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 |  موضوع: كتاب Theory of Structures الأربعاء 08 يناير 2025, 11:21 pm | |
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Theory of Structures
R.s. Khurmi
[A Textbook for the students of B.E., B.Tech, B.Arch., B.Sc. Engg.,
Section ‘B’ of AMIE (I), UPSC (Engg. Services), Diploma Courses and
Other Engineering Examinations]
(SI UNITS)
و المحتوى كما يلي :
CONTENTS
PART - 1
STATICALLY DETERMINATE STRUCTURES
1. INTRODUCTION 3-12
1. Definition. 3
Units 3
2. Fundamental Units. 3
3. Derived Units. 3
4. Systems of Units.
5. S.I. Units (International Systems of Units). 4
6. Metre. 4
7. Kilogram. 4
8. Second. 4
9. Presentation of Units and Their Values. 5
10. Rules for S.I. Units. 5
Mathematical Review 5
11. Useful Data. 5
12. Algebra. g
13. Trigonometry. 7
14. Differential Calculus. 9
Basic Concepts jq
15. Applied Mechanics 10
16. Strength of Materials 11
17. Types of Structures 11
18. Statically Determinate Structures u
19. Statically Indeterminate Structures 12
20. Internally Indeterminate Structures 12
21. Externally Indeterminate Structures 12
2. ROLLING LOADS 13 _ 56
L Introduction 13
2. Effects of rolling loads. 13
3. Sign conventions. 14
4. A single concentrated load. 14
5. A uniformly distributed load, longer than the span. 17
0. A uniformly distributed load, shorter than the span. 21
7. Two concentrated loads. 26
8« Several concentrated loads. 33
Proposition for the maximum bending moment under any given load. 33
10. Absolute maximum bending moment. 36
11. Proposition for the maximum bending moment at any given section on the span. 40
12. Equivalent uniformly distributed load. 46
(xiii)J Principles for the influence lines for forces in the mcmbcnt of trussed bridges. 79
5’ Influence lines for a Pratt truss with parallel chords. 79
w14. combined dead
load.
51
52
57
- 77
, INFLUENCE UNES 57
1, Introduction. • 57
2.
3.
Uses of Influence lines. |cd |oad.
Influence lines for a single d |ongcr than thc span. 58
61
4. Influence lines for a . ^bu|ed |oad shorter than the span.
>■
4. influence lines for TRUSSED BRIDGES
63
68
71
119
1. Introduction. /0
in
2. Through type trusses. 78
6. Influence lines for an inclined Pratt truss. 91
7. Influence lines for a deck type Warren girder. 100
8. Influence lines for a composite truss. 108
5. DIRECT AND BENDING STRESSES 120 - 140
1. Introduction. 120
2. Eccentric Loading. 120
3. Columns with Eccentric Loading. 121
4. Symmetrical Columns with Eccentric Loading about One Axis. 121
5. Symmetrical Columns with Eccentric Loading about Two Axes. 126
6. Unsymmetrical Columns with Eccentric Loading. 129
7. Limit of Eccentricity. 133
8. Wind Pressure on walls and Chimneys. 136
6. DAMS AND RETAINING WALLS 141 - 188
1. Introduction. 141
2. Rectangular Dams. 141
3. Trapezoidal Dams with Water Face Vertical. 146
4. Trapezoidal Dams with Water Face Inclined. 153
S. Conditions for the Stability of a Dam. 156
6. Condition to Avoid Tension in the Masonry of the Dam at its Base. 157
7. Condition to Prevent the Overturning of the Dam. 157
8. Condition to Prevent the Sliding of Dam. 158
9.
10.
Condition to Prevent the Crushing of Masonry at the Base of the Dam.
Minimum Base Width of a Dam.
