Chapter 8 - الصفحات الشخصيةsite.iugaza.edu.ps/mhaiba/files/2013/09/CH8-Screws...Chapter 8 Screws, Fasteners, and the Design of Nonpermanent Joints 10/23/2015 1 Mohammad

Chapter 8

Screws, Fasteners, and the Design of Nonpermanent Joints

10/23/2015

Mohammad Suliman Abuhaiba, Ph.D., PE1

Chapter Outline

Mohammad Suliman Abuhaiba, Ph.D., PE

10/23/20152

Thread Standards & Definitions

Mechanics of Power Screws

Threaded Fasteners

Joints—Fastener Stiffness

Joints—Member Stiffness

Bolt Strength

Tension Joints—The External Load

Relating Bolt Torque to Bolt Tension

Statically Loaded Tension Joint with Preload

Gasketed Joints

Fatigue Loading of Tension Joints

Bolted and Riveted Joints Loaded in Shear

Thread Standards and Definitions


Fig. 8–1

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Pitch: distance between adjacentthreads

Major diameter: largest diameter ofthread

Minor diameter: smallest diameter ofthread

Pitch diameter: theoretical diameterbetween major & minor diameters,

where tooth & gap are same width


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Lead l: distance the nut moves parallel toscrew axis in one turn

For a single thread, lead = pitch

In a double-threaded screw, lead =

twice pitch

In a triple-threaded screw, lead = 3

times the pitch


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All threads are RH unless otherwise noted

If the bolt is turned cw, the bolt advances

toward the nut.


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American National (Unified) thread

UN: normal thread

UNR: greater root radius for fatigue

applications

Metric thread

M series: normal thread

MJ series: greater root radius


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Thread Standards and Definitions Coarse series UNC

General assembly & Frequent disassembly

Not good for vibrations

Fine series UNF

Good for vibrations & adjustments

Automotive & aircraft

Extra Fine series UNEF

Good for shock and large vibrations

High grade alloy

Instrumentation & AircraftMohammad Suliman Abuhaiba, Ph.D., PE

10/23/20158


Basic profile for metric M and MJ threads


Fig. 8–2

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Table 8-1: Diameters & Areas for Metric Threads


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Table 8-2: Diameters & Areas for Unified Screw Threads


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Tensile Stress Area

Tensile stress area, At: area of anunthreaded rod with the same tensile

strength as a threaded rod.

Effective area of a threaded rod to be

used for stress calculations.

Diameter of this unthreaded rod:

average of pitch diameter & minor

diameter of the threaded rodMohammad Suliman Abuhaiba, Ph.D., PE

10/23/201512

Unified threads designation

Unified threads are specified by

stating nominal major diameter,

number of threads per inch, and

thread series,

Ex: 5/8 in-18 UNRF or 0.625 in-18 UNRF

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13

Metric threads designation

Metric threads are specified by

writing diameter and pitch in

millimeters

M12 × 1.75: a thread having a

nominal major diameter of 12 mm

and a pitch of 1.75 mm

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14

Square and Acme ThreadsSquare & Acme threads are used when

threads are intended to transmit power


Fig. 8–3

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Square and Acme Threads


Table 8-3: Preferred Pitches for Acme Threads

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Mechanics of

Power Screws

Power screw

Used to change

angular motion into

linear motion

Transmits power

Examples: vises,

presses, jacks, lead

screw on lathe


Fig. 8–4

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Mechanics of Power

Screws Torque to raise or lower a

load

Unroll one turn of a thread

Treat thread as inclined

plane and Do force analysis


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For raising the load


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For lowering the load


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Eliminate N & solve for P to raise & lower the

load


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Divide numerator & denominator by cosl,

knowing tanl = l /p dm


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Raising and Lowering Torque

Torque = Force × mean radius


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If lowering torque is negative, the load will

lower itself by causing the screw to spin

without any external effort.

If the lowering torque is positive, screw is

self-locking

Self-locking Condition


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Self-locking condition: p f dm > l

l / p dm = tan l, the self-locking conditioncan be seen to only involve the coefficient

of friction and the lead angle.

Self-locking Condition


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Power Screw Efficiency

Torque needed to raise the load with no

friction losses can be found from Eq. (8–1)

with f = 0.

Efficiency of the power screw


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Thread angle creates a

wedging action

Friction components are

increased

Torque to raise a load is

found by dividing friction

terms in Eq. (8–1) by cosa:

Power Screws with

Acme Threads


Fig. 8–7

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Collar Friction

Additional component

of torque is often

needed to account for

friction between a

collar & the load.

