aisc-boltedjointpaper

STEEL CONSTRUCTION VOLUME 35 NUMBER 1, MARCH 20011

AN ENGINEERING INSIGHT TO THE FUNDAMENTAL BEHAVIOUROF TENSILEBOLTED JOINTS

Dr Saman FernandoAjax Technology Centre

76-88 Mills Road, Braeside Vic 3195

1. INTRODUCTIONThe threaded fastener (nut and bolt) has played asignificant role in the industrial revolution even thoughthe exact date of its conception is not known. Theconcept of a helical thread was first introduced byArchimedes in the 3rd century B.C. Some archeologistsargue that the threaded fastener was in existence evenbefore Archimedes at the Hanging Gardens ofBabylon. It is accepted that the common forms ofthreaded fastener assemblies have been in existence forat least 500 years. Threaded fasteners are probably thebest choice to apply a desired clamp load to assemble ajoint, at a low cost, with the option to disassemble if andwhen necessary. Furthermore, the simplicity of itsmechanism of developing and maintaining the desiredclamp force made it very popular and it has become oneof the most accepted engineering products. In anegative sense, this simplicity may have made someusers complacent and therefore to disregard someimportant issues associated with a bolted joint.

2. BOLTED JOINT

Based on the service loads there are two types boltedjoints. In tensile joints the bolts are loaded parallel tothe bolt axis while in shear joints the bolts are loadedpredominantly perpendicular to the bolt axis. Forexample the connection of two flanges of a pressurevessel constitute a tensile joint while the connection of abeam to a column can be considered as a shear joint.

In a typical shear joint the bolt acts as a shear pin. Theanalysis of a shear joint is quite straightforward. Thebolt does not need to maintain a specific tensile load. Inthis case the tensile load is applied only to prevent thenut from loosening. When the shear load on the joint

changes the corresponding stress field in the bolt alsochanges. Under dynamic loading this can lead topossible fatigue failure of the bolts.

Consider however that, a shear force can betransmitted with the help of friction forcesperpendicular to the bolt axis, which are created bythe tensile force on the bolt and friction between theplates/bolt/nut etc. Even though the joint supports ashear load, in this instance, it is considered as a tensilejoint or more specifically as a friction joint.Essentially, for this joint the body of the bolt need nottouch the joining members. In a friction joint avariation in the shear force does not cause a variationon the tensile force on the bolt. As a result fordynamic loading situations a friction joint willeliminate possible fatigue failure.

In most situations involving dynamic loading thetensile joint becomes a requirement and moreattention is needed in the design of this joint.Therefore the rest of the discussion will be focussedon the tensile joint.

In order to shed some light on to the behaviour of ageneric tensile bolted joint a comprehensive 3D Non-linear Elasto-Plastic Finite Element model analysishas been conducted. Results of this work will bepublished in the near future. Although most of thecomplexities of a generic tensile bolted joint can beaddressed with the above comprehensive approach,cost and the effort requires does not qualify it as ageneric engineering tool for wider applications.Therefore, an attempt has been made to develop asimple analytical method using fundamental theoryand first order approximations. Although theapproach presented here can be substantiated andcalibrated by the aforementioned FEM analysis andexperimental data, the emphasis made in thispublication is to qualitatively highlight the importanceof the various critical parameters associated with ageneric tensile bolted joint.

The optimum pre-tension of a bolt in a joint has beena subject of confusion.

STEEL CONSTRUCTION VOLUME 35 NUMBER 1, MARCH 2001 2

3. IMPORTANCE OF PRE-TENSIONIn order to emphasize the importance of pre-tension orpre-load on the bolts in a bolted joint, the following firstorder analysis based on fundamental engineeringprinciples is carried out. In a typical bolted joint one ofthe main functions of the bolt is to maintain an adequatepositive clamping force during the service life of thejoint in order to prevent leaks, relative movement, wearand fretting, etc. To achieve a particular service liferequirement for a bolted joint it is very important tounderstand the effect of bolt pre-tension (Fi) and theapplied load (Fa) on the Clamping force (Fc).

For simplified analysis purposes, two types of tensionjoint load configurations may be considered:a) An external load is applied at the surface adjacent tothe nut and the head (Type A, Figure 1(a)),b) An external load is applied at the jointed interface(Type B, Figure 1(b)). These two types share theapplied load differently between the fastener and theclamping force. However, in reality a typical joint willbe a combination of the above Type A and Type BJoints.

