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1030 Appendix C <strong>Structural</strong> Aids Table C.7 Maximum and Minimum Moments in Equal-Span Continuous Beams 7. Uniform loads: M = wL2 K where w = (D.L. + L.L.) D.L. = Uniform dead load L.L. = Uniform live load per unit length Values of coefficient K First span AB Second support B (positive moment) (negative moment) Ratio Number of spans Number of spans DL/w 2 3 4 5 2 3 4 5 0.0 10.5 10.0 10.2 10.1 8.0 8.6 8.3 8.3 0.1 10.8 10.2 10.4 10.3 8.0 8.7 8.4 8.5 0.2 11.1 10.4 10.6 10.6 8.0 8.8 8.5 8.6 0.3 11.4 10.6 10.9 10.8 8.0 9.0 8.6 8.7 0.4 11.8 10.9 11.1 11.0 8.0 9.1 8.6 8.8 0.5 12.1 11.1 11.4 11.3 8.0 9.2 8.8 8.9 0.6 12.5 11.4 11.7 11.6 8.0 9.4 8.9 9.0 0.7 12.9 11.6 12.0 11.9 8.0 9.5 9.0 9.1 0.8 13.3 11.9 12.3 12.2 8.0 9.7 9.1 9.2 0.9 12.8 12.2 12.6 12.5 8.0 9.8 9.2 9.4 1.0 14.3 12.5 13.0 12.8 8.0 9.9 9.3 9.5 Second span BC (positive moment) Third support C (negative moment) Third span CD (positive moment) Interior Interior Ratio span support Number of spans Spans Span (positive (negative DL/w 3 4 5 4 5 5 moment) moment) 0.0 13.4 12.4 12.7 9.3 9.0 11.7 12.0 8.8 0.1 14.3 13.2 13.5 9.7 9.3 12.3 12.6 9.1 0.2 15.4 14.0 14.3 10.0 9.6 12.9 13.3 9.8 0.3 16.7 14.9 15.3 10.4 9.9 13.6 14.1 9.5 0.4 18.2 16.0 16.5 10.8 10.2 14.3 15.0 9.9 0.5 20.0 17.2 17.9 11.5 10.5 15.2 16.0 10.1 0.6 22.2 18.7 19.5 11.7 10.9 16.2 17.2 10.5 0.7 25.0 20.4 21.4 12.2 11.3 17.3 18.4 10.8 0.8 28.6 22.4 23.8 12.7 11.7 18.5 20.0 11.2 0.9 33.3 24.9 26.6 13.3 12.2 20.0 21.8 11.6 1.0 40.0 28.3 30.0 14.0 12.7 21.7 24.0 12.0 (continued)
Appendix C <strong>Structural</strong> Aids 1031 Table C.7 (Continued) Example: K values 1. 2. DL w = 0.4 DL w = 1.0 8. Concentrated loads: P ′ = concentrated dead load P ′′ = concentrated live load ( ) P ′ M = + P′′ L K 1 K 2 First Span AB Second Support B K 1 (DL) K 2 (LL) K 1 (DL) K 2 (LL) Number of Spans 2 3 4 2 3 4 2 3 4 2 3 4 Central load 6.40 5.71 5.89 4.92 4.70 4.76 5.35 6.67 6.22 5.33 5.71 5.53 One-third-point loads 4.50 4.09 4.20 3.60 3.46 3.50 3.00 3.75 3.50 3.00 3.21 3.11 One-fourth-point loads 3.67 3.20 3.34 2.61 2.46 2.50 2.13 2.67 2.49 2.13 2.28 2.21 Second Span BC Third Support C K 1 K 2 K 1 K 2 Number of Spans 3 4 3 4 4 4 Central load 10.00 8.61 5.71 5.46 9.33 6.22 One-third-point loads 15.00 9.00 5.00 4.50 5.25 3.50 One-fourth-point loads 8.00 6.05 3.20 3.01 3.72 2.49 Example: K values ( P ′ K 1 (dead load) M AB (max) = 5.71 + P′′ 4.7 ( P ′ −M B (max) = 6.67 + P′′ 5.71 ( P ′ K 2 (live load) M BC (max) = 10 + P′′ 5.71 ) L ) L ) L
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Structural Concrete
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Portions of this publication reprod
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vi Contents 2.9 Shear Modulus 24 2.
