bolted joint design

1

Bolted Joint Design - Input Datawww.boltsecuring.com

Bolted Joint Design

2


PROBLEMS CREATED BY INCORRECT PRELOAD• Static failure of the fastener: If you apply too much preload, the threads will strip.

• Static failure of joint members: Excessive preload can also crush or gall or warp orfracture joint members such as castings and flanges.

• Vibration loosening of the nut: No amount of preload can �ght extreme transversevibration, but in most applications, proper preload can eliminate vibration looseningof the nut.

• Fatigue failure of the bolt: Most bolts that fail in use do so in fatigue. Higher preloaddoes increase the mean stress in a fastener, and therefore threatens to shorten fatiguelife. But higher preload also reduces the load excursions seen by the bolt. The net e�ectis that higher preload almost always improves fatigue life.

• Stress corrosion cracking: Stress corrosion cracking (SCC), like fatigue, can cause abolt to break. Stresses in the bolt, created primarily by preload, will encourage SCC ifthey’re above a certain threshold level.

• Joint separation: Proper preload prevents joint separation; this means that it reduces orprevents such things as leaks in a fluid pipeline or blow-by in an engine. The latter, ofcourse, means that proper preload allows the engine to produce more horsepower.

• Joint slip: Many joints are subjected to shear loads at right angles to the axis of thebolt. Many such joints rely for their strength on the friction forces developed betweenjoint members, forces created by the clamping force exerted by the bolt on the joint.Again, therefore, it is preload that determines joint integrity. If preload is inadequate,the joint will slip, which can mean misalignment, cramping, fretting, or bolt shear.

• Excessive weight: If we could always count on correct preload, we could use fewer andsmaller fasteners, and o�en smaller joint members. This can have a signi�cant e�ecton the weight of our products.

• Excessive cost: The cost of many products is proportional to the number of assemblyoperations. Correct preload means fewer fasteners and lower manufacturing costs—aswell as lower warranty and liability costs.

3


The lowest strain is obtained with concentric continuously applied force. For eccentric continuously applied force the bolt is placed under additional bending strain. High shearing force requires a strong bolt, because a very high residual clamping force is required for bolts.

Tapped blind hole jointThread depth Bore depth

LoadStatical Dynamic Centrically applied axial load Eccentrically applied load Transverse load

Tight of the boltWith screwdriver With torque wrench Rotation-angle controlled or yield point controlled

Axial load FA (N) Transverse load FQ (N)

4


BoltISO standard Dimension Thread pitch Property class Material Allowance class

Bolt to drawingDrawing no Dimension Thread pitch Property class Material Allowance class

HOW MUCH PRELOAD?We always want the maximum possible preload, but in choosing this, we must consider:• Strength of the bolt and of the joint members under static and dynamic loads• Accuracy with which we expect to tighten the bolts• Importance of the joint, i.e., the factor of safety required• Operating environment the joint will experience in use (temperature, corrosive fluids, seismic shock, etc.)• Operating or working loads which will be placed on the joint in use

5


NutISO standard Dimension Thread pitch Property class Material Allowance class

Nut to drawingDrawing no Dimension Thread pitch Property class Material Allowance class

Clamping platesDimension Thikness Material

6


FrictionCoe�cient of friction in thread Coe�cient of friction in head seat

Min

Max

EmbeddingLoss of preload by embedding Amount of embedding (mm)

Tightening procedureBolt driven Nut driven

Tightening procedureYield point factor for tightening Tightening torque MA max

Tightening procedureTightening factor alpha A

MINIMIZING EMBEDMENT: We can minimize embedment relaxation by chamfering holes, by insisting on flat and parallel joint surfaces, by speci�ing that holes should be drilled perpendicular to joint surfaces, or by speci�ing hard washers.

7


FACTORS THAT AFFECT THE WORKING LOADS ON BOLTS• Sequence=procedure: The procedure with which a group of bolts are tightened cana�ect �nal results substantially. Procedure includes such things as the sequence withwhich they’re tightened, whether they’re tightened with a single pass at the �naltorque, or in several passes at steadily increasing torques, etc.

• Residual preloads: The preloads le� in the bolts a�er embedment and elastic interactions.

• External loads: External loads add to or subtract from the tension in the bolts, andtherefore from the clamping force on the joint. Such loads must be predicted andaccounted for when the joint is designed and when the ‘‘correct’’ preload is chosen.External loads are created by such things as pressure in the pipeline or engine, snow onthe roof, inertia, earthquakes, the weight of other portions of the structure, etc.

