Strength calculation and Dimension of Joints.pptx

by
NIGUSSIE ADEM
November
21, 2022
CHAPTER THREE
Strength Calculation and
Dimensioning of Joints

Welded
Joints
Riveted
Joints
Power
Screws
Bolt
Materials
and
Strength
Bolted
Connections
CONTENTS
NIGUSSIE ADEM, DEPT. OF MANUF. TECH., 2

3
NIGUSSIE ADEM DEPT. OF MANF. TECH.
Introduction
 The helical-thread screw was undoubtedly an extremely
important mechanical invention. It is a basis of power screws
which change angular motion to linear motion to transmit
power or to develop large forces (presses, jacks, etc.), and
threaded fasteners, an important element in nonpermanent
joints.
 A fastener is any device used to connect or join two or more
components. Literally hundreds of fastener types and
variations are available. The most common are threaded
fasteners referred to by many names, among them bolts,
screws, nuts, studs, lag screws, and set screws.

4
Introduction cont…
 Typical methods of fastening or joining parts use such devices
as bolts, nuts, cap screws, setscrews, rivets, spring retainers,
locking devices, pins, keys, welds, and adhesives.
 A bolt is a threaded fastener designed to pass through holes in the
mating members and to be secured by tightening a nut from the
end opposite the head of the bolt.

5
Introduction cont…
 A screw is a threaded fastener designed to be inserted through
a hole in one member to be joined and into a threaded hole in
the mating member.
 Machine screws, also called cap screws, are precision fasteners
with straight-threaded bodies that are turned into tapped holes.
 A popular type of machine screw is the socket head cap screw.

6
Bolt Materials and Strength
 Most fasteners are made from steel because of its high
strength, high stiffness, good ductility, and good
machinability and formability.
 Three strength ratings are frequently available: the familiar tensile
strength and yield strength plus the proof strength.
 Proof strength, similar to the elastic limit, is defined as the stress
at which the bolt or the screw would undergo permanent
deformation.
 It usually ranges between 0.90 and 0.95 times the yield strength.

7
Bolt Materials and Strength cont…
 Aluminum is used for its corrosion resistance, light weight,
and fair strength level.
 Brass, copper, and bronze are also used for their corrosion
resistance. Ease of machining and an attractive appearance are
also advantageous.
 Nickel and its alloys, such as Monel and Inconel (from the
International Nickel Company), provide good performance at
elevated temperatures while also having good corrosion
resistance, toughness at low temperatures, and an attractive
appearance.
 Stainless steels are used primarily for their corrosion resistance

8
Thread Standards and Deﬁnitions

9
Thread Standards and Deﬁnitions cont…
 Pitch:
The pitch is defined as the distance measured parallel to the axis of the screw
from a point on one thread to the corresponding point on the adjacent
thread.
It is denoted by the letter p.
 Lead:
It is defined as the distance measured parallel to the axis of the screw which
the nut will advance in one revolution of the screw.
It is denoted by the letter l.
For a single-threaded screw, the lead is same as the pitch. For double-
threaded screw, the lead is twice of the pitch, and so on.

10
 Nominal Diameter(Major diameter):
Nominal diameter is the largest diameter of the screw. It is also called major diameter.
It is denoted by the letter d.
 Core Diameter (minor diameter):
The core diameter is the smallest diameter of the screw thread. It is also called minor
diameter.
It is denoted by the letter dr.
 Helix Angle:
The helix angle is defined as the angle made by the helix of the thread with a plane
perpendicular to the axis of the screw. It is also called lead angle.
It is denoted by α.

11
 There are different types of thread standards.
 The American National (Unified) thread standard has been approved in many
countries for use on all standard threaded products. The thread angle is 600 and
the crests of the thread may be either flat or rounded.

12
 The M profile replaces the inch class and is the basic ISO 68 profile with 60°
symmetric threads.
 The MJ profile has a rounded fillet at the root of the external thread and a
larger minor diameter of both the internal and external threads. This profile is
especially useful where high fatigue strength is required.
 Two major Unified thread series are in common use: UN and UNR. The
difference between these is simply that a root radius must be used in the UNR
series.
 Unified threads are specified by stating the nominal major diameter, the
number of threads per inch, and the thread series, for example, 5/8 in-18
UNRF or 0.625 in-18 UNRF.

