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Appendix A
Metrication
Since 1983, the American Concrete Institute has issued separate metric editions of the 318 building code. The companion metric code and commentary to the 1995 inch-pound code and commentary is "Building Code Requirements for Structural Concrete (ACI 318M-95) and Commentary-ACI 318RM-95." The style, format, and content of ACI 318M-95 and ACI 318RM-95 closely follow the 1995 inch-pound code. Each section in the metric code and commentary matches up with the corresponding section in the inch-pound code and commentary. Except for the necessary modications of numerical values and units, and the expressions which are impacted by the units of parameters, such as fc or Jy ' the provisions in ACI 318M-95 are identical to the corresponding provisions in ACI 318RM-95.
At press time, federal government-funded construction projects were required to be metric, i.e., designed in metric units and built with metric materials. Private sector projects, however, were not under any such mandate regarding units. An aspect of the federal government's metric initiative which impacts non-metric construction is soft metric reinforcing bars. In early 1997, several steel producing mills began to phase in the production of soft metric reinforcing bars. It is anticipated that virtually all production will soon be soft metric bars. If the mills follow through with shifting their production to only soft metric bars, it is expected that the production of inch-pound bars will be discontinued. As a consequence of the steel mills' initiative to produce only soft metric reinforcing bars, it is likely then that soft metric bars will be furnished to non-metric construction projects. Since the body of this Guide is concerned with the inchpound version ofthe 1995 ACI Building Code, the authors believe it is essential to include basic information regarding soft metric reinforcing bars in this appendix. Thus, the purpose of the following discussion is to acquaint the reader with the impact of soft metric reinforcing bars on non-metric construction projects.
ASTM has metricated several of the steel reinforcement specifications which are referenced in ACI 318M-95. The ASTM specifications for steel reinforcement, which have been metricated, are presented in a "dual-units" format. A dual-units format means that a single document, e.g., Specification
Appendix A Metrication / 445
A615/A615M-96a, contains inch-pound units and SI* metric units, and the specification prescribes the requirements for both metric and inch-pound billet-steel bars. Thus, in ACI 318M-95, billet-steel reinforcing bars are required to conform to ASTM A615M-96a. Similarly, low-alloy steel reinforcing bars are required to meet the requirements of ASTM A706M-96a. The other two ASTM Specifications are A6161 A616M -96a for rail-steel and A617 I A617M -96a for axle-steel reinforcing bars. The metric bar sizes in these two specifications have also been soft converted. These specifications are not discussed here, because rail-steel and axle-steel rebars are not generally available except in a few areas of the country.
The main differences in the metric provisions in the ASTM specifications for reinforcing bars, as compared with the requirements for inch-pound bars, are concerned with:
• Designations of the bar sizes • Minimum yield strengths or grades • Bar marking • Substitution of metric bars for inch-pound bars
DESIGNATIONS OF BAR SIZES. Soft metric conversions of the eleven inch-pound sizes are now the standard sizes of metric bars. The one-to-one correspondence of bar sizes is shown in Table A-I. Each metric bar size has the same physical characteristics as its corresponding inch-pound bar size. For example, consider a #13 metric bar. The corresponding inch-pound bar size is
TABLE A-1 ASTM Standard Metric Reinforcing Bars
Nominal Dimensions(b)
Bar Diameter Cross-Sectional Weight Size(·) mm [in.] Area, mm2 [in.2] kg/m [Ibslft]
#10 [#3] 9.5 [0.375] 71 [0.11] 0.560 [0.376] #13 [#4] 12.7 [0.500] 129 [0.20] 0.994 [0.668] #16 [#5] 15.9 [0.625] 199 [0.31] 1.552 [1.043] #19 [#6] 19.1 [0.750] 284 [0.44] 2.235 [1.502] #22 [#7] 22.2 [0.875] 387 [0.60] 3.042 [2.044] #25 [#8] 25.4 [1.000] 510 [0.79] 3.973 [2.670] #29 [#9] 28.7 [1.128] 645 [1.00] 5.060 [3.400] #32 [#10] 32.3 [1.270] 819 [1.27] 6.404 [4.303] #36 [#11] 35.8 [1.410] 1006 [1.56] 7.907 [5.313] #43 [#14] 43.0 [1.693] 1452 [2.25] 11.38 [7.65] #57 [#18] 57.3 [2.257] 2581 [4.00] 20.24 [13.60]
(.) Equivalent inch-pound bar sizes are the designations enclosed within brackets. (b) The equivalent nominal dimensions of inch-pound bars are the values enclosed within brackets.
* SI stands for International System of Units.
446 / Structural Design Guide to the ACI Building Code
a #4. The #13 metric bar's nominal diameter, cross-sectional area, and weight per unit of length-except for being expressed in metric units and its weight more properly called "mass" in metric terminology-are exactly the same as the nominal diameter, area and weight of its counterpart #4 inch-pound bar. In addition, the height and spacing ofthe #13 metric bar's deformations are the same as the #4 bar's deformations. The end result of the soft conversion of the inch-pound bar sizes is that the soft metric bars are physically the same as the inch-pound bars.
YIELD STRENGTHS OR GRADES. Minimum yield strengths in metric units are 300, 420 and 520 MPa (megapascals), which are equal to 43,000, 60,900 and 75,400 psi, respectively. Metric Grade 420 is the counterpart of standard Grade 60.