Figure 1(a): Type A Joint

Figure 1(b): Type B Joint

Type A Joint:

Figure 2: Mechanical representation ofType A joint

The bolt is represented by a tension spring of stiffnesskb while the joint is represented by a compressionspring of stiffness kc. With initial pre-load (Fi) and noexternal load applied, the spring system will be inequilibrium with,Fb = Fi (1)Fc = Fi (2)where Fb is bolt tension and Fc is clamping force.

b

bbb L

EAk . (3)

where Ab is the effective stress area of the bolt, EbYoungs modulus of bolt material and Lb the effectivelength of the bolt.where D is the nominal diameter of the bolt.

c

ccc L

EAk . (5)

where Ac is the effective stress area of the jointmembers, Ec Youngs modulus of joint material andLc the effective length of the joint.If Dj < Db

where Dj the joint diameter, Db bolt under head/washer bearing diameter and Dh the hole diameter.If joint thickness t


If Dj > 3Db then,

where Lg is the grip length of the joint.

In general, due to the larger stress area (Ac>Ab), kc > kb(Eqn (3), (5)). The applied force Fa will generate anoverall displacement as shown in the Figure 2. Thisdisplacement imparts an additional load of kb. on thebolt.

The new bolt tension may now be represented by,

Fb = Fi + kb.. (9)

The same displacement relaxes the compression forceon the joint members by kc. resulting a new clampingforce of:

Fc = Fi kc. (10)

For the equilibrium of forces:Fa = Fb - Fc = kb. + kc.. (11)

The resultant overall joint stiffness ka can be defined as;Fa = ka. (12)

By substituting (12) in (11);ka. = kb. + kc.

ka = kb + kc (13)

Combining (12) and (13)

)( cba

a

a

kkF

kF

(14)

by substituting (14) in (9) and (10) respectively;

)(.

cb

abib kk

FkFF

(15)

)(.

cb

acic kk

FkFF

(16)

Equation (15) confirms that only a component of theapplied load is contributing to increase the tension of thebolt. Typically kc is larger than kb and hence, theincrease in the bolt tension will be less than the decreasein the clamping force. Therefore the parameter kc/kb hasa significant impact on the performance of the joint.

The Figure 3 shows the relationship between Fi, Fb, Fcand Fa for bolted joint in the elastic range.

Load

cb

abib kk

FkFF

.

Fa0 Fa

bc

acic kk

FkFF

.Fi

Load F

Figure 3: Variation of Fb and Fc with Fa in theElastic regionFrom this graph it can be seen that Fc = 0 when

c

icba k

FkkF ).(0

. (17)

This relationship proves that as high as possible pre-tension Fi will provide the best load carrying capacityfor the joint. As discussed earlier, one of the mainfunctions of a fastener is to keep the joint together.Therefore, it can be considered that the joint is failedwhen the applied load reaches Fa0.

The bolt tension when Fc = 0 is (combining (15), (16)and (17)),

00).(

ac

icbb Fk

FkkF (18)

shall be smaller than the breaking load of the fastener.

For clamping load to become zero before the boltreaches yield;

)(.

cb

cyi kk

kFF

(19)

where, Fy is the yield strength of the fastener.

In order to obtain a feel for the relative magnitudes ofthe above parameters the following example is given;

3.1 Example 1:M20:Property Class 8.8 Bolt(Property Class X .Y is defined as Ultimate Tensile StrengthUTS =X *100 MPa and Proof Strength YS= 0.1* Y * UTS)UTS = 8 * 100 = 800 MPaYS = 0.1 * 8 * 800 = 640 MPa.Effective Area = 245 mm2Proof Load = 147kNBreaking Load = 203kNBearing Diameter (Db) = 40mmEffective Grip Length = 100mmYoungs Modulus = 200GPakb(eq.(3)) =245*200/100 kN/mm

=490 kN/mm

)8(104

22

h

gbc D

LDA


Joint:Youngs Modulus =200GPaJoint Diameter (Dj) > 120mmHole Diameter (Dh) =22mmLength =100mmEffective Area (eq(8)) =1583.5mm2kc (eq.(5)) =1583.5*200/100 kN/mm

=3167kN/mmNote: In reality the bolt effective-length will be slightlylarger than the joint effective-length. Joint effectivearea is based on using a high tensile washer on eitherend.

Now, kc/kb = 3167/490 = 6.46.

For most common applications this number is between 4and 8.