158
161
11. Maximum Height of a Dam. 166
11 Retaining Walls. 167
13.
fl 4
14. Active Earth Pressure Earth Pressure. on a Retaining Wall. 167 167
15. Passive Earth Pressure. 167
Uh’)
16. Theories of Active Earth Pressure
17. Rankine's Theory for Active Earth Pressure
18.
19.
Coulomb s Wedge Theory for Active Earth Pressure
Graphical Method for Active Earth Pressure
20. Graphical Method for Rankine's Theory
21.
22.
Rchbann's Graphical Method for Coulomb's Tlieorv
Conditions for thc Stability of a Retaining wall
7. DEFLECTION OF BEAMS
189
1. Introduction.
2. Curvature of thc Bending Beam.
3. Relation between Slope, Deflection and Radius of Curvature
4. Methods for Slope and Deflection at a Section.
5. Double Integration Method for Slope and Deflection.
6. Simply Supported Beam with a Central Point Load.
7. Simply Supported Beam with an Eccentric Point Load.
8. Simply Supported Beam with a Uniformly Distributed Load.
9. Simply Supported Beam with a Gradually Varying Load.
10. Macaulay's Method for Slope and Deflection.
11. Beams of Composite Section.
8. DEFLECTION OF CANTILEVERS 217
1. Introduction.
2. Methods for Slope and Deflection at a Section.
3. Double Integration Method for Slope and Deflection.
4. Cantilever with a Point Load at the Free End.
5. Cantilever with a Point Load not at the Free End.
6. Cantilever with a Uniformly Distributed Load.
7. Cantilever Partially Loaded with a Uniformly Distributed Load.
8. Cantilever Loaded from the Free End.
9. Cantilever with a gradually Varying Load.
10. Cantilever with Several Loads
11. Cantilever of Composite Section.
9. DEFLECTION BY MOMENT AREA METHOD 235
1. Introduction.
2. Mohr's Theorems.
3. Area and Position of the Centre of Gravity of Parabolas.
4. Simply Supported Beam with a Central Point Load.
5. Simply Supported Beam with an Eccentric Point Load.
6. Simply Supported Beam with a Uniformly Distributed Load.
7. Simply Supported Beam with a Gradually Varying Load.
8. Cantilever with a Point Load at the Free end.
9. Cantilever with a Point Load at any Point.
10. Cantilever with a Uniformly Distributed Load.
11. Cantilever with a Gradually Varying Load.
252
10. DEFLECTION BY CONJUGATE BEAM METHOD
1. Introduction.
2. Conjugate Beam.
1. Introduction 272
1 Perfect frames 273
3. Types of deflections. 273
A Statical deflection. 273
5.
6.
Horizontal deflection.
Methods for finding out the deflection. 273
274
7. Unit load method for deflection. 291
8. Graphical method for deflection. 291
9.
10.
11.
Williot diagram for deflects
X5Z££"- join‘ “ of ,he 291
294
11 vXx diagram for the frames with only one joint fixed. 297
297
13. Mohr diagram.
12. CABLES AND SUSPENSION BRIDGES 302 -343
1. Introduction. 302
•> Equilibrium of cable under a given system of loading. 303
3. Equation of the cable. 304
4. Horizontal thrust on the cable. 304
5. Tension in the cable. 305
6. Tension in the cable supported at the same level. 306
7. Tension in the cable supported at different levels. 309
8. Anchor cables. 312
9. Guide pulley support for suspension cable. 312
10. Roller support for suspension cable. 313
11. Length of the cable. 316
11 Length of the cable, when supported at the same level. 316
13. Length of the cable, when supported at different levels. 319
14. Effect on the cable due to change in temperature. 322
15. Stiffening girders in the suspension bridges. 325
16. Suspension bridges with three-hinged stiffning girder. 325
17. Influence lines for moving loads over the suspension bridges with
three-hinged stiffening girders. 327
18.
19.