BAR MARKING. Soft metric rebars are required to be identified or marked distinctively for size and minimum yield strength or grade. For example, consider the marking requirements for a #25, Grade 420 metric bar. The ASTM Specifications require the number "25" to be rolled onto the surface of the metric bar to indicate its size. For identifying or designating the minimum yield strength or grade, the ASTM Specifications provide an option. A mill can choose to roll a "4" (the first digit in the grade number) onto the bar, or roll on a single longitudinal rib or grade line to indicate Grade 420. Marking requirements for metric rebars are shown in Figure A-I.
SUBSTITUTION. The ASTM Specifications contain a provision for substitution of metric bars for corresponding inch-pound size bars and strength level. For example, Section 20.3.5 is the substitution provision in the A615/A615M-96a Specification for billet-steel rebars. It states:
"20.3.5 It shall be permissible to substitute: a metric size bar of Grade 300 for the corresponding inch-pound size bar of Grade 40, a metric size bar of Grade 420 for the corresponding inch-pound size bar of Grade 60, and a metric size bar of Grade 520 for the corresponding inch-pound size bar of Grade 75."
The substitution clause in the A 7061 A 706M -96B Specification for low-alloy steel rebars states:
"16.3.5 It shall be permissible to substitute a metric size bar of Grade 420 for the corresponding inch-pound size bar of Grade 60."
Appendix A Metrication / 447
Main Ribs
S lor Billet (A61S"',
W lor Low-Alloy (A706"',
Grade Mark
(One line only)
* Bars marked with a Sand W meet both A615M and A70sM
GRADE 420
"'.::roo_--Main RibS-----l...,
Letter or Symbol -_____.1(( tor Producing Mill
Bar Size #43 --~~~~
Type Steel ----tIY S lor Billet (A6tS"',
Grade Mark
Grade Lines (Two lines only)
GRADE 520
Figure A-I Marking requirements for metric reinforcing bars
MECHANICAL PROPERTIES. Requirements for tensile and bending properties in the current ASTM specifications for reinforcing bars are presented in Table A-2. The metric bar sizes and criteria for tensile and bending properties in metric units comprise the requirements in ASTM A615M-96a and A706M-96b. Similarly, the data for inch-pound bars, which are enclosed within brackets in Table A-2, reflect the requirements in the inch-pound parts of the two specifications.
The tabulated data in Table A-2 serve to further illustrate soft conversion. Since the tensile property requirement "minimum percentage of elongation" is non-dimensional and related to bar size, the stipulated values are exactly the same for soft metric bars and corresponding inch-pound bar sizes_ Note the gage length of 8 in. has also been soft-converted to (8)(25.4) = 203.2 mm. The minimum tensile strengths for Grade 60 and Grade 75 have been rounded
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Appendix A Metrication I 449
slightly: 90,000 psi = 620.7 MPa, rounded to 620 MPa; 100,000 psi = 689.7 MPa, rounded to 690 MPa; and 80,000 psi = 551.7 MPa, rounded to 550 MPa. Since bend test requirements are a function of bar size, the pin diameters required for soft metric rebars are exactly the same as those for corresponding inch-pound bar sizes.
DESIGN ASPECTS
Soft metric bar sizes are identical to corresponding inch-pound bar sizes with respect to cross-sectional area (Table A-I). The minimum yield strength, t;., of metric bars is slightly larger than the correspondingt;. of inch-pound bars. Thus, in all cases with respect to the reinforcement, the calculated design strength of a structural member, which is reinforced with soft metric bars, will be slightly larger than the design strength of the same member with inch-pound bars of equivalent size and yield strength.
For example, compare the design strength of a structural member reinforced with 4-#36 Grade 420 bars versus the design strength of the same member reinforced with 4-#11 Grade 60 bars. From Table A-I, the area of a #36 bar is 1,006 mm2; the area of a #11 bar is 1.56 in.2 The design strength of the member would be equal to the product of the strength-reduction factor, l/J, and the nominal strength of the reinforcement, A.t;., where l/J = 0.90 for flexure, l/J = 0.70 for compression in a tied column, and so forth. Since A.fy for the metric rebars exceeds that of the inch-pound rebars, consequently l/JA...fy of the member reinforced with the metric bars is greater than l/JA...fy of the member reinforced with the inch-pound bars. See Table A-3.
This straightforward example can also serve as a basis to discuss substitution of soft metric bars for inch-pound bars in a non-metric construction project. Suppose a tied column in a non-metric designed building is reinforced with 4-#11, Grade 60 bars; ties are #4. If 4-#36 Grade 420 bars and #13 ties are substituted, determine the effect on the design strength of the column. With respect to the reinforcement, the design strength, l/JA.t;. of the soft metric bars is (0.70)(380 kips) = 266 kips. The design strength of the inch-pound bars is (0.70)(374.4) = 262 kips. Substitution of the soft metric bars does not have an adverse effect on the design strength of the column. Instead the soft metric bars provide a slight increase in design strength.
