Bolted joint design

1
Bolted Joint Design - Input Data
www.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 or
fracture joint members such as castings and flanges.
• Vibration loosening of the nut: No amount of preload can Ȳght extreme transverse
vibration, but in most applications, proper preload can eliminate vibration loosening
of the nut.
• Fatigue failure of the bolt: Most bolts that fail in use do so in fatigue. Higher preload
does increase the mean stress in a fastener, and therefore threatens to shorten fatigue
life. But higher preload also reduces the load excursions seen by the bolt. The net eȩect
is that higher preload almost always improves fatigue life.
• Stress corrosion cracking: Stress corrosion cracking (SCC), like fatigue, can cause a
bolt to break. Stresses in the bolt, created primarily by preload, will encourage SCC if
they’re above a certain threshold level.
• Joint separation: Proper preload prevents joint separation; this means that it reduces or
prevents such things as leaks in a fluid pipeline or blow-by in an engine. The latter, of
course, 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 the
bolt. Many such joints rely for their strength on the friction forces developed between
joint 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 and
smaller fasteners, and oȵen smaller joint members. This can have a signiȲcant eȩect
on the weight of our products.
• Excessive cost: The cost of many products is proportional to the number of assembly
operations. Correct preload means fewer fasteners and lower manufacturing costs—as
well as lower warranty and liability costs.

3
Load
Statical Dynamic Centrically applied axial load Eccentrically applied load Transverse load
Tight of the bolt
With screwdriver With torque wrench Rotation-angle controlled or yield point controlled
Axial load FA (N) Transverse load FQ (N)
Tapped blind hole joint
Thread depth Bore depth
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.

4
Bolt
ISO standard Dimension Thread pitch Property class Material Allowance class
Bolt to drawing
Drawing 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
Nut
ISO standard Dimension Thread pitch Property class Material Allowance class
Nut to drawing
Drawing no Dimension Thread pitch Property class Material Allowance class
Clamping plates
Dimension Thikness Material

6
Friction
CoeȬcient of friction in thread CoeȬcient of friction in head seat
Min
Max
Embedding
Loss of preload by embedding Amount of embedding (mm)
Tightening procedure
Yield point factor for tightening Tightening torque MA max
Bolt driven Nut driven
Tightening factor alpha A
MINIMIZING EMBEDMENT: We can minimize embedment relaxation by chamfering holes,
by insisting on flat and parallel joint surfaces, by speciȹing that holes should be drilled
perpendicular to joint surfaces, or by speciȹing hard washers.

7
FACTORS THAT AFFECT THE WORKING LOADS ON BOLTS
• Sequence=procedure: The procedure with which a group of bolts are tightened can
aȩect Ȳnal results substantially. Procedure includes such things as the sequence with
which they’re tightened, whether they’re tightened with a single pass at the Ȳnal
torque, or in several passes at steadily increasing torques, etc.
• Residual preloads: The preloads leȵ in the bolts aȵer embedment and elastic interactions.
• External loads: External loads add to or subtract from the tension in the bolts, and
therefore from the clamping force on the joint. Such loads must be predicted and
accounted 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 on
the roof, inertia, earthquakes, the weight of other portions of the structure, etc.
• Service conditions: Severe environments can aȩect operating conditions in the joint
and bolts. This is especially true of operating temperatures. These can create diȩerential
expansion or contraction, which can signiȲcantly alter bolt tensions and clamping
force. Corrosion can cause change as well. Contained pressure will aȩect clamping
forces.
• Long-term relaxation: There are some long-term relaxation eȩects that must also be
considered: 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 performance
from the joint, unless the parts are the right size, are hardened properly, and are in
good condition. This factor can’t be handled separately; it gets in the act by aȩecting
the others. If the bolts are soȵ, for example, we won’t get the expected preload
for a given torque, and relaxation will be worse. If joint members are warped or
misaligned, it may take an abnormal amount of tension in the bolts (created by an
abnormal amount of preload) to create the necessary clamping force between joint
members.

Sample only
Cond. Modification Date Name
Date Name
Compl.
Check
Stand.
App
Copying of this document and giving it to other and the use
or communication of the contents therof, are forbidden with-out
of damages. All rights are reserved in the event of the grant
of a patent or the registration of a utility model or design.
express authority. Offenders are liable to the payment
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

