R.S. K}IURMI
CONTENTS
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PART 1 STATICALLY DETERMINATE STRUCTURES
3-12
[\TR.ODUCTION
L
Dellnition.
3
Ii rrit-r
: j 4. : !r" N" u
3
Fundamental Units.
3
Derii'ed Units.
3
Sl stems
of Units.
I. Ljnits (International Systems of Units). \Ietre. S
4 4
Kilogram. S:.'ond. Pesentation of Units and Their Values. l,t|t- Rules for S.I. Units. l',&,uftematical Review
:i.
L-.eful Data.
:f. :4
T:ieonometry.
+
4 5 5
6 6 6
.uJ
)lt-erential Calculus. illu;iu Concepts
l0
-i
i,:plied Mechanics :,nt., S::ength of Materials :* T",pes of Structures
10
Slrically Determinate Structures -'0. S;rically Indeterminate Structures .llr. -::ernally Indeterminate Structures ::. lriemally Indeterminate Structures
l1
-
9
11 11
{',
12
t2 12
TI.{.LNG LOADS
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13-56
,---:oduction
:::e;ts of rolling
IJ
loads.
IJ
S-rn conventions.
14
-r single concentrated load.
t4
{ :rnif-ormly distributed load, longer than the span. i :rnitbrmly distributed load, shorter than the span. l;.-i concentrated loads.
2l
t
>;-' eral concentrated loads.
JJ
I
i:-,losition for the maximum bending moment under any given load.
JJ
I ,IL
-fl!"
rrolute r[aximum bending moment. 1: pr'rsition for the maximum bendin! moment :;,iralent uniformly distributed load. (xiii)
tl
26
36
at any given section on the span. 40 46
13. 14. 3.
f,.
6.
for the combined dead 51
Focal length due to combined dead load and live load'
52
s7
INFLUENCE LINES
1. 2. 3. 4. 5. 6. 7. 4.
Shear force and bending moment diagrarn load and iive load.
-77 51
Introduction. Uses of Influence lines. lnfluence lines for a single concentrated load' Influence lines for a uniformly distributed load longer than the span. Influence lines for a uniformly distributed load shofter than the span. Influence lines for two concentrated loads' Influence lines for several concentrated loads'
INFLUENCE LINES FOR TRUSSED
BRIDGES
51 61
63 68 1T
78
-
TI9
78 1. Introduction. 78 2. Through type trusses. 78 3. Deck type trusses. "79 bridges' of trussed 4. Principles for the influence lines for forces in the members 19 5. Influence lines for a Pratt truss with parallel chords' 91 6. Influence lines for an inclined Pratt truss' 100 7. Influence lines for a deck type Warren girder' 108 8. Influence lines for a composite truss. 120'T4O DIRECT AND BENDING STRESSES 120 1. Introduction. "120 2. Eccentric Loading. l2l 3. Columns with H'ccentric Loading. 4.SymmetricalColumnswithEccentricLoadingaboutoneAxis.12| 5.SymmetricalColumnswithEccentricLoadingaboutTwoAxes.126 129 6, Unsymmetrical Columns with Eccentric Loading' ll3 7, Limit oi EccentricitY. -136 8. Wind Pressure on walls and Chimneys' 141 - 188 DAMS AND RETAINING WALLS l4l 1. Introduction. 141 2. Rectangular Dams. 146 3. Trapezoidal Dams with Water Face Vertical' 153 4. Trapezoidal Dams with Water Face Inclined' 156 5. Conditions tbr the Stability of a Dam' 6.ConditiontoAvoidTensionintheMasonryoftheDamatitsBase'|51 157 7. Condition to Prevent the Overturning of the Dam' 158 8. Condition to Prevent the Slicling of Darn' 158 Dam. of the Base the at Masonry 9. Conilition to Prevent the crushing of 161 il). \linrmunr Base Width of a Dam. 166 11 ',1:' r--.,.:r Hersht of a Dam. ' 161 : *_' 16'7 -: :, : . .--: , .' -,- ' - R:trinir,g Wall. 16'7 : { i
:
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,
:..,:
'16'7
16. 17. 18. 19. 20. 11. 12.
Theories of Active Earth Pressure. Rankine's Theory for Active Earth Pressure. Coulomb's Wedge Theory for Active Earth Pressure. Graphical Method for Active Earth Pressure. Graphical Method for Rankine's Theory Rehbann's Graphical Method for Coulomb"s Theory Conditions for the Stability of a Retaining wail
168 168
10. 11.