DEVELOPMENT AND LAP SPLICES. ACI 318M-95, similar to the inchpound code, requires anchorage or embedment length, the location and length of lap splices, and the type and location of mechanical splices and welded splices to be included on design drawings or in project specifications (Sections 1.2.1-h and 1.2.1-1 in either Code). Consider an example concerning substitution of soft metric reinforcing bars for inch-pound bars. Suppose the embedment
450 I Structural Design Guide to the ACI Building Code
TABLE A-3 Comparison of design strengths, metric bars vs. inch-pound bars
4-136 Grade 420
4(1006) = Area of bars, A, 4,024mm2
or 6.24 in.2
Minimum 420 MPa(a) yield strength, /y or 60.9 ksi
(4,024)(420) = Nominal strength 1.69 X 1(1 of the bars, A,/y Newtons
or 380 kips
4-#11 Grade 60
4(1.56) = 6.24 in.2
or 4,024 mm2
60 ksi or 413.7 MPa(b)
(6.24)(60) = 374.4 kips
or 1.66 X l<fi Newtons
(.) Expressing strength or stress values in MPa is inconvenient in the authors' opinion. For convenience in design calculations, the minimum yield strength value of 420 MPa can be taken as 420 Newtons per mm2 or 420 N/mm2• To convert Newtons to kips, divide the value in Newtons by 4.45 x 10'. In this case, (1.69 x 106) .;- (4.45 Xla') = 380 kips. (b) To convert ksi to Megapascals, multiply the value in ksi by 6.895 x 106 to get Pascals. Then divide the result by 106 to get Megapascals. In this case, (60) (6.895 x 106) .;- 106 = 413.7 MPa.
and lap splice requirements for Grade 60 reinforcing bars are specified on the design drawings or in the project specifications for an inch-pound construction project. If soft metric Grade 420 bars are substituted for the inch-pound bars, will the embedment and lap splice lengths specified for the Grade 60 bars be suitable for the metric Grade 420 bars? Development lengths and lap splice lengths of reinforcing bars, whether tension or compression, are directly proportional to the specified yield strength, f" of the bar. The ratio of the minimum yield strengths, metric vs. inch-pound, is (60.9/60) = 1.015 or a variance of 1.5 percent. Because of the nearly identical minimum yield strengths, the anchorage or embedment lengths and lap splice lengths which the designer has specified for the Grade 60 rebars will be suitable for the substitute Grade 420 rebars.
FABRICATION AND DETAILS OF REINFORCEMENT
Since soft metric rebars are physically the same as corresponding sizes of inchpound bars, all aspects of fabricating and detailing soft metric rebars will be identical to the fabricating and detailing practices used for inch-pound bars. CRSI has prepared and published Hook Details for ASTM Standard Metric Rebars-dimensions of end hooks, stirrup hooks, and seismic stirrupltie hooks-soft-converted values of the standard hook dimensions used for inchpound bars. See Figure A-2.
Appendix A Metrication I 451
RECOMMENDED END HOOKS, ALL GRADES OF STEEL
ALL GRADES OF STEEL o = Finished inside bend diameter db = Nominal bar diameter Min. 0 = 6 cit. tor .10 lhrough #25 Min. 0 = 8 cit. for '29, .32 and '36 Min. 0 = 10 cit. tor .43 and .57
Hook A orG
n
o
BAR SIZE .10 .13 .1& .19 1122 125 t29 .32 .36 .43 '57
Beam
4. STIRRUP HOOKS (TIe Bends Similar)
BAR D -'0' 135' SIZE AorG AorG '10 40 105 105 '13 50 115 115 .16 65 155 140 .11 115 305 205 1122 135 355 230 125 155 410 270
-H dimension is approximate. NOTE: All dimensions are in milRmeters (mm).
If" 65 80 95
115 135 155
D lBO'HOOKS eo'HOOKS
AorG J AorG 60 125 80 150 80 150 105 200 95 175 130 250
115 200 155 300 135 250 180 375 155 275 205 425 240 375 300 475 275 425 335 550 305 475 375 600 465 675 550 775 610 925 725 1050
SEISMIC STIRRUP I TIE
BAR 135' SEISMIC HOOK
SIZE D AorG If" .10 40 110 80 .13 50 115 80 .16 65 140 95 .19 115 205 115 .22 135 230 135 .25 155 270 155
-H dimension is approximate. NOTE: All dimensionS are in millimeters (rnm).