Assuming load is

concentrated at mean

collar diameter dc


Fig. 8–7

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Stresses in Body of Power Screws

Maximum nominal shear stress in torsion of

the screw body

Axial stress in screw body


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Stresses in Threads of Power Screws

Bearing stress in

threads,

nt = number of

engaged threads


Fig. 8–8

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Stresses in Threads

of Power Screws

Bending stress at root of

thread,


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Stresses in Threads

of Power Screws

Transverse shear stress at

center of root of thread,


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Consider stress element

at top of root “plane”

Obtain von Mises stress

Stresses in Threads

of Power Screws


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Largest stress in threads of a

screw-nut combination

Experiments indicate that:

1st thread carries 38% of load

2nd thread 25%

3rd thread 18%

7th thread is free of load

To find largest stress in 1st thread of a screw-

nut combination, use 0.38F in place of F,

and set nt = 1Mohammad Suliman Abuhaiba, Ph.D., PE

10/23/201534

Example 8-1A square-thread power

screw has a major

diameter of 32 mm and

a pitch of 4 mm with

double threads. The

given data include f = fc

= 0.08, dc = 40 mm, and F

= 6.4 kN per screw.


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Example 8-1Find:

a) Thread depth, thread width, pitch diameter,

minor diameter, and lead

b) Torque required to raise and lower the load

c) Efficiency during lifting the load

d) Body stresses, torsional and compressive

Bearing stress

e) Thread bending stress at the root of thread

f) Von Mises stress at the root of thread

g) maximum shear stress at the root of thread


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Coefficient of friction in screw threads

Ham and Ryan showed that the coefficient

of friction in screw threads is:

independent of axial load

independent of speed

decreases with heavier lubricants

shows little variation with combinations of

materials, and is best for steel on bronze.

Sliding coefficients of friction in power

screws are about 0.10 – 0.15

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37

Power Screw Safe Bearing Pressure

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38

Table 8–4: Screw Bearing Pressure pbSource: H. A. Rothbart and T. H. Brown, Jr., Mechanical Design Handbook, 2nd ed., McGraw-Hill,

New York, 2006.

Power Screw Friction Coefficients

Table 8–5: Coefficients of Friction f for

Threaded Pairs

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39

Source: H. A. Rothbart and T. H. Brown, Jr., Mechanical Design Handbook, 2nd ed., McGraw-Hill,

New York, 2006.

Power Screw Friction Coefficients

Table 8–6: Thrust-Collar Friction Coefficients

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40

Source: H. A. Rothbart and T. H. Brown, Jr., Mechanical Design Handbook, 2nd ed., McGraw-Hill,

New York, 2006.

Hexagon-Head Bolt

Table A–29: Standard dimensions

W ≈1.5 times nominal diameter


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Hexagon-Head BoltThreaded Length


Metric

English

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Hexagon-Head Bolt

Ideal bolt length: one or two threads

project from the nut after it is tightened.

Bolt holes may have burrs or sharp edges

after drilling. These could bite into the fillet

and increase stress concentration.

Therefore, washers must always be used

under the bolt head.


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Hexagon-Head Bolt

Washers should be of hardened steel and

loaded onto the bolt so that the rounded

edge of the stamped hole faces the

washer face of the bolt.

When tightening, if possible, hold the bolt

head stationary and twist the nut; in this

way the bolt shank will not feel the thread-

friction torque.


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Head Type of Bolts

Hexagon head bolt

Usually uses nut

Heavy duty

Hexagon head

cap screw

Thinner head

Often used as

screw (in threaded

hole, without nut)


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Socket head cap screw

Usually more precision applications

Access from the top

Machine screws

Usually smaller sizes

Slot or Philips head common

Threaded all the way

Typical cap-screw heads


Fig. 8–10

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a) Fillister head

b) Flat head

c) Hexagonal

socket head

Machine Screws

Mohammad Suliman Abuhaiba, Ph.D., PEFig. 8–11

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Machine Screws


Fig. 8–11

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Nuts


a) End view

b) Washer-faced, regular

c) Chamfered both sides, regular

d) Washer-faced, jam nut

e) Chamfered both sides, jam nut

Fig. 8–12

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Nuts

Appendix A–31: typical specifications

First three threads of nut carry majority of

load

Localized plastic strain in the first thread is

likely, so nuts should not be re-used in

critical applications.


