كتاب A Textbook of Strength of Materials - Mechanics of Solids
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منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب A Textbook of Strength of Materials - Mechanics of Solids

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A Textbook of Strength of Materials - Mechanics of Solids
(In S.I. Units)
For Degree, U.P.S.C. (Eng g. Services), GATE and Other Competitive Examinations
By
Dr. R.K. BANSAL
B.Sc. Engg. (Mech.), M. Tech., Hons. (I.I.T., Delhi)
Ph.D., M.I.E. (India)
Formerly Professor and Head
Department of Mechanical Engineering,
(University of Delhi)
Delhi College of Engineering, Delhi

كتاب A Textbook of Strength of Materials - Mechanics of Solids  A_t_b_12
و المحتوى كما يلي :


CONTENTS
Chapters Pages
Chapter 1. Simple Stresses and Strains 1—58
1.1. Introduction 1
1.2. Stress 1
1.3. Strain 2
1.4. Types of Stresses 2
1.5. Elasticity and Elastic Limit 5
1.6. Hooke’s Law and Elastic Modulii 6
1.7. Modulus of Elasticity (or Young’s Modulus) 6
1.8. Factor of Safety 6
1.9. Constitutive Relationship between Stress and Strain 6
1.10. Analysis of Bars of Varying Sections 14
1.11. Analysis of Uniformly Tapering Circular Rod 24
1.12. Analysis of Uniformly Tapering Rectangular Bar 27
1.13. Analysis of Bars of Composite Sections 30
1.14. Thermal Stresses 42
1.15. Thermal Stresses in Composite Bars 44
1.16. Elongation of a Bar Due to its Own Weight 50
1.17. Analysis of Bar of Uniform Strength 51
Highlights 53
Exercise 54
Chapter 2. Elastic Constants 59—84
2.1. Introduction 59
2.2. Longitudinal Strain 59
2.3. Lateral Strain 59
2.4. Poisson’s Ratio 60
2.5. Volumetric Strain 62
2.6. Volumetric Strain of a Cylindrical Rod 68
2.7. Bulk Modulus 70
2.8. Expression for Young’s Modulus in Terms of Bulk Modulus 70
2.9. Principle of Complementary Shear Stresses 73
2.10. Stresses on Inclined Sections when the Element is Subjected to Simple
Shear Stresses 74
2.11. Diagonal Stresses Produced by Simple Shear on a Square Block 76
2.12. Direct (Tensile and Compressive) Strains of the Diagonals 77
2.13. Relationship between Modulus of Elasticity and Modulus of Rigidity 78
Highlights 81
Exercise 82
Chapter 3. Principal Stresses and Strains 85—142
3.1. Introduction 85
3.2. Principal Planes and Principal Stresses 85
3.3. Methods of Determining Stresses on Oblique Section 85
3.4. Analytical Method for Determining Stresses on Oblique Section 85x
Chapters Pages
3.5. Mohr’s Circle 123
3.6. Strain on an Oblique Plane 133
3.7. Mohr’s Strain Circle 137
Highlights 137
Exercise 139
Chapter 4. Strain Energy and Impact Loading 143—170
4.1. Introduction 143
4.2. Some Definitions 143
4.3. Expression for Strain Energy Stored in a Body when the Load is Applied
Gradually 143
4.4. Expression for Strain Energy Stored in a Body when the Load is Applied
Suddenly 145
4.5. Expression for Strain Energy Stored in a Body when the Load is Applied
with Impact 152
4.6. Expression for Strain Energy Stored in a Body due to Shear Stress 165
Highlights 166
Exercise 167
Chapter 5. Centre of Gravity and Moment of Inertia 171—236
5.1. Centre of Gravity 171
5.2. Centroid 171
5.3. Centroid or Centre of Gravity of Simple Plane Figures 171
5.4. Centroid (or Centre of Gravity) of Areas of Plane Figures
by the Method of Moments 171
5.5. Important Points 173
5.6. Area Moment of Inertia 195
5.7. Radius of Gyration 196
5.8. Theorem of the Perpendicular Axis 196
5.9. Theorem of Parallel Axis 197
5.10. Determination of Area Moment of Inertia 198
5.11. Mass Moment of Inertia 212