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viii Contents 8 Design of Deep Beam
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x Contents 14.9 Design Requirements
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xii Contents 21.5 Circular Beam Sub
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xiv Preface 5. To explain the failu
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xvi Preface A companion Web site fo
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xviii Notation C c C m C r C s C t
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xx Notation M 1s Factored end momen
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xxii Notation ζ Parameter for eval
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xxiv Conversion Factors To Convert
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CHAPTER1 INTRODUCTION Water Tower P
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1.3 Advantages and Disadvantages of
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1.6 Units of Measurement 5 A second
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1.7 Loads 7 Table 1.2 Density and S
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1.10 Structural Concrete Design 9 F
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1.12 Concrete High-Rise Buildings 1
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References 13 Concrete bridge, Knox
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CHAPTER2 PROPERTIES OF REINFORCED C
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2.2 Compressive Strength 17 Table 2
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2.4 Tensile Strength of Concrete 19
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2.6 Shear Strength 21 The splitting
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2.8 Poisson’s Ratio 23 For practi
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2.12 Creep 25 3. Type, Amount, and
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2.13 Models for Predicting Shrinkag
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2.14 Unit Weight of Concrete 69 Det
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2.17 Lightweight Concrete 71 Castin
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2.19 Steel Reinforcement 73 have pr
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2.19 Steel Reinforcement 75 Table 2
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2.19 Steel Reinforcement 77 Table 2
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References 79 Section 2.14 The unit
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Problems 81 2.10 Determine the modu
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CHAPTER3 FLEXURAL ANALYSIS OF REINF
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3.3 Behavior of Simply Supported Re
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3.3 Behavior of Simply Supported Re
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3.4 Types of Flexural Failure and S
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3.5 Load Factors 91 h c b d d t A s
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3.6 Strength Reduction Factor φ 93
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3.8 Equivalent Compressive Stress D
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3.8 Equivalent Compressive Stress D
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3.9 Singly Reinforced Rectangular S
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3.11 Adequacy of Sections 109 accom
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3.11 Adequacy of Sections 111 2. Ch
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3.12 Bundled Bars 113 2. Check ρ m
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3.13 Sections in the Transition Reg
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3.14 Rectangular Sections with Comp
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3.15 Analysis of T- and I-Sections
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3.18 Sections of Other Shapes 137 3
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3.19 Analysis of Sections Using Tab
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3.20 Additional Examples 141 Soluti
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3.21 Examples Using SI Units 143 Fo
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Summary 145 SUMMARY Flowcharts for
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Summary 147 Note that (A s f y −
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Problems 149 3.2 Rectangular sectio
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Problems 151 Figure 3.41 Problem 3.
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4.2 Rectangular Sections with Tensi
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4.3 Spacing of Reinforcement and Co
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4.4 Rectangular Sections with Compr
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4.5 Design of T-Sections 169 3. Com
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4.5 Design of T-Sections 171 The de
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4.5 Design of T-Sections 173 A s Fi
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4.6 Additional Examples 175 Example
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4.6 Additional Examples 177 1.5 2.3
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4.7 Examples Using SI Units 179 Sol
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Summary 181 SUMMARY Sections 4.1-4.
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Summary 183 There are two cases: Ca
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Problems 185 No. M u (K⋅ft) b (in
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5.2 Shear Stresses in Concrete Beam
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5.3 Behavior of Beams without Shear
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5.4 Moment Effect on Shear Strength
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5.5 Beams with Shear Reinforcement
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5.5 Beams with Shear Reinforcement
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5.6 ACI Code Shear Design Requireme
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5.7 Design of Vertical Stirrups 201
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5.7 Design of Vertical Stirrups 203
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5.8 Design Summary 205 5.8 DESIGN S
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5.8 Design Summary 207 Choose no. 3
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5.9 Shear Force Due to Live Loads 2
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5.9 Shear Force Due to Live Loads 2
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5.10 Shear Stresses in Members of V
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5.10 Shear Stresses in Members of V
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5.11 Examples Using SI Units 217 M
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5.11 Examples Using SI Units 219 Ta
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5.11 Examples Using SI Units 221 5.
