Mechanical Fasteners Tensile and Shear Stress Areas

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Mechanical Fasteners

–

Tensile and Shear Stress Areas

Lecture 28

Engineering 473

Machine Design

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Threaded Fasteners

Bolt

Bolt – Threaded fastener designed to

pass through holes in mating members and to be secured by tightening a nut from the end opposite the head of the bolt.

Screw

Screw – Threaded fastener designed to

be inserted through a hole in one

member and into a threaded hole in a mating member.

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Bolts

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Machine Screws

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Sheet Metal and

Lag Screws

Sheet metal screws are often self-tapping.

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Set Screws

Set screws are used to develop a normal force between two objects (e.g. collar and shaft).

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Thread Standards

(Inch Series) (Inch Series) American Standard B1.1 American Standard B1.1--19491949

First American standard to cover the Unified Thread Series agreed upon by the United Kingdom, Canada, and the United States. Represents the basic American standard for fastener threads. Threads made to this standard are called “unified threads”.

ANSI B1.1

ANSI B1.1--1989/ASME B1.11989/ASME B1.1--19891989

Revised standard that still incorporates much of the original standard.

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Thread Standards

(Metric Series) (Metric Series) ANSI B1.13M ANSI B1.13M--1983 (R1989)1983 (R1989)

Contains system of metric threads for general

fastening purposes in mechanisms and structures. Fasteners made to this standard are often referred to as M-series.

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Thread Profiles

The pitch line or diameter is located at ½ the height of the theoretical sharp v-thread profile.

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Thread Series

Unified Coarse

Unified Coarse--Thread Series (UNC or UNRC)Thread Series (UNC or UNRC) Thread Series

Thread Series – groups of diameter-pitch combinations

distinguished from each other by the number of threads per inch applied to a specific diameter.

Most commonly used in the bulk production of bolts, screws, nuts for general engineering applications.

Unified Fine

Unified Fine--Thread Series (UNF or UNRF)Thread Series (UNF or UNRF) Use when more threads per inch are required (i.e. where are short length of engagement is available).

M

M--SeriesSeries

Metric system of diameters, pitches, and tolerance/allowances.

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Thread Classes

Thread Classes

Thread Classes – Define the amount of tolerance

and allowance associated with a particular thread. Classes 1A, 2A, 3A

Classes 1A, 2A, 3A – apply to external threads.

Class 2A is the most commonly used. Classes 1B, 2B, 3B

Classes 1B, 2B, 3B – apply to internal

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Thread Designations

(Inch Series) (Inch Series)

2A

20UNC

4

1

−

Nominal Size

Threads per inch

Thread Series

Thread Class

External Thread The following is an example of the standard method used to designate bolt and screw thread requirements on a drawing or in a specification.

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Thread Designations

(Metric Series) (Metric Series)

4g6g(22)

M6x1

−

The following is an example of the standard method used to designate bolt and screw thread requirements on a drawing or in a specification.

Metric Series

Nominal Diameter Pitch (mm)

Tolerance Classification

Lowercase=> external thread

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Material and Strength

Designations

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Designations

(Continued)

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Designations

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Tensile Stress Area

The average axial stress in a fastener is computed using a “tensile stress area”.

2 p r t

2

D

4

π

A

ú

û

ù

ê

ë

é

+

=

t ave

A

F

σ

=

stress axial Average σ Area Stress Tensile A Diameter Pitch D Diameter Root D Force Axial F ave t p r ≡ ≡ ≡ ≡ ≡

Tests of threaded rods have shown that an unthreaded rod having a

diameter equal to the mean of the pitch diameter and the minor diameter will have the same tensile strength as the threaded rod.

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Tensile Stress Area

(Continued) (Continued)

( )

° ⋅ = ÷ ø ö ç è æ ₊ − = 60 tan 2n 1 H H 16 3 H 8 3 2 d D_t _b threads/in p 1 n thread of height l theoretica H bolt of diameter d plane critical at diameter D b t = ≡ ≡ ≡ ≡

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Tensile Stress Area

( )

n 16 3 9 d D 16 3 8 3 n 60 tan d D 60 tan 2n 1 H H 16 3 H 8 3 2 d D b t b t b t − = ÷ ø ö ç è æ ₊ ° − = ° ⋅ = ÷ ø ö ç è æ ₊ − = 2 b t 2 t t n 0.9743 d 4 π A D 4 π A ÷ ø ö ç è æ ₋ = ⋅ =

This is the formula used by manufacturers of inch series fasteners to publish the tensile area in their catalogs.