175 175 178
.
182
189'216
DEFLECTION OF BEAMS
1. :. 3. {. 5. 6. 7. 8. 9.
1',74
,
Introduction. Curvature of the Bending Beam. Relation between Slope, Deflection and Radius of Curvature. Methods for Slope and Deflection at a Section. Double Integration Method for Slope and Deflection. Simply Supported Beam with a Central Point Load. Simply Supported Beam with an Eccentric Point Load. Simply Supported Beam with a Uniformly Distributed Load. Simply Supported Beam with a Gradually Varying Load. Macaulay's Method for Slope and Deflection. Beams of Composite Section.
DEFLECTION OF CANTILEVERS
189 189 190 101
192 192 194 240 203 205 zt-')
217
l. Introduction. 2. Methods for Slope and Deflection at a Section. 3. Double Integration Method for Slope and Deflection.
* 234 . 2r1 211 217 217 220
.1. 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. r+,
DEFLECTION BY MOMENT AREA METHOD
1. 2. 3. 1. 5. 6. 7. 8. 9.
221
223 a1/l
226
228 232
235
251.
235
Introduction.
235
Mohr's Theorems.
Area and Position of the Centre of Gravity of Parabolas. Simply Supported Beam with a Central Point Load. Simply Supported Beam with an Eccentric Point Load. Simply Supported Beam with a Uniformly Distributed Load. Simply Supported Beam with a Gradually Varying Load. Cantilever with a Point Load at the Free end. Cantilever with a Point Load at any Point. 10. Cantilever with a Uniformly Distributed Load. 11. Cantilever with a Gradually Varying Load.
i{. DEFLECTION BY CONJUGATE BEAM METHOD 1. Introduction.
2.
-
Conjugate Beam. (l;1/
l
236 236
238 240 243 246 241 249
250 252
- 27r 252 252
3. Relation between an Actual Beam and the Conjugate Beam. 4. Cantilever with a Point Load at the Free End. '.; 5. Cantilever with a Uniformly Distributed Load. 6. Cantilever with a Gradually Varying Load. 7. Simply Supported Beam with Central point Load. 8. Simply Supporred Beam with an Ecceniric point Loacl. 9. Simply Supporred Beam with a Uniformly Distribured Load.
10. Simply 11.
/-)
')<
25E
260 263
26s 272
1.
Introduction. 2. Perfect frames. 3. Types of deflections. 4. Vertical deflection. 5. Horizontal deflecrion. 6. Methods for tinding out the cleflection. 7. {Jnit load method for deflection. 8. Graphical rnethod for deflection. 9. Williot diagram for deflection. 10. Williot diagram lbr the frames, with two joints fixed. 11. williot diagram for the frames with one ioint and the direction of the other fixed. 12. Williot diagram for the frames with only one joint fixed.
-
273 aa1
zt3 al l zt)
-t1A
291 291 291 294 291 297
..
CABLES AND SUSPENSION BRIDGES
L
2. 3. 4-
5. 6.
18. 9.
302
lntroduction.
Equilibrium of cabie under a given system of loading. Equation of the cable. E{
Anchor cables. Guide pulley support tbr suspension cable.
10. Roller support for suspension cable. 11. Length of the cable. 12. Length of the cable, when supported at the sarrre level. 13. Length of the cable, when supported at differenr levels. 14. Effect on the cable due to change in temperature. 15. Stiffening girders in the suspension bririges. 16. Suspension bridges with three-hinged stiffning girder. 17' Influence lines for moving loads over the suspe'sion bridges with
301 212 212 273
13. Mohr diagrarn. 12.
three-hinged stift-ening girders. concentraied loatl rolli'g over the suspension bridge with three-hinged stifTening girders. Influence lines for a uniformly distributed road rofling over the suspension bridge with three-hinged stiffening girders.
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343 302 303
304 304 305 306 3DD ar^ Jtl
312
3r3 316 316 319 322 325
325
18. Influence lines fbr a single
JZt
19.
32'7
(.ryl)
i
25,i
Supported Beam with a Gradually Varying Load.
DEFLECTION OF PERFECT FRAMES
_
25j
JJ.']