Load Extension Diagram
F [N]
250E3
200E3
150E3
Load:
FVmin,req= 94000 N
FM,Re =202528 N
FM,max =182275 N
FMmax,req=150399 N
FMmin,req= 94000 N
FAmax= 100000 N
FKreq= 1000 N
FSA = 7000 N
FPA = 93000 N
FZ = 0 N
Coefficients:
n = 0.30
phi n = 0.070
alpha a = 1.60
Functions:
FSA= phi n * FA
FV = FA+FKR-FSA
FA = FSA+FPA
FMmin,req = FVreq+FZ
FMmax,req=FMmin,req*al.a
100E3
50E3
0
-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 only
-0.1 -0.05 0 0.05 0.1
Sample Cond. Modification Date Name
Date Name
Compl.
Check
Stand.
App
Copying of this document and giving it to other and the use
or communication of the contents therof, are forbidden with-out
of damages. All rights are reserved in the event of the grant
of a patent or the registration of a utility model or design.
express authority. Offenders are liable to the payment
2013/11/06
Page
Pg.
f [mm]
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
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

Sample only
-
MA [Nm]
M-alpha-Diagram (Proj.from elastic origin)
MA Rm = 951.9 Nm
MA Re = 756.9 Nm
MA,max = 681.2 Nm
0 10 20 30 40 50 60 70 alpha [°]
1000
800
600
400
200
0
μmin
MA,min = 425.8 Nm
μ=0
MG (μG=0.14) = 411.3 Nm
ISO 4014-M24x120-8.8 d>16
μG = 0.140
μK = 0.100
K = M/(d*F) = 0.155
nue Re = 0.90
MA,max = 681.2 Nm
FM,max = 182275 N
alpha max = 37.98 deg
MA,Re = 756.9 Nm
FM,Re = 202528 N
alpha Re = 42.20 deg
MA μ0 = 98.84 Nm
FM μ0 = 207018 N
alpha μ0= 43.13 deg
MA min = 425.8 Nm
FM/al.A= 113922 N
R MA = 17.94 Nm/°
FM,max/FMmax,req = 1.212
SF=Re/Sig.redB=1.153
SD=Sig.AS/Sig.a= 4.367
Sp=pG/pmax=1.386

Sample only
-
FM-alpha-Diagram (Proj.from elastic origin)
FM [N]
300E3
250E3
200E3
150E3
100E3
FM Re (μG=μK=0) = 230020 N
0 10 20 30 40 50 60 70 alpha [°]
50E3
0
FM,Rm = 254695 N
FM,Re = 202528 N
FM,max = 182275 N
FM,min = 113922 N
ISO 4014-M24x120-8.8 d>16
μG = 0.140
μK = 0.100
K = M/(d*F) = 0.155
nue Re = 0.90
MA,max = 681.2 Nm
FM,max = 182275 N
FZ = 0 N
FVmax = 182275 N
MA,Re = 756.9 Nm
FM,Re = 202528 N
MA μ0 = 98.84 Nm
FM μ0 = 207018 N
MA min = 425.8 Nm
FM/al.A= 113922 N
R FM = 4800 N/°
Sp=pG/pmax=1.386

Sample only
-
FM-MA-Diagram
FM [N]
300E3
250E3
200E3
150E3
100E3
0 200 400 600 800 1000 MA [Nm]
50E3
0
FM,Re = 202528 N
FM,max = 182275 N
FM,min = 113922 N μ=0
μmin
FM Re μ0
ISO 4014-M24x120-8.8 d>16
μG = 0.140
μK = 0.100
K = M/(d*F) = 0.155
nue Re = 0.90
MA,max = 681.2 Nm
FM,max = 182275 N
FZ = 0 N
FVmax = 182275 N
MA,Re = 756.9 Nm
FM,Re = 202528 N
MA μ0 = 98.84 Nm
FM μ0 = 207018 N
MA min = 425.8 Nm
FM/al.A= 113922 N
R FM = 4800 N/°
Sp=pG/pmax=1.386

MA-FM-Diagram
Sample only
MA [Nm]
0 50E3 100E3 150E3 200E3 FM [N]
700
600
500
400
300
200
100
0
MA = 681.2 Nm
MAmin = 425.8 Nm
μmin
ISO 4014-M24x120-8.8 d>16
μG = 0.140
μK = 0.100
K = M/(d*F) = 0.155
nue Re = 0.90
MA,max = 681.2 Nm
FM,max = 182275 N
FZ = 0 N
FVmax = 182275 N
MA,Re = 756.9 Nm
FM,Re = 202528 N
MA μ0 = 98.84 Nm
FM μ0 = 207018 N
MA min = 425.8 Nm
FM/al.A= 113922 N
R FM = 4800 N/°
Sp=pG/pmax=1.386