Figure A-2 Hook details for ASTM standard metric reinforcing bars (courtesy of Concrete Reinforcing Steel Institute)
Subject Index
Acceptance tests, 1-4, 8-10 Admixtures, chloride containing, 10 Aggregates, 12 Air-entrained concrete, 384 American Society for Testing & Materials
(ASTM),1 American Welding Society (A WS), 5 Analogous columns
column analogy examples, 98-100,104, 157-159, 161
Analysis (see Chapter 2)
approximate vs. "exact," 23-25 lateral loads, 306-312 one-way slab, example, 39-47 two-way slab frames, 29-31, 306--312 two-way slab systems (see Chapters 5, 6,
7,8) Analysis, direct design method examples, 80,
144,179 Analysis, equivalent frame method examples,
97, 156 Analysis, two-way slab-beam (see Chapter 9)
examples, 205, 206, 208 shear and moment, 209, 221-226 torsion, 209, 226-235
Anchorage (see Development), 356, 366, 370 Approximate Analysis, 18-22 Axial load, combined with bending (see
Columns)
Balanced conditions, 33, 268, 282 Beams (see Chapter 9)
code requirements, 216 crack control, 241 deep, 219 depth, minimum, 241 examples, 220, 242 slab systems, two-way, 121,209 slender, 218 spandrel, 121, 210, 242 torsion, 189,209,226,243
Bearing column-footing, 340, 341 walls, 269-278, 324, 327
Beta, sub-one (f3l)' 32, 268 Biaxial bending, columns, 288-295 Bond (see Development), 354 Bonded tendons, 394 Brackets (see Beams, deep), 110, 119 Buckling (see Slender columns) Bundled bars, 284, 320
Calcium chloride, 11 Cantilever edge, two-way systems, 131, 199 Carbon equivalent, 5-7 Carry-over factors, 104, 160 Cements, 11 Coefficient of variation, 9 Column capitals, 120, 155 Column design for walls, 269 Column shape, 130
comparisons, 284 shear constants, 133-136, 164, 165, 171-174 two-way shear, 130, 338
Columns (see Chapter 10; also see Walls, Chapter 11)
analogous, examples, 98, 100, 104, 157, 161 base-stress transfer to footings (see Bearing) biaxial bending, 288-295 capitals, round, 154 design, 266 details, 269, 314-323 effective length, 303 equivalent, 94 frames, 296, 305, 306, 312 interaction curves, 275, 280--288 maximum load, 268, 279 minimum eccentricity, 266, 306 minimum size, 266 sidesway, 267, 306--314 slender, 267, 295-303 stiffness, Kc ' 95, 155
454 / Subject Index
Columns (continued) ties. 319. 321-323
Compressive strength. specified. 12 statistical evaluation. 13 tests. 12-14
Compressive stress block. 32-34. 268 Computer calculation
building permits. 18 Concrete (see Compressive strength)
lightweight structural (see Chapter 15) modulus of elasticity. 17 normal weight. 17 plain structural (see Chapter 16) properties. proportioning. 12 quality. 12 tests of. 13 trial mixtures. II. 12 water-cementitious materials ratio. II
Corbels (see Brackets) Core tests. 13. 14 Corners and joints. 384-387 Cover. 383
columns. 269 fire requirements. 59 joists. 59 precast concrete. 383 prestressed concrete. 391 walls. 269. 325
Crack control. 35. 39. 46. 47. 91. 241 Curing. 12
Dead load. 16 Deflection
allowable. 40 computed. 44-46. 66--72 lateral. 304. 308. 310 long-term. 45. 70 minimum thickness. 40. 80. 205
Design alternate method. 15 limit. 25-27 strength method. 15.31-34
Design aids closed (torsion) stirrups. 254-259 columns. in flat plate. 136--141 columns tied. 278 embedment and lap splices. 357. 359. 362.
365.366.369 flexural. 261. 262 longitudinal bars. torsion. 260 round columns with capitals. 154
slender columns. 298. 300--302 stiffness. Kec. 96 stiffness. Kc. 99 stiffness. K,. 101 stiffness. K,. 96 stirrups. 251. 252. 405.406 two-way shear constants. 133-136. 164. 165.
171-174 Design drawings. 17.354.373 Details of reinforcement (see Chapter 13).
314-323 Development (see Chapter 13; also Splices and
Anchorage). 235-240 compression. 26. 27. 356--359 dowels. footing. 357 end-bearing splices. 282. 376 hooks. 365. 366.371. 374 slabs. 42 tension. 359 top bars. 237 welded wire fabric. 379. 380
