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ME-328 Machine DesignLecture 7Instructor: Dr. Samiur Rahman ShahNUST School of Mechanical and Manufacturing EngineeringScrews, keys and non-permanent fasteners:Design of Screws, Fasteners, and ConnectionsThread Standards & definitionsPower ScrewsThread StressesThreaded FastenersBolted Joints In Tension & CompressionTorque requirementsStrength SpecificationsSelection of the NutBolt Pre-Load & Fatigue StrengthPage 22Screws, Keys and Couplings, Screws:Gasket JointsBolt & Riveted Joints in ShearCentroid of Bolt/ Rivet GroupsEccentric Loading of Bolt & Rivet JointsKeys, Pins & Retainers.Page 33Page 4Coefficients of friction and safe working pressures

Page 5Stresses concentrated at the fillet, at the start of the threads, and the thread-root filletsThe thread length of metric bolts, where D is the nominal diameter in mm is given at rightIdeally, only one or two threads should surpass the nutWashers should always be used to avoid stress concentrations due to burrsThreaded fasteners

Page 6Washers should always be used to avoid stress concentrations due to burrsRounded face should contact bolt headWashers may be used under the nut tooClamping load elongates the bolt This elongation ensures a pre-loadBolt should be held stationary so that no torsional loads be imposed on the bolt bodyDuring tightening of nuts, generally the first thread yields, work hardens, and then spreads load over three threadsNuts should not be reused

Threaded fastenersPage 7

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Page 9Twisting the nut provides pre-tension or preloadThis load exists even without external load PA variation of fastening in Fig 8-14 may be to use studsA spring rate can be defined for a bolt determine stiffness of the bolt systemThe grip is the total thickness of the connected materialJoints Fastener stiffness

Page 10Stiffness of bolt consists of two partsThreadedNon-threaded

WhereAt = tensile stress arealt = length of threaded portion of gripAd = major diameter of area of fastenerld = length of unthreaded portion in grip

Page 11Substituting in earlier equation, we get

Wherekb is the estimated effective stiffness of the bolt in the clamped zoneFor short fasteners, where threaded area is longer, kT may be usedFor long fasteners where unthreaded area is longer, kd may be used

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Page 15In earlier section, stiffness of fastener was determined in clamped zoneIn this section, stiffness of member must be known in the clamped zoneBoth must be known to know what happens when an external loading is applied to this assembled connectionThere may be more than two members in the grip of the fastener, each acting as a spring in seriesTotal spring rate is given by

Joints Member stiffness

Page 16A pressure cone may be used to calculate stress distribution in clamped memberVariable proposed by Ito et al.1 complicatedFixed Little2 and Osgood3 much simplerA fixed cone angle of 30o will be usedY. Ito, J. Toyoda and S. Nagata, Interdace Pressure Distribution in a Bolt-Flange Asse;mbly, ASME paper np. 77-WA/DE-11, 1977R. E. Little, Bolted Joints: How Much Give?, Machine Design, Nov. 9, 1967C. C. Osgood, Saving Weight on Bolted Joints, Machine Design, Oct. 25, 1979

Page 17Referring to figure, elongation of an element of the cone of thickness dx subjected to a tensile force P is

The area of the element is

Page 18Integrating, we get the elongation as

Using a table of integrals, we get

Thus the spring rate or stiffness of this frustum is

Page 19With =30o, this becomes

The last two equations must be solved separately for each frustum in the jointIndividual stiffnesses are assembled to give km (series stiffness)If the members have the same Youngs modulus E with identical frusta back-to-back, we treat them as two identical springs in series

Page 20Using grip as l =2tdw as the diameter of the washer faceWe find the spring rate of the members to be

The washer external dia is usually 50% greater than inner dia for normal hexagonal nuts and cap screws, thus dw = 1.5dIf we also use =30o

Page 21Thank you