Influence lines for a single concentrated load rolling over the suspension
bridge with three-hinged stiffening girders. 327
Influence lines for a uniformly distributed load rolling over the suspension
bndge with three-hinged stiffening girders. 333
(xvi)
20. Suspension bridges with two-hinged stiffening girders. 337
21. Influence lines for a single concentrated load rolling over the suspension
bridge with two- hinged stiffening girders. 337
13. THREE-HINGED ARCHES 344 - 377
1. Introduction. 344
2. Theoretical arch or line of thrust. 344
3. Actual arch. 345
4. Eddy’s theorem for bending moment. 346
5. Proof of Eddy’s theorem. 346
6. Use of Eddy’s theorem. 346
7. Types of three-hinged arches. 346
8. Three-hinged parabolic arch. 347
9. Three-hinged circular arch. 347
10. Horizontal thrust In a three-hinged arch. 348
11. Three-hinged parabolic arch supported at different levels. 356
12. Straining actions in a three-hinged arch. 360
13. Effect of change in temperature on a three-hinged arch. 364
14. Influence lines for the moving loads over three-hinged arches. 365
15 Influence lines for a concentrated load moving over three-hinged TAX
circular arches. JOO
16. Influence lines for a concentrated load moving over three-hinged TAG
parabolic arches.
17. Influence lines for a uniformly distributed load moving over three-hinged
parabolic arches.
PART - 2
STATICALLY INDETERMINATE STRUCTURES
« XXI -
14. PROPPED CANTILEVERS AND BEAMS 403
381
1. Introduction. 381
2. Reaction of a Prop. 382
3. Propped Cantilever with a Uniformly Distributed Load. 389
4. Cantilever Propped at an Intermediate Point. 389
5 Propped Cantilever with a point load panned
6. W, Supponed .». U»d »d 397
at the Centre. 401
7. Sinking of the Prop.
- 431
15. FIXED BEAMS 404
1. Introduction. 404
2. Advantages of Fixed Beams. 404
3. Bending Moment Diagrams for Fixed Beams. 406
4.
5.
6.
7.
Fixing Moments of a Fixed Beam.
Fixing Moments of a Fixed Beam Eccentric Point Load.
Fixing Moments of a Fixed Beam 3071 । Distributed Load.
Fixing Moments of a Fixed Beam Carrymg a Umformty
407
410
415
(xvf’O17.
432
458
SLOPE DEFLECTION METHOD
Continuous
Continuous
Continuous
Continuous
Continuous
Beams
Beams
1.
1
3.
4.
5.
6.
7.
8.
9.
. Beam MH•
, nMMow* ’HZre al o« Ena 10 « „Sinking of a Suppon.
9 Fixing Moments of a Fixed t>
THEOREM Of THREE moments
Beams with a Sinking Support.
Beams Subjected to a Couple.
Introduction.
f Continuous Beams.
Typcs
with Fixed End Supports.
with End Span Overhanging.
I.
2.
3.
4.
5.
6.
7.
8.
Introduction.
Assumption in slope deflection method.
Sign conventions.
Slope deflection equations.
Slope deflection equations when the supports arc at the same level.
Slope deflection equations when one of the supports is at a lower level.
Application of slope deflection equations.
Continuous beams.
9. Simple frames.
10. Portal frames.
11. Symmetrical portal frames.
12. Unsymmetrical portal frames.
18. MOMENT DISTRIBUTION METHOD
1. Introduction.
2. Sign Conventions.
3. Carry Over Factor.
4. Cany Over Factor for a Beam Fixed at One End and Simply Supported
at the Other.
5. Cany Over Factor for a Beam. Simply Supported at Both Ends.
6. Stiffness Factor.
7. Distribution Factors.
8. Application of Moment Distribution Method to Various Types of
Continuous Beams.
9. Beanes with Fixed End Suppons.
10. Beams with Simply Supponed Ends.
11. Beanes with End Span Overhanging.
12. Beams With a Sinking Support.
13. Simple Frames
14. Portal frames
15. Symmetrical portal frames
Mii)
4jt
432
432
432
33.)
