Strength of materials. Part.1
Timoshenko, Stephen
Strength of materials. Part.1 elementary theory and prblems - New Delhi CBS Pub. and dist. pvt. ltd. 2002 - xiv,442p.
CONTENTS
TENSION AND COMPRESSION WITHIN THE ELASTIC LIMIT 1
1. Elasticity ................... 1
2. Hooke'sLaw ................. 2
3. The Tensile Test Diagram ........... 6
4. Working Stress ................ 8
5. Stress and Strain Produced in a Bar by Its Own
Weight ................... 14
6. Statically Indeterminate Problems in Tension and
Compression ................ 20
7. Assembly and Thermal Stresses ......... 26
8. Extension of a Circular Ring .......... 31
II. ANALYSIS OF STRESS AND STRAIN .......... 37
9. Stress on Inclined Planes for Simple Tension and
Compression ................ 37
10. Mohr's Circle ................. 40
11. Tension or Compression in Two Perpendicular Di¬rections 44
12. Mohr's Circle for Combined Stresses ....... 46
13. Principal Stresses ............... 49
14. Lateral Contraction .............. 53
15. Strain in the1 Case of Tension or Compression in Two
Perpendicular Directions ........... 54
16. Pure Shear. Modulus in Sheai- ......... 57
17. Working Stresses in Shear ........... 62
18. Tension or Compression in Three Perpendicular Di¬rections 65
III. BENDING MOMENT AND SHEARING FORCE ....... 70
19. Types of Beams ................ 70
20. Bending Moment and Shearing Force ...... 72
21. Relation between Bending Moment and Shearing Force 76
22. Bending Moment and Shearing Force Diagrams . .78
IV. STRESSES IN LATERALLY LOADED SYMMETRICAL BEAMS . 92
23. Pure Bending ................. 92
24. Various Shapes of Cross Sections of Beams 100
25. General Case of Laterally Loaded Symmetrical Beams ....... 105
26. Shearing Stresses in Bending .......... 113
27. Distribution of Shearing Stresses in the Case of a Circular Cross Section ............ 120
28. Shearing Stresses in I Beams .......... 122
29. Principal Stresses in Bending .......... 125
30. Stresses in Built-up Beams ........... 130
V. DEFLECTION OF LATERALLY LOADED SYMMETRICAL BEAMS ................... 137
31. Differential Equation of the Deflection Curve . . 137
32. Bending of a Uniformly Loaded Beam ...... 140
33. Deflection of a Simply Supported Beam Loaded by a
Concentrated Load ........143
34. Determination of Deflections by the Use of the Bending Moment Diagram. Area-Moment Method 147
35. Deflection of a Cantilever Beam by the Area-Mo¬ment Method ................ 149
36. Deflection of a Simply Supported Beam by the Area-Moment Method .....154
37. Method of Superposition ............ 162
38. TKe Deflection of Beams with Overhangs ..... 167
39. Effect of Shearing Force on the Deflection of Beams 170
VI. STATICALLY INDETERMINATE PROBLEMS IN BENDING . . 176
40. Redundant Constraints ............. 176
41. Beam Built In at One End and Supported at the Other 179
42. Beam with Both Ends Built In ......... 186
43. Frames .................... 190
44. Beams on Three Supports ........... 198
45. Continuous Beams ............... 202
VII. SYMMETRICAL BEAMS OF VARIABLE CROSS SECTION.
BEAMS OF Two MATERIALS .......... 210
46. Beams of Variable Cross Section . ........ 210
