##### Document Text Contents

Page 1

1 fUNDAMENTALS OF MACHINE DESIGN

P.ORlOV

TRANSLATED FROM THE RUSSIAN

BY YU. TRAVNICHEV

MIR PUBLISHERS . MOSCOW

Page 2

Aa

B~

r'l'

M

Ee

q

Ht]

€Ie

FIrst published 1976

THE RUSSIAN ALPHABET AND TRANSLITERATION

Aa a KK k Xx kh

B6 b JIJI I 1\1\ Is

Be v MM m 'I" ch

rr g HR n illm sh

lJ.11, d 00' 0' II\", shch

Ee e TIn p 1> .. "

Ee e Pp r bI IiI Y

lRlK .h Cc s bb

,

3. Z TT t a. e

Ihr Yy u IOroyu

lU y <ll<J! f an ya

THE GREEK ALPHABET

Alpha It IO'ta Pp RhO'

Beta K" Kappa l:a Sigma

Gamma A)" Lambda T.~ Tau

Delta Mj.t Mu Yu UpsilO'n

EpsilO'n Nv Nu <ll<p Phi

Zeta Ss Xi Xx Chi

Eta 00' Omicron '!'1j> Psi

Theta TI" Pi g", ,. Omega

'@ English translation, iVIir Publishers, 1976

I

'\

Page 260

260 Chapter 4. Rigidity of Structures

surpassing the elastic limit of all steels. The relative deformation s

under the action of this force (line aa) for steels 1 to 3 will respective-

ly be equal to 0.5, 1 and 2.5%. Thereby, the deformation of a part

made from the strongest steel is 1/0.5 = 2 times less than that in

the case of steel 2 and 2.5/0.5 = 5 times less than that for steel 3.

The advantages of high-strength steels in the considered case can

be illustrated in some other way. Let the given limit relative defor-

mation " = 1 % (line bbl. The part made from'the strongest steell,

will have this deformation under a 9.5-tf load; from steel 2 - under

a 7.5-tf load, and from steel 3 - under a 6-tf load.

Thus, from the above it is clear that the rigidity of a system in the

plastic deformatiou area is determined mostly by the strength

factors.

(c) Rigidity of Thin-Walled and Composite Structures

In thin-walled and particularly shell structures stability of the

system is of great importance. Constructions of such a nature are in

certain conditions at stresses which are safe from the viewpoint

of nominal strength and rigidity calculations prone to abrupt local

oi;.,general deformations braring the character of collapse.

The main means in the battle against the loss of stability (apart

from improvement in material strength) is the reinforcement of easi-

ly deformable sections in the system by the introduction of stiffen-

ing elements, or braces, between the deforming sections and rigid

units. '

In composite strll,ctures (Le., in systems, composed of several parts

by tight fits) ,the rigidity will depend also upon a factor, sel-

dom considered,buthaving great practical significance, namely,

the rigidity of matched units. Presence of gaps or clearances in such

matched units often results in deformations which surpass many times

the natural {inherent) recoverable strains of the structural elements.

When dealing with such units special attention must be paid to

the rigidity of fastening and built-up parts.

Other efficient ways at enhancing the rigidity of composite systems

are dead tightening of joint units, interference fits, larger bearing

surfaces and providing greater rigidity at connection points.

4.2. Specific Rigidity Indices of Materials

-"To compare the indices of rigidity, strength and weight of parts

made from different materials, four main cases must be considered:

,1. Parts identical. in shapes (with equal loads the parts have the

s'anie stresses). '

·"2. Parts ,of equal stiffness (have equal deformations with different

seCtionsaud stresses). "

Y ••

Page 261

4.2. Speci/tc Rigidity 1ndices of Materials 261

3. Parts of equal strength (have identical safety factors, different

sections and stresses proportional to the ultimate strength of the

material).

4. Parts having identical weight.

The first case (changing the material of a part for another material

but leaving its geometrical dimensions the same) is encountered in

practice when the sectional sizes of the part are suited to the manu-

facturing conditions (e.g., cast housing components). It is the same

for parts not specially designed, with small or indeterminate stres-

ses.