Now maximum clamp load Fimax is (eq. (19));

kN

kkkF

Fcb

cyi

3.127)3167490(

3167147

)(.

max

This gives the maximum pre-tension load for this jointas 127.3/147*100% = 86.6% of the proof load.

The corresponding maximum applied load for theseparation of the joint is (eq.(18));

00).(

ac

icbb Fk

FkkF = 147kN,

i.e., the proof load of the fastener. This confirms thatthe tensile load applied on the joint at separation will beequal to the load on the fastener.The Load vs Displacement graph for the above case isshown in Figure 4.

Fb=Fi+kbLoad

Fa=ka.

Fc=Fi-kc.

Fimax

ka = kb + kc

kbkc

Fy

Fa

Figure 4: Load Displacement graph in the elasticzone.

Now, lets investigate what happens if the fastener wasunder tensioned. For example only 30% of the yieldload, Fi2= 0.3*147 = 44.1kN.

The force at separation is (eq.(18));

c

icba k

FkkF 202

).(

Fa02 = (490+3167)*44.1/3167 = 50.9kNThis is a significant reduction from 147kN ascalculated earlier. By reducing the pre-load from127.3kN to 44.1kN (86.6% yield to 30% yield) theload carrying capacity of the joint has fallen from147kN to 50.9kN. However, it is important to noticethat the bolt will yield at a joint load of 48.9kN eventhough the joint has already failed by that time due toseparation.A graphical representation of the above process isshown in Figure 5.

Load

Fa02 Fa0

Fimax

Fi2

Fa

Fb

Fc

Fb

cb

abib kk

FkFF

.

bc

acic kk

FkFF

.

Figure 5: Effect of reduced pre-load.As shown in Figure 5, when the pre-load is reducedfrom Fimax to Fi2 the separation load is reduced fromFa0 to Fa02. In this case, when the joint has failed thebolt is still far from its yield load. If the applied loadis increased after separation of the joint, the totalapplied load will then be transferred to the bolt. Thebolt load will increase at the same rate as the increaseof applied load. As the joint is already separated, thiswill lead to further failure mechanisms such as boltbending, fretting, joint wear, fracture etc. It is nowclear that this is not the most economical way of usinga bolt.

As discussed earlier, in eq. (15,16) the ratio kc/kb is animportant parameter for a bolted joint. Thisdetermines the contribution of applied load to the boltload. The larger this factor, the smaller is the effecton the bolt. This implies that the thinner and longerthe bolts are better it is. However, it should be kept inmind that the load carrying capacity of a bolt isproportional to the square of the bolt diameter andtherefore a reduction in diameter will have somenegative effects. In general, a larger number of smalldiameter bolts are better than a small number of largerdiameter bolts, especially under dynamic loading.


4. EFFECT OF DYNAMIC LOADING:Most mechanical connections are subject to dynamicloads. Rotating and reciprocating machinery generatessignificant cyclic loads. One of the main failure modesassociated with cyclic loading is fatigue. The fatiguelife of a bolt can be estimated by a combination of S-Nand Sa vs Sm diagrams, where Sa is the fluctuatingstress, Sm is mean stress and N is number of cycles forfailure. This theory is well established and reportedelsewhere. A simple example is presented here in orderto highlight the importance of pre-load on the fatiguelife of a bolted joint.Figure 6 shows the effect of the peak fluctuating stress(Sa) on the lifetime of the product when subject to aregular cyclic load. The lifetime is given as the numberof cycles that the product can undergo before fatiguefailure. As we decrease the magnitude of the fluctuatingstress, in this case less than 421MPa, the life time willapproach infinity as it will not subject to fatigue failure.Similarly, if we increase the peak alternating stress thelifetime will decrease. In this example, as the peakalternating stress approaches 772MPa, failure will occuraround 103 cycles.In general, wind and earthquake dynamic loads willhave irregular frequency and amplitudes. Although thesame theory stated here can be used to estimate thefatigue life the treatment would be somewhatcomplicated.

Figure 6: Peak alternating stress Savs Life N cyclesgraph (S-N Curve) for Class 10.9 Steel

Figure 7 shows the effect of peak alternating stress andthe mean tensile stress on fatigue failure. As can beexpected, when the mean stress reaches ultimatestrength (Su), the sample will fail without anyfluctuating load. On the other hand, when the peakalternating stress is 772 MPa and mean stress is zero, itwill fail around 103 cycles. The effect of combiningalternating and mean stresses on fatigue life is shown inFigure 7.