5.12. Determination of Mass Moment of Inertia 213
5.13. Product of Inertia 219
5.14. Principal Axes 220
5.15. Principal Moments of Inertia 221
Highlights 229
Exercise 230
Chapter 6. Shear Force and Bending Moment 237—294
6.1. Introduction 237
6.2. Shear Force and Bending Moment Diagrams 237
6.3. Types of Beams 237
6.4. Types of Load 238
6.5. Sign Conventions for Shear Force and Bending Moment 239
6.6. Important Points for Drawing Shear Force and Bending Moment Diagrams 240
6.7. Shear Force and Bending Moment Diagrams for a Cantilever with a
Point Load at the Free End 241
6.8. Shear Force and Bending Moment Diagrams for a Cantilever with a
Uniformly Distributed Load 244xi
6.9. Shear Force and Bending Moment Diagrams for a Cantilever
Carrying a Gradually Varying Load 252
6.10. Shear Force and Bending Moment Diagrams for a Simply
Supported Beam with a Point Load at Mid-point 254
6.11. Shear Force and Bending Moment Diagrams for a Simply
Supported Beam with an Eccentric Point Load 256
6.12. Shear Force and Bending Moment Diagrams for a Simply
Supported Beam Carrying a Uniformly Distributed Load 258
6.13. Shear Force and Bending Moment Diagrams for a
Simply Supported Beam Carrying a Uniformly
Varying Load from Zero at Each End to w Per Unit Length at the Centre 266
6.14. Shear Force and B.M. Diagrams for a Simply Supported Beam
Carrying a Uniformly Varying Load from Zero at one End to w Per Unit
Length at the Other End 268
6.15. Shear Force and Bending Moment Diagrams for Over-hanging Beams 272
6.16. S. F. and B. M. Diagrams for Beams Carrying Inclined Load 281
6.17. Shear Force and Bending Moment Diagrams for Beams Subjected
to Couples 286
6.18. Relations between Load, Shear Force and Bending Moment 289
Highlights 290
Exercise 291
Chapter 7. Bending Stresses in Beams 295—344
7.1. Introduction 295
7.2. Pure Bending or Simple Bending 295
7.3. Theory of Simple Bending with Assumptions Made 296
7.4. Expression for Bending Stress 297
7.5. Neutral Axis and Moment of Resistance 298
7.6. Bending Stresses in Symmetrical Sections 300
7.7. Section Modulus 303
7.8. Section Modulus for Various Shapes or Beam Sections 303
7.9. Bending Stress in Unsymmetrical Sections 315
7.10. Strength of a Section 323
7.11. Composite Beams (Flitched Beams) 330
Highlights 340
Exercise 341
Chapter 8. Shear Stresses in Beams 345—380
8.1. Introduction 345
8.2. Shear Stress at a Section 345
8.3. Shear Stress Distribution for Different Sections 351
Highlights 376
Exercise 377
Chapter 9. Direct and Bending Stresses 381—412
9.1. Introduction 381
9.2. Combined Bending and Direct Stresses 381
9.3. Resultant Stress when a Column of Rectangular Section is Subjected to
an Eccentric Load 382
9.4. Resultant Stress when a Column of Rectangular Section is Subjected to a
Load which is Eccentric to both Axes 390
Chapters Pagesxii
9.5. Resultant Stress for Unsymmetrical Columns with Eccentric Loading 397
9.6. Middle Third Rule for Rectangular Sections (i.e., Kernel of Section) 402
9.7. Middle Quarter Rule for Circular Sections (i.e., Kernel of Section) 404
9.8. Kernel of Hollow Circular Section (or Value of Eccentricity
for Hollow Circular Section) 405
9.9. Kernel of Hollow Rectangular Section (or Value of
Eccentricity for Hollow Rectangular Section) 406
Highlights 409
Exercise 410
Chapter 10. Dams and Retaining Walls 413—468
10.1. Introduction 413
10.2. Types of Dams 413
10.3. Rectangular Dams 413
10.4. Stresses Across the Section of a Rectangular Dam 417
10.5. Trapezoidal Dam having Water Face Inclined 428
10.6. Stability of a Dam 434