FM [N]: 148099 ± 34177 -> 0.27 % (Sigma=3)
FM [N]: 148099 ± 34177 -> 0.27 %
113922 .. 182275: -> 0.27 %
113922 .. 182275: -> 0.27 %
Sample only
0.27%
113922
0.135%
-3
0.27%
182275
99.8650%
3
115000
120000
125000
130000
135000
140000
145000
150000
155000
160000
165000
170000
175000
180000
FM [N]
0.0032
0.0233
0.1350
0.6210
2.2750
6.6807
15.8655
30.8538
50.0000
69.1462
84.1345
93.3193
97.7250
99.3790
99.8650
99.9767
99.9968
per cent
-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
Sigma
ISO 4014-M24x120-8.8 d>16
μG = 0.140
μK = 0.100
K = M/(d*F) = 0.155
nue Re = 0.90
MA,max = 681.2 Nm
FM,max = 182275 N
FZ = 0 N
FVmax = 182275 N
MA,Re = 756.9 Nm
FM,Re = 202528 N
MA μ0 = 98.84 Nm
FM μ0 = 207018 N
MA min = 425.8 Nm
FM/al.A= 113922 N
R FM = 4800 N/°
Sp=pG/pmax=1.386

Sample only
-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1
f [mm]
F [N]
250E3
200E3
150E3
100E3
50E3
0
Load:
FVmin,req= 94000 N
FM,Re =202528 N
FM,max =182275 N
FMmax,req=150399 N
FMmin,req= 94000 N
FAmax= 100000 N
FKreq= 1000 N
FSA = 7000 N
FPA = 93000 N
FZ = 0 N
Coefficients:
n = 0.30
phi n = 0.070
alpha a = 1.60
Functions:
FSA= phi n * FA
FV = FA+FKR-FSA
FA = FSA+FPA

Load Extension Diagram (Assembly req.)
Sample only
-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1
f [mm]
F [N]
250E3
200E3
150E3
100E3
50E3
0
Load:
FVmin,req= 94000 N
FM,Re =202528 N
FM,max =182275 N
FMmax,req=150399 N
FMmin,req= 94000 N
FAmax= 100000 N
FZ = 0 N
Coefficients:
alpha a = 1.60
Functions:

Load Extension Diagram (Assembly )
Sample only
-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1
f [mm]
F [N]
250E3
200E3
150E3
100E3
50E3
0
Load:
FVmin,req= 94000 N
FM,Re =202528 N
FM,max =182275 N
FVmax =182275 N
FVmin =113922 N
FAmax= 100000 N
FZ = 0 N
Coefficients:
alpha a = 1.60
Functions:
FM,max= FMRe * nue
FVmax = FM,max - FZ
FVmin = FM,min - FZ

Load Extension Diagram (Working condition req.)
Sample only
f [mm]
-0.2 -0.15 -0.1 -0.05 0 0.05
F [N]
120E3
100E3
80E3
60E3
40E3
20E3
0
Load:
FVmin,req= 94000 N
FAmax= 100000 N
FKreq= 1000 N
FSA = 7000 N
FPA = 93000 N
Coefficients:
n = 0.30
phi n = 0.070
Functions:
FSA= phi n * FA
FV = FA+FKR-FSA
FA = FSA+FPA
FKR = FV - FPA

Load Extension Diagram (Working condition max.)
Sample only
-0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1
f [mm]
F [N]
200E3
150E3
100E3
50E3
0
Load:
FVmax =182275 N
FAmax= 100000 N
FKreq= 1000 N
FSA = 7000 N
FPA = 93000 N
Coefficients:
n = 0.30
phi n = 0.070
Functions:
FSA= phi n * FA
FV = FM - FZ
FA = FSA+FPA
FKR = FV - FPA

Sample only
-
Load Extension Diagram (Working condition min.)
f [mm]
-0.2 -0.15 -0.1 -0.05 0 0.05
F [N]
140E3
120E3
100E3
80E3
60E3
40E3
20E3
0
Load:
FVmin =113922 N
FAmax= 100000 N
FKreq= 1000 N
FKR = 20923 N
FSA = 7000 N
FPA = 93000 N
Coefficients:
n = 0.30
phi n = 0.070
Functions:
FSA= phi n * FA
FV = FM - FZ
FA = FSA+FPA
FKR = FV - FPA

