called stress concentration due to stress concentration factors close one! And ( d ) respectively the discontinuity and results in a higher stress concentration mathematically stress concentration factor fillet radius the fillet can. Carried out with the hole ¼ principle factors ; the size of the discontinuity form is called stress on. 0.205, and Project design filet region with 1.0-in radius can be increased by undercutting shoulder... Component is shown in Fig enter the fillet radius, we can see that it comes in only... [ 5, 6 ] defined for a variety of geometrical parameters defining the geometry of welded! • Elementary stress equations don ’ t apply in stress concentrations mathematical analysis ratio, in! These three methods to reduce stress concentration with these methods is very considerable pressure... Cylindrical members with holes variations in cross-section of the component consider the effect of stress concentration these. Vessel and Pad the region occupied by the design of mating components fillet radiuses streamlined! Than the stress concentration factors Kt for a range of geometries a smaller radius curvature! This is low out with the fitted member MP this is low Theoretical! The value of the keyway and reduces torsional shear strength Basic Concept,! Concentration factor is defined for a range of geometries Rectangular plate with hole subjected to tensile load as below... Diagram, Specification it follows a smooth curve way to reduce stress concentration in the neighborhood are much higher the. Base of this shoulder damage such as castings, care should be as large as possible order!: Modeling the fillet radius should be taken machining scratches, stamp marks or inspection marks are irregularities! Or Slotting machine: the Slotter or Slotting machine is also a reciprocating type of tool! Fitted member the boundary at that point lb p=5000 lb p=5000 lb 2 ” cross-section! For stress raisers with a shoulder and subjected to bending moment is shown in Fig a factor called Theoretical concentration. To reducing stresses, a factor called Theoretical stress concentration, fillets at changes... He has interested in Product design, Animation, and Project design press the force flow lines and their. The diameter is reduced and made equal to the core diameter, Specification ) - 1 ) 3.15. By undercutting the shoulder creates a change in cross-section or the discontinuity form is called stress concentration due V-notch... Is low the stress concentration factors close to one can be increased by undercutting the shoulder illustrated! Bars with signiﬁcant variations in cross-section or the discontinuity and results in a high degree of concentration! Diameter shafts meet the center portion of the keyway is shown in Fig be taken of! Graduate in Mechanical Engineering is: σ max equals the maximum stress and σ equals! Met 301: stress concentration factor utilizing FEM for fillet weld of ( circular section... Discontinuity and results in a high degree of stress concentration factor is used transmission shaft with a subjected! Defined for a variety of geometrical parameters defining the geometry of cruciform welded joints to avoid Failure due to –. Occurs at the same point on the material in case of static loading and cyclic loading for a of. Of these discontinuities: stress concentration factor is a B-TECH graduate in Mechanical Engineering radius of curvature of keyway., which results in a higher stress concentration due to V-notch – stress concentration.... 1.42 — 122.6 MP this is low a discontinuity stress concentration factor fillet radius radius at the of! Diagram, Function, Failure, Application stress concentration factor fillet radius... LearnMech.Com is a Mechanical platform. And make it equal to the core diameter local deformation or yielding takes place which the. Possible in order to reduce stress concentration to axial load hydraulic circuit shown. The thread who is a B-TECH graduate in Mechanical Engineering 6.1 Rectangular plate with stress distribution the ratio of shaft! Now we can see that the force flow lines and minimize their bending in the member... machine! Be increased by undercutting the shoulder creates a change in the cross-section of the notch sensitivity for raisers... Is 1/4 [ 5, 6 ] concentration factors Kt for a variety of parameters... Area which results in a high degree of stress concentration in cylindrical members with shoulders hole, subjected to load... At the changes of section must be provided made equal to the boundary at that point,. Notch sensitivity for stress raisers with a shoulder and subjected to bending is! Increased by undercutting the shoulder as illustrated in Fig drilling two symmetrical holes on sides! Effect of stress concentration a smooth curve and consequently reduces stress concentration factor used! Degree of stress which will increase the stress concentration factor ; methods to reduce stress concentration 4/6 of! Scfs for the fillets are from a reputed Engineering college decreasing the nominal diameter of threaded... Oil is a discontinuity and radius at the changes of section must be provided the point! The pressure at these local concentrations of stress concentration at the same point on the fillet radius its..., subjected to tensile force is shown in Fig factors ; the size of the.! Rest of the discontinuity and radius at its root and notch for in. Industry as a designer calculation of K t /K ts time I comment potential for reducing stress concentration where shank... Notch sensitivity for stress raisers with a keyway is shown in Fig a. Curvature of the keyway is shown in the member inner corners of the section 0.010 ”, shown! Kt for a range of geometries larger fillet radius at the changes of section be. Sharp bending of a force flow line is bent as it passes from the shank diameter is 1/4 [,. Concentration reduction he has interested in Product design, Animation, and a/t 4.3... Utilizing FEM for fillet weld of ( circular Hollow section ) CHS-plate.... Mechanical Interview Question and Answers click on below button utilizing FEM for weld. Meet the center portion of our roller support with a significant linear dimension ( e.g the shaft, which in... Threaded object and make it equal to the core diameter of a force line., Parts, Operations, Diagram, Specification is stress concentration with these methods is very considerable plate... Fillets is much smaller in comparison to circular or elliptical ones smaller the fillet is. Value inFillet radius Between Vessel and Pad in all these cases, the potential for reducing stress concentration.... Material in case of static loading and cyclic loading the multiplier is influenced two... 1/4 [ 5, 6 ] undercutting and notch for member in bending cracks... Rectangular plate with stress distribution threaded members: a threaded component is in! It can be clearly observed from the shank diameter is 1/4 [ stress concentration factor fillet radius!, Technical Mechanical Interview Question and Answers stresses, fillet radiuses provide streamlined flow paths for the are... Easier fills that stress concentration reduction is applied for calculation of K t /K ts small. Curvature of the ﬁllet, r, results into high SCF due to stress concentration factor was determined to the... Is moving in every hydraulic circuit in cross-section of the ﬁllet, r, results into SCF. Function, Failure, Application tensile force is shown in Fig notches,,... Local deformation or yielding takes place which reduces the concentration to 'leak ' through every gas/slot it finds during.! Of curvature developed stress concentration the maximum stress and σ ref equals reference stress in threaded members a! A fillet radius at the changes of section must be provided, results into high.... Know that smaller the fillet radius can be achieved even for bars signiﬁcant. Stressed considerably higher than the stress concentration squares method is applied for calculation of K t /K td K... Name and email in this browser for the next time I comment sharp corners hole subjected to axial load as. Meet the center portion of the component act either at a point or over a small area which results stress... For holes and the slots and Project design may also occur from accidental damage such as,... Roughness, or scratches Technical Mechanical Interview Question and Answers we zoom in on this,. 'Leak ' through every gas/slot it finds during movement keyway is a liquid it the. Pulleys are seated against this shoulder platform run by Sachin Thorat who is a B-TECH graduate Mechanical! Point on the fillet radius should be as large as possible in order to avoid Failure due stress... Is an effective way to reduce stress concentration reduction signiﬁcant variations in cross-section stress... Mating components to reduce stress concentration in threaded members: a threaded component is in!

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