10.7. Retaining Walls 447
10.8. Rankine’s Theory of Earth Pressure 449
10.9. Surcharged Retaining Wall 459
10.10. Chimneys 462
Highlights 464
Exercise 466
Chapter 11. Analysis of Perfect Frames 469—514
11.1. Introduction 469
11.2. Types of Frames 469
11.3. Assumptions Made in Finding Out the Forces in a Frame 470
11.4. Reactions of Supports of a Frame 470
11.5. Analysis of a Frame 471
Highlights 508
Exercise 508
Chapter 12. Deflection of Beams 515—558
12.1. Introduction 515
12.2. Deflection and Slope of a Beam Subjected to Uniform Bending Moment 515
12.3. Relation between Slope, Deflection and Radius of Curvature 517
12.4. Deflection of a Simply Supported Beam Carrying a
Point Load at the Centre 519
12.5. Deflection of a Simply Supported Beam with an Eccentric Point Load 523
12.6. Deflection of a Simply Supported Beam with a Uniformly Distributed Load 530
12.7. Macaulay’s Method 535
12.8. Moment Area Method 550
12.9. Mohr’s Theorems 552
12.10. Slope and Deflection of a Simply Supported Beam Carrying a Point Load at
the Centre by Mohr’s Theorem 553
12.11. Slope and Deflection of a Simply Supported Beam Carrying a
Uniformly Distributed Load by Mohr’s Theorem 554
Highlights 555
Exercise 556
Chapters Pagesxiii
Chapter 13. Deflection of Cantilevers 559—582
13.1. Introduction 559
13.2. Deflection of a Cantilever with a Point Load at the Free End by Double
Integration Method 559
13.3. Deflection of a Cantilever with a Point Load at a Distance ‘a’ from
the Fixed End 561
13.4. Deflection of a Cantilever with a Uniformly Distributed Load 562
13.5. Deflection of a Cantilever with a Uniformly Distributed Load for a
Distance ‘a’ from the Fixed End 566
13.6. Deflection of a Cantilever with a Uniformly Distributed Load for a
Distance ‘a’ from the Free End 566
13.7. Deflection of a Cantilever with a Gradually Varying Load 572
13.8. Deflection and Slope of a Cantilever by Moment Area Method 576
Highlights 580
Exercise 581
Chapter 14. Conjugate Beam Method, Propped
Cantilevers and Beams 583—618
14.1. Introduction 583
14.2. Conjugate Beam Method 583
14.3. Deflection and Slope of a Simply Supported Beam with a Point
Load at the Centre 583
14.4. Simply Supported Beam Carrying an Eccentric Point Load 585
14.5. Relation between Actual Beam and Conjugate Beam 597
14.6. Deflection and Slope of a Cantilever with a Point Load at the Free End 597
14.7. Propped Cantilevers and Beams 602
14.8. S.F. and B.M. Diagrams for a Propped Cantilever Carrying a Point Load
at the Centre and Propped at the Free End 603
14.9. S.F. and B.M. Diagrams for a Propped Cantilever Carrying
a Uniformly Distributed Load and Propped at the Free End 604
14.10. S.F. and B.M. Diagrams for a Simply Supported Beam with
a Uniformly Distributed Load and Propped at the Centre 610
14.11. Yielding of a Prop 614
Highlights 615
Exercise 616
Chapter 15. Fixed and Continuous Beams 619—678
15.1. Introduction 619
15.2. Bending Moment Diagram for Fixed Beams 620
15.3. Slope and Deflection for a Fixed Beam Carrying a Point Load at the Centre 624
15.4. Slope and Deflection for a Fixed Beam Carrying an Eccentric Point Load 628
15.5. Slope and Deflection for a Fixed Beam Carrying a Uniformly Distributed
Load Over the Entire Length 644
15.6. Fixed End Moments of Fixed Beam Due to Sinking of a Support 654
15.7. Advantages of Fixed Beams 657
15.8. Continuous Beams 658
15.9. Bending Moment Diagram for Continuous Beams 658
Highlights 675
Exercise 676
Chapters Pagesxiv
Chapter 16. Torsion of Shafts and Springs 679—746
16.1. Introduction 679