Figure 7: Sa vs Sm curve for class 10.9 steel.

To understand the effect of pre-load on fatigue life,the following example is considered:

4.1 Example 2:

Bolt:M20, Class 10.9, eff. grip length 100mmSu = 1000MPa kb = 168kN/mmSy = 900MPa kc = 1050 kN/mmFy = 203kN Fa = 58 kN (mean)Fu = 255kN Fa = 81.2kN (peak alternating)

Case 1:

Pre-Load = Fi = 60% Fy = 121.8 kN

)(.

cb

abib kk

FkFF

Fb (mean) = 121.8+490*58/(3167+490)= 129.6kN= 100*129.6/203 %Fy= 63.8%Fy

Sm = 0.638 * 900 = 574MPa

c

icba k

FkkF ).(0

Fa0 = (490+3167)*121.8/3167 = 140.6 kNFb = 81.2*490/(490+3167) = 10.9kN = 5.4% FySa = 0.054*900 = 48.6 MPa

Case 2:Pre-Load = Fi = 25% Fy = 0.25*203= 50.75kN

)(.

cb

abib kk

FkFF

Log

Log Sa

106105104103

772634517421

Axial loading stress in MPa

200

200

400

400

600

600

800

800

1000

1000

Sm

Su

Sy

Sy

103

104

105

106

Sa

Axial stress in MPa

j

k


Fb (mean) = 50.75+490*58/(3167+490)= 58.5 kN = 28.8% Fy

Sm = 0.288 * 900 = 259MPa

c

icba k

FkkF ).(0

Fa0 = (490+3167)*50.75/3167 = 58.6 kNFb= (58+81.2-58.6)+58.6-58.5= 80.7kN= 39.75%FySa = 0.3975*900 = 357.75 MPa

The above parameters for Case 1 and Case 2 are shownin Figure 8. For Case 1, a pre-load of 60%Fy is applied.The mean applied load of 58kN result in a mean boltload of 129.6kN. An applied load of 140.6kN willseparate the joint.

Load

cb

abib kk

FkFF

.

bc

acic kk

FkFF

.

58.6 140.6

121.8

50.75

Fa

Fb

58.0 81.2

58.5

129.6

10.9

80.7

Figure 8: Loading diagram for example 2.

The peak fluctuating component of the 81.2kN appliedload imparts a fluctuating bolt load of 10.9kN. As thetotal maximum applied load (58+81.2=139.2kN) is lessthan 140.6kN the joint will not separate under appliedload conditions. The mean (Sm) and peak fluctuatingstress (Sa) for Case 1 are 574MPa and 48.6MParespectively. This point is shown as point in Figure 7and is in the area where no fatigue failure will occur.

In Case 2, the pre-load is only 25%Fy=50.75kN. Thismay be a result of tightening error of the bolt. As aresult the clamp separation load is reduced to only58.6kN. That means when the joint load of 58+81.2kNis applied, the joint will separate (this may beconsidered as failure) and the load excess of 58.6kNwill be transmitted directly to the bolt. Under the meanload of 58kN, the bolt will experience a mean load of58.5kN resulting a mean stress Sm of 259MPa. Thefluctuating load of 81.2kN imparts a fluctuating boltload of 80.7kN resulting a peak fluctuating stress Sa of357.3MPa. This point is shown as in Figure 7. This

point is clearly within the life span of 106 cycles limit.This implies that the bolt will fail around 106 cycles.

This example clearly identifies importance of properlytightening the bolts in dynamic situations. Reductionof pre-load from 60% Yield to 25% Yield will alterthe joint from no fatigue failure to fatigue failure.

A similar problem may occur if the bolts are overtightened. The following example shows the effect ofover-tightening the bolts.

Case 3:If the initial pre-load is set up at 95% of the yield load(Fi=192.9kN) in Case 1 of the previous example, thebolt load at mean applied load (58 kN) is;

Fb = 192.9+490*58/(3167+490)= 200.7kN

When the fluctuating component of 81.2kN is appliedas shown in Case 1, this will impart a fluctuating loadof 10.9kN on the bolt. Now the total applied load of211.8 kN (200.7 + 10.9) will exceed the yield load(203kN) of the bolt and will be subject to plasticdeformation. When the fluctuating component isreleased momentarily the pre-tension of the bolt is lostdue to plastic deformation. The loss of pre-tensionmakes it similar to Case 2 and leads to failure by bothjoint separation and fatigue.Therefore it is crucial that the bolt pre-tension has tobe within a very specific range to achieve correct andoptimum performance of the joint.

