Chapter 4 Design of Nonpermanent Joints 4.0 Introduction4.1 Thread Standards and Definitions4.2 The Mechanics of Power Screws  4.2.1 Force Analysis for Trapezoidal Threads  4.2.2 Collar Friction4.3 Threaded Fastener4.4 Joints – Fastener Stiffness 4.5 Joints – Member Stiffness4.6 Bolt Strength4.7 Tension Joints – The External Load4.8 Relating Bolt Torque to Bolt Tension4.9 Statically Loaded Tension Joint – Preload4.10 Shear Joints

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Introduction

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Tensioning the fastener by turning the nut differentiates a bolt from a screw, which is tightened by turning its head.

Bolts are generally manufactured from metals, but bolts made of other materials, such as nylon, also commercially available.

The properties of some bolting metals are modified by heat treatment and other means to increase yield strength.

Bolt heads have various shapes to suit different applications

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Thread Standards and Definitions

4/ 32Terminology of screw threads.

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Pitch, p The distance between adjacent thread forms measured parallel to the thread axis. The pitch in U.S. units is the reciprocal of the number of thread forms per inch N. Major

diameter, dThe largest diameter of a screw thread. 

minor diameter, dr or dl

The smallest diameter of a screw thread. 

Lead, l The distance the nut moves parallel to the screw axis when the nut is given one turn. For a single thread, as in Figure, the lead is the same as the pitch.

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Basic thread profile for metric M and MJ threads.

D(d)=basic major diameter

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d dr

pP/2

P/2

pP/2

P/2

d dr

29

(a) Square Thread (b) Acme thread

•Metric threads are specified by writing the diameter and pitch in millimetres, in that order. •Thus, M12 x 1.75 is a thread having a nominal major diameter of 12 mm and a pitch of 1.75 mm. •Note that the letter M, which precedes the diameter, is the clue to the metric designation.

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The Joyce worm-gear screw jack

The Mechanics of Power Screws a square-threaded power screw with single

thread having a mean diameter dm, a pitch p, a lead angle , and a helix angle is loaded by the axial compressive force F.

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For lifting the load

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dm

l

N

W

N P

0cossin NNPFH

0cossin NNWFV

For lowering the load

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dm

l

N

W

NP

0cossin NNPFH

0cossin NNWFV

Therefore, torque required to raise the load as equation 8-1

Therefore, torque required to lower the load as equation 8-2

Efficiency of power screw as equation 8-4

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o T

Fle

2

fld

fdlFdT

m

mmR

2

fld

lfdFdT

m

mmL

2

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• When screw is loaded axially, a thrust or collar bearing must be employed between the rotating and stationary members in order to carry the axial component. Figure above is a typical thrust collar which the load is to be concentrated.

• Where dc = mean collar diameter

• And fc = coefficient of collar friction

2cc

c

dFfT

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EXAMPLE:

A bolted joint is to have a grip consisting of two 14-mm steel plates and one 14R metric plain washer to fit under the head of the M14 2 hex-head bolt, 50 mm long.

(a) What is the length of the thread LT for this diameter metric course-pitch series bolt?

(b) What is the length of the grip LG?

(c) What is the height H of the nut?

(d) Is the bolt long enough? If not, round to the next larger preferred length (Table A-17).

(e) What is the length of the shank and threaded portions of the bolt within the grip? These lengths are needed in order to estimate the bolt spring rate kb.

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SOLUTION:

(a) LT = 2D + 6 = 2(14) + 6 = 34 mm Ans.

(b) From Table A-33, the maximum washer thickness is 3.5 mm. Thus, the grip is,

LG = 14 + 14 + 3.5 = 31.5 mm Ans.

(c) From Table A-31, H = 12.8 mm

(d) LG + H = 31.5 + 12.8 = 44.3 mm

This would be rounded to L = 50 mm.

The bolt is long enough. Ans.

(e) ld = L - LT = 50 - 34 = 16 mm Ans.

lt = LG - ld = 31.5 - 16 = 15.5 mm Ans.

These lengths are needed to estimate the bolt spring rate kb.

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Work out the Example 8-1 (page 405)

Threaded Fasteners

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•The threaded length of inch-series bolt (8-13)

•For metric bolt (8-14)

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Joints – Fastener Stiffness

21/ 32dttd

tdb lAlA

EAAk

Joints – Member Stiffness

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))(tan(

))(tan(ln2

tan

ddddl

ddddlEd

k

ww

wwm

)/exp( lBdAEd

km

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Bolt Strength

Read at Home (RAH) **page 417 - 421

Tension Joints – The External Load

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iimb

bibb FCPF

kk

PkFPF

Resultant bolt load

Resultant load on the connected members

iimb

mimm FPCF

kk

PkFPF

)1(

Relating Bolt Torque to Bolt Tension

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Statically Loaded Tension Joint – Preload

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ptp SAF

Shear Joints Joints can and should be loaded in shear so that the

fasteners see no additional stress beyond the initial tightening.

The shear loading is resisted in two principal ways:The shear load is carried by friction between the

members and ensured by the clamping action of the bolts or cap screws. Should the friction be insufficient, the shear load is carried by only two of the fasteners in the pattern. This occurs because errors in hole size and placement preclude a uniform sharing of the shear load. The analysis problem involves identifying the two fasteners that represent the worst case.

The shear load is carried by dowel pins in reamed holes, placed in both parts while clamped together to ensure alignment. The dowels will carry the shear load. Pins are often tapered to allow firm setting and easy removal if necessary.

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n

i

n

ii

A

xAx

1

1

n

i

n

ii

A

yAy

1

1

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Centroid of pins, rivets or bolts

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........222''

CBA

nn rrr

MrF

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Work out the Example 8-7 (page 441)

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The path to our destination is not always a straight one. We go down the wrong road, we get lost, we turn back. Maybe it doesn't matter which road we embark on. Maybe what matters is that we embark. Barbara Hall, Northern Exposure, Rosebud, 1993  

The chief obstacle to the progressof the human race is the human race. Don Marquis (1878 - 1937)

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EXERCISE:

A double-threaded power screw, with ISO metric trapezoidal threads, is used to raise a load of 300 kN. The nominal diameter is 100 mm and the pitch is 12 mm. The coefficient of friction at screw threads is 0.5. Neglecting collar friction, calculate:

i) Torque require to raise the load;ii) Torque required to lower the load, and iii) Efficiency of the screw.

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~ END ~THANK YOU FOR YOUR

KIND ATTENTION.