The second aud the third cases .occur when not only the material

of a part but also its sectional sizes are changed (designed parts in

which stresses and deformations are determined rather closely and

specified so as to make the maximum use of the material's

strength and rigidity).

The fourth case is when the weight of a structure is determined

by its function and conditions of use.

During the comparison of strength, weight and rigidity indices

of parts made from different materials, we assume that the parts

have equal length and their sections (for the last three cases) are

changed in a geometrically similar manner.

1. Parts of similar shapes (cr = const). For tension-compression,

the rigidity coefficient

),_ EF

-I

where F and I = cross-sectional area and length, respectively;

E = Young's modulus

Given: I = const, and F = const, hence

),=constE (4.11)

Le., the rigidity of parts in this case is dependent only on the value

of Young's modulus.

Safety factor

% n=-

(J

where crb = ultimate tensile strength;

cr = acting stress in a part

Given: cr = const, hence

n= constcrb (4.12)

The value n defines the maximum load which the part can sustain

Pm==nP

Page 519

Other Books for Your Library

1. APPLIED MECHANICS. By M. Kostryktn.

2. MACHINE DESIGN. By M. Mountn and D. Goltztker.

3. MACHINE ELEMENTS. By V. Dobrovolsky et 01.

4. MACHINE TOOL DESIGN. VOL.!. By N. Acherkan et 01.

5. MACHINE TOOL DESIGN. VOL. II. By N. Ackerkan et 01.

6. MACHINE TOOLS. By N. Chernov.

7. MANUFACTURING ENGINEERING. A GENERAL

COURSE. By V. Dantlevsky et 01.

8. MECHANISMS OF MODERN ENGINEERING. VOL. I.

By I. Artobolevsky.

9. MECHANISMS OF MODERN ENGINEERING. VOL. II.

By I. Artobolevsky.

10. METAL CUTTING AND CUTTING TOOLS. By A. Ar-

shinov and C. A lexeyev.

11. THEORETICAL MECHANICS. By A. Movnin and A. Iz-

rayelit.

1 fUNDAMENTALS OF MACHINE DESIGN

P.ORlOV

TRANSLATED FROM THE RUSSIAN

BY YU. TRAVNICHEV

MIR PUBLISHERS . MOSCOW

Page 2

Aa

B~

r'l'

M

Ee

q

Ht]

€Ie

FIrst published 1976

THE RUSSIAN ALPHABET AND TRANSLITERATION

Aa a KK k Xx kh

B6 b JIJI I 1\1\ Is

Be v MM m 'I" ch

rr g HR n illm sh

lJ.11, d 00' 0' II\", shch

Ee e TIn p 1> .. "

Ee e Pp r bI IiI Y

lRlK .h Cc s bb

,

3. Z TT t a. e

Ihr Yy u IOroyu

lU y <ll<J! f an ya

THE GREEK ALPHABET

Alpha It IO'ta Pp RhO'

Beta K" Kappa l:a Sigma

Gamma A)" Lambda T.~ Tau

Delta Mj.t Mu Yu UpsilO'n

EpsilO'n Nv Nu <ll<p Phi

Zeta Ss Xi Xx Chi

Eta 00' Omicron '!'1j> Psi

Theta TI" Pi g", ,. Omega

'@ English translation, iVIir Publishers, 1976

I

'\

Page 260

260 Chapter 4. Rigidity of Structures

surpassing the elastic limit of all steels. The relative deformation s

under the action of this force (line aa) for steels 1 to 3 will respective-

ly be equal to 0.5, 1 and 2.5%. Thereby, the deformation of a part

made from the strongest steel is 1/0.5 = 2 times less than that in

the case of steel 2 and 2.5/0.5 = 5 times less than that for steel 3.

The advantages of high-strength steels in the considered case can

be illustrated in some other way. Let the given limit relative defor-

mation " = 1 % (line bbl. The part made from'the strongest steell,

will have this deformation under a 9.5-tf load; from steel 2 - under

a 7.5-tf load, and from steel 3 - under a 6-tf load.