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Tensile Stress Area

(Continued) (Continued) 2 b t

n

0.9328

d

4

π

A

÷

ø

ö

ç

è

æ

−

=

The following formula may be obtained in a similar manner for metric series threads.

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Shear Area of External

Thread

Consideration of the interaction between mating threads must be considered to establish the shear area of an external thread.

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Shear Area of External Threads

( )

gap 0.75H 0.5t 30 tan n t K π A e e max n, e s, − = ° ⋅ ⋅ ⋅ = inch per threads n plane shear critical at thread external of thickness t thread internal of diameter minor maximum K thread external of area shear A e max n, e s, ≡ ≡ ≡ ≡

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Threads

( )

÷÷ø ö ççè æ − ° ⋅ = = ° = − = ° ⋅ ⋅ ⋅ = gap 2n 3 0.75 30 tan 2 t 2n 3 60 tan 2n 1 H gap 0.75H 0.5t 30 tan n t K π A e e e max n, s,e

(

s,min n,max

)

e min s, max n, e min s, max n, K E 3 1 2n 1 t E 2n 3 2 1 K 2 1 2n 3 4 3 3 1 2 t E 2n 3 2 1 K 2 1 gap − + = ú ú û ù ê ê ë é ÷÷ø ö ççè æ − + − ⋅ = ÷÷ø ö ççè æ − + =

The gap equation is based on tolerance data.

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Threads

(

)

_úûù êë é ₊ ₋ ⋅ ⋅ ⋅

= _n,_max _s,_min _n,_max

e s, E K 3 1 2n 1 K n π A

This equation appears in the ANSI standards and gives the shear area per unit length of engagement. It must be multiplied by the length of engagement, L_e, to obtain the actual shear area. This area is often reported in

manufacturers data sheets for bolts and screws.

(

s,min n,max

)

e max n, e s, E K L 3 1 2n 1 K n π A ⋅ úû ù êë é ₊ ₋ ⋅ ⋅ ⋅ =

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Shear Area of Internal

Threads

n

t

D

π

A

_s,_i

=

⋅

_s,_min

⋅

_i

⋅

plane) (critical thread internal of thickness t thread) (external diameter major Minimum D i min s, ≡ ≡

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Shear Area of Internal

Threads

(

)

threads

internal

the

of

diameter

pitch

maximum

E

D

3

1

2n

1

n

D

π

A

max n, max n, min s, min s, i s,

≡

úû

ù

êë

é

+

−

⋅

=

Similar to the previous derivation, an equation that takes into account the tolerances of the thread system can be derived to compute the shear area of the internal thread.

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Length of Engagement

(Equal Strength Materials)

If the internal thread and external thread material have the same strength, then

t max t

A

F

S

=

e i s, max t

L

A

F

0.5S

⋅

=

i s, t e e i s, t t t max

A

2A

L

A

0.5S

A

S

F

=

Tensile Strength Tensile Strength (External Thread) (External Thread) Shear Strength Shear Strength (Internal Thread) (Internal Thread)

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Length of Engagement

(Unequal Strength Materials) (Unequal Strength Materials)

If the internal thread and external thread do not have the same material, then

t max e t,

A

F

S

=

e i s, max i t,

L

A

F

0.5S

⋅

=

i t, i s, e t, t e e i s, i t, t e t, max

S

A

S

2A

L

A

0.5S

A

S

F

⋅

=

Tensile Strength Tensile Strength (External Thread) (External Thread) Shear Strength Shear Strength (Internal Thread) (Internal Thread)

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Bolt/Nut Design Philosophy

ANSI standard bolts and nuts of equal grades are designed to have the bolt fail before the threads in the nut are stripped.

The engineer designing a machine element is

responsible for determining how something should fail taking into account the safety of the operators and public. Length of engagement is an important consideration in designing machine elements with machine screws.

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Assignment

A 5/16-18UNC-2A fastener is made from a material having a yield strength of 120 ksi. The fastener will be engaged with a nut made from the same material. Compute the tensile stress area, shear stress area per length of engagement, and

minimum length of engagement. Dimensional information on the threads is given below.

The minimum pitch diameter of the external thread is 0.2712 in., and the maximum minor diameter of the internal thread is 0.265 inch, minimum major diameter of the external thread is 0.3026 in, and the maximum pitch diameter of the internal threads is 0.2817 (reference Table 4, page1544, Machinery’s Handbook).