mow227 2014 fasteners 2 - varsity field · • turn the nut not the bolt if possible. ... typical...

Department of Mechanical and Aeronautical Engineering

SCREWS, FASTENERS AND NON

PERMANENT JOINTS

2

MOW 227 2014


•Yielding take place in the first thread with cold work

strengthening

•Never re-use nuts in structural connections because their

thread gets damaged

•


• Washers underneath bolt head

• Purpose of a bolt is to clamp two or more parts

together

• Turn the nut not the bolt if possible. Why?


countersunk


h

t2

BOLTED JOINTS STIFFNESS

ll`

Table 8.7


BOLT STIFFNESS

Tensile Stress Area


COMPRESSION OF BOLTED MEMBERS

• There may be more than two members in the grip of

the bolt

• The total member stiffness of the joint

– If one of the members is a gasket the stiffness is

so soft relative to the other members that for all

practical purpose, the others can be neglected

and only the gasket used

nm kkkkk

11111

321

++++= L


m

kd

kt


COMPRESSION OF BOLTED

MEMBERS

( )2 2

2 2

0tan

2 2

tan tan2 2

i

D dA r r x

D d D dx x

π π α

π α α

= − = + −

+ − = + +


(2 tan )( )ln

tan (2 tan )( )

tan

(2 tan )( )ln(2 tan )( )

P t D d D d

Ed t D d D d

P Edk

t D d D d

t D d D d

αδ

π α α

π α

αδ

α

+ − +=

+ + −

= =+ − +

+ + −

The contraction of an element in the cone of thickness dx,

subjected to a compressive force P is:

Substituting A into the previous equation and integrating the

resulting equation from 0 to t gives.

Pdxd

EAδ =


COMPRESSION OF BOLTED MEMBERS

• Assuming:

– dw = 1.5 d, and α = 30°, and l=2t

+⋅

+⋅

⋅⋅⋅=

dl

dl

dEkm

5.25774.0

5.05774.05ln2

5774.0 π


� Bolt strength is specified by:

1. minimum proof strength Sp

2. or minimum proof load Fp, 3. and minimum tensile strength, Sut

� The proof load is the maximum load (force)

that a bolt can withstand without acquiring a

permanent set.

� The proof strength is the quotient of the

proof load and the tensile-stress area.

Table 8-9 to 8-11

Bolt Strength


• Read section 8-6

*Use same grade nuts as the bolt

Department of Mechanical and Aeronautical EngineeringFi

P

BOLTED JOINTS IN TENSION

• Clearance between the bolt and hole

• Preload - Fi

• External tensile load – P

• External shear load – Ps

• Collar friction: fc

• Thread friction: ft


BOLTED JOINTS

Fi

P

σm<0

σb>0


BOLTED JOINTS

• Purpose of preload is to place the bolted member

components in compression for better resistance to

the external tensile load and to create a friction force

between the parts to resist shear load

• Joint has failed when

– resulting loading between members equals 0

– The load in the bolt exceeds yield


BOLTED JOINTS

Spring constant or stiffness constant

– δ : Deflection

– F : Force

– A : Area

– E : Modulus of elasticity (Steel: E=200GPa)

Stiffness constant, k

L

EAFk

⋅==

δ

EA

LF

⋅

⋅=δ


BOLTED JOINTS

• P – total external load on bolted assembly

• Fi – Preload due to tightening

• Pb – Portion of P taken by bolt

• Pm – Portion of P taken by members

• Fb – Resultant bolt load = Pb + Fi

• Fm – Resultant load on members = Pm - Fi

• C – Fraction of P taken by bolt

mb PPP +=


BOLTED JOINTS

• Increase in deformation of the bolt

• Compression of members

b

b

k

P=∆δ

m

m

k

P=∆δ


BOLTED JOINTS

• On the assumption that the members have not separated, the

increase in deformation of the bolt must equal the decrease in

deformation of the members

– But

– rearranging

m

m

b

b

k

P

k

P==δ

mb PPP +=

PCPkk

kP

mb

bb ⋅=⋅

+=


BOLTED JOINTS

• The resultant load on the bolt is

• The resultant load on the member is

THESE EQUATIONS ARE ONLY VALID AS LONG AS SOME OF

THE INITIAL COMPRESSION REMAINS IN THE MEMBERS

iibb FPCFPF +⋅=+=

iimm FPCFPF −⋅−=−= )1(

mb

b

kk

kC

+=


RELATING BOLT TORQUE TO BOLT TENSION

• Torque to produce preload:

• Simplifying

collarthreads TTT +=

2sec

sec

2

cci

m

mmi dfF

lfd

dfldFT

⋅⋅+

⋅−⋅

⋅⋅+⋅=

απ

απ

dFKT i ⋅⋅=

*K = Torque factor


• Tension, not torque, indicates proper joint tightness.

– Often, preload can be set more accurately by

controlling the number of turns rather than input

torque.