16.2. Derivation of Shear Stress Produced in a Circular Shaft Subjected to Torsion 679
16.3. Maximum Torque Transmitted by a Circular Solid Shaft 681
16.4. Torque Transmitted by a Hollow Circular Shaft 683
16.5. Power Transmitted by Shafts 684
16.6. Expression for Torque in Terms of Polar Moment of Inertia 694
16.7. Polar Modulus 695
16.8. Strength of a Shaft and Torsional Rigidity 695
16.9. Flanged Coupling 702
16.10. Strength of a Shaft of Varying Sections 705
16.11. Composite Shaft 713
16.12. Combined Bending and Torsion 717
16.13. Expression for Strain Energy Stored in a Body Due to Torsion 720
16.14. Springs 728
Highlights 741
Exercise 743
Chapter 17. Thin Cylinders and Spheres 747—788
17.1. Introduction 747
17.2. Thin Cylindrical Vessel Subjected to Internal Pressure 747
17.3. Stresses in a Thin Cylindrical Vessel Subjected to Internal Pressure 748
17.4. Expression for Circumferential Stress (or Hoop Stress) 748
17.5. Expression for Longitudinal Stress 749
17.6. Efficiency of a Joint 753
17.7. Effect of Internal Pressure on the Dimensions of a Thin Cylindrical Shell 757
17.8. A Thin Cylindrical Vessel Subjected to Internal Fluid Pressure and a Torque 768
17.9. Wire Winding of Thin Cylinders 772
17.10. Thin Spherical Shells 777
17.11. Change in Dimensions of a Thin Spherical Shell Due to an Internal Pressure 778
17.12. Rotational Stresses in Thin Cylinders 780
Highlights 783
Exercise 784
Chapter 18. Thick Cylinders and Spheres 789—816
18.1. Introduction 789
18.2. Stresses in a Thick Cylindrical Shell 789
18.3. Stresses in Compound Thick Cylinders 797
18.4. Initial Difference in Radii at the Junction of a Compound Cylinder for
Shrinkage 802
18.5. Thick Spherical Shells 808
Highlights 813
Exercise 814
Chapter 19. Columns and Struts 817—880
19.1. Introduction 817
19.2. Failure of a Column 817
19.3. Assumptions Made in the Euler’s Column Theory 818
Chapters Pagesxv
19.4. End Conditions for Long Columns 818
19.5. Expression for Crippling Load When Both the Ends of the Column are Hinged 819
19.6. Expression for Crippling Load When One End of the Column is Fixed and
the Other End is Free 820
19.7. Expression for Crippling Load When Both the Ends of the Column are Fixed 822
19.8. Expression for Crippling Load When One End of the Column is Fixed and
the Other End is Hinged (or Pinned) 825
19.9. Effective Length (or Equivalent Length) of a Column 827
19.10. Limitation of Euler’s Formula 829
19.11. Rankine’s Formula 844
19.12. Straight Line Formula 856
19.13. Johnson’s Parabolic Formula 856
19.14. Factor of Safety 857
19.15. Formula by Indian Standard Code (I.S. Code) for Mild Steel 857
19.16. Columns with Eccentric Load 858
19.17. Columns with Initial Curvature 862
19.18. Strut with Lateral Load (or Beam Columns) 867
Highlights 875
Exercise 877
Chapter 20. Riveted Joints 881—910
20.1. Introduction 881
20.2. Types of Riveted Joints 881
20.3. Chain Riveted Joint 882
20.4. Zig-Zag Riveted Joint 882
20.5. Diamond Riveted Joint 882
20.6. Failure of a Riveted Joint 886
20.7. Strength of a Riveted Joint 889
20.8. Efficiency of a Riveted Joint 890
20.9. Design of a Riveted Joint 902
Highlights 905
Exercise 907
Chapter 21. Welded Joints 911—930
21.1. Introduction 911
21.2. Advantages and Disadvantages of Welded Connections 911
21.3. Types of Welded Joints 912
21.4. Analysis of a Compound Weld 916
21.5. Analysis of Unsymmetrical Welded Sections which are Loaded Axially 918
Highlights 925
Exercise 927
Chapter 22. Rotating Discs and Cylinders 931—968
22.1. Introduction 931
22.2. Expression for Stresses in a Rotating Thin Disc 931