Direct design method. two-way slab systems (see Chapters 5. 6. 7. 8)
code requirements for. 79.143 examples. 80. 144. 179. 205
Drawings (design). 17.354.373 Drawings (placing). 321. 434 Drop panels. 143. 145
Embedment (see Anchorage; Chapter 13) End-bearing. splices. 282. 376 Equivalent column concept. 94 Equivalent frame method (see Chapters 5. 6. 7)
concept. 94 examples. 97. 156
Exposure. 35. 36
Fixed-end moment factors. 104. 161 Flat plate (see Chapter 5)
defined. 76 examples. 80. 97
Flat slab (see Chapter 6) carry-over factors. 160 defined. 142 examples. 144. 156 stiffness. 158
Flexural members (see Beams) Folded plate. 436 Footings (see Bearing; Development;
Chapter 12) column. 338-344 combined. 349
depth (thickness), minimum, 337 design, 344 dowels, 342 pile,337 plain concrete, 336, 338, 426 wall, 340, 426
Form removal, 435 Frames (see Analysis)
Hooks (see Development), 371 standard, 374
Inspection (see Chapter 17) concreting, 434 form removal, 435 materials, 433 responsibility, 432
Interaction curves (see Columns)
Joist construction cover, 59, 60 crack control, 57 definition, 55 distribution ribs, 74 examples, 62-72 fire resistance, 59, 60 lightweight concrete, 61, 62 limitations, 55, 56 one-way (see Chapter 4) shear, 60-62, 64,65 "skip-joist," 73 two-way (see Chapter 7) wide-module, 72, 73
Laterally unbraced (see Analysis) Lightweight concrete (see Chapter 15)
definition, 419 deflection, 420-422 example, 421 joists, 60, 61, 62 shear, 61, 62
Limit design, 25-27 Load factors, 15,31 Load factors, critical, 217 Load tests (see Chapter 18),
analytical, 439 code requirements, 437, 438 criteria, 439 example, 440 pattern, 439 procedure, 438
Loads
actual, 15, 16 dead, 16 factored, 15, 18, 217 factors, 15,33,217 live, 15 reductions, 15, 16,76 service, 15,217 specified, 15, 16
Mats (footings), 349
Subject Index I 455
Mechanical connections, 318, 376, 378 Metrication (see Appendix A), 444-451 Minimum reinforcement
flexural,260 shrinkage and temperature, 263 spacings, 264
Model analysis, 18 Modulus of elasticity (see Concrete) Moment-area method, examples, Moment coefficients, 18-22
limitations on use of, 18 recommendations vs. frame analysis, 23 two-way slabs, 27-29, 81-83
Moment redistribution (see Limit design), 25-27
Openings slabs, 151 two-way joists, 187
Pattern loading, 18,236,439 Pedestal, 338 Phi, 4>, factors, 15, 31 Pile cap design, 349 Pile capacity (see Footings), 336 Plain structural concrete (see Chapter 16)
definition, 423 design, 424 examples, 427, 429 footings, 426 joints, 424 pedestals, 426 walls, 425
Post-tensioning (see Chapter 14) Precast concrete, cover, 383 Prestressed concrete (see Chapter 14)
bonded reinforcement, 394 cover, 391 deflection, 398,411,412 design example, 407-418 design moment strength, 393 exceptions, 17,388
456 / Subject Index
Prestressed concrete (continued) loss of prestress, 392 post-tensioning, 388 pre-tensioning, 388 reinforcement, 2,389-391 service load, 398 shear, 398,399,401-405 specifications (project), 17, 18 stresses, permissible (allowable), 399, 400
Pre-tensioning (see Prestressed concrete) Proportioning (see Concrete), 11
Reinforcement anchorage (see Chapter 13; also
Development) balanced ratios, 33 bar mats, 4 bar spacing (see Crack Control), 46 billet -steel bars, 2, 3 bundled bars, 284, 320, 376 closed stirrups, 248-250 coated bars, 4 columns, special details, 314-323 compression, beams, 34 deformed, 1, 2 development (see Chapter 13) distribution (see Crack Control) headed bars, 371 high-strength alloy steel bars, 389, 390 hooks, 371, 374 low-alloy steel bars, 2, 3 maximum, 33, 38, 56, 91 metric bars (see Appendix A), 444-451 minimum, 38, 56, 91, 260, 263 plain (smooth), 1 prestressed concrete, minimum bonded, 405,
406 ratio, prestressed to non-prestressed, 405 shear, 187,224,245,404 strand, prestressing, 389, 390 torsion, 126, 191,231,245 welded wire fabric (WWF), 8 welding, 5-8 wires, 1,8