– Turn-of-nut method

• After the snug-tightening procedure is

completed, each bolt in the connection is pre-

tensioned additionally by the applicable amount

of relative rotation


STATICALLY LOADED TENSION JOINT

• Tensile stress failure

– Stress in bolt

– Introducing a load factor n:

• Where Sp is the proof stress

ib FPCF +⋅=

t

i

t

bA

F

A

PC+

⋅=σ

p

t

i

t

b SA

F

A

PnC=+

⋅⋅=σ


STATICALLY LOADED TENSION JOINT

• Joint separation

– The value of the load that will cause separation = P0

– At Joint Separation

• The Bolt Is Carrying All The Load

– Safety factor against separation, n0:

0PFb =

0)1( 0 =−⋅−= im FPCF

P

Pn 0

0 =

Portion of external

load carried by member

)1( CP

Fn i

o−−−−

====

Ratio of opening load

compared to external load


PRELOAD

• It is recommended that for static and fatigue

loading the following be used for preload

– Fi = 0.75 Fp (reused connections)

– Fi = 0.90 Fp (permanent connections)

– Where Fp is the proof load

ptp SAF ⋅=


BOLT MATERIALS


FATIGUE LOADING

• Already corrected for notch sensitivity and surface finish

• Peterson – typical bolt failures

– 15% under head

– 20% at end of shank

– 65% in the thread

• usually safe to assume that the fasteners have rolled threads –unless specific information is available

• Use machined finish for the body of the bolt if nothing is stated


Endurance Limit

• Fully corrected (including Kf) axial endurance

strength for rolled threads


FATIGUE LOADING• External load fluctuates between 0 and some

maximum force P

– Fmax = Fb

– Fmin = Fi

– Alternating component:

• Fa = (Fmax - Fmin)/2 = (Fb - Fi)/2

– Mean component:

• Fm = (Fmax+ Fmin)/2= (Fb + Fi)/2

– Alternating stress:

– Mean stress:

tt

ii

t

iba

A

PC

A

FFPC

A

FF

⋅

⋅=

⋅

−+⋅=

⋅

−=

22

)()

2(σ

t

i

tt

ii

t

ibm

A

F

A

PC

A

FFPC

A

FF+

⋅

⋅=

⋅

++⋅=

⋅

+=

22

)()

2(σ

iam σσσ +=

Load + pre-tension

Pre-tension


Mean Stress

• Goodman

• Soderberg

• Gerber

• ASME elliptic

1=+u

m

e

a

SS

σσ

1)( 2 =+u

ma

e

a

SS

σσ

1=+y

m

e

a

SS

σσ

1)()( 22 =+y

m

e

a

SS

σσ


FATIGUE LOADING

• Goodman

– But

(Applying the load factor to the alternating component only)

1=+u

m

e

a

SS

σσ

iam σσσ +=

1=+

+u

ia

e

a

SS

σσσ

1=+⋅

+⋅

u

iaf

e

af

S

n

S

n σσσ

)(

)(2

eu

ituef

SSPC

FASSn

+⋅

−⋅⋅=


160 kN

40 mm Table A-29 nut thickness 14.8 mm

20

20

M16 x 60 Grade 8.8

4 mm

40 + 14.8 + 4 =58.8 mm

..


60 mm

2 x 16 + 6 = 38 mm

60 – 38 = 22 mm

18 mm 157 mm2

0.0162 201 m m2

6102215718201

207157201

×+×

××

923.68 MN/m

100 GPa

⋅+⋅

⋅+⋅

⋅

165.2405774.0

165.0405774.05ln2

161005774.0 π

1609.08 MN/m

mMN

e

/19.1594

77871.016100 40/1661616.0

=

⋅⋅= ⋅


365.008.160968.923

68.923=

+

11, Sp=600MPa

(157)600 = 70.65kN

96.470650157600

1602365.0=

−⋅

⋅⋅

5

02.2)5160000(365.0

70650157600=

−⋅

5

0.9


Gasketed Joints

[[[[ ]]]]

63

)1(

)1(

≤≤≤≤≤≤≤≤

−−−−−−−−====

−−−−−−−−====

−−−−====

Nd

D

A

NCnPFp

FnPCF

NA

Fp

b

g

i

im

g

m

ππππ

Pressure p on gasket

Forces on members

Load Factor

Gasket pressure

To maintain adequate uniformity of pressure the bolts must

be spaced, not more than six diameters apart (rough rule)


Summary: BOLT SIZING

• Factors used during bolt sizing

– Bolt size

– Number of bolts

– Bolt material

– Type of loading

– Bolt preload

– Safety factor

– Load/pressure at failure

– Member material

• Note:

– Any of the above can be used as an entry point for

the sizing of a bolted connections

mow227 2014 fasteners 2 - varsity field · • turn the nut not the bolt if possible. ... typical...

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