22.3. Disc of Uniform Strength 948
22.4. Long Cylinders 952
Highlights 965
Exercise 967
Chapters Pagesxvi
Chapters Pages
Chapter 23. Bending of Curved Bars 969—1016
23.1. Introduction 969
23.2. Assumptions Made in the Derivation of Stresses in a Curved Bar 969
23.3. Expression for Stresses in a Curved Bar 969
23.4. Determination of Factor ‘h2’ for Various Sections 976
23.5. Resultant Stress in a Curved Bar Subjected to Direct Stresses and Bending
Stresses 989
23.6. Resultant Stress in a Hook 990
23.7. Stresses in Circular Ring 999
23.8. Stresses in a Chain Link 1005
Highlights 1012
Exercise 1014
Chapter 24. Theories of Failure 1017—1050
24.1. Introduction 1017
24.2. Maximum Principal Stress Theory 1017
24.3. Maximum Principal Strain Theory 1018
24.4. Maximum Shear Stress Theory 1022
24.5. Maximum Strain Energy Theory 1026
24.6. Maximum Shear Strain Energy Theory 1030
24.7. Graphical Representation of Theories for Two Dimensional Stress System 1032
24.8. Important Points from Theories of Failures used in Design 1036
24.9. Energy of Distortion (or Shear Strain Energy) 1045
Highlights 1048
Exercise 1048
Chapter 25. Unsymmetrical Bending and Shear Centre 1051—1090
25.1. Introduction 1051
25.2. Properties of Beam Cross-section 1051
25.3. Stress in Unsymmetrical Bending 1053
25.4. Deflection of Beams in Unsymmetrical Bending 1055
25.5. Shear Centre 1073
25.6. Determination of Shear Centre for Channel Section 1073
25.7. Determination of Shear Centre for I-Section 1080
Highlights 1088
Exercise 1089
Chapter 26. Objective Type Questions 1091—1142
26.1. Objective Type Questions Generally Asked in Competitive Examinations 1091
26.2. Answers of Objective Type Questions 1118
26.3. Objective Type Questions from Competitive Examinations 1119
26.4. Answers with Explanations 1127
Subject Index 1143
SUBJECT INDEX
1143
A
Analysis of bars of varying
sections, 14
– of composite sections, 30
Analysis of a compound weld, 916
Area moment method, 550
Assumption made in the theory of
simple bending 296
B
Bar of uniform strength, 51
– composite sections, 30
– varying sections, 14
Beams, continuous, 658
– fixed, 619
– deflection of beams, 515
– propped, 609
– columns, 867
Bending, 291
– plane, 296
– moment, 237
– moment and shear force, 237
– stresses in beams, 295
– of curved bars, 969
Bulk modulus, 70
Buckling load, 818
Butt joint, 881
– weld 912
C
Cantilever, 237
– propped, 602
– truss, 476
Centre of gravity, 171
Circumferential stress, 748
Centroid, 171
Chain riveting, 882
Chimneys, 462
– wind pressure, 462
Clapeyron’s equation, 659
Columns and struts, 817
– long, 817
– beams, 868
– with eccentric load, 858
– with initial curvature, 862
Combined direct and bending, 381
Composite shaft, 713
Composite sections, 30
Combined bending and torsion, 717
Complementary shear stresses, 73
Compressive stress, 3
– strain, 3
Conjugate beam method, 583
Continuous beams, 658
Coupling, 702
Crippling load, 818
Critical load, 818
Curved bars, 969
– Rectangular, 977
– Triangular, 978
– Circular, 981
– Trapezoidal, 980
Cylinders, thin, 747
– thick, 786
D
Dams, 413
Deflection of beams, 515
– in unsymmetrical bending, 1055
– of cantilever, 559
Thin cylindrical shell, 784
Riveted joint, 892
Diamond riveting, 882
Direct and bending stress combined, 381
Disc of uniform strength, 948
E
Earth pressure, 449
Eccentric loading, 397
Elasticity, 5
Elastic constants, 59
Elastic limit, 5
Elastic modulii, 6
Efficiency of a joint, 753, 890
Energy of distortion, 1033
Effective length, 827
Euler’s theory, 818