• Service conditions: Severe environments can a�ect operating conditions in the jointand bolts. This is especially true of operating temperatures. These can create di�erentialexpansion or contraction, which can signi�cantly alter bolt tensions and clampingforce. Corrosion can cause change as well. Contained pressure will a�ect clampingforces.

• Long-term relaxation: There are some long-term relaxation e�ects that must also beconsidered: relaxation caused by corrosion, or stress relaxation or creep, or vibration.And again, we want correct bolt loads for the life of the joint, not just for a while.

• The quality of parts: We won’t get correct preload, or satisfactory performancefrom the joint, unless the parts are the right size, are hardened properly, and are ingood condition. This factor can’t be handled separately; it gets in the act by a�ectingthe others. If the bolts are so�, for example, we won’t get the expected preloadfor a given torque, and relaxation will be worse. If joint members are warped ormisaligned, it may take an abnormal amount of tension in the bolts (created by anabnormal amount of preload) to create the necessary clamping force between jointmembers.

Sample o

nly

Cond. Modification Date Name

Date Name

Compl.

Check

Stand.

App

Copy

ing

of th

is d

ocum

ent a

nd g

ivin

g it

to o

ther

and

the

use

or c

omm

unica

tion

of th

e co

nten

ts th

erof

, are

forb

idde

n w

ith-

out e

xpre

ss a

utho

rity.

Offe

nder

s ar

e lia

ble

to th

e pa

ymen

tof

dam

ages

. All

right

s ar

e re

serv

ed in

the

even

t of t

he g

rant

of a

pat

ent o

r the

regi

stra

tion

of a

util

ity m

odel

or d

esig

n.

2013/11/06

Page

Pg.

ISO 4014 - M24 x 120 - 8.8 d>16 SW36

i de [mm] di [mm] l [mm] material 1 120.0 25.0 40.0 0.6020 GJL-200 (GG-20) 2 120.0 25.0 40.0 0.6020 GJL-200 (GG-20)

through bolted joint with nut (DSV) ISO 4032 - SW 36 h M mm 21.5 m tr mm 21.5

LOAD FA max N 100000 FA min N 0 FQ N 0 FKreq N 1000 FKR min N 20923 FM,Re N 202528 FM,max N 182275 FMmax,req N 150399 FMmin,req N 94000 fz mm 0 Fz N 0 FV min,req N 94000 FV min N 113922 FV max N 182275 FSA max N 7000 FPA max N 93000 FS max N 189276 FS,Re N 231600 FS,Rm N 291254

FRICTION min max μG 0.140 0.140 μK 0.100 0.100 μTr 0.120 K 0.155

ASSEMBLY (Bolt driven) nue Rp 0.90 alpha A 1.60 MA max/min Nm 681.2 / 425.8 alpha max/min deg 37.98 / 23.74

FACTORS OF SAFETY safety against loosening FM,max/FMmax,req 1.21 safety yield point red.B SF=Rp/Sig.redB 1.15 safety ag.fatigue fract.(centr.) SD=Sig.AS/Sig.a 4.37 safety plate surface pressure Sp=pG/pmax 1.39

Sample o

nly

Cond. Modification Date Name

Date Name

Compl.

Check

Stand.

App

Copy

ing

of th

is d

ocum

ent a

nd g

ivin

g it

to o

ther

and

the

use

or c

omm

unica

tion

of th

e co

nten

ts th

erof

, are

forb

idde

n w

ith-

out e

xpre

ss a

utho

rity.

Offe

nder

s ar

e lia

ble

to th

e pa

ymen

tof

dam

ages

. All

right

s ar

e re

serv

ed in

the

even

t of t

he g

rant

of a

pat

ent o

r the

regi

stra

tion

of a

util

ity m

odel

or d

esig

n.

2013/11/06

Page

Pg.

input tensile load max. FA max N 100000 tensile load min. FA min N 0 transverse load FQ N 0 reqd.residual clamp.load FKR N 1000 amount of embedding fz mm 0 loss of preload by embedding Fz N 0 tightening factor alpha A N 1.6 tightening torque (max.) MA Nm 681.2

Load Extension Diagram FSA / FA phi n 0.07 additional bolt load from FA FSA max N 7000 additional plate load from FA FPA max N 93000

Load, required req. preload FV = FKR + FA - FSA N 94000 req. assembly preload min. FM min = FV + Fz N 94000 req. assembly preload max. FM max = FM min * alpha A N 150399

Load, real real assembly preload (max) FM (zul,max) N 182275 assembly preload at Rp FM 0.2 N 202528 real assembly preload max. FV max = FM - Fz N 182275 real assembly preload min. FV min = FM / alphaA - Fz N 113922 real residual clamp.load FKR min = FV min - FPA N 20923 bolt load max. FS max = FV max + FSA N 189276 bolt fracture load F Rm N 291254 yield load, bolt F Rp N 231600