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Problems 223 3. R. C. Fenwick and T
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Problems 225 11.1 K/ft Figure 5.25
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6.2 Instantaneous Deflection 227 Ta
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6.2 Instantaneous Deflection 229 wh
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6.2 Instantaneous Deflection 231 (a
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6.3 Long-Time Deflection 233 Then c
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6.5 Deflection Due to Combinations
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6.6 Cracks in Flexural Members 243
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6.6 Cracks in Flexural Members 245
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6.7 ACI Code Requirements 247 have
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6.7 ACI Code Requirements 249 Check
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6.7 ACI Code Requirements 251 Choos
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References 253 2. Maximum crack wid
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CHAPTER7 DEVELOPMENT LENGTH OF REIN
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7.2 Development of Bond Stresses 25
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7.3 Development Length in Tension 2
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7.3 Development Length in Tension 2
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7.4 Development Length in Compressi
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7.5 Summary for Computation of I d
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7.6 Critical Sections in Flexural M
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7.6 Critical Sections in Flexural M
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7.7 Standard Hooks (ACI Code, Secti
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7.7 Standard Hooks (ACI Code, Secti
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7.8 Splices of Reinforcement 277 Fi
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7.8 Splices of Reinforcement 279 So
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7.9 Moment-Resistance Diagram (Bar
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7.9 Moment-Resistance Diagram (Bar
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Summary 285 Let A s = 0.018(10)(17)
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Problems 287 7. C. O. Orangum, J. O
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Problems 289 Figure 7.17 (33 kN/m).
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8.3 Strut-and-Tie Model 291 D B D D
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8.4 ACI Design Procedure to Build a
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8.5 Strut-and-Tie Method According
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8.6 Deep Members 303 This equation
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8.6 Deep Members 305 that cause cra
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8.6 Deep Members 307 P u = 768 K D
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8.6 Deep Members 309 Strut Nodal zo
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8.6 Deep Members 311 V u = 160 K CL
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8.6 Deep Members 313 Centroid of st
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8.6 Deep Members 315 2. Check if be
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8.6 Deep Members 317 9. Check ancho
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8.6 Deep Members 319 Pu = 766 K 6.0
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References 321 No. 9 bar @3.5" c/c
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Problems 323 11.3’ 11.3’ W LL W
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9.1 Types of Slabs 325 (a) (b) (c)
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9.2 Design of One-Way Solid Slabs 3
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9.6 Distribution of Loads from One-
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9.7 One-Way Joist Floor System 335
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9.7 One-Way Joist Floor System 337
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References 339 One-way ribbed slab
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Problems 341 9.6 Repeat Problem 9.4
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10.2 Types of Columns 343 Figure 10
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10.4 ACI Code Limitations 345 (a) (
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10.5 Spiral Reinforcement 347 Table
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10.8 Long Columns 349 reinforced co
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10.8 Long Columns 351 3. Design of
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References 353 Section 10.5 Minimum
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Problems 355 Number f ′ c (ksi) P
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11.1 Introduction 357 B C H A A D V
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11.3 Load-Moment Interaction Diagra
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11.4 Safety Provisions 361 11.4 SAF
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11.5 Balanced Condition: Rectangula
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11.6 Column Sections under Eccentri
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11.7 Strength of Columns for Tensio
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11.7 Strength of Columns for Tensio
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11.8 Strength of Columns for Compre
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11.10 Rectangular Columns with Side
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11.10 Rectangular Columns with Side
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11.11 Load Capacity of Circular Col
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11.12 Analysis and Design of Column
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11.12 Analysis and Design of Column
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11.13 Design of Columns under Eccen
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11.14 Biaxial Bending 397 5 no. 10
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11.15 Circular Columns with Uniform
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11.15 Circular Columns with Uniform
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11.17 Parme Load Contour Method 403
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11.18 Equation of Failure Surface 4
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11.19 SI Example 411 3. Compute the
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Summary 413 SUMMARY Sections 11.1-1
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Problems 415 REFERENCES 1. B. Brest
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Problems 417 16 no. 10 bars Figure
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Problems 419 11.12 Repeat Problem 1
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12.2 Effective Column Length (Kl u
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12.3 Effective Length Factor (K) 42
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12.4 Member Stiffness (EI) 425 Long
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12.5 Limitation of the Slenderness
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12.6 Moment-Magnifier Design Method
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Summary 439 3. The value of K can b
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Problems 441 7. R. Green and J. E.