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Joints—Fastener StiffnessTension Loaded Bolted Joint


Fig. 8–13

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Joints—Fastener StiffnessTension Loaded Bolted Joint

Grip length l includes everything

being compressed by bolt preload,

including washers

Washer under head prevents burrs

at the hole from gouging into the

fillet under the bolt head


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Joints—Fastener StiffnessPressure Vessel Head

Only part of the

threaded length

of the bolt

contributes to

the effective

grip l


Fig. 8–14

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Procedure for

Finding Fastener

Stiffness

Effective Grip Length for

Tapped Holes

Fastener length (round

up using Table A–17)


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Procedure for Finding Fastener Stiffness


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Effective Grip Length for Tapped Holes

l = thickness of all material squeezed between face of

bolt and face of nut

Fastener length

(round up using

Table A–17)

Procedure to Find Bolt Stiffness

Threaded Length, LT


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Procedure to Find Bolt Stiffness


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Bolt Effective Stiffness Axially loaded rod, partly threaded and partly

unthreaded

Consider each portion as a spring

Combine as two springs in series


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Member Stiffness Model compressed members as if they are frusta

spreading from the bolt head and nut to the

midpoint of the grip

Each frustum has a half-apex angle of a

Find stiffness for frustum in compression


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Member Stiffness

Mohammad Suliman Abuhaiba, Ph.D.,

PE

10/23/201560

10/23/201561

Member Stiffness


PE

Member Stiffness

With typical value of a = 30º,

Use Eq. (8–20) to find stiffness for each

frustum

Combine all frusta as springs in series


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Member Stiffness for Common

Material in Grip

If the grip consists of any number of

members all of the same material, two

identical frusta can be added in series.

dw = washer face diameter = 1.5d, and

with a = 30º,


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FEA Approach to Member Stiffness

Figure 8–16


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Exponential curve-fit of finite element results

can be used for case of common material

within the grip


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Table 8–8: Stiffness Parameters of Various

Member MaterialsSource: J. Wileman, M. Choudury, and I. Green, “Computation of Member Stiffness in Bolted

Connections,” Trans. ASME, J. Mech. Design, vol. 113, December 1991, pp. 432–437.

Example 8-2

As shown in Fig. 8–17a, two plates are clamped by

washer-faced ½ in-20 UNF × 11/2 in SAE grade 5 bolts

each with a standard ½ N steel plain washer.

a) Determine the member spring rate km if the top

plate is steel and the bottom plate is gray cast

iron.

b) Using the method of conical frusta, determine the

member spring rate km if both plates are steel.

c) Using Eq. (8–23), determine the member spring

rate km if both plates are steel. Compare the

results with part (b).

d) Determine the bolt spring rate kb.Mohammad Suliman Abuhaiba, Ph.D., PE

10/23/201567

Example 8-2


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Bolt Materials

Proof load: maximum load that a boltcan withstand without acquiring a

permanent set

Proof strength = proof load / At

Corresponds to proportional limit

Typically used for static strength of bolt

Good bolt materials have stress-strain

curve that continues to rise to fracture


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Bolt Materials


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Figure 8–18: Typical stress-strain

diagram for bolt materials showing

proof strength Sp, yield strength Sy,and ultimate tensile strength Sut

Table 8–9: SAE Specifications for Steel Bolts


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Table 8–9: SAE Specifications for Steel Bolts


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Table 8–10: ASTM Specification for Steel Bolts


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Table 8–10: ASTM Specification for Steel Bolts


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Table 8–11: Metric Mechanical-

Property Classes for Steel Bolts


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Table 8–11: Metric Mechanical-

Property Classes for Steel Bolts


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Unified Bolt Specification


Nominal diameter

¼-20 x ¾ in UNC-2 Grade 5 Hex head bolt

Threads per inch

length

Thread series

Class fit

Material grade

Head type

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Metric Bolt Specification


M12 x 1.75 ISO 4.8 Hex head bolt

Metric

Nominal diameter

Pitch

Material class

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Fi = preload

Ptotal = Total external tensile load applied to joint

P = external tensile load per bolt = Ptotal / N

Pb = portion of P taken by bolt

Pm = portion of P taken by members

Fb = Pb + Fi = resultant bolt load

Fm = Pm − Fi = resultant load on members

C = fraction of external load P carried by bolt

1 − C = fraction of external load P carried by

members

N = Number of bolts in the jointMohammad Suliman Abuhaiba, Ph.D., PE


10/23/201579


During bolt preload

bolt is stretched

members in grip are

compressed

When external load P

is applied

Bolt stretches an

additional amount d

Members in grip

uncompress same

amount dMohammad Suliman Abuhaiba, Ph.D., PE

Fig. 8–13

10/23/201580

P = Pb + Pm

The stiffness constant of the joint C:

C indicates proportion of external load P that the

bolt will carry

A good design target is around 0.2


10/23/201581


The resultant bolt load is

The resultant load on the members is

These results are only valid if the load onthe members remains negative, indicatingthe members stay in compression.