Load Extension Diagram

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

f [mm]0

50E3

100E3

150E3

200E3

250E3

F [N]Load:FVmin,req= 94000 NFM,Re =202528 NFM,max =182275 NFMmax,req=150399 NFMmin,req= 94000 NFAmax= 100000 NFKreq= 1000 NFSA = 7000 NFPA = 93000 NFZ = 0 N Coefficients:n = 0.30phi n = 0.070alpha a = 1.60 Functions:FSA= phi n * FAFV = FA+FKR-FSAFA = FSA+FPAFMmin,req = FVreq+FZFMmax,req=FMmin,req*al.a

Sample o

nly

-

M-alpha-Diagram (Proj.from elastic origin)

0 10 20 30 40 50 60 70 alpha [°]

0

200

400

600

800

1000

MA [Nm]

μmin

MA Rm = 951.9 Nm

MA Re = 756.9 Nm

MA,max = 681.2 Nm

MA,min = 425.8 Nm

μ=0

MG (μG=0.14) = 411.3 Nm

ISO 4014-M24x120-8.8 d>16 μG = 0.140μK = 0.100K = M/(d*F) = 0.155nue Re = 0.90MA,max = 681.2 NmFM,max = 182275 Nalpha max = 37.98 degMA,Re = 756.9 NmFM,Re = 202528 Nalpha Re = 42.20 degMA μ0 = 98.84 NmFM μ0 = 207018 Nalpha μ0= 43.13 degMA min = 425.8 NmFM/al.A= 113922 NR MA = 17.94 Nm/°FM,max/FMmax,req = 1.212SF=Re/Sig.redB=1.153SD=Sig.AS/Sig.a= 4.367Sp=pG/pmax=1.386

Sample o

nly

-

FM-alpha-Diagram (Proj.from elastic origin)

0 10 20 30 40 50 60 70 alpha [°]

0

50E3

100E3

150E3

200E3

250E3

300E3

FM [N]

FM,Rm = 254695 N

FM,Re = 202528 N

FM,max = 182275 N

FM,min = 113922 N

FM Re (μG=μK=0) = 230020 N

ISO 4014-M24x120-8.8 d>16 μG = 0.140μK = 0.100K = M/(d*F) = 0.155nue Re = 0.90MA,max = 681.2 NmFM,max = 182275 Nalpha max = 37.98 degFZ = 0 NFVmax = 182275 NMA,Re = 756.9 NmFM,Re = 202528 Nalpha Re = 42.20 degMA μ0 = 98.84 NmFM μ0 = 207018 Nalpha μ0= 43.13 degMA min = 425.8 NmFM/al.A= 113922 NR FM = 4800 N/°FM,max/FMmax,req = 1.212SF=Re/Sig.redB=1.153SD=Sig.AS/Sig.a= 4.367Sp=pG/pmax=1.386

Sample o

nly

-

FM-MA-Diagram

0 200 400 600 800 1000 MA [Nm]

0

50E3

100E3

150E3

200E3

250E3

300E3

FM [N]

FM,Re = 202528 N

FM,max = 182275 N

FM,min = 113922 Nμ=0

μmin

FM Re μ0


Sample o

nly

MA-FM-Diagram

0 50E3 100E3 150E3 200E3 FM [N]

0

100

200

300

400

500

600

700

MA [Nm]

MA = 681.2 Nm

MAmin = 425.8 Nm

μmin


Sample o

nly

FM [N]: 148099 ± 34177 -> 0.27 % (Sigma=3)FM [N]: 148099 ± 34177 -> 0.27 %

113922 .. 182275: -> 0.27 %113922 .. 182275: -> 0.27 %

0.27%1139220.135%-3

0.27%18227599.8650%3

1150

00

120

00

0

1250

00

130

00

0

1350

00

140

00

0

1450

00

150

00

0

1550

00

160

00

0

1650

00

170

00

0

1750

00

180

00

0

FM [N

]

0.0

032

0.0

233

0.1

350

0.6

210

2.2

750

6.6

807

15.

8655

30

.853

8

50

.00

00

69.

1462

84.

1345

93.

3193

97.

7250

99.

3790

99.

8650

99.

9767

99.