Safety analytical investigation, 14, 439 brittle vs. ductile failure, 33, 397 form removal, 435 load tests, 14, 439 strength evaluation, 13, 14, 437
Sennceload,15,62,69
Serviceability requirements, 15,35,39,241 crack control, 35, 39, 57, 91, 241 deflection, 35, 241 stresses (see Prestressed Concrete and
Alternate Design Method) Shear (see Beams)
brackets, 119 combined with torsion, 121,226,243 design, beams, 221 footings, 337, 426 reinforcement, 225, 251 shear constants, 133-136, 164, 165, 171-174 slabs (one-way), 43 two-way examples, 81,106 two-way rectangular, 346
Shear wall, 324 Shearhead, 113 Slab systems (see Chapters 3, 4, 5, 6, 7 and 8)
direct design method, 27-29 one-way, 37 one-way joist systems, 55 openings, 151 two-way systems, 76,142,178,203
Slenderness approximate evaluation, columns, 267, 295 beams, 218 shortcut evaluation, columns, 295-306 walls, 331
Soil pressure, 336, 344, 429 Spacing of reinforcement, 57, 91, 382 Specifications (materials), 1-4,8-12,389-391 Specifications (project), 17, 354, 432 Spiral, 1,284 Splices (see Chapter 13), 314-320, 369, 373,
375-382 compression, 373 end-bearing, 282, 376 mechanical connections, 376, 378 tension, 377 welded wire fabric, 379-382
Splitting tensile strength, 13 Statistical evaluation, 9, 10, 13 Stirrups
design for shear, 223, 404 shear and torsion, 231, 245 spacing, shear and torsion, 232, 247
Strength actual failure, 33 design method, 15,31 specified, 8, 10, 33
Strength-reduction factors, cj>, 15,31 Strength tests
concrete (see Compressive strength), 12-14 reinforcing bars, 2-4
Structural integrity, 64, 220 Structural plain concrete (see Chapter 16)
Tack welding, 7, 8 Tendon (see Prestressed Concrete) Tests
example, load, 440 load, 439-443 strength, (see Strength tests)
Thin shell, 436 Ties (see Chapter to), 319, 321-323 Torsion (see Chapter 9)
combined with shear, 192,209,232,243 reinforcement, design, 127, 191, 231, 245
Torsional stiffness (see Chapters 5, 6, 7, 8) chart, 96 design limit, 230 slab,95 slab with beam, 209 slab with drop, 159 waffle slab, 202
Two-way construction examples, flat plate, 80, 97 examples, flat slab, 144, 156 examples, waffle slab, 179, 181 examples, with beams, 205, 206, 208 two-way slab on beams, 211
Subject Index I 457
Unified design provisions, 34
Waffle flat slab (see Chapter 7) defined, 178 examples, 179,181
Walls (see Chapter to) bearing,327,328 deep beam, 334 defined,324 design as columns, 269 empirical design, 327 nonloadbearing, 326 plain concrete, 334 rational design, 328 retaining, 324 shear, 324 slenderness effects, 331 two-way, 213,335
Water, 10, 11 WeldabiJity,5 Welded wire fabric, 1,8,61
example, 52 wire sizes, 54
Welding, 5-8
Yield strength, 2-4 specified vs. actual, 33
Commentary Section Index
Commen- Commen- Commen-tary tary tary Section Pages Section Pages Section Pages
R1.2.1 354 Rl1.5.2 404 R13.5.1.2 30 RIA 438 Rl1.5.5 399 R13.6.l.8 77 R5.l0 435 Rl1.5.6 404 R13.6.3.3 28.143.211 R7.l0.5 288 RlI.6.3.5 229 R13.7A 94 R7.l2.1.2 39 RlI.6.3.6 191 R13.7.5 79 R1O.5.l 261 Rl1.8.1 219 R13.7.7.l 103 RI0.5A 263 Rl1.12.l.1 130 RI8.1.1 388 R1O.6 199 Rl 1.12. 1.2 130 RI8.1.3 388 R1O.6A 35.46.57 Rl1.12.4.7 115 R18A 398 RI0.l0 31 Rl1.12.6 85 R20.1 438 RI0.11 31 Rl1.12.6.2 87. Ill. 112. R20.1.3 440 R1O.12.l 299.307 133. 134 R20.5.3 438 R 1O.l 2.3 298 RI2.11.3 42 R20.5A 438 RI0.l2.3.2 299 R12.l6A 376 R20.5.5 438 RI0.l7 425 RI2.17.2.1 318 R22.3 424 Rll.4 403 R13.3.8.5 77 R22A.4 424 Rl1.4.1 402 R13.5.1.1 29.30
Code Section Index
Code Code Code Section Pages Section Pages Section Pages
1.2.1 12,17,354 4.2.3 11 7.2 373 1.2.2 18,219 4.3.1 11,384,419 7.2.2 374 1.3 432 4.3.2 11 7.3 434 1.3.1 432 4.4.1 11 7.4.1 434 1.3.4 434 4.4.2 11,419 7.4.2 434 1.4 213,334,384, 5.1.3 12 7.5.1 434
419,438 5.1.4 13,420 7.5.2 434 2.1 17,76,80, 5.1.5 420 7.5.2.2 434