13
 Metric threads are specified by writing the diameter and pitch in millimeters,
in that order. Thus, M12 × 1.75 is a thread having a nominal major diameter of
12 mm and a pitch of 1.75 mm.
 M stands for metric.

14
Stress Area
 The stress area is the effective cross-sectional area of the bolt that resists bolt
fracture.

15
Threaded Fasteners cont…
 The thread length of inch-series bolts, where d is the nominal diameter, is
and for metric bolts is
where the dimensions are in millimeters.

16
Fastener Stiffness
 The purpose of the bolt is to clamp the two, or more, parts together. Twisting
the nut stretches the bolt to produce the clamping force. This clamping force
is called the pretension or bolt preload.
 The grip 𝑙 of a connection is the total thickness of the clamped material. In
the above figure, the grip is the sum of the thicknesses of both members and
both washers.

17
Fastener Stiffness cont…
 The stiffness of the portion of a bolt or screw within the clamped zone will
generally consist of two parts, that of the unthreaded shank portion and that
of the threaded portion.
 The spring rates of the threaded and unthreaded portions of the bolt in the
clamped zone are

18
Fastener Stiffness cont…
 Therefore, the estimated effective stiffness of the bolt or cap screw in the
clamped zone is

19
Suggested Procedure for Finding Fastener Stiffness

20
Suggested Procedure for Finding Fastener Stiffness

21
Stiffness of the Clamped Parts (Member stiffness)
The clamped parts may consist of a combination of different materials.
Hence, the total spring rate of the members is:
Shigley and Mischke proposed the following expression for the joint
stiffness:

22
Stiffness of the Clamped Parts (Member stiffness)
Wileman et al. obtained an exponential expression using finite element
analysis:

23
Tension Joints—The External Load
Preload 𝐹𝑖 , has been correctly applied by tightening the nut before P is
applied.
𝑃𝑡𝑜𝑡𝑎𝑙 = Total external tensile load applied to the joint

24
Tension Joints—The External Load cont…
The load P is tension, and it causes the connection to stretch, or elongate, through some
distance δ.

25
Tension Joints—The External Load cont…

26

27
Power Screws
 A power screw is a mechanical device used for converting rotary motion
into linear motion and transmitting power. Its also called as translation
screw.
 Power screw has three essential parts screw ,nut and part to hold either the
screw or the nut in its place.
 Depending upon the holding arrangement power screw operate in two
different ways. In first case the screw rotates in its bearing, while the nut has
axial motion eg. Lead screw. In second case the nut is kept stationary and
the screw moves in axial direction eg. Screw jack, machine vice.

28
Power Screws cont…
 The main applications of power screws are as follows:
i. To raise the load, e.g., screw-jack;
ii. To obtain accurate motion in machining operations, e.g., lead-screw of
lathe;
iii. To clamp a work piece, e.g., a vice; and
iv. To load a specimen, e.g., universal testing machine.

29
Force analysis of square thread:
From fig.
And , dm is the mean diameter of the screw.
It is given by,

30
Force analysis of square thread cont…
Considering the right angle triangle, the relationship between the helix
angle, mean diameter and lead can be expressed in the following form:
30

31
𝟏.Lifting load:
The screw is considered as an inclined plane with inclination α as
shown in fig.
Forces act at a point on inclined plane
• Load F
• Normal reaction N
• Frictional force µN
• Effort 𝑃𝑅
𝑃𝑅
N
µN
F
l
π𝑑𝑚
𝐹𝑜𝑟𝑐𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚 𝑓𝑜𝑟 𝑙𝑖𝑓𝑡𝑖𝑛𝑔 𝑙𝑜𝑎𝑑
α

32
𝑃𝑅 =
𝐹(𝜇 cos 𝛼 +sin 𝛼)
(cos 𝛼 − 𝜇 sin 𝛼)
Dividing right hand side by cos α
𝑃𝑅 =
𝐹( µ + tan α )
(1 − µ tan α )
(c)
µ = 𝑐𝑜𝑒𝑓𝑓𝑖𝑒𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑓𝑟𝑖𝑐𝑡𝑖𝑜n