9968

per c

ent

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Sigm

a


Sample o

nly

Load Extension Diagram

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

f [mm]0

50E3

100E3

150E3

200E3

250E3

F [N]Load:FVmin,req= 94000 NFM,Re =202528 NFM,max =182275 NFMmax,req=150399 NFMmin,req= 94000 NFAmax= 100000 NFKreq= 1000 NFSA = 7000 NFPA = 93000 NFZ = 0 N Coefficients:n = 0.30phi n = 0.070alpha a = 1.60 Functions:FSA= phi n * FAFV = FA+FKR-FSAFA = FSA+FPAFMmin,req = FVreq+FZFMmax,req=FMmin,req*al.a

Sample o

nly

Load Extension Diagram (Assembly req.)

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

f [mm]0

50E3

100E3

150E3

200E3

250E3

F [N]Load:FVmin,req= 94000 NFM,Re =202528 NFM,max =182275 NFMmax,req=150399 NFMmin,req= 94000 NFAmax= 100000 NFZ = 0 N Coefficients:alpha a = 1.60 Functions:FMmin,req = FVreq+FZFMmax,req=FMmin,req*al.a

Sample o

nly

Load Extension Diagram (Assembly )

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

f [mm]0

50E3

100E3

150E3

200E3

250E3

F [N]Load:FVmin,req= 94000 NFM,Re =202528 NFM,max =182275 NFVmax =182275 NFVmin =113922 NFAmax= 100000 NFZ = 0 N Coefficients:alpha a = 1.60 Functions:FM,max= FMRe * nueFVmax = FM,max - FZFVmin = FM,min - FZ

Sample o

nly

Load Extension Diagram (Working condition req.)

-0.2 -0.15 -0.1 -0.05 0 0.05

f [mm]0

20E3

40E3

60E3

80E3

100E3

120E3

F [N]Load:FVmin,req= 94000 NFAmax= 100000 NFKreq= 1000 NFSA = 7000 NFPA = 93000 N Coefficients:n = 0.30phi n = 0.070 Functions:FSA= phi n * FAFV = FA+FKR-FSAFA = FSA+FPAFKR = FV - FPA

Sample o

nly

Load Extension Diagram (Working condition max.)

-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1

f [mm]0

50E3

100E3

150E3

200E3

F [N]Load:FVmax =182275 NFAmax= 100000 NFKreq= 1000 NFSA = 7000 NFPA = 93000 N Coefficients:n = 0.30phi n = 0.070 Functions:FSA= phi n * FAFV = FM - FZFA = FSA+FPAFKR = FV - FPA

Sample o

nly

-

Load Extension Diagram (Working condition min.)

-0.2 -0.15 -0.1 -0.05 0 0.05

f [mm]0

20E3

40E3

60E3

80E3

100E3

120E3

140E3

F [N]Load:FVmin =113922 NFAmax= 100000 NFKreq= 1000 NFKR = 20923 NFSA = 7000 NFPA = 93000 N Coefficients:n = 0.30phi n = 0.070 Functions:FSA= phi n * FAFV = FM - FZFA = FSA+FPAFKR = FV - FPA

Sample

only

hexagon head bolt ISO 4014 - M24 x 120 - 12.9 SW36i de [mm] di [mm] l [mm] A [mm²] x [mm] delta mm/N

1 24.00 0.00 60.00 452.4 60.00 0.632E-6G3 20.27 0.00 20.00 322.7 80.00 0.295E-6G2 22.00 0.00 40.00 380.3 120.00

major diameter d mm 24allowance class 6gmajor diameter max dmax mm 23,952major diameter min dmin mm 23,577thread pitch P mm 3stress cross-section As mm² 350,9diameter to As ds mm 21,137minor diameter d3 mm 20,271minor diameter nom. d3 nom mm 20,319minor diameter max. d3 max mm 20,271minor diameter min. d3 min mm 19,958pitch diameter d2 mm 22,003pitch diameter nom. d2 nom mm 22,051pitch diameter max. d2 max mm 22,003pitch diameter min. d2 min mm 21,806minimum cross-section A0 mm² 350,9yield point Re,Rp0,2 MPa 1100tensile strength min Rm MPa 1220tensile strength max Rm,max MPa 1464Young`s modulus ES MPa 210000shear stress coefficient Dose betaB 0,577bolt length up to head l mm 120thread length lG mm 60width across flats SW mm 36min.bear.surface dia dw mm 33,6clamping length lk mm 80

Sample

only

CLAMPED PLATES (DIMENSIONS)i de [mm] di [mm] l [mm] x[mm] Aequ[mm²] de pmax

1 120.00 25.00 40.00 40.00 1974.6 56.02 120.00 25.00 40.00 80.00 1974.6 56.0

CLAMPED PLATES (MATERIAL AND LOAD)i material E [MPa] pperm pBmax d.[mm/N] a.[mm/K]