266, 324, 388, 5.2 13 7.5.3 51,73 419,423 5.2.1 383 7.5.4 8,434
3.1.2 433 5.2.3 11, 12 7.6 315 3.2.1 11 5.3 11,13 7.6.2 383 3.2.2 11 5.4.1 13 7.6.3 317,342,383 3.3.1 12,419 5.4.2 13 7.6.4 342 3.3.2 383 5.5 13 7.6.5 39,42,47,91, 3.4.2 10 5.6 11,13 326,383 3.4.3 11 5.6.2.2 12 7.6.6 217,382 3.5 1 5.6.3.4 12 7.7 263, 315, 373, 3.5.3 393 5.6.4.2 13 383 3.5.3.1 4 5.6.4.4 14 7.7.1 39,41,58,73, 3.5.3.3 4 5.6.4.5 14 217,221,242, 3.5.3.4 8 5.7.1 434 269,315,325, 3.5.3.5 1, 8, 9, 51 5.9.1 434 363,383 3.5.3.6 2,8,9,51 5.9.2 434 7.7.2 58, 325, 383, 3.5.3.7 4 5.10 217 391 3.5.3.8 8 5.10.1 434 7.7.3 325,383 3.5.4.1 1 5.11 435 7.7.3.2 384,391 3.5.4.2 5.12 435 7.7.3.3 384 3.5.5.1 2,389,390 5.13 435 7.7.5 58, 384, 391, 3.5.5.2 2,389,391 6.1 433 392 3.5.6.1 2 6.2.1 435 7.7.7 58,384,391 3.5.6.2 2 6.3 56 7.8 315,318,376 3.6.1 10 6.4 217 7.8.1.1 315 3.6.3 10 6.4.4 435 7.8.1.3 315 3.8.1 6.4.5 435 7.8.1.5 318,376 4.1.1 11 6.4.6 435 7.9 217,322,323, 4.2.1 384 7.1 371,372,373 364,368,384 4.2.2 11 7.1.3 374 7.10 315
462 / Code Section Index
Code Code Code Section Pages Section Pages Section Pages
7.10.4 284,319,359, 8.6.1 20,23 9.5.2 35,69 375 8.6.2 38 9.5.2.1 20,40,66,71,
7.10.4.6 322 8.7 39 241 7.10.4.7 217,323 8.7.1 20,22,23 9.5.2.2 80 7.10.5 284,319,375 8.7.2 23 9.5.2.3 44, 50, 68, 69, 7.10.5.1 269 8.7.3 66 72, 150,261, 7.10.5.2 323 8.9 39 411,420,422 7.10.5.3 284,288,321, 8.9.2 23 9.5.2.4 70
322 8.10 216 9.5.2.5 45,71,412 7.10.5.4 315,322 8.10.2 57,222,388 9.5.2.6 412 7.10.5.5 217,319,322, 8.10.3 388 9.5.3 35,143
323 8.10.4 388 9.5.3.1 205 7.11 217,321,384 8.10.5.2 58 9.5.3.2 80, 144 7.11.1 375 8.11 37,72,73, 9.5.3.3 150,206, 7.11.3 235,250,321 178,389 209 7.12 37,38,51,53, 8.11.1 55 9.5.3.4 80, 150, 151
56,59,91, 8.11.2 55,56 9.5.4 398 262,334 8.11.3 55,56,72 9.5.4.1 411
7.12.1 213 8.11.4 37,56 9.6 15 7.12.1.2 38,263 8.11.5 383 10.0 267,303,309 7.12.2 41,42,383 8.11.5.3 59 10.2 32,267,268, 7.12.2.1 39 8.11.6 56 393, 412,420 7.12.2.2 58,263,264 8.11.7 56 10.2.3 32 7.13.2 217,354 8.11.8 61,65,73, 10.2.4 393 7.13.2.1 64,220 178,179,197 10.2.6 33 7.13.2.2 220,242,248 9.0 150,205,206, 10.2.7 33 7.13.2.3 220 350 10.3 268,328 8.0 18,20 9.1 31 10.3.2 33,34,268, 8.1.2 15,267 9.1.1 15,31 332,389 8.1.3 34,268 9.1.2 15,31 10.3.3 33, 34, 56, 64, 8.2.2 15 9.2 15, 16, 18,31, 91,216,222, 8.2.3 17 217,325,397, 268,389 8.2.4 17 398,439 10.3.4 180 8.3 18,23 9.2.1 41,52,217, 10.3.5 268,278 8.3.1 18,216,218 221 10.3.5.1 278,281 8.3.2 243 9.2.2 217 10.3.5.2 281 8.3.3 18,39,41,51, 9.2.3 217 10.4 216,218
52,53,63, 9.2.4 217,325,326 10.5 193,216,219, 216,218,221, 9.2.5 217,325 260,389 235 9.2.6 217 10.5.1 56,64
8.4 18,23,91, 9.2.7 217 10.5.2 57 216,218,236, 9.3 31,61,325, 10.5.3 64, 199,260, 388 439 262,263
8.4.1 25,26,27,31 9.3.1 15,393 10.5.4 37, 38, 42, 58, 8.5 45 9.3.2 33 262 8.5.1 17,31,330, 9.3.2.2 282 10.6 15, 35, 39, 46,
411,412,420 9.3.5 334,424 58,216 8.5.3 391 9.5 15,39,45, 10.6.2 91 8.6 39 216,399 10.6.3 241
Code Section Index / 463
Code Code Code Section Pages Section Pages Section Pages
10.6.4 35,39,46,57, 11.1.3.2 399 11.6.3.5 126,257 241 11.2 13,420 11.6.3.6 191,245,257
10.6.5 57,58 11.2.1.1 61 11.6.3.7 127, 192,234, 10.6.6 57 11.2.1.2 61,62 257 10.7 216,219,220, 11.2.2.1 145 11.6.3.8 227,234,247
334 11.3 61,73 11.6.4.1 121,248 10.7.4 219,334 11.3.1 124, 143,209, 11.6.5.2 192,233,247 10.8.4 269,280 244 11.6.5.3 127,192,247, 10.9 266 11.3.1.1 43,61,65, 257 10.9.1 269,280,389 187,197,223, 11.6.6 234,244 10.9.2 288 337 11.6.6.1 192 10.9.3 284,359 11.3.2 209 11.6.6.2 127,247 10.10 31,266,267, 11.3.2.1 43,62,65, 11.6.6.3 247
278, 296, 306, 179,253,338 11.7 350 310,312,328 11.4.1 402, 403, 404, 11.8 219,220,350
10.10.1 31,296 415,418 11.8.1 219 10.11 31,266,267, 11.4.2 404,416,418 11.8.4 354
278,296,306, 11.4.2.1 403 11.8.5 350 307, 311, 11.4.2.2 403 11.8.6 350 328,331 11.4.2.3 399,403 11.8.7 350