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10/23/201583


Table 8–12: Computation of Bolt and Member

Stiffnesses. Steel members clamped using a ½

in-13 NC steel bolt.


Best way to measure bolt preload is by

relating measured bolt elongation and

calculated stiffness

measuring bolt elongation is not practical

Measuring applied torque by a torque

wrench

Find relation between applied torque and

bolt preload


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Power screw equations, Eqs. 8–5 & 8–6, we

get

tanl = l/pdm,

Collar diameter: dc = (d + 1.5d)/2 = 1.25d


PE

10/23/201585


Define term in brackets as torque coefficient K


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Table 8–15: recommended Torque factors

K for use with Eq. (8-27)

K = 0.2 when bolt condition is not stated


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Table 8–13: Distribution of Preload Fi for 20Tests of Un-lubricated Bolts Torqued to 90

N.m

Mean value = 34.3 kN

Standard deviation = 4.91KN


10/23/201588


Table 8–14: Distribution of Preload Fi for 10Tests of Lubricated Bolts Torqued to 90 N.m

Mean value = 34.18 kN (un-lubricated 34.3 kN)

Standard deviation = 2.88 kN (un-lubricated 4.91

kN)

Lubrication made little change to average preload

vs torque

Lubrication significantly reduces the standard

deviation of preload vs torque


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Example 8-3


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Axial Stress:

Yielding Factor of Safety:

Load Factor:

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Joint Separation Factor of safety:

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Safe joint: External load be smaller than that needed to

cause the joint to separate

If separation does occur, the entire external load will be

imposed on the bolt.

P0 = value of the external load that would cause joint

separation.

At separation, Fm = 0 in Eq. (8–25):

Statically Loaded Tension Joint with

Preload - Recommended Preload


10/23/201593

For other materials, an approximate value is

Sp = 0.85Sy

Example 8-4

Figure 8–19 is a cross section of a grade 25

cast-iron pressure vessel. A total of N bolts are

to be used to resist a separating force of 36

kip.

a) Determine kb, km, and C.

b) Find the number of bolts required for a load factor

of 2 where the bolts may be reused when the joint

is taken apart.

c) With the number of bolts obtained in part (b),

determine the realized load factor for overload,

the yielding factor of safety, and the load factor

for joint separation.Mohammad Suliman Abuhaiba, Ph.D., PE

10/23/201594

Example 8-4


Fig. 8–19

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Gasketed Joints

For a full gasket compressed between

members of a bolted joint, the gasket

pressure p is found by dividing the force in

the member by the gasket area per bolt.

The force in the member, including a load

factor n,


10/23/201596

Gasketed JointsThus the gasket pressure is

To maintain adequate uniformity of

pressure, adjacent bolts should not be

placed more than six nominal diametersapart on the bolt circle.

For wrench clearance, bolts should be at

least three diameters apart


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Distribution of typical bolt failures:

15% under the head

20% at the end of the thread

65% in the thread at the nut face


10/23/201598


Table 8–16: Fatigue stress-concentration

factors for threads and fillet


10/23/201599

Endurance Strength for BoltsTable 8–17: Fully Corrected Endurance

Strengths for Bolts and Screws with Rolled

Threads*


10/23/2015100

Endurance Strength for Bolts

Fatigue stress-concentration factor Kf isincluded as a reducer of the endurance

strength

So it should not be applied to bolt stresses


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Fatigue Stresses

With an external load on a per bolt basis fluctuating

between Pmin and Pmax,


10/23/2015102

Typical Fatigue Load Line for BoltsFigure 8–20: Designer’s fatigue diagram

showing a Goodman failure line and a load line

for a constant preload and a fluctuating load.


10/23/2015103

Typical Fatigue Load Line for Bolts

Equation of load line:

Equation of Goodman line:

Solving (a) and (b) for intersection point,


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Fatigue Factor of Safety

Fatigue factor of safety based on

Goodman line and constant preload load

line,


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Repeated Load Special Case

External load fluctuates between 0 and Pmax

Setting Pmin = 0 in Eqs. (8-35) and (8-36),

With constant preload load line,

Load line has slope of unity for repeated load

caseMohammad Suliman Abuhaiba, Ph.D., PE

10/23/2015106



Load line:

Goodman:

Gerber:

ASME-elliptic:

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Goodman:

Gerber:

ASME-elliptic:

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Further Reductions for Goodman

For convenience, sa & si can besubstituted into any of the fatigue factor of

safety equations.