Thus, from the above it is clear that the rigidity of a system in the

plastic deformatiou area is determined mostly by the strength

factors.

(c) Rigidity of Thin-Walled and Composite Structures

In thin-walled and particularly shell structures stability of the

system is of great importance. Constructions of such a nature are in

certain conditions at stresses which are safe from the viewpoint

of nominal strength and rigidity calculations prone to abrupt local

oi;.,general deformations braring the character of collapse.

The main means in the battle against the loss of stability (apart

from improvement in material strength) is the reinforcement of easi-

ly deformable sections in the system by the introduction of stiffen-

ing elements, or braces, between the deforming sections and rigid

units. '

In composite strll,ctures (Le., in systems, composed of several parts

by tight fits) ,the rigidity will depend also upon a factor, sel-

dom considered,buthaving great practical significance, namely,

the rigidity of matched units. Presence of gaps or clearances in such

matched units often results in deformations which surpass many times

the natural {inherent) recoverable strains of the structural elements.

When dealing with such units special attention must be paid to

the rigidity of fastening and built-up parts.

Other efficient ways at enhancing the rigidity of composite systems

are dead tightening of joint units, interference fits, larger bearing

surfaces and providing greater rigidity at connection points.

4.2. Specific Rigidity Indices of Materials

-"To compare the indices of rigidity, strength and weight of parts

made from different materials, four main cases must be considered:

,1. Parts identical. in shapes (with equal loads the parts have the

s'anie stresses). '

·"2. Parts ,of equal stiffness (have equal deformations with different

seCtionsaud stresses). "

Y ••

Page 261

4.2. Speci/tc Rigidity 1ndices of Materials 261

3. Parts of equal strength (have identical safety factors, different

sections and stresses proportional to the ultimate strength of the

material).

4. Parts having identical weight.

The first case (changing the material of a part for another material

but leaving its geometrical dimensions the same) is encountered in

practice when the sectional sizes of the part are suited to the manu-

facturing conditions (e.g., cast housing components). It is the same

for parts not specially designed, with small or indeterminate stres-

ses.

The second aud the third cases .occur when not only the material

of a part but also its sectional sizes are changed (designed parts in

which stresses and deformations are determined rather closely and

specified so as to make the maximum use of the material's

strength and rigidity).

The fourth case is when the weight of a structure is determined

by its function and conditions of use.

During the comparison of strength, weight and rigidity indices

of parts made from different materials, we assume that the parts

have equal length and their sections (for the last three cases) are

changed in a geometrically similar manner.

1. Parts of similar shapes (cr = const). For tension-compression,

the rigidity coefficient

),_ EF

-I

where F and I = cross-sectional area and length, respectively;

E = Young's modulus

Given: I = const, and F = const, hence

),=constE (4.11)

Le., the rigidity of parts in this case is dependent only on the value

of Young's modulus.

Safety factor

% n=-

(J

where crb = ultimate tensile strength;

cr = acting stress in a part

Given: cr = const, hence

n= constcrb (4.12)

The value n defines the maximum load which the part can sustain

Pm==nP

Page 519

Other Books for Your Library

1. APPLIED MECHANICS. By M. Kostryktn.

2. MACHINE DESIGN. By M. Mountn and D. Goltztker.

3. MACHINE ELEMENTS. By V. Dobrovolsky et 01.

4. MACHINE TOOL DESIGN. VOL.!. By N. Acherkan et 01.

5. MACHINE TOOL DESIGN. VOL. II. By N. Ackerkan et 01.

6. MACHINE TOOLS. By N. Chernov.

7. MANUFACTURING ENGINEERING. A GENERAL

COURSE. By V. Dantlevsky et 01.

8. MECHANISMS OF MODERN ENGINEERING. VOL. I.

By I. Artobolevsky.

9. MECHANISMS OF MODERN ENGINEERING. VOL. II.

By I. Artobolevsky.

10. METAL CUTTING AND CUTTING TOOLS. By A. Ar-

shinov and C. A lexeyev.

11. THEORETICAL MECHANICS. By A. Movnin and A. Iz-

rayelit.