331
:ri. Suspension bridges with two-hinged stifTening girders' :1. Influence lines for a single concentfated load rolling over the suspension bridge with two- hinged stiffening $irders.
,lF
344
THREE-HINGEDARCHES
l. :. i. J. 5. h.
337
- 377 344 344
Introduction. Theoretical arch or line of thrust.
345 346
Actual arch. Eddy's theorem for bending moment. Proof of EddY's theorem.
346 346
Use of EddY's theorem. Types of three-hinged arches. t. Three-hinged Parabolic arch. q. Three-hinged circular arch. 10. Horizontal thrust [n a three-hinged arch' 11. Three-hinged parabolic arch supported at different levels' 12. Straining actions in a three-hinged arch' 13. Effect of change in temperature on a three-hinged arch' l.l. Influence lines for the moving loads over three-hinged arches. 15. Influence lines for a concentrated load moving over three-hinged
circular
346
3+l
J+t 348 356 360
364 365 366
arches.
16. Influence lines for a concentrated loacl moving over three-hinged
369
parabolic arches. 17. Influence lines for a uniformly distributed load moving over three-hinged oarabolic arches.
3tl
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PART 2 STATICALLY INDETERMINATE STRUCTURES
.,{
381
PROPPED CANTILEVERS AND BEAMS
-
381
1. Introduction. 2. Reaction of a ProP. 3. Propped Cantilever with a Uniiormly Distributed Load' -1. Cantilever Propped at an Itltermediate Point' 5. Propped Cantilever with a point load
-381
382 3'39
389
6.SimplySupportedBearnwithaUniformlyDistributedLoadandPropped
7. :5.
391
at the Centre. Sinking of the ProP.
40i 404
FIXED BEAMS
1. 2, 3. 4. 5. 6. 7.
403
Introduction. Advantages of Fixed Beams. Bending Moment Diagrams for Fixed Beams' Fixing Moments of a Fixed Beam' Fixing Moments of a Fixed Beam Carrying a Central Point Load' Fixing Moments of a Fixed Beam Carrying an Eccentric Point Load. Fixing Moments of a Fixed Beam carrying a uniformly Distributed (:rvii)
-
431
444 404
404 406 40'7
L,oad.
410 4l,5
8. 9. 16.
THEOREM OF THREE MOMENTS
1. 2, 3. 4. 5. 6. 7. 8. 9. 17.
Fixing Moments of a Fixed Beam Carrying a Gradually Varying Load from Zero at One End to n per unit length at the Other. Fixing Moments of a Fixed Beam due to Sinking of a Suppoft.
426
-
+J./-
+51 +JZ
334
334 339 444 448 555
458
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Introduction. Assurnption in slope deflection method. Sign conr entions. Slope detlection equations. Slope deflection equations when the supports are at the same level. Slope deflection equations when one of the supports is at a lower level. Application of slope cleflection equations. Continuous beams t Simple frames.
452 462 470 476 476 479
MOMENT DISTRIBUTION METHOD
1. 2. 3. 4.
Introduction. Sign Conventions.
5. 6. 7. 8.
Cany Over Factor for a Beam, Simply Supponed at Both Ends.
Carry Over Factor. Carry Over Factor for a Beam Fixed at One End and Simply Supported at the Other. Stiffness Factor.
l)istribution
495 458 458 459 459 459 461
10. Portal frames. 11. Symmetrical portal frames. 12. Unsymrnetrical portal frames. 18.
457 ia^
Introduction. Bending Moment Diagrams tbr Continuous Beams. Claypeyron's Theorem of Three Moments. Application of Clapeyron's Theorem of Three Moments to various Types of Continuous Beams. Continuous Beams with Simply Supported Ends. Continuous Beams with Fixed End Supports. Continuous Beams with End Span Overhanging. Continuous Beams with a Sinking Support. Continrious Beams Subjected to a Couple.
SLOPE DEFLECTION METHOD
1. 2. 3. 4. 5. 6. 7. 8. 9.
432
42."
F'actors.
496
-
557
493 493 493 491 498 499 500
Application of Moment Distribution Method to Various Types of
Continuous Beams. 9. Beams with Fixed End Supports. 1.0. Beams with Simply Supported Ends.
11. Beams with End Span Overhanging. 12. Beams With a Sinking Support. 13. Simple Frames 14. Portai fiames 15. Symmetrical portal frames (xviii)
502 502 506 509
5r7 \,ta
527
5)7