5. TORQUE TENSION RELATIONSHIP:Now that the importance of the bolt pre-tension isestablished it is important to investigate how this canbe reliably achieved.Torque has been considered synonymous with tensionin the past with the unavailability of an economicaland reliable bolt tensioning method. Severalapproximations has been used in the design of boltedjoints at varying success and confident level in orderto relate the torque to tension.The Nut Factor approach is the most commonly used.The simplified torque tension relationship;

T=K.D.Fwhere K Nut Factor, D Bolt Diameter and F is theBolt Tension.

This formula can be further expanded to;

T = F.D.(K1+K2+K3).where K1, K2 and K3 are contributions due to boltstretch, thread friction and under-head/under-nutbearing friction respectively. The following chartdescribes these parameters.


Using energy balance principals a first orderrelationship between the torque (T) and Tension (F) canbe derived as follows;

In a rotation of the nut by ;work done by torque = T.work done by tension = F.p /2work done by thread friction = Frt t/coswork done by under head friction = F.rb.b

where, p thread pitch, thread flank angle, rt effectivethread radius, rb effective bearing radius, and t and bare thread and bearing friction coefficients respectively.

Now for energy balance;

Figure 9: Parameters associated with Torque-Tension Relationship.Term K1D represent the contribution of the torquetowards bolt elongation and joint compression, K2D thefraction of torque spent on overcoming thread frictionand K3D the fraction of torque spent on overcomingunder head friction.

For a M12 bolt;Pitch p = 1.75mmThread friction t = 0.15Thread radius rt = 6mmThread angle = 30Under head friction b = 0.15Effective under head radius = 8mm

Now;T = F (0.28+1.04+1.2)K1:K2:K3 = 0.28:1.04:1.2 = 11:41:48 %

From this simple analysis it is evident that typically,around 10% of the effort is going to the stretch of thebolt and compression of the joint, 40% of effort isgoing to overcome thread friction and the remaining50% is going to overcome bearing friction. Thisimplies that approximately 90% effort is going toovercome friction while only 10% is doing usefulwork.There are a large number of parameters such as,surface finish, hardness, lubricants, among otherthings, that can alter the friction coefficientsassociated with a bolted joint. A 10% reduction infriction contribution (from 90% - 81%) will increasethe bolt stretch-joint compression contribution from10% - 19% which is a 90% increase.As such, it shall be understood that the torque tensionrelationship is not a reliable way of ensuring thetension of the bolt under most situations. The value ofK can vary from approximately 0.2 to 2.0 dependingon the condition of the bolt and the bolted joint.Any irregularity or damage to the thread can also beseen as an increased friction hence adding to theoverall variability of the friction coefficient.Therefore, if the torque is used as a measure of tensionit shall be made sure that the thread is in perfectshape. Galling of threads can also contribute tosignificantly large friction forces.Torque tension scatter varies largely with the size ofthe bolt, coatings, interface friction, and jointgeometry. With large bolts (>M30) this scatter maybe as high as 300%.

Figure 10 shows the torque vs tension relationshipmeasured for M8, property class 8.8, Zinc electroplated bolts and nuts (without any lubricant) tightenedon the same joint. Each bolt assembly is used onlyonce. The solid line shows the theoretical relationshipbetween tension and torque assuming typical frictionvalues for Zn coated interfacing surfaces. The spreadbetween the six samples are quite significant. Therecommended assembly torque for the above bolts is15.4Nm to achieve a tension of 13.8kN which is 65%of the proof load. At 15.4 Nm torque the six samples

K

K1 K3K2

D p t D rt D rb

).(.cos2

..

cos2

321 KKKDFTD

rD

rD

pDFT

Frr

FFpT

bbtt

bbtt


achieved tension values from 11 to 17 kN. The spreadof 6kN is a 43% variation on the desired tension value.If a 90% of the proof load was desired (19.1kN) thetorque values from 17.5Nm to 33Nm were required toachieve the desired tension on different bolts. If a33Nm torque is applied to each bolt, that would havefailed several of the above bolts!!!

Figure 10: Torque Tension Relationship; M8, Class8.8, Zinc plated bolts, first tightening six samples. Asplated, no lubrication. Proof Load 21.2kN, BreakingLoad 29.2kN.