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CHAPTER13 FOOTINGS Office building
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13.2 Types of Footings 445 Vertical
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13.2 Types of Footings 447 Figure 1
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13.4 Design Considerations 449 Figu
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13.4 Design Considerations 451 This
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13.4 Design Considerations 453 c Co
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13.5 Plain Concrete Footings 459 th
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13.5 Plain Concrete Footings 461 No
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13.5 Plain Concrete Footings 463 c
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13.5 Plain Concrete Footings 465 Th
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13.5 Plain Concrete Footings 467 8'
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13.5 Plain Concrete Footings 469 14
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13.5 Plain Concrete Footings 471 Fi
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13.6 Combined Footings 473 Figure 1
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13.6 Combined Footings 475 (Assumed
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13.6 Combined Footings 477 16″ ×
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13.8 Footings under Biaxial Moment
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13.8 Footings under Biaxial Moment
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13.10 Footings on Piles 483 13.9 SL
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Summary 485 V Required d = u (1000)
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Problems 487 Section 13.5 Plain con
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Problems 489 Table 13.3 Problem 13.
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14.2 Types of Retaining Walls 491 F
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14.4 Active and Passive Soil Pressu
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14.4 Active and Passive Soil Pressu
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14.5 Effect of Surcharge 497 The ac
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14.7 Stability Against Overturning
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14.9 Design Requirements 501 Figure
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14.10 Drainage 503 Example 14.1 The
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14.10 Drainage 505 c. The flexural
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14.10 Drainage 507 Figure 14.12 Exa
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14.10 Drainage 509 The total resist
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14.10 Drainage 511 concrete on the
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14.11 Basement Walls 513 Figure 14.
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14.11 Basement Walls 515 No. 4 @ 12
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Summary 517 Figure 14.17 Example 14
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Problems 519 Figure 14.18 Problem 1
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Problems 521 the coefficient of fri
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CHAPTER15 DESIGN FOR TORSION Apartm
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15.3 Torsional Stresses 525 Figure
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15.3 Torsional Stresses 527 Table 1
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15.6 Torsion Theories for Concrete
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15.8 Torsion in Reinforced Concrete
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15.9 Summary of ACI Code Procedures
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References 551 Equation U.S. Custom
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Problems 553 3 no. 9 Figure 15.17 P
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CHAPTER16 CONTINUOUS BEAMS AND FRAM
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16.2 Maximum Moments in Continuous
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16.2 Maximum Moments in Continuous
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16.3 Building Frames 561 2 no. 9 4
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16.4 Portal Frames 563 Figure 16.8
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16.6 Design of Frame Hinges 565 For
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16.6 Design of Frame Hinges 567 Fig
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16.6 Design of Frame Hinges 573 d.
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16.6 Design of Frame Hinges 575 Fro
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16.6 Design of Frame Hinges 577 iii
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16.7 Introduction to Limit Design 5
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16.8 The Collapse Mechanism 581 tra
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16.11 Limit Analysis 583 Example 16
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16.11 Limit Analysis 585 Figure 16.
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16.12 Rotation of Plastic Hinges 58
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16.13 Summary of Limit Design Proce
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16.13 Summary of Limit Design Proce
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16.14 Moment Redistribution of Maxi
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Summary 605 A B C D E F Typical sec
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Problems 607 Table 16.1 gives the d
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17.2 Types of Two-Way Slabs 611 Fig
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17.2 Types of Two-Way Slabs 613 Fig
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17.4 Design Concepts 615 Slabonbeam
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17.4 Design Concepts 617 Figure 17.
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17.5 Column and Middle Strips 619 T
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17.6 Minimum Slab Thickness to Cont
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17.6 Minimum Slab Thickness to Cont
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17.7 Shear Strength of Slabs 625 Fi
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17.7 Shear Strength of Slabs 627 Fi
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17.8 Analysis of Two-Way Slabs by t
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17.10 Transfer of Unbalanced Moment
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(a) Figure 17.33 (a) Planofthewaffl
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17.11 Waffle Slabs 675 Table 17.12
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17.11 Waffle Slabs 677 (a) (b) M 0
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17.11 Waffle Slabs 679 Table 17.13
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17.12 Equivalent Frame Method 681 b
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17.12 Equivalent Frame Method 683 t
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17.12 Equivalent Frame Method 685 T
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17.12 Equivalent Frame Method 687 F
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17.12 Equivalent Frame Method 689 F
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17.12 Equivalent Frame Method 691 T
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Problems 693 Section 17.12 1. In th
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Problems 695 17.5 (Flat slabs) Use
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18.1 Introduction 697 Figure 18.1 P
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18.2 Types of Stairs 699 Figure 18.
