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604 Chapter 16 Continuous Beams and Frames Table 16.4 Final Moments of Example 16.8 after Moment Redistribution Section Location Case 1 Case 2 Case 3 Case 4 Case 5 DL Moments LL Maximum Negative LL Maximum Positive DL + LL (1) + (2) Maximum Negative DL + LL (1) + (3) Maximum Positive Support A 0 0 0 0 0 B −308.5 −260.4 +21.4 −568.9 a −287.1 C −205.7 −231.5 — −437.2 a −205.7 D −308.5 −260.4 +21.4 −568.9 a −287.1 E 0 0 0 0 0 Midspan AB 245.8 −71.3 228.7 ±174.5 ±474.5 a BC 142.9 −118.6 181.2 ±24.3 ±324.1 a CD 142.9 −118.6 181.2 ±24.3 ±324.1 a DE 245.8 −71.3 228.7 ±174.5 ±474.5 a a Final maximum and minimum design moments. 8. The final maximum and minimum moments after moment redistribution are shown in Table 16.4. The moment envelope is shown in Fig. 16.32h. 9. In this example, the midspan sections are used for simplicity: The midspan moments are not necessarily the maximum positive moments. In the case of the end spans AB and DE, the maximum moment after 10% moment redistribution is equal to (w D L 2 )/12.2 and occurs at 0.4L from A and D. Example 16.9 Use the ACI Code limitation, determine the permissible redistribution of negative moments at supports B, C, D, andE of the continuous beam ABCDEF shown in Fig. 16.33. The beam has a rectangular section, b = 12 in., h = 22 in., and d = 19.5 in., and it is reinforced as shown in the following table (f ′ c = 4ksi and f y = 60 ksi). Solution 1. For f c ′ = 4ksi and f y = 60 ksi, ρ b = 0.0285. The ACI Code redistribution factor was given as follows: ) ρ − ρ′ q = 20 (1 − (Eq. 16.25) ρ b 2. The ACI Code redistribution factor is a function of the net tensile strain, ε t , and varies between 7.5 and 20%, as shown in Fig. 16.31. q ′ = 1000ε t ε t = 0.003 + f y ∕E s ρ∕ρ b − 0.003
Summary 605 A B C D E F Typical section at support 2.5" Tension bars A s 22" 2.5" 12" Compression bars A' s Figure 16.33 Example 16.9. and ε t = 0.005 ρ∕ρ b − 0.003 (for f y = 60 ksi) The following table shows the values of q and q ′ , which are not compatible. Support Tension Bars (A s ) ρ Compression ρ − ρ ′ Bars (A ′ ) S ρ′ ρ b q% ε t q ′ B 3 no. 9 0.01282 0 0 0.45 11.0 0.0113 11.3 C 3 no. 10 0.0160 0 0 0.56 8.8 0.006 0 D 3 no. 6 0.00564 0 0 0.198 16.0 0.0226 20 E 4 no. 8 0.01342 3 no. 6 0.0056 0.273 14.5 0.0153 15.3 SUMMARY Sections 16.1–16.3 In continuous beams, the maximum and minimum moments are obtained by considering the dead load acting on all spans, whereas pattern loading is considered for live or moving loads, as shown in Figs. 16.2 and. 16.3. The ACI moment coefficients described in Chapter 9 may be used to compute approximate values for the maximum and minimum moments and shears. Sections 16.4 and 16.5 A frame subjected to a system of loads may be analyzed by the equivalent frame method. Frames may be statically determinate or indeterminate.
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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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17.8 Analysis of Two-Way Slabs by t
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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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Problems 723 Figure 18.23 Problem 1
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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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Appendix A Design Tables (U.S. Cust
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1006 Appendix B Design Tables (SI U
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1014 Appendix C Structural Aids Tab
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1034 Index Beams (continued) stress
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1036 Index F Factored loads, 91 Fai
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1038 Index Seismic design (continue
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Structural Concrete - Hassoun

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