Figure 11: Repeated tightening of the above Sample2 for five times.

Figure 11 shows the first and subsequent four tighteningof the Sample 2 bolt in the above experiment. For atightening torque of 15.4Nm, tension values from 6 to

13kN were achieved depending on how many timesthe bolt was tightened. Again the spread on thedesired tension is over 50%. The above figures aretypical for all bolt sizes, however, the large bolts willhave greater variations in the torque tensionrelationship.

Torque vs Tension-M8, Class8.8,Zinc Plated, Tightening Sample 2 Five times

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

Torque (Nm)

TheorySeries1Series2Series3Series4Series5

Torque vs Tension - M8, Class 8.8, Zinc Plated, First Tightening of six assembliesProof Load 21.2kN, Breaking Load 29.2kN

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

Torque (Nm)

TheorySample 1Sample 2Sample 3Sample 4Sample 5Sample 6


6. CONVENTIONAL METHODS OFTIGHTENINGAlthough, most of the practitioners understand theimportance of bolt tension in a bolted joint theconventional tightening methods only provide a vagueindication of the bolt tension. Extensive researchcarried out on torque-tension relationships prove thatunder most uncontrolled situations using torque as ameasure of tension can lead to a error as large as 50%.Even under controlled conditions torque on its own isnot a reliable measure of tension. On the other hand, thereliable tension measuring systems are cumbersome andexpensive. A comparison of various methods availablefor achieving pre-load in terms of their reliability andrelative cost are shown in Figure 12.

Figure 12: Comparison of common tighteningmethods

Another commonly used method is the turn of the nutmethod. This method, in fact, is the recommendedmethod by Australian Steel Codes AS4100. In thismethod the nut is tightened to a snug tight positionand then tighten further fraction of a turn depending onthe joint geometry. However, the standard does notspecifically define the snug tight position. Accordingto the theory, the snug tight position is where a stepchange in the gradient of the torque vs angle curveoccurs. In order to carry out this process with anyaccuracy a torque sensor and an angle encoder shall beused. Then by calibrating on the desired joint with adirect tension measureing device the required nutrotation after the snug tight position can be determined.This will then provide a method of tightening with somedegree of accuracy. However, for example, fortightening slew-ring bolts this method may not besuitable. Snug tight position for one bolt may change

with the tightening of the remaining bolts hencemaking this method not reliable at all.Load Indicating Washer (LIW) is another commonmethod of assuring desired tension. Again thismethod will not give satisfactory results for tighteningslew-ring bolts as the firstly tightened bolts willbecome loosen when tightening the subsequent bolts.LIWs are capable of indicating the tension only intheir first tightening.Hydraulic Bolt Tensioning is relatively popular inheavy industries due to its simplicity. However, whenusing this method, the bolt tension is known onlywhen the hydraulic pressure is applied (by measuringthe hydraulic pressure). Once the hydraulic pressureis removed and the load is transferred from the jack tothe nut, bolt and the tightening flanges, the appliedtension on the bolt is relaxed. In one experimentcarried out by ATC on a large rock crusher showed

that at a 8bar hydraulic pressure applied on three M64Flange bolts resulted in a 80 -90% of proof loadinitially and then relaxed to 45 56% proof load oncethe pressure is removed. It was found that therelaxation is a function of bolt/nut size, number ofthreads engaged, and the flange dimensions amongother parameters. However, it was not possible toestablish a firm relationship with the applied hydraulicpressure and the final bolt tension.Heating the bolts at tightening is another method ofobtaining a pre-load. The bolt is heated to a knowntemperature with the help of a concentrated heatsource. This will elongate the bolt. The nut istightened at this point and let the joint to cool down.The shrinkage of the bolt will impart a pre-tension onthe joint. This method is not very advisable fortightening high tensile bolts as the tensile strength ofthe bolt may be significantly affected by heating thebolt. Control of the bolt temperature is extremelydifficult and large variations in temperature may be

0 5 10 15 20 25 30 35 40

Ordinary Spanner

Torque W rench

Torque Control Bolt

Turn of the Nut Method

Torque Angle Signature

Load Indicating Washers

Heating the Bolt

Hydraulic Bolt Tensioning

Ultrasonic

Mechanical Tension Indication

Strain Guages

Smart Bolt System

% ERROR / RELATIVE COST

% ErrorRelative Cost


observed over the bolt. This may result in variablematerial properties over the bolt.Another factor that affects the bolt tension is the jointtemperature. Especially if the joint is made ofdissimilar materials, the differential thermal expansionof the bolt and joint materials will cause variations inthe bolt tension. Even if the bolts are tightenedaccurately to the desired tension value, if the joint issubject to temperature variations the working tension onthe bolt may change. It is not possible to theoreticallyestimate these changes to a sufficient accuracy. Onlydirect tension measurement will provide the engineerwith the real time working tensions on such bolts.