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18.2 Types of Stairs 707 Free-stand
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18.2 Types of Stairs 711 For a symm
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18.3 Examples 713 2. The width of s
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18.3 Examples 715 Let d = 7.9 − 0
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18.3 Examples 717 1 no. 3 / step No
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18.3 Examples 719 6. The transverse
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Summary 721 3. Calculate the reinfo
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19.1 Prestressed Concrete 725 Figur
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19.1 Prestressed Concrete 727 f ′
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19.1 Prestressed Concrete 729 Addin
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19.1 Prestressed Concrete 731 may b
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19.1 Prestressed Concrete 733 Figur
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19.2 Materials and Serviceability R
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19.3 Loss of Prestress 737 Table 19
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19.3 Loss of Prestress 739 and ( Fi
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19.3 Loss of Prestress 741 where P
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19.3 Loss of Prestress 743 2. Loss
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19.3 Loss of Prestress 745 4. Loss
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19.4 Analysis of Flexural Members 7
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19.5 Design of Flexural Members 757
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19.6 Cracking Moment 763 The maximu
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19.7 Deflection 765 called camber.
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19.8 Design for Shear 767 The cambe
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19.8 Design for Shear 769 Figure 19
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19.8 Design for Shear 771 3. The mi
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19.8 Design for Shear 773 Use d p =
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19.9 Preliminary Design of Prestres
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19.10 End-Block Stresses 777 The co
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19.10 End-Block Stresses 779 Figure
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Summary 781 Section 19.5 The nomina
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Problems 783 27. Y. Guyon. Prestres
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Problems 785 b. Locate the tendons
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20.2 Seismic Design Category 787 20
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20.2 Seismic Design Category 789 Ta
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20.2 Seismic Design Category 791 Fi
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20.2 Seismic Design Category 795 Ta
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20.2 Seismic Design Category 803 St
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20.3 Analysis Procedures 805 Table
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20.3 Analysis Procedures 807 The la
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20.3 Analysis Procedures 809 Step 5
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20.3 Analysis Procedures 811 Table
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20.3 Analysis Procedures 813 Exampl
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20.3 Analysis Procedures 815 254 6
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20.3 Analysis Procedures 817 9. Det
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20.5 Special Requirements in Design
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Problems 857 20.5 Design the transv
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21.2 Uniformly Loaded Circular Beam
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21.3 Semicircular Beam Fixed at End
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21.3 Semicircular Beam Fixed at End
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21.4 Fixed-End Semicircular Beam un
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21.4 Fixed-End Semicircular Beam un
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21.5 Circular Beam Subjected to Uni
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21.6 Circular Beam Subjected to a C
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21.6 Circular Beam Subjected to a C
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21.7 V-Shape Beams Subjected to Uni
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21.8 V-Shape Beams Subjected to a C
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21.8 V-Shape Beams Subjected to a C
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Summary 885 Figure 21.12 Example 21
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CHAPTER22 PRESTRESSED CONCRETE BRID
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22.2 Typical Cross Sections 889 22.
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22.3 Design Philosophy of AASHTO Sp
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22.4 Load Factors and Combinations
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22.4 Load Factors and Combinations
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22.5 Gravity Loads 897 Table 22.10
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22.5 Gravity Loads 899 Design tande
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22.6 Design for Flexural and Axial
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22.7 Design for Shear (AASHTO 5.8)
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22.8 Loss of Prestress (AASHTO 5.9.
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22.9 Deflections (AASHTO 5.7.3.6) 9
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CHAPTER23 REVIEW PROBLEMS ON CONCRE
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Review Problems on Concrete Buildin
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Design and Analysis Flowcharts 971
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Page 1007 and 1008: Design and Analysis Flowcharts 979
Page 1023 and 1024: Appendix A Design Tables (U.S. Cust
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Page 1034 and 1035: 1006 Appendix B Design Tables (SI U
Page 1042 and 1043: 1014 Appendix C Structural Aids Tab
Page 1062 and 1063: 1034 Index Beams (continued) stress
Page 1064 and 1065: 1036 Index F Factored loads, 91 Fai
Page 1066 and 1067: 1038 Index Seismic design (continue
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Structural Concrete - Hassoun

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