334
339
444
448
555
495
458
458
459
459
459
461
462
462
470
476
476
479
- 557
493
493
493
497
498
499
500
502
502
506
509
517
524
527
527
16.
17.
18.
19.
20.
Unsymmetrical portal frames
Ratio of sway moments at the joints of column heads and beam
Ratio of sway moments at the joints of column heads and beam, when
both the ends arc hinged.
Ratio of sway moments at the joints of column heads and beam, when
both the ends are fixed.
Ratio of sway moments at the joints of the column heads and beam, when
one end is fixed and the oilier hinged.
19. COLUMN ANALOGY METHOD
1. Introduction.
2, Sign convention.
3, Theory of column analogy.
4. Application of column analogy method.
5. Fixed beams.
6. Portal frames.
7. Symmetrical Portal frames.
g. Portal frame with hinged legs.
9. Unsymmetrical portal frames.
20. two-hinged ARCHES 583 -
1. Introduction.
2. Horizontal thrust in two-hinged arches.
3. Horizontal thrust by strain energy.
4. Horizontal thrust by flexural deformation.
5. Types of two-hinged arches.
6 Horizontal thrust in a two-hinged parabolic arch carrying a concentrated load.
7. Horizontal thrust in a two-hinged circular arch carrying a concentrated load.
8 Horizontal thrust in a two-hinged parabolic arch carrying a uniformly
distributed load over the entire span.
9. Effect of change in temperature in a two-hinged arch.
10. Straining actions in a two-hinged arch.
11. Influence lines for moving loads over two-hinged arches
21. FORCES IN REDUNDANT FRAMES 614
1. Introduction.
2. Redundant frame.
3. Casligliano’s first theorem.
4. Proof of Castigliano’s first theorem.
5 Maxwell’s method for the forces in redundant frames.
t pZX”
7. Frames with two —or mmore re redundant reg*-.members. —<•*•—“
8. Trussed beams. _
22. COLUMNS AND STRUTS
1. Introduction.
2. Failure of a Column or Strut.
3. Euler’s Column Theory.
4. Assumptions in the Euler’s Column Theory.
531
532
532
542
551
- 582
558
558
559
560
560
570
570
571
574
613
583
583
584
584
586
587
590
594
599
602
608
- 641
614
614
615
615
616
627
630
636
667
642
642
643
64323.
* of Columns.
7. columns with the Other Free,
s Columns with One End
’• Colun,ns and the Other Hinged.
£ X7fX^ of a column
12. Slenderness Ratio.
13. Limitations of Euler’s Formu a.
14 Empirical Formulae for Columns.
15. Rankine's Formula for Columns.
16. Johnson's Formula for Columns.
17. Johnson s Straight Line Formula for Columns.
1g. Johnson s Parabolic Formula for Columns.