1 0.6040 GJL400 ( 135000 1000 781 0.15E-6 9,00E-062 0.6040 GJL400 ( 135000 1000 825 0.15E-6 9,00E-06

BOLTED JOINT: through bolted joint with nut (DSV)hexagon nut ISO 4032 - SW 36min.bear.surface dia nut dw M mm 33,2height of nut h M mm 21,5thread length engaged m geo mm 21,5engaged thread length m tr mm 21,5

ELASTIC RESILIENCEelastic resilience head delta SK mm/N 1,26E-07elastic resilience bolt sect. delta is mm/N 6,32E-07elastic resilience free thread del.Gew mm/N 2,95E-07elastic resilience thread delta G mm/N 1,77E-07elastic resilience nut delta M mm/N 1,01E-07elastic resilience bolt delta S mm/N 1,33E-06elastic resilience plates delta P mm/N 3,00E-07

SPRING RATEspring rate bolt R S N/mm 7,51E+05spring rate plates R P N/mm 3,33E+06

ELONGATION

Sample

only

elongation bolt at FM,max fSM mm 0,404shortening plates at FM,max fPM mm 0,091

BENDING RESILIENCEclamp.length ratio lk/d 3,33bending resilience bolt beta S 1/Nmm 3,87E-08

LOADcalculation base FM, MA VDI 2230-2003max. axial force FA max N 100000min. axial force FA min N 0transverse load FQ N 0reqd.residual clamp.load FKreq N 1000min.residual clamp.load at FAmax FKRmax N 95390min.residual clamp.load at FAmin FKRmin N 189870theor.preload at Rp0.2 FM0.2 N 337547assembly preload FMzul,max FM,max N 303792assembly preload FMzul,min FM,min N 189870max.req.assembly preload FMmax,req N 152769min.req.assembly preload FMmin,req N 95481total amount of embedding fz mm 0loss of preload by embedding Fz N 0req.preload FVmin,req N 95481min.preload FVmin N 189870max.preload FVmax N 303792additional bolt load from FA FSAmax N 5519additional plate load from FA FPAmax N 94481total bolt load FS max N 309312bolt fracture load FS Rm N 428108yield load, bolt FS Re N 385999prestressing load factor FM/FA 3,038

Sample

only

DISTRIBUTION OF LOADintrod.of load (in): to clamping plate 1load introduction factor n1 0,3share of elast.on introd. FA(in) delta1 1,05E-07

introd.of load (out): to clamping plate 2load introduction factor n2 0,3share of elast.on introd. FA(out) delta2 1,05E-07

load ratio phi K 0,184load ratio phi n 0,055load introduction factor n 0,3

FATIGUE STRESSperm.fatigue stress RTBHT ±sig.ASV MPa 44fatigue stress on bolt (centr.) ±sigma a MPa 8safety ag.fatigue fract.(centr.) SD=Sig.AS/Sig.a 5,54number of load cycles NZ 3,40E+08

FRICTIONcoeff.of friction in thread μG 0,14coeff.of friction in head seat μK 0,1coeff.of friction at interface μTr min 0,12friction rate K=M/(d*F) 0,155

ASSEMBLY (tightening torque)yield point tightening factor nue Re 0,9tightening factor alpha A 1,6dispersion of assembly load Tol FM % 23,1tightening procedure: Nut driventightening torque MA MA,max Nm 1132

Sample

only

tightening torque MA,min Nm 707,7tightening torque MA,nom Nm 920tolerance tightening torque Tol MA % 23,1loosening torque MA- Nm 834,7tightening torque f yield point MA Re Nm 1258tightening angle al.max deg 59,5tightening angle al.min deg 37,2rate for tightening torque R MA Nm/deg 19,04rate for prestressing load R FM N/deg 5109

STRESSmax.tensile stress at FM+FSA Sigma 0 MPa 881Max.shear stress tau max MPa 370Max.comparative stress(k tau=0.5) Sig.redB MPa 938

FACTORS OF SAFETYsafety against loosening FM,max/FMmax,req 1,99safety yield point red.B SF=Re/Sig.redB 1,17safety ag.fatigue fract.(centr.) SD=Sig.AS/Sig.a 5,54safety plate surface pressure Sp=pperm/pmax 1,21

We Help Companies Secure Bolted Joints Bolt Securing 1.6180 AB | Lilla Bommen 6 | SE-411 04 Gothenburg

Phone: +46-317 810 608 | Fax: +46-313 011 858www.boltsecuring.com

bolted joint design

Engineering

proper preload

excessive preload

joint separation

joint slip

joint integrity

maximum possible preload

oen smaller joint members

warp orfracture joint