33
33
Substituting tan 𝛼 =
𝑙
𝜋𝑑𝑚
in to equation (C)
𝑃𝑅 =
𝐹(µ +
𝑙
𝜋𝑑𝑚
)
( 1 −
µ𝑙
𝜋𝑑𝑚
)
or
𝑃𝑅 =
𝐹 µ𝜋𝑑𝑚 + 𝑙
𝜋𝑑𝑚 − µ𝑙
The torque required to raise the load is given by
𝑇𝑅 = 𝑃𝑅
𝑑𝑚
2
𝑇𝑅 = 𝐹
𝑑𝑚
2
(
µ𝜋𝑑𝑚 + 𝑙
𝜋𝑑𝑚 − µ𝑙
)

34
34
34
𝟐.Lowering load:
The forces acting at a point on the inclined plane as shown in
fig.
µN
N
𝑃𝐿
F
l
π𝑑𝑚
𝐹𝑜𝑟𝑐𝑒 𝑑𝑖𝑎𝑔𝑟𝑎𝑚 𝑓𝑜𝑟 𝑙𝑜𝑤𝑒𝑟𝑖𝑛𝑔 𝑙𝑜𝑎𝑑
α
Considering the equilibrium of horizontal & vertical forces
𝑃𝐿 = µ𝑁 cos α − 𝑁 sin α (a)
𝐹 = 𝑁 cos α + µ𝑁 sin α (b)

35
Dividing (a) by (b)
𝑃𝐿 =
𝐹(𝜇 cos 𝛼 − sin 𝛼)
(cos 𝛼 + 𝜇 sin 𝛼)
Dividing right hand side by cos α
𝑃𝐿=
𝐹( µ − tan α )
(1+ µ tan α )
(c)
Substituting tan 𝛼 =
𝑙
𝜋𝑑𝑚
in to equation (C)
𝑃𝐿 =
𝐹(µ −
𝑙
𝜋𝑑𝑚
)
( 1 +
µ𝑙
𝜋𝑑𝑚
)
or
𝑃𝐿 =
𝐹 µ𝜋𝑑𝑚 − 𝑙
µ𝑙 + 𝜋𝑑𝑚

36
 The torque required to lower the load is:
𝑇𝐿 = 𝑃𝐿
𝑑𝑚
2
𝑇𝐿 = 𝐹
𝑑𝑚
2
(
µ𝜋𝑑𝑚 − 𝑙
µ𝜋𝑑𝑚 + 𝑙
)

37
Self-locking Screw
 When a positive lowering torque is obtained, the screw is said to be self-
locking. Thus the condition for self-locking is
µ𝜋𝑑𝑚 > 𝑙
Dividing both sides of the equation by 𝜋𝑑𝑚
µ > tan 𝛼
 This relation states that self-locking is obtained whenever the coefﬁcient of
thread friction is equal to or greater than the tangent of the thread lead angle.
 A self-locking screw will hold the load in place without a brake.
 This property is used in screw jack application.

38
Collar Torque
 When the 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.
 If 𝑓𝑐 is the coefﬁcient of collar friction, the
torque required is

39
Efficiency
 An expression for efﬁciency is also useful in the evaluation of power screws. If we let
μ = 0 in Eq. (8–1), we obtain
𝑇0 =
𝐹𝑙
2𝜋
which, since thread friction has been eliminated, is the torque required only to raise the
load. The efﬁciency is therefore
𝜂0 =
𝑊𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡
𝑊𝑜𝑟𝑘 𝑖𝑛𝑝𝑢𝑡
=
𝑇0
𝑇𝑅
=
𝐹𝑙
2𝜋𝑇𝑅
39

40
Stresses in screw
40
The body of the screw is subjected to an axial
force F and torsional moment 𝑇as shown in
fig.
The direct compressive stress σ𝑐
σ𝑐 =
𝐹
(
π
4
𝑑𝑟
2
)
The torsional shear stres
τ =
16 𝑇
π𝑑𝑟
3
The principal shear stress
τ𝑚𝑎𝑥 = (
σ𝑟
2
)2+τ2

41
 The transverse shear stress τ𝑡 at the center of the root of the
thread due to load F is
τ𝑡 =
3𝑉
2𝐴
=
3𝐹
2π 𝑑𝑟 𝑧(
𝑝
2
)
=
3𝐹
π 𝑑𝑟 𝑧𝑝
τ𝑡= transverse shear stress at the root of the screw (𝑁 𝑚𝑚2
)
𝑝 = thread thickness at the core diameter (mm)
z = number of threads in engagement with the nut.
 The bending stress at the root of the thread 𝜎𝑏 is found from:
𝜎𝑏 =
𝑀𝑐
𝐼
=
𝐹𝑝
4
∗ (
𝑝
4
)
1
12
∗ 𝜋 ∗ 𝑑𝑟 ∗ 𝑧 ∗ (
𝑝
2
)3
=
6𝐹
𝜋 ∗ 𝑑𝑟 ∗ 𝑝 ∗ 𝑧