22. Indian Standard Code for Columns.
20. Long Columns subjected to Eccentric Loading.
643
643
644
645
646
647
649
649
650
654
654
659
659
660
660
662
PLASTIC THEORY 668 - 685
1. Introduction
1 Assumptions in plastic theory.
3. Plastic hinge.
4. Plastic moment or collapse moment.
5. Collapse load.
6. Load factor.
7. Shape factor.
8. Collapse load for different types of beams.
9. Collapse load for a simply supported beam with a central point load.
10. Collapse load for a simply supported beam with an eccentric point load.
11. Collapse load for a simply supported beam with a uniformly distributed load.
12. Collapse load for a propped cantilever with a central point load.
13. Collapse load for a propped cantilever with an eccentric point load.
14. Collapse load for a propped cantilever with a uniformly distributed load.
15. Collapse load for a fixed beam with a central point load.
16. Collapse load for a fixed beam with an eccentric load.
17. Collapse load for a fixed beam with a uniformly distributed load.
668
668
669
669
670
670
670
672
672
672
673
674
675
678
680
680
682
APPENDIX
INDEX 686
697
- 696
-702
(«)
LIST OF SYMBOLS
(Theory of Structures)
Quantity Symbol (Symbol Name) Units
Area of cross section A
Rankine’s constant a
Width B, b
Shear modulus of Rigidity C N/mm2
Depth D, d
Diameter D, d
KU 2
Young's Modulus of Elasticity E _ ••— N/mm
Linear Strain e
Eccentricity e
Centre of Gravity G
Centroid of Area or Lamina G
Height
Moment of Inertia
H. h
I
m
mm1
mm4
Polar Moment of Inertia J N/mm2
Bulk Modulus of Elasticity K
Radius of Gyration k N/mm
Stiffness of Spring
Length
sL
I m
Effective Length Le
M, m kg
Mass N-m
Bending Moment
Number
M n
P, F N
 Force N/mm2
Pressure
Radius
P
R. r
r
Resultant Force V
Reaction or Reacting Force A
Vertical Reaction
Ky
Horizontal Reaction s
T t
Time T
Twisting Moment T
Tensile Force
(xrDSlenderness Ratio
Strain Energy
•Volume
Load or Weight
Load per unit length
Specific Weight
Cartesian co-ordinates
Distance
Deflection
Section Modulus
Radius of Gyration
Co-efficient of Linear Expansion
Angle
Poisson’s ratio
Frequency
Efficiency
Strain
Shear Strain
Slope
Deflection
Deflection
Change in Length
Co-efficient of Friction
Normal Stress
Shear Stress
Polar Co-ordinates
Theory of Structures
(SubjectArticlesCorrelatedwithPageNumbersandArticleNumbers)
Absolute maximum bending moment,
36(2.10)
Active earth pressure on retaining walls,
167(6.13)
_ Rankine's Theory for, 168 (6.1 7)
_ Coulomb's Wedge Theory for, 174
(6.18)
Actual arch, 345(13.3)
Advantages of fixed beams, 404 (15.2)
Algebra (useful data), 6(11.12)
Anchor cables, 312(12.8)
Angle of Repose, 686 (Appendix)
Application of Clapeyron’s theorem of
three moments, 435 ( 16.4)
-Column analogy method, 560(19.4)
-Momentdistribution method,502
Slope deflection equations, 462(17.7)
Applied Mechanics, 10(1.15)
Arch,
-Circular, 347 (13.9)
-Parabolic, 347 (13.8)
Assumptions in Euler's column theory, 643
(22.4)
-in plastic theory, 668 (23.2)
-in slope deflection method, 458(17.2)
Bending moment diagrams for continuous
^5,432(16.2)
-For combined dead load and live load,
51 (2.13)
-for fixed beams 404 (15.3)
Cables,
-Anchor, 312(12.8)
-Equation of, 304 (9.3)
Castigliano's first theorem, 615 (21.3)
-Proof of, 615 (21.4)
Cantilever with a point load, 217 (8.4), 220
(8.5)
-with u.d.l. 221 (8.6), 382 (14.3)
-with a gradually varying load, 226 (8.9)
- with several loads, 228 (8.10)
Carry over factor, 496 (18.3)
-for a beam fixed at one end, and
simply supported at the other, 497
(18.4)
-simply supported beam 498 (18.5)
C.G.S.units,4(1.4)
Circular arch, 347 (13.9)
Clapeyron's theorem of three moments, 432
(16.3)
-Application of, 435 (16.4)
-Proof of, 433 (16.4)
Collapse moment,669 (23.4)
Collapse load,670(23.5)
-for different types of beams 672(23.8)
-for fixed beams, 680 (23.15),
680(23-16), 682 (23.17).