– limitations of, 829
F
Factor of safety, 6, 857
Failure of a column, 817
Failure of riveted joints, 886
SUBJECT INDEX
Fixed beams, 619
Formula – Johnson’s, 856
– I.S.Code, 857
– straight line, 856
Frames, 469
Flanged coupling, 702
G
Graphical method, 501
– principal stresses, 85
Guest’s theory, 1022
Gyration, radius, 196
H
Haigh’s theory, 1026
Helical spring, 728
Hooke’s Law, 6
Hoop stress, 748
I
Impact loading, 143
– load, 152
Inclined loads, 281
I-section, 359
J
Johnson’s formula, 856
Joints, 881
– riveted, 881
– welded, 911
K
Kernel, 408
– of hollow circular section, 408
– of hollow rectangular section, 408
L
Lap joint, 881
– weld, 911
Lateral strain, 59
Leaf springs, 728
Long columns, 817
Longitudinal, strain, 59
– stress, 742
M
Macaulay’s method, 535
Maximum principal stress theory,
1017STRENGTH OF MATERIALS
1144
– strain theory, 1018
– shear stress theory, 1022
– strain energy theory, 1026
– shear strain energy theory, 1030
Middle third rule, 402
Middle quarter rule, 404
Mises-Henky theory, 1030
Method of joints, 471
– sections, 492
Modulus, bulk, 70
– of elasticity, 6
– of rigidity, 6
Mohr’s circle, 123
Mohr’s strain circle, 137
Mohr’s theorem, 552
Moment area method, 550
Moment of inertia, 195
– resistances, 298
N
Neutral axis, 297
– layer, 296
O
Oblique, 85
Overhanging beams, 237
P
Pitch of rivets, 902
Poisson’s ratio, 60
Polar moment of inertia, 694
Polar Modulus, 695
Power transmitted by shafts, 684
Principal planes, 85
– Strain, 85
– Stress, 85
Principle of complementary
stresses, 73
Proof resilience, 143
Propped cantilevers and beams, 583
R
Rankine’s formula, 844
Rankine theory, 449
Relationship between modulus of
elasticity, 78
– S.F. and B.M. 286
Resilience, 143
– proof, 143
Resistance of moment, 299
Riveted joints, 881
– failure, 886
– strength, 889
– efficiency, 890
– design, 902
Rotational stress, 780
– in a thin cylinder, 780
– in a thin disc, 931
S
Safety factor, 6
Simple bending, 295
Section modulus, 303
Shafts, torsion of, 679
Shafts, composite, 713
Shear centre, 1073
Shear force, 241
– for cantilevers, 241
– for a simply supported beam,
254
Shear in strain energy, 1033
Shear modulus, 6
Spherical shells, 771
Springs, 728
– leaf, 728
– helical, 728
Straight line formula, 856
Strain, 2
– types of, 2
– compressive, 2, 3
– shear, 2
– tensile, 2
Strain energy, 143
Stress, 1, 2
– in a curved bar, 969
– in unsymmetrical bending, 1053
– compressive, 3
– shear, 4
– principal, 85
– tensile, 2
– thermal, 42
– types of, 2
Strength of a shaft, 695
– riveted joint, 889, 892
Struts, 867
– with lateral load, 867
T
Thermal stresses, 42
Tensile, 2
– strain, 2
– stress, 2
Thick cylinder, 789
Thick spherical shells, 808
Thin cylinder, 747
– spherical shells, 777
Theorem of
– parallel axis, 197
– perpendicular axis, 196
Theories of failure, 1036
Theory of
– maximum principal stress,1017
– maximum principal strain,1018
– maximum shear stress, 1022
– maximum strain energy, 1026
– maximum shear strain energy,
1036
Torsion of shafts, 679
Torsional rigidity, 695
Types of riveted joints, 881
– welded joints, 911
– beams, 237
– load, 237
U
Uniform strength, 51
V
Value of h2 for curved
– rectangular bar, 977
– triangular bar, 978
– circular bar, 981
– trapezoidal bar, 980
Volumetric strain, 62
V-butt joint, 912
W
Walls retaining, 447
Welded joints, 911
– butt weld joint, 912
– fillet weld joint, 912
– compound weld joint, 916
Winkler-Bach Formula, 964
Wind pressure on chimneys, 462
Y
Young’s modulus, 6, 59
Z
Zig-Zag riveted joint, 882


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