47. Symmetrical Beams of Two Different Materials . 217
48. Reinforced-Concrete Beams ........... 221
49. Shearing Stresses in Reinforced-Concrete Beams . . 225
VIII. BENDING OF BEAMS IN A PLANE WHICH Is NOT A PLANE OF SYMMETRY . 227
50. Pure Bending in a Plane Which Is Not a, Plane of
Symmetry ................. 227
51. Bending of Beams Having Two Planes of Symmetry 233
52. Bending of Beams in a Principal Plane Which Is
Not a Plane of Symmetry .......... 235
IX. COMBINED BENDING AND AXIAL LOAD. THEORY OF
COLUMNS .................. 245
53. Bending Accompanied by Tension or Compression . 245
54. Eccentric Loading of a Short Strut ....... 249
55. The Core of a Section ............. 254
56. Eccentric Compression of a Slender Symmetrical
Column ............... . . . 258
57. Critical Load ................. 263
58. Critical Stress; Design of Columns ........ 268
59. Design of Columns on the Basis of Assumed Inac¬curacies . 274
60. Empirical Formulas for Column Design ..... 277
X. TORSION AND COMBINED BENDING AND TORSION ... 281
61. Torsion of a Circular Shaft ........... 281
62. Torsion of a Hollow Shaft ........... 287
63. Shaft of Rectangular Cross Section ....... 289
64. Helical Spring, Close Coiled ........... 290
65. Combined Bending and Torsion of Circular Shafts . 295
XI. STRAIN ENERGY AND IMPACT . . . \-^.'. ...... 301
66. Elastic Strain Energy in Tension ........ 301
67. Tension Produced by Impact .......... 305
68. Elastic Strain Energy in Shear and Torsion .... 312
69. Elastic Strain Energy in Bending .... . . . . 316
70. Deflection Produced by Impact ......... 320
71. The General Expression for Strain Energy .... 325
72. The Theorem of Castigliano . .......... 328
73. Deflection of Trusses. ............. 335
74. Application of Castigliano Theorem in Solution of
Statically Indeterminate Problems ....... 340
75. The Reciprocal Theorem ............ 351
76. Exceptional Cases . . ... .......... 359
XII. CURVED BARS .................. 362
77. Pure Bending of Curved Bars .......... 362
78. Bending of Curved Bars by.Fofces Acting in the
Plane of Symmetry ............. 366
79. Particular Cases of Curved Bars ......... 368
80. Deflection of Curved Bars ........... 378
81. Arch Hinged at the Ends ............ 394.
82. Stresses in a Flywheel ............ . 398
83. Deflection Curve for a Bar with a Circular Center
Line .................... 401
84. Bending of Curvetl Tubes. ........... 405
85. Bending of a Curved Bar Out of Its Plane of Initial
Curvature ........... 410
APPENDIX A
MOMENTS OF INERTIA OF PLANE AREAS ........ 417
I. The Moment of Inertia of a Plane Area with Respect to
an Axis in Its Plane ............. 417
II. Polar Moment of Inertia of a Plane Area ....... 420
III. Parallel-Axis Theorem ............... 422
IV. Product of Inertia. Principal Axes ......... 423
V. Change of Direction of Axes. Determination of the
Principal Axes ................ 425
APPENDIX E
TABLES OF STRUCTURAL SHAPES ........... 429
AUTHOR INDEX ..................... 435
SUBJECT INDEX ..................... 437
8123910304
620.112 / TIM
Strength of materials. Part.1 elementary theory and prblems - New Delhi CBS Pub. and dist. pvt. ltd. 2002 - xiv,442p.