-for propped cantilevers, 674 (23.12),
697698 Theory of Structures
678 (23.14)
- for simply supported beams, 672
(23.9)
672 (23.10), 673 (23.11)
Conditions for the stability ofdam,
156(6.5)
157(6.6), 158(6.8), 158(6.9)
-retaining wall, 182(6.22)
Columns with eccentric loading, 121 (5.3)
-Symmetrical, about one axis, 121 (5.4)
-Symmetrical,about twoaxis, 126(5.5)
-Unsymmetrical, 129(5.6)
Columns with both ends fixed, 646 (22.9)
-hinged, 644(22.7)
— with one end fixed and the other free,
645 (22.8)
- with one end fixed and the other
hinged 647 (22.10)
Continuous beams subjected to a couple,
455(16.9)
-with end span overhanging,444(16.7)
509(18.11)
-with fixedend supports, 439(16.6),
502 (18.9)
-withsinkingsupport,448(16.8),
517(18.12)
-with simply supported ends, 435 (16.5)
506(18.10)
Conjugate beam method, 252 ( 10.2)
Coulomb's wedge theory, 174 (6. 1 8)
Curvature of the bending beam, 189 (7.2)
Dams, 141 (6.1)
-Conditions for the stability, 156(6.5)
-Rectangular, 141 (6.2)
-Trapezoidal, 146(6.3), 153(6.4)
Deck type trusses, 78 (4.3)
Deflection at a section 2 17 (8.2)
Deflection of perfect frames, 272 (||.2)
-Horizontal, 273(11.5)
-Vertical, 273 (11.4)
Detereminate structures, 11 (1.18)
Differential calculus (useful data), 9(].|4)
Distribution factors, 500(18.7)
Double integration method,2 17 (8.3)
Earth pressure on retaining walls,167(6.13)
-Active. 167 (6.14)
- Passive, 167 (6.15)
Eccentric loading, 120(5.2)
Eccentricity,Limit of, 133(5.7)
Eddy's theorem for bending moments, 346
(13.4)
-Proof of 346 (13.5)
-Use of 346 (13.6)
Effect of change in temperature in a twohinged arch, 599 (20.9)
-three-hinged arch, 364 (13.13)
-rollingloads, 13(2.1)
Effect on the cable due to change in
temperature, 322 (12.14)
Empirical formulae forcolumns,654(22.14)
-I.S.Code, 660 (22.22)
-Johnson's,659(22.16),660(22.18)
-Rankine's 654 (22.15)
Equation of the cable, 304 (9.3)
Equivalent lengthofa column, 649(22.1 1)
Equilibrium ofcable under a given system
ofloading,303 (12.2)
Equivalent u.d,l.,46(2.12)
Euler's column theory, 643 (22.3)
-formula.Limitationsof650(22.13)
Externally indeterminate structures,12(1-2)
F
Factor, Carry over, 496 (18.3)
-Distribution,500(18.7)
I
-Stiffness. 499 (18.6)
failure ofa column or a strut, 642 (22.2)
Fixingmoment of a fixed beam, 406 ( 15 4)
560(19-5)
-carrying a central point load,407( 15.5)
-carrying an eccentric point load, 4 10
(15.6)
-carryinga uniformlydistributed load,
415(15.7)
-due to gradually varying load, 422
(15.8)
_ due to siniking of a support, 426 (15.9)
Focal length due to the combined dead
load and live, 52(2.14)
Forces due to error in the length of a
number in a redundant frame, 627 (2 1.6)
F P.S. units, 4 (1.4)
Frames, Portal, 476 ( 1 7.10), 527 (18.14),
570(19.6)
Frames with two or more redundant
members, 630 (21.7)
Fundamental units, 3 ( 1.2)
Graphical method for active earth