7. LOADING BEYOND YIELDIn most situations the pre-tension load will be less thanthe yield load, however, due to the applied loads the boltexceeds yield load. The work hardening materialsgenerally exhibit elastic plastic behavior. Forsimplicity, perfectly linear-elastic and perfectly linearplastic behavior of the bolt material is assumed. Thetypical stress strain relationship for such material isshown in Figure 13. The gradient of the elastic zone isthe Youngs Modulus (E) and the gradient of the plasticzone is the plastic modulus (Ep). For all elastic plasticmaterials Ep


8. BOLTING TO YIELDIn some occasions in order to get the highest clampingforce the bolts are tightened beyond yield. Especially,when relying on torque to tension the bolt, a bettercertainty can be achieved when the bolts are tightenedbeyond the yield, as the effect of variation in torque onthe tension is lower. This has to be done carefully,especially with high tensile bolts where the separationbetween the yield and the failure load is relativelynarrow. Furthermore, if a bolt is yielded it shall not bereused, as this will alter the geometry and themechanical properties of the bolt.

Figure 16: Bolt tension and clamping force variationbeyond yield

In the authors opinion this method is suitable for frictiongrip joints where the joint is loaded in shear and there isno possibility of extra tensile load applied on the bolt.

This method shall not be used to tighten the bolts ifthere is any uncertainty on whether any additionaldynamic or static tensile load will be applied on thejoint during its life span.

The relationship between Fi, Fb, Fc and Fa for a jointtightened beyond yield is shown in Figure 16. This isvery similar to the Figure 14, without the elastic zone inthe bolt tension. When unloading the joint the bolttension follows a line parallel to the elastic line and endup with a residual plastic displacement which leads to areduction in pre-tension to Fi2. Gbp, Gb, Gcp and Gc arethe gradients as defined earlier.

As kbp is always smaller than kb Gbp will always besmaller than Gb. Similarly, Gcp will be larger inmagnitude to Gc.As shown in Figures 16 and 17 if the applied load isincreased and then reduced in a joint where the bolts aretightened to yield the bolts will lose pre-load due toplastic deformation. Therefore, tightening to yield is

not suitable for joints where the bolts may be subjectto additional tensile loads.

Figure 17: Load displacement curve beyond yield

9. VIBRATION LOOSENING:It is common experience that some bolts will beloosened when subject to vibrations and dynamicloading. There were several attempts to understandthe mechanism of vibration loosening. A large groupof researchers believe that the mechanism issomewhat similar to that of vibratory bowl feedersand vibratory conveyors. In general, it is acombination of the inertial forces generated byparticular vibration, and friction forces.Through proper design it is possible to developmechanical systems where the bolts have a tendencyto be tightened under applied loads (eg., some LawnMower Bolts, Wheel Nuts). On the other hand,certain situations promote vibration loosening eitherdue to lack of consideration at design level or due tomere complexity of a particular joint. Especiallywhen the joint incorporates soft gasket materialsand/or different member materials the complexityincreases significantly.There are several devices available in the market toprevent vibration loosening. Lock nuts, Nylok Nuts,serrated washers, spring washers, Cottor pins, to namea few. All of these devices provide additional frictionforce or interlock to the bolt/nut. Depending on thenature of vibrations and other conditions there will bea finite resultant loosening torque that the fastenersystem has to resist. The said devices help resistingthis torque.The fact that 90% of the applied torque is going toovercome frictional forces, as discussed earlier, maybe of value to prevent vibration loosening. Thefrictional torque is directly proportional to theremaining tensile load on the bolt. Therefore, if thebolts are tightened to a particular pre-load, in such away that the remaining tension on the bolt underapplied load is adequate to generate a friction torque

Fi

Fi2

kbp

kb

ka=kb+kc

Fa= ka

2

F

Fi

Fi2

Fb

Fc

GcpGc

Gbp Gb

Fa


larger than the loosening torque vibration loosening willnot occur. The tests carried out by ATC confirmed thatif a typical bolted joint is tightened to a pre-load higherthan 65% of the yield load of the fastener vibrationloosening will not occur even under severe vibrationconditions.There may be some special occasions where it may notbe feasible to apply such pre-loads to the joint. Asuitable anti-loosening device may be used in suchsituations.

