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218 Chapter 5 Shear and Diagonal Tension 8¢ 0″ d = 19.5″ 17.6″ 14.5″ 12″ 10.75″ d = 9.5″ α (a) 2304 K·in. 1726 0 18″ 48″ 912 396 183 BMD 24″ 12″ 12″ (b) SFD 34 K 30.25 K 24 K (c) 19 K 16.5 K 14 K 0 126 Resisted by concrete 0 126 psi 148 S = 152 8.8″ 3 # 9 160 173 182 196 psi 7.2″ 6″ 5.3″ 4.75″ (d) Bent bars if needed 4″ 2 # 3 3 × 8″ 3 × 7″ 10 × 4.5″ 2″ 962 (e) Figure 5.20 Example 5.4: Web reinforcement for beam of variable depth.
5.11 Examples Using SI Units 219 Table 5.4 Shear Reinforcement Formulas U.S. Customary Units V u = design shear SI Units V u = design shear Maximum ( design V u at distance d from face of support. V c = 2.0λ √ ) ( f c ′ b w d V c = 0.17λ √ ) f c ′ b w d [ V c = 1.9λ √ ( )] [ f c ′ V + 2500ρ u d w b M w d V c = 0.16λ √ ( )] f c ′ V + 17.2ρ u d w b u M w d u V u d V u d ρ w = A s b w d V c ≤ ( 3.5λ √ f ′ c ≤ 1.0 M) u ρ w = A s b w d b w d V c ≤ ( 0.29λ √ f ′ c ≤ 1.0 M u ) b w d V u = φV c + φV s V u = φV c + φV s Vertical stirrups φV s = V u −φ V c S = A v f yt d/V s Minimum A v = 50b w S ≤ f yt 0.75 √ ( ) bw f c ′ S f yt Maximum S = A v f yt 50b w ≥ φV s = V u − φ V c S = A v f yt d/V s Minimum A v = 0.35b w S ≤ f yt 0.0062 √ ( ) bw f c ′ S f y A v f yt 0.75 √ Maximum S = A v f yt ≥ f c ′ b 0.35b w w For vertical web reinforcement Maximum S = 1 d ≤ 24 in. 2 Maximum S = 1 d ≤ 600 mm 2 If V s ≤ 4.0 √ ( f c ′ bw d ) If V s ≤ 0.33 √ ( f c ′ bw d ) Maximum S = d∕4 = 12 in. Maximum S = d∕4 = 300 mm If V s > 4.0 √ ( f c ′ bw d ) If V s > 0.33 √ ( f c ′ bw d ) V s ≤ 8 √ ( f c ′ bw d ) V s ≤ 0.67 √ ( f c ′ bw d ) Otherwise increase the dimensions of the section. Series of bent bars or inclined stirrups V A v = s S f yt d (sin α + cos α) For α = 45 ∘ , S = 1.4A υ f y d∕V s V A v = s S f yt d (sin α + cos α) For α = 45 ∘ , S = 1.4A υ f y d∕V s For single bent bar or group of bars, parallel and bent in one position A v = V s A f yt sin α v = V s f yt sin α For α ( = 45 ∘ , A y = 1.4V s ∕f yt For α = 45 ∘ , A v = 1.4V s ∕f yt V s ≤ 3 √ ) ( f c ′ b w d V s ≤ 0.25 √ ) f c ′ b w d A v f y 0.062 √ f ′ c b w
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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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4.4 Rectangular Sections with Compr
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Page 197 and 198: 4.5 Design of T-Sections 169 3. Com
Page 199 and 200: 4.5 Design of T-Sections 171 The de
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Page 203 and 204: 4.6 Additional Examples 175 Example
Page 205 and 206: 4.6 Additional Examples 177 1.5 2.3
Page 207 and 208: 4.7 Examples Using SI Units 179 Sol
Page 209 and 210: Summary 181 SUMMARY Sections 4.1-4.
Page 211 and 212: Summary 183 There are two cases: Ca
Page 213 and 214: Problems 185 No. M u (K⋅ft) b (in
Page 215 and 216: Problems 187 Figure 4.17 Problem 4.
Page 217 and 218: 5.2 Shear Stresses in Concrete Beam
Page 219 and 220: 5.3 Behavior of Beams without Shear
Page 221 and 222: 5.4 Moment Effect on Shear Strength
Page 223 and 224: 5.5 Beams with Shear Reinforcement
Page 225 and 226: 5.5 Beams with Shear Reinforcement
Page 227 and 228: 5.6 ACI Code Shear Design Requireme
Page 229 and 230: 5.7 Design of Vertical Stirrups 201
Page 231 and 232: 5.7 Design of Vertical Stirrups 203
Page 233 and 234: 5.8 Design Summary 205 5.8 DESIGN S
Page 235 and 236: 5.8 Design Summary 207 Choose no. 3
Page 237 and 238: 5.9 Shear Force Due to Live Loads 2
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Page 241 and 242: 5.10 Shear Stresses in Members of V
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Page 245: 5.11 Examples Using SI Units 217 M
Page 249 and 250: 5.11 Examples Using SI Units 221 5.
Page 251 and 252: Problems 223 3. R. C. Fenwick and T
Page 253 and 254: Problems 225 11.1 K/ft Figure 5.25
Page 255 and 256: 6.2 Instantaneous Deflection 227 Ta
Page 257 and 258: 6.2 Instantaneous Deflection 229 wh
Page 259 and 260: 6.2 Instantaneous Deflection 231 (a
Page 261 and 262: 6.3 Long-Time Deflection 233 Then c
Page 263 and 264: 6.5 Deflection Due to Combinations
Page 271 and 272: 6.6 Cracks in Flexural Members 243
Page 273 and 274: 6.6 Cracks in Flexural Members 245
Page 275 and 276: 6.7 ACI Code Requirements 247 have
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Page 281 and 282: References 253 2. Maximum crack wid
Page 283 and 284: Problems 255 Figure 6.13 Problem 6.
Page 285 and 286: CHAPTER7 DEVELOPMENT LENGTH OF REIN
Page 287 and 288: 7.2 Development of Bond Stresses 25
Page 289 and 290: 7.3 Development Length in Tension 2
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Page 293 and 294: 7.4 Development Length in Compressi
Page 295 and 296: 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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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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