pressure, 175 (6.19)
-for deflection, 291 (11.8)
- for Rankine's theory, 175 (6.20)
Guidepulley support for suspension cable,
312(12.9)
lorizontal deflection of perfect frames,
273(1L5)
onzontal thrust in cable, 304 (9.4)
ln three-hinged arch, 348 (13.10)
hinged 583 (20.2),
7(20.6), 590 (20.7), 594 (20.8)
•ndex a
~ flexural defn
'"^wlines.STGjj
- for COnCentraledl^d. 58(3 3)
63(^jnn|yd«tributedlo9d,61(34)t
-“ses of, 57(32)
lnde,erminate structures, 12(| 19)
-Externally, 12(12|)
“Internally, 12(120)
-India Standard code forcolumns,
659(22.22)
l.L. for trussed bridges, 78 (4.1)
- for a composite truss, 108 (4.8)
- for a deck type-Warren truss 100
(4.7)
- for an inclined Pratt truss,91 (4.6)
- for a Pratt truss with parallel chords,
79(4.5)
l.L. for moving loads over three-hinged
arches, 360(13.12),369(13.16),
371(10.17)
- over two-hinged arches, 608 (20.11)
-over suspension bridges, 327(12.17),
333(12.19), 337(12.21)
Integral calculus (useful data), 11(1.14)
J
Johnson's formula for column, 659 (22.16)
-parabolic, 660(22.18)
-straight line,659(22.17)700 Theory of Structures
K
Kilogram, 4(1.7)
L
Length ofthc cable. 316(12 1 1)
- when supported al different eve
319(12.13)
— when supported at same leve ,
316(12.12)
Line of thrust, 344 ( 13.2)
Limit ofeccentricity, 133 (5.7)
-of Euler's formula, 650(22.13)
Load factor, 670(23.6)
Longcolumns subject to eccentric loading,
662(22.20)
M
Macaulay's method. 205 (7.10)
Maximum height of dam, 166 (6.1 )
Maxwell's method for the forces in
redundant frame, 616 (21.5)
Methods for findingout the deflect.on. 273
(11.6)
-graphical method, 291(118,
-unit load method,274 (11.7)
Metre, 4 (1.6)
Minimum base width of a dam, 161 (6.1 )
M.K.S. units, 4(1 4)
Mohr diagram, 297(11 13)
- theorem, 235 (9.2)
Moment area method. 235 (9.1)
P
Parabolic arch. 347 (13.8)
Passive earth pressure due to retaining
Walls. 167(6.15)
po'^ frames. 476(17.10). 527(1834)
<70(19.6)
Symmetrical, 476(17.11)
527(18.15), 570(19.7)
Unsvmmetrical, 479(17.12)
531(18.16), 574(19.9)
-with hinged legs. 571 (19.8)
Pratt truss, Influence lines for, 79(4.5),
91 (4.6)
Priniciples for the influence lines for the
forces in the members of the trussed
bridges, 79(4.4)
Proposition for maximum B.M. under any
given load, 33 (2.9)
- at any section in the span, 40 (2.11)
Propped beam with u.d.I., 397 (14.6)
Propped cantilever, 381 (14.1)
-withpoint load,389 (14.4)
-with u d.L, 382 (14.3)
Proof of Clapeyron's theorem of three
moments, 433 (16.3)
-Castigliano's first theorem, 615 (21.4)
- Eddy's theorem, 346 (13.5)
-Unit load method for deflection,
274 (11.7)
Rankine's formula for columns, 654 (22.15)
- theory for active earth pressure.
168(6.17) . .
Ratio of sway moments at the joints o
column heads and beams, 532 (18-
- when both the ends are fixe ,-
(18.19)
u. . 5,2
- when both the ends are hingeo.