For Goodman criteria in Eq. (8–45),

If there is no preload, C = 1 and Fi = 0,

resulting in


10/23/2015109

Further Reductions for Goodman

Preload is beneficial for resisting fatigue

when nf / nf0 is greater than unity. This puts

an upper bound on the preload,


10/23/2015110

Yield Check with Fatigue Stresses


10/23/2015111

Example 8-5Figure 8–21 shows a connection using cap

screws. The joint is subjected to a fluctuating

force whose maximum value is 5 kip per

screw. The required data are: cap screw, 5/8

in-11 NC, SAE 5; hardened-steel washer, tw =

1 /16 in thick; steel cover plate, t1 = 5/8 in, Es

= 30 Mpsi; and cast-iron base, t2 = 5/8 in, Eci =

16 Mpsi.

a) Find kb, km, and C using the assumptions

given in the caption of Fig. 8–21.

b) Find all factors of safetyMohammad Suliman Abuhaiba, Ph.D., PE

10/23/2015112

Example 8-5


10/23/2015113

Bolted and Riveted Joints

Loaded in ShearPossible Failure

modes:

(a) Joint loaded

in shear

(b) Bending of

bolt or

members

(c) Shear of bolt

(d) Tensile failure

of members


Fig. 8–23

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Bolted and Riveted Joints

Loaded in ShearPossible failure

modes

e) Bearing stress

on bolt or

members

f) Shear tear-

out

g) Tensile tear-

outMohammad Suliman Abuhaiba, Ph.D., PE

10/23/2015115

Fig. 8–23

Failure by Bending

Bending moment is approximately M = Ft /2, where t is the grip length

I/c is for the weakest member or for the

bolt(s)


10/23/2015116

Failure by Shear of Bolt Simple direct shear

Use total cross sectional area of

bolts that are carrying the load.

For bolts, determine whether the

shear is across the nominal area or

across threaded area. Use area

based on nominal diameter or

minor diameter, as appropriate.Mohammad Suliman Abuhaiba, Ph.D., PE

10/23/2015117

Failure by Tensile Rupture of Member

Simple tensile failure

Use smallest net area of the

member, with holes removed


10/23/2015118

Failure by Bearing or crushing Stress

Bolt or member with lowest

strength will crush first

Assume uniform stress distribution

over projected contact area, A =

td

t = thickness of thinnest plate

d = bolt diameter


10/23/2015119

Failure by Shear-out or Tear-out

Edge shear-out or tear-out is avoided by

spacing bolts at least 1.5 diameters away

from the edge


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Example 8-6

Two 1- by 4-in 1018 cold-rolled steel bars

are butt-spliced with two ½ - by 4-in 1018

cold-rolled splice plates using four ¾ in-16

UNF grade 5 bolts as depicted in Fig. 8–24.

For a design factor of nd = 1.5 estimate the

static load F that can be carried if the bolts

lose preload.


10/23/2015121

Example 8-6


Fig. 8–24

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Shear Joints with Eccentric Loading

The load does not pass along a line of

symmetry of the fasteners.

Find moment about centroid of bolt

pattern

Centroid location


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Shear Joints with

Eccentric

Loading


Fig. 8–27

10/23/2015124

Shear Joints with

Eccentric Loading

Primary Shear

Secondary Shear, due to

moment load around

centroid


10/23/2015125

Shear Joints with

Eccentric Loading

Force taken by each bolt

depends upon its radial

distance from the centroid

Bolt farthest from the centroid

takes the greatest load

Nearest bolt takes the

smallest


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Example 8-7Shown in Fig. 8–28 is a 15- by 200-mm

rectangular steel bar cantilevered to a 250-

mm steel channel using four tightly fitted

bolts located at A, B, C, and D. For F = 16 kN

load, find:

a) The resultant load on each bolt

b) The maximum shear stress in each bolt

c) The maximum bearing stress

d) The critical bending stress in the barMohammad Suliman Abuhaiba, Ph.D., PE

10/23/2015127

Example 8-7


Fig. 8–28

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Example 8-7


Fig. 8–29

10/23/2015129

Documents

Chapter 8 - الصفحات الشخصيةsite.iugaza.edu.ps/mhaiba/files/2013/09/CH8-Screws...Chapter 8 Screws, Fasteners, and the Design of Nonpermanent Joints 10/23/2015 1 Mohammad