CONTENTS
TENSION AND COMPRESSION WITHIN THE ELASTIC LIMIT 1
1. Elasticity ................... 1
2. Hooke'sLaw ................. 2
3. The Tensile Test Diagram ........... 6
4. Working Stress ................ 8
5. Stress and Strain Produced in a Bar by Its Own
Weight ................... 14
6. Statically Indeterminate Problems in Tension and
Compression ................ 20
7. Assembly and Thermal Stresses ......... 26
8. Extension of a Circular Ring .......... 31
II. ANALYSIS OF STRESS AND STRAIN .......... 37
9. Stress on Inclined Planes for Simple Tension and
Compression ................ 37
10. Mohr's Circle ................. 40
11. Tension or Compression in Two Perpendicular Di¬rections 44
12. Mohr's Circle for Combined Stresses ....... 46
13. Principal Stresses ............... 49
14. Lateral Contraction .............. 53
15. Strain in the1 Case of Tension or Compression in Two
Perpendicular Directions ........... 54
16. Pure Shear. Modulus in Sheai- ......... 57
17. Working Stresses in Shear ........... 62
18. Tension or Compression in Three Perpendicular Di¬rections 65
III. BENDING MOMENT AND SHEARING FORCE ....... 70
19. Types of Beams ................ 70
20. Bending Moment and Shearing Force ...... 72
21. Relation between Bending Moment and Shearing Force 76
22. Bending Moment and Shearing Force Diagrams . .78
IV. STRESSES IN LATERALLY LOADED SYMMETRICAL BEAMS . 92
23. Pure Bending ................. 92
24. Various Shapes of Cross Sections of Beams 100
25. General Case of Laterally Loaded Symmetrical Beams ....... 105
26. Shearing Stresses in Bending .......... 113
27. Distribution of Shearing Stresses in the Case of a Circular Cross Section ............ 120
28. Shearing Stresses in I Beams .......... 122
29. Principal Stresses in Bending .......... 125
30. Stresses in Built-up Beams ........... 130
V. DEFLECTION OF LATERALLY LOADED SYMMETRICAL BEAMS ................... 137
31. Differential Equation of the Deflection Curve . . 137
32. Bending of a Uniformly Loaded Beam ...... 140
33. Deflection of a Simply Supported Beam Loaded by a
Concentrated Load ........143
34. Determination of Deflections by the Use of the Bending Moment Diagram. Area-Moment Method 147
35. Deflection of a Cantilever Beam by the Area-Mo¬ment Method ................ 149
36. Deflection of a Simply Supported Beam by the Area-Moment Method .....154
37. Method of Superposition ............ 162
38. TKe Deflection of Beams with Overhangs ..... 167
39. Effect of Shearing Force on the Deflection of Beams 170
VI. STATICALLY INDETERMINATE PROBLEMS IN BENDING . . 176
40. Redundant Constraints ............. 176
41. Beam Built In at One End and Supported at the Other 179
42. Beam with Both Ends Built In ......... 186
43. Frames .................... 190
44. Beams on Three Supports ........... 198
45. Continuous Beams ............... 202
VII. SYMMETRICAL BEAMS OF VARIABLE CROSS SECTION.
BEAMS OF Two MATERIALS .......... 210
46. Beams of Variable Cross Section . ........ 210
47. Symmetrical Beams of Two Different Materials . 217
48. Reinforced-Concrete Beams ........... 221
49. Shearing Stresses in Reinforced-Concrete Beams . . 225
VIII. BENDING OF BEAMS IN A PLANE WHICH Is NOT A PLANE OF SYMMETRY . 227
50. Pure Bending in a Plane Which Is Not a, Plane of
Symmetry ................. 227
51. Bending of Beams Having Two Planes of Symmetry 233
52. Bending of Beams in a Principal Plane Which Is
Not a Plane of Symmetry .......... 235
IX. COMBINED BENDING AND AXIAL LOAD. THEORY OF
COLUMNS .................. 245
53. Bending Accompanied by Tension or Compression . 245
54. Eccentric Loading of a Short Strut ....... 249
55. The Core of a Section ............. 254
56. Eccentric Compression of a Slender Symmetrical
Column ............... . . . 258
57. Critical Load ................. 263
58. Critical Stress; Design of Columns ........ 268
59. Design of Columns on the Basis of Assumed Inac¬curacies . 274
60. Empirical Formulas for Column Design ..... 277
X. TORSION AND COMBINED BENDING AND TORSION ... 281
61. Torsion of a Circular Shaft ........... 281
62. Torsion of a Hollow Shaft ........... 287
63. Shaft of Rectangular Cross Section ....... 289
64. Helical Spring, Close Coiled ........... 290
65. Combined Bending and Torsion of Circular Shafts . 295
XI. STRAIN ENERGY AND IMPACT . . . \-^.'. ...... 301
66. Elastic Strain Energy in Tension ........ 301
67. Tension Produced by Impact .......... 305
68. Elastic Strain Energy in Shear and Torsion .... 312
69. Elastic Strain Energy in Bending .... . . . . 316
70. Deflection Produced by Impact ......... 320
71. The General Expression for Strain Energy .... 325
72. The Theorem of Castigliano . .......... 328
73. Deflection of Trusses. ............. 335
74. Application of Castigliano Theorem in Solution of
Statically Indeterminate Problems ....... 340
75. The Reciprocal Theorem ............ 351
76. Exceptional Cases . . ... .......... 359
XII. CURVED BARS .................. 362
77. Pure Bending of Curved Bars .......... 362
78. Bending of Curved Bars by.Fofces Acting in the
Plane of Symmetry ............. 366
79. Particular Cases of Curved Bars ......... 368
80. Deflection of Curved Bars ........... 378
81. Arch Hinged at the Ends ............ 394.
82. Stresses in a Flywheel ............ . 398
83. Deflection Curve for a Bar with a Circular Center
Line .................... 401
84. Bending of Curvetl Tubes. ........... 405
85. Bending of a Curved Bar Out of Its Plane of Initial
Curvature ........... 410
APPENDIX A
MOMENTS OF INERTIA OF PLANE AREAS ........ 417
I. The Moment of Inertia of a Plane Area with Respect to
an Axis in Its Plane ............. 417
II. Polar Moment of Inertia of a Plane Area ....... 420
III. Parallel-Axis Theorem ............... 422
IV. Product of Inertia. Principal Axes ......... 423
V. Change of Direction of Axes. Determination of the
Principal Axes ................ 425
APPENDIX E
TABLES OF STRUCTURAL SHAPES ........... 429
AUTHOR INDEX ..................... 435
SUBJECT INDEX ..................... 437
8123910304
620.112 / TIM