Mathcad - Bolt Loading VDI M39

7/29/2019 Mathcad - Bolt Loading VDI M39

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Bolt Loading VDI M39.xmcd

MARYLAND METRICS -- THREAD DATA CHART: Metric Thread -- Coarse Pitch

NominalSize

ISO M

ThreadFormType

MajorDiameter

mmd=D

Pitchmmp

RootRadius

mmr

PitchDiameter

mmd2=D2

MinorDiameterMale Thd.

d3

MinorDiameter

Female Thd.D1

ThreadHeight

Male Thd.h3

ThreadHeight

Female Thd.H1

TapDrill

Diametermm

39.00 M 39.00 4.00 0.577 36.402 34.093 34.670 2.454 2.165 35.00copyright maryland metrics-- all rights reserved filnam:isomlee.xls ver t3a

Fastner size M39

Diameter at stress cross-sect ion A.s (Minor dia of male thread) DS 34.093 mm:=

Shank diameter of bolt neck DT 34.093 mm:=

Outside diameter of the consact area under the head of the driven fastner DW 60 mm:=

Effect ive diameter for friction at the contact of the head of the driven fastner Dkm60 mm 42 mm+

2:=

Dkm 51 mm=

Effective tensile stress cross-section of the bolt thread AS 976 mm2

:=

Pitch of the bolt thread P 4 mm:=

Ry 210 MPa:=Actual proof stress of the bolt

Minimum 2% Proof stess fo bolt material ISO 898 grade 50

stated in eurocode

Rp.0.2 210 MPa:=

Outside diameter of bolt at the smallest cross section d0 34.093 mm:=

Pitch diameter of the bolt thread d2 36.402 mm:=

Minor Diameter of bolt thread d3 34.093 mm:=

Minimum cross section area of the bolt A0

d02

4912.894 mm

2=:=

Half flank angle of blt thread

th

6

0.524=:=

Coefficien of friction between bolt and nut thread G 0.14:=

Coefficien of friction at the contact of the driven head K 0.14:=

Degree of explotiaiton of bolt yield stress desired at max assembly condition 90%:=

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lK 550 mm:=

Bolt c lamp Length

Shank length l1 lK:=

Joint coefficient w 1:=

Clamped parts hole diameter dh 42 mm:=

dw 410 mm:=

DA 220 mm:=

atan 0.6( ) 30.964 deg=:=

Rp.0.2.min 210 MPa:=

Esteel 200 GPa:=

Econc 30 GPa:=

Ep Econc:=

AS Rp.0.2 204.96 kN=

Maximum assembly preload

expected from tightening to specified

torque

FM.Tab

AS Rp.0.2

1 34

1 d3d2

+

P

d2

G

cos th( )

+

2

+

151 kN=:=

Note this is not with in the VDI spec and should normally be taken from tables

A Preload to resist a maximum force of:- FA.max 125 kN:=

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R1 tightening factor in acordance with table 8 A 1.4:=

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bolt diameter to clamping lengthlK

d0

16.132=For friction coefficient class B

FKRmin 0 N:=

R2 Required minimum clamp load.

The joint is symetrically clamped

FKerf FKRmin:= FKerf 0 kN=

R3 Splitting the working load, elastic resilience and load introduction factor

S

lK

AS Esteel:=

S 2.818 106

mm

N

=

P

2

w dh tan ( )ln

dw dh+( ) DA dh( )

dw dh( ) DA dh+( )

2

DA2

dh2

lK DA DW( )

w tan ( )

+

Ep :=

P 1.434 107

mm

N=

Load factor with the application under the bolt head

K

P

P S+0.048=:=

K:=

n2d 0.15:=

n n2d

P

P S+ 7.264 10

3=:=

fZ 3.5 m:= fZ 3.5 106

m=R4 Preload changes

See table 5.4/1 P64

FZ

fZ 5

P S+6 kN=:= 5 no interfaces

conservative

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R5 Determinine the minimum assembly preload

No temperature reqirementsFM.min FKerf 1 n( ) FA.max+ FZ+:=

FM.min 130 kN=

R6 Determine maximum assembly preload

FM.max A FM.min:=

FM.max 182 kN=

R7 Determine the assembly stress

red.Mzul Rp.0.2.min:=

red.Mzul 189 MPa=

FMzul

A0 Rp.0.2.min

1 33

2

d2

d0

P

d21.55 G+

+

:=

FMzul 116 kN=

FA.max 6.053 kN=

0.1 Rp.0.2.min AS 20.496 kN=

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R8 Determine the working stress

n FA.max 0.908 kN=

FS.max FMzul n FA.max+:=

FS.max 117 kN=

Z.max

FS.max

A0

:=

Z.max 128.11 MPa=

max

Mg

W

p

:=

Mg

d ??????????

FS.max 117 kN=

FM.max 182 kN=

FM.min 130 kN=

GS.max.x

FS.max S

0 mm

FS.max P

:=GM.max.x

FM.max S

0 mm

FM.max P

:=GM.min.x

FM.min S

0 mm

FM.min P

:=

GS.max.y

0 kN

FS.max

0 kN

:=GM.max.y

0 kN

FM.max

0 kN

:=GM.min.y

0 kN

FM.min

0 kN

:=

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GZ.x

FM.min FZ+( ) S

0 mm

FM.min FZ+( ) P

:= GKerf.x

FKerf( ) S

0 mm

FKerf( ) P

:=

GZ.y

0 kN

FM.min FZ( )

0 kN

:= GKerf.y

0 kN

FKerf( )

0 kN

:=

yieldx

0.6 mm

0 mm

0.3 mm

:=

yieldy

AS Rp.0.2

AS Rp.0.2

AS Rp.0.2

:=

25

50

75

100

125

150

175

200

225

250

GS.max.y

kN

GM.max.y

kN

GM.min.y

kN

GZ.y

kN

GKerf.y

kN

yieldy

kN

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0.6 0.4 0.2 0 0.2 0.4

F s max

max preloadmin preload

Loss of preload

Required clamp force

trace 6

GS.max.x

mm

GM.max.x

mm,

GM.min.x

mm,

GZ.x

mm,

GKerf.x

mm,

yieldx

mm,

Fset

FM.max FM.min+

2156 kN=:=

Fset

AS Rp.0.276.114 %=

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P 4 mm=

150 kN S

P

rev 38.038 deg=

GM.max.x

0.513

0

0.026

mm=

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Mathcad - Bolt Loading VDI M39

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