10. CONCLUSIONS:A simple approximate analytical approach is presented.This may help engineers to better understand theperformance of bolted joints.In general, the following specific conclusions are made;1. The contribution of applied load on the bolt load in

a pre-loaded tensile joint depends on the stiffnessratio of the bolt and the joint.

2. Large number of slender bolts is better than a smallnumber of large bolts for a tensile joint subject todynamic loads.

3. If feasible, longer bolts provide better properties fora dynamic joint than shorter bolts.

4. Correct pre-load (pre-tension) is paramount inachieving high-performance dynamic tensile joints.

5. Calibrated torque wrench is not a reliable method ofachieving a desired bolt tension.

6. Common Hydraulic bolt tensioning methods doesnot adequately account for the relaxation of thejoint.

7. LIWs are not suitable for most group-bolted joints.Tightening sequence and process is critical tooptimize the use of LIW.

8. Heating the high tensile bolts may result in poorquality joints.

9. Tightening to yield is not suitable for tensile joints.10. No anti-loosening devices are necessary if the bolts

are tightened to at least 65% of the yield load.11. Most joint failures are due to insufficient pre-load in

the bolts.

11. BIBLIOGRAPHY:Bickford, John H., An Introduction to the Design andBehaviour of Bolted Joints, Marcel Dekker, Inc, NewYork 1990.Juvinall, Robert C., Fundamentals of MachineComponents Design, John Wiley & Sons, New York,1983.Ziada, H.H., Abd-El-Latif, A.K., Areas of contact andpressure distribution in gasketed bolted joints, 1E(1)Journal-ME, Vol 62, November, 1981, pp 77-83.Finkelston, R.J., Wallace, P.W., Advances in High-performance mechanical fastening, Paper 800451,SAE, New York, N.Y., Feb 20, 1980.

Fisher, J.W., Struik, J.H.A., Guide to Design Criteriafor Bolted and Riveted Joints, John Wiley and Sons,New York, 1974.Gorenc, B., Tinyou,R., Syam, A., Steel DesignersHandbook, 6th Edition, UNSW Press, 1996Australian Standard AS4100-1998, Steel Structures.

11. NOMENCLATUREAb Effective Stress Area of BoltAc - Effective Stress Area of ClampD - Diameter of Bolt ShankDb - Bearing Diameter of Bolt HeadDh -Hole DiameterDj -Effective Diameter of JointE - Youngs Modulus of ElasticityEb - Youngs Modulus of Elasticity BoltEc - - Youngs Modulus of Elasticity ClampF - ForceFa - Applied ForceFa - Applied Peak Fluctuating ForceFa0 - Applied Force to Separate the ClampFa02 - Applied Force to Separate the Clamp after a

plastic cycleFb - Bolt Tension ForceFb - Peak Fluctuating Bolt Tension ForceFb0 - Bolt Tension at Separation of the ClampFc - Clamping ForceFi - Initial Bolt Tension Pre-loadFimax - Maximum Pre-LoadFi2 - Pre-load remaining after a plastic load cycleFy - Yield Load of the BoltG - Gradient of Graph Fb, Fc vs FaK - Nut FactorK1 - Nut Factor due to bolt stretchK2 - Nut Factor due to thread frictionK3 - Nut Factor due to Under head/nut Frictionk - Stiffnesska - Joint Stiffnesskb - Bolt Stiffnesskc - Clamp StiffnessL - LengthLb - Effective Bolt LengthLc - Effective Clamp LengthLg -Joint Grip Lengthp - Thread Pitchr - Radiusrt - Thread Effective Radiusrb - Under Head/Nut Effective RadiusSa - Peak Fluctuating StressSm - Mean StressSu - Ultimate Tensile Stress (UTS)Sy - Yield Stress (YS)T - Torque

Greek Symbols; -Infinitesimal Bolt Rotation - Elongation


- Variation - Friction Coefficientb - Under Head/Nut Friction Coefficientt - Thread Friction Coefficient - Flank Angle of the Thread

Indices:p - Plastic Stateb - Boltc - Clampi - Initial

aisc-boltedjointpaper

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