Sample only
hexagon head bolt ISO 4014 - M24 x 120 - 12.9 SW36
i 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-6
G3 20.27 0.00 20.00 322.7 80.00 0.295E-6
G2 22.00 0.00 40.00 380.3 120.00
major diameter d mm 24
allowance class 6g
major diameter max dmax mm 23,952
major diameter min dmin mm 23,577
thread pitch P mm 3
stress cross-section As mm² 350,9
diameter to As ds mm 21,137
minor diameter d3 mm 20,271
minor diameter nom. d3 nom mm 20,319
minor diameter max. d3 max mm 20,271
minor diameter min. d3 min mm 19,958
pitch diameter d2 mm 22,003
pitch diameter nom. d2 nom mm 22,051
pitch diameter max. d2 max mm 22,003
pitch diameter min. d2 min mm 21,806
minimum cross-section A0 mm² 350,9
yield point Re,Rp0,2 MPa 1100
tensile strength min Rm MPa 1220
tensile strength max Rm,max MPa 1464
Young`s modulus ES MPa 210000
shear stress coefficient Dose betaB 0,577
bolt length up to head l mm 120
thread length lG mm 60
width across flats SW mm 36
min.bear.surface dia dw mm 33,6
clamping 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 56.0
2 120.00 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-06
2 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 36
min.bear.surface dia nut dw M mm 33,2
height of nut h M mm 21,5
thread length engaged m geo mm 21,5
engaged thread length m tr mm 21,5
ELASTIC RESILIENCE
elastic resilience head delta SK mm/N 1,26E-07
elastic resilience bolt sect. delta is mm/N 6,32E-07
elastic resilience free thread del.Gew mm/N 2,95E-07
elastic resilience thread delta G mm/N 1,77E-07
elastic resilience nut delta M mm/N 1,01E-07
elastic resilience bolt delta S mm/N 1,33E-06
elastic resilience plates delta P mm/N 3,00E-07
SPRING RATE
spring rate bolt R S N/mm 7,51E+05
spring rate plates R P N/mm 3,33E+06
ELONGATION

Sample only
elongation bolt at FM,max fSM mm 0,404
shortening plates at FM,max fPM mm 0,091
BENDING RESILIENCE
clamp.length ratio lk/d 3,33
bending resilience bolt beta S 1/Nmm 3,87E-08
LOAD
calculation base FM, MA VDI 2230-2003
max. axial force FA max N 100000
min. axial force FA min N 0
transverse load FQ N 0
reqd.residual clamp.load FKreq N 1000
min.residual clamp.load at FAmax FKRmax N 95390
min.residual clamp.load at FAmin FKRmin N 189870
theor.preload at Rp0.2 FM0.2 N 337547
assembly preload FMzul,max FM,max N 303792
assembly preload FMzul,min FM,min N 189870
max.req.assembly preload FMmax,req N 152769
min.req.assembly preload FMmin,req N 95481
total amount of embedding fz mm 0
loss of preload by embedding Fz N 0
req.preload FVmin,req N 95481
min.preload FVmin N 189870
max.preload FVmax N 303792
additional bolt load from FA FSAmax N 5519
additional plate load from FA FPAmax N 94481
total bolt load FS max N 309312
bolt fracture load FS Rm N 428108
yield load, bolt FS Re N 385999
prestressing load factor FM/FA 3,038

Sample only
DISTRIBUTION OF LOAD
introd.of load (in): to clamping plate 1
load introduction factor n1 0,3
share of elast.on introd. FA(in) delta1 1,05E-07
introd.of load (out): to clamping plate 2
load introduction factor n2 0,3
share of elast.on introd. FA(out) delta2 1,05E-07
load ratio phi K 0,184
load ratio phi n 0,055
load introduction factor n 0,3
FATIGUE STRESS
perm.fatigue stress RTBHT ±sig.ASV MPa 44
fatigue stress on bolt (centr.) ±sigma a MPa 8
safety ag.fatigue fract.(centr.) SD=Sig.AS/Sig.a 5,54
number of load cycles NZ 3,40E+08
FRICTION
coeff.of friction in thread μG 0,14
coeff.of friction in head seat μK 0,1
coeff.of friction at interface μTr min 0,12
friction rate K=M/(d*F) 0,155
ASSEMBLY (tightening torque)
yield point tightening factor nue Re 0,9
tightening factor alpha A 1,6
dispersion of assembly load Tol FM % 23,1
tightening procedure: Nut driven
tightening torque MA MA,max Nm 1132

Sample only
tightening torque MA,min Nm 707,7
tightening torque MA,nom Nm 920
tolerance tightening torque Tol MA % 23,1
loosening torque MA- Nm 834,7
tightening torque f yield point MA Re Nm 1258
tightening angle al.max deg 59,5
tightening angle al.min deg 37,2
rate for tightening torque R MA Nm/deg 19,04
rate for prestressing load R FM N/deg 5109
STRESS
max.tensile stress at FM+FSA Sigma 0 MPa 881
Max.shear stress tau max MPa 370
Max.comparative stress(k tau=0.5) Sig.redB MPa 938
FACTORS OF SAFETY
safety against loosening FM,max/FMmax,req 1,99
safety yield point red.B SF=Re/Sig.redB 1,17
safety ag.fatigue fract.(centr.) SD=Sig.AS/Sig.a 5,54
safety plate surface pressure Sp=pperm/pmax 1,21

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Bolted joint design

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