(1818) L ,h,r
-when one end is fixed and the othe
hinged,55 1 (18.20)
Reaction of a prop, 381(14-2)
Rectangular dam, 141 (6.2)
Redundant frames, 614(21.2)
- with two or more redundant members
630(21.7)
Rehbann's graphical method for coulomb's
theory. 178(6.21)
Relation between slope, deflection and
radius of curvature. 190(7.3)
Retaining walls. 167(6.12)
- Earth pressure on, 167 (6.13)
Roller support for suspension cables, 3 13
(12.10)
Rollingloads 13(2! I)
_ Effects of 13 (2.2)
s
Second, 4(1-8)
Several concentrated rolling loads, 33 (2.8),
68 (3.6)
S.F. diagram for the combined dead load
and live load, 51 (2.13)
Shape factor, 670 (23.7)
Sign conventions for columns and struts,
643 (22.5)
-for column analogy method, 558(19.2)
-for rolling loads, 14(2.3)
-formomentdistributionmethod,496
(18.2)
-for slope deflectionmethod, 459(17.4)
Simple frames, 470( 17.9), 524 (18.13)
Simply supported beam with central point
load, 192(7.6)
- with an eccentric point load, 194 (7.7)
-with gradually varying load, 203 (7.9)
- with u.d.L, 200(7.8), 397 (14.6)
Single concentratedrollingload, 14(2.4)
Sinkingofsupport, 426(15.9)
-ofprop, 401 (14.7)
Slenderness ratio, 649(22.12)
Sl°peatapoint, 191 (7.4)
-deflection equations,459(17.4),461
•ndex a 7q’
- m a twohinged arch,602 (20 10»
^ength of Materials, 1 1 (ijgj °
Suspension bridges,302(12 1)
‘^O-hingedstiffeninggirders.337
Sway moments, 53 1 (18.16)
Symmetrical columns with eccentric
loading, 121(5.3)
-about one axis, 121 (5.4)
- about two axes, 126 (5.5)
-portal frames, 476(17.11),527(18 15),
570(19.6) ’ A
System of units, 4 (1.4)
(17.6)
^biltyofdarnJS6
Statically deter 5)
-indeVXT5^
Tension in the cable, 305 (9.5)
-supported at different levels,309(12.7)
-supported at same level,306 (9.6)
Theorem,Castigliano's first,615 (21.3)
Theoretical arch or line of thrust, 344 (13.2)
Theory of active earth pressure, 168 (6.16)
-columnanalogy,559(19.3)
Three-hinged arches, 347 (13.8),347 (13.9)
- supported at different levels,356
(13.11)
Through type trusses, 78 (4.2)
Trapezoidal dams having water face
inclined, 153(6.4)
-vertical 146(6.3)
Trigonometry (useful data), 7(1.13)
Trussed702 Theory of Structures
- beams, 636 (21.8)
-bridges,Influencelines for.79(4.4)
Two concentratedrolling loads, 26 (2.7),
68 (3.6)
Types ofdeflections. 273 ( 1 1.3)
-horizontal,273 (11.5)
-vertical, 273 (11.4)
Types of three-hinged arches, 346 (13.7)
-two-hinged arches, 586 (20.5)
-endconditionsofcolumns,643 (22.6)
- structures, 11 (1.17)
— influence lines, 57 (3. 1)
Useful data, 6(II0
Uses of Eddy's theorem, 346 (13.6)
-influence lines, 57 (3.2)
V
Vertical deflection of perfect frames, 273
(11-4)
u w
Uniformlydistributedrollingload,
- longer than the span, 17(2.5), 61 (3.4)
-shorter than the span,21(2.6),63(3.5)
Unit load method for deflection, 274(11.7)
-Proof of, 274 (11.7)
Units,Fundamental, 3 (1.2)
Unsymmetrical columns with eccentric
loading,129(5.6)
-portal frame, 479(17.12),574(19.9)
-useofEddy's theorem, 346(13.6)
Warren girder, Influence lines for, 100(4.7)
Wedge theory for active earth pressure,
174(6.18)
Wi11iot diagram for deflectionof frames,
291(11.9)
-withonly onejoint fixed,297(11.12)
-withonejoint and thedirectionofother
fixed,294(11.11)
-with twojoints fixed,291 (11.10)
Wind pressure on walls and chimneys, 136
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