42
42
 The bearing stress is
𝜎𝑏𝑒𝑎𝑟𝑖𝑛𝑔 = −
𝐹
𝜋𝑑𝑚𝑧
𝑝
2
= −
2𝐹
𝜋𝑑𝑚𝑧𝑝

43
43

44
44

45
Riveted Joints
 A Rivet is a short cylindrical rod having a head and a tapered tail. The main body of the
rivet is called shank.
 Riveting is an operation whereby two plates are joined with the help of a rivet.

46
Riveted Joints cont…
 Steps of riveting joints
1. Smooth holes are drilled (or punched and reamed) in two plates to be joined and the
rivet is inserted.
2. Holding the head by means of a backing up bar as shown in figure below, necessary
force is applied at the tail end with a die until the tail deforms plastically to the required
shape.
 Depending upon whether the rivet is initially heated or not, the riveting operation can be of
two types:
A. Cold riveting is done at ambient temperature and
B. Hot riveting rivets are initially heated before applying force

47
Types of Riveted Joints
 Riveted joints are mainly of two types.
 1. Lap Joints: the plates that are to be joined are brought face to face such
that an overlap exists. Rivets are inserted on the overlapping portion.

48
Types of Riveted Joints cont…
 2. Butt Joints: in this type of joint, the plates are brought to each other
without forming any overlap. Riveted joints are formed between each of the
plates and one or two cover plates.

49
Modes of failure of rivet joints
 1. Tearing of the plate at the edge: occurs due to insufficient margin. This
type of failure can be avoided by keeping margin, m = 1.5d, where d is the
diameter of the rivet.
 2. Tearing of the plate across a row of rivets: the main plate or cover plates may
tear-off across a row of rivets.

50
Modes of failure of rivet joints cont…
 3. Shearing of rivets: Rivets are in single shear in lap joints and in double
shear in double strap butt joints.

51
Modes of failure of rivet joints cont…
 4. Crushing of rivets (plates): When the joint is loaded, compressive stress is
induced over the contact area between rivet and the plate.

52
Welded Joints
 Welding can be deﬁned as a process of joining metallic parts by heating to a
suitable temperature with or without the application of pressure.
 Welding is an economical and efﬁcient method for obtaining a permanent joint
of metallic parts.
 The strength of welded joint is high. Very often, the strength of the weld is
more than the strength of the plates that are joined together.

53
Types of Welded Joints
 Welded joints are divided into two groups—butt joints and ﬁllet joints.
1. Butt Joint: butt joint can be deﬁned as a joint between two components lying
approximately in the same plane. A butt joint connects the ends of the two plates.

54
Types of Welded Joints
 Welded joints are divided into two groups—butt joints and fillet joints.
2. FILLET JOINTS:A fillet joint, also called a lap joint, is a joint between two
overlapping plates or components. A fillet weld consists of an approximately
triangular cross-section joining two surfaces at right angles to each other.
There are two types of fillet joints— transverse and parallel.

55
STRENGTH OF BUTT WELDS
A butt welded joint, subjected to tensile force P, is shown below. The average
tensile stress in the weld is given by,

56
STRENGTH OF PARALLEL FILLET WELDS
The shear stress in the ﬁllet weld is given by,

57
STRENGTH OF TRANSVERSE FILLET WELDS
The minimum cross section of the weld is at the throat. The tensile stress in the
transverse ﬁllet weld is given by,
Usually, there are two welds of equal length on two sides of the plate as shown
in the above figure. In such cases,

58
Example: A plate, 75 mm wide and 10 mm thick, is joined with
another steel plate by means of single transverse and double parallel
ﬁllet welds, as shown in Fig. 8.11. The joint is subjected to a
maximum tensile force of 55 kN. The permissible tensile and shear
stresses in the weld material are 70 and 50
𝑁
𝑚𝑚2 respectively.
Determine the required length of each parallel ﬁllet weld.

59

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