10.11.1 31,296,299, 11.5 73 11.8.9 219,350 304,307 11.5.1.1 401 11.8.10 219,350
10.11.2 305,329,330 11.5.2 401,404 11.9 350 10.11.4.1 297 11.5.4 251 11.9.3.2.1 398 10.11.4.2 267,296 11.5.4.1 189,224,245, 11.10 324 10.11.5 329,331 401, 404 11.11.1 209 10.11.5.1 310 11.5.4.3 224,245,404 11.11.2.1 130 10.12 266,296 11.5.5 73,216,401 11.11.4.9 119 10.12.1 267,298 11.5.5.1 37,125, 188, 11.12 97, 113, 151, 10.12.2 267,305,331 221,224,415 326,337 10.12.3 297,309,332 11.5.5.2 399 11.12.1 345 10.12.3.2 266,296 11.5.5.3 188, 224, 226, 11.12.1.1 89, 122, 130, 10.13 296,312 247,251,401 179,186,338, 10.13.1 267,298 11.5.5.4 401 350 10.13.2 267,318 11.5.6 61,245 11.12.1.2 85, 130, 132, 10.13.4.2 310,311,312 11.5.6.1 62,225,404 143,179,186, 10.13.4.3 312 11.5.6.2 223,250 209,338,349, 10.13.5 303 11.5.6.8 224, 340, 404, 350 10.13.6 303 414 11.12.2 179,209,338, 10.13.7 218 11.6 216,229,405 352 10.15 316 11.6.1 121,191,210, 11.12.2.1 130, 143, 145, 10.15.2 319,320 226,227,229, 186,346,353 10.17.1 340,357 235,243,253 lLl2.3 115 11.0 124,219,232 11.6.2.2 126,191,230, 11.12.3.1 340 ILl 124 243 11.12.3.2 115,340 11.1.1 44,53,60,61, 11.6.2.4 190,228,243 11.12.4 110,115
145,223 11.6.3 230,231 11.12.4.1 115 11.1.3 349,350 11.6.3.1 126, 191,245, 11.12.4.5 118 11.1.3.1 44,223 253 11.12.4.6 116
464 I Code Section Index
Code Code Code Section Pages Section Pages Section Pages
11.12.4.7 115 12.10.5 237,238,239, 12.17.4 283,318,377 11.12.4.8 115 240,363 12.18 51 11.12.4.9 119 12.10.5.1 367 12.18.1 381 11.12.5 131,187 12.11 236,364 12.18.2 381 11.12.5.1 151 12.11.1 25, 26, 42, 43, 12.18.3 381 11.12.6 79,85,97, 216,363 12.19 51,52
154 12.11.2 27,216,238, 12.19.1 379 12.1 340,364,367 364 12.19.2 380 12.1.1 319,356,371 12.11.3 43, 239, 355, 13.0 79,89,94, 12.2 340, 342, 359, 363 103, 110, 122,
378 12.12 236,364 144, 179, 182, 12.2.1 367 12.12.1 216,237 184,205 12.2.2 322, 359, 360, 12.12.2 239,323 13.1.1 213
361,362,369, 12.12.3 237,239,367 13.1.2 110,119,182, 371,380,381 12.13 236,248,250 211,213
12.2.3 347,359,360, 12.13.2 8,73,249 13.2 94 361,380,381 12.13.2.1 73,248,249 13.2.1 207
12.2.4 13,93,360, 12.13.2.2 249,250 13.2.4 121,182,183, 361 12.13.2.4 73 184,200,205,
12.2.4.3 420 12.13.3 248,253,407 210,229 12.2.5 359 12.13.5 121,250 13.3 90,91, 199 12.3 26,27,315, 12.14 315 13.3.1 213,214
319,320, 12.14.1 354 13.3.2 90,91,199, 342 12.14.2.1 284, 343, 376, 383
12.3.1 356 378 13.3.3.2 124 12.3.2 356 12.14.2.3 382 13.3.6 153 12.3.2.2 248 12.14.3 377,379 13.3.7.1 143 12.3.3.2 357 12.14.3.1 378 13.3.7.2 143 12.4 320, 356, 360, 12.15 318,319,321, 13.3.7.3 143
376 369,381 13.3.8.5 181 12.5 340,342,371 12.15.1 344,377 13.4 151 12.5.2 365,371 12.15.2 318,378 13.4.1 151 12.5.3 371,372 12.15.3 318 13.4.2 151 12.5.3.2 365,373 12.15.4 318 13.5.2 183,235 12.5.3.3 373 12.15.4.1 379 13.5.3 79,94,122 12.5.3.5 373 12.16 315,373,375 13.5.3.1 86, 107, 190 12.5.4 372,373 12.16.1 283,375 13.5.3.2 81,90,107, 12.5.5 342,343,356, 12.16.2 344, 358, 376, 112, 147, 148,
371 378 154, 190,227, 12.6 371 12.16.4 283,317,376 235 12.7 51,52 12.16.4.3 376 13.5.3.3 77,110,154 12.7.2 52,381 12.16.6.3 384 13.5.4 79,94 12.7.3 381 12.17 315,318 13.6 79,307,349 12.7.4 381 12.17.2 318,376 13.6.1 28,204,211 12.8 51,379 12.17.2.1 281 13.6.1.2 206 12.10 364 12.17.2.2 282 13.6.1.4 213 12.10.3 237,239,363, 12.17.2.4 315,319,344, 13.6.1.5 77, 156
364,367 375 13.6.1.6 204,207,209 12.10.4 237,239,367 12.17.2.5 344,.375 13.6.2.2 81, 145
Code Section Index / 465
Code Code Code Section Pages Section Pages Section Pages
13.6.2.5 110, 120, 183, 14.1.2 324,326 18.6.2 393 210,211 14.2.1 213,324 18.7 393,394,412
13.6.3 145 14.2.6 324 18.7.2 394 13.6.3.1 91,110,180 14.2.7 324,326,327, 18.7.3 397,407 13.6.3.2 146, 179,205 328 18.8 389 13.6.3.3 27,28,81, 14.3 219,324,389 18.8.1 395
146,211 14.3.2 269,280,326 18.8.3 397 13.6.3.5 110,122 14.3.3 326 18.9.2 405 13.6.3.6 77,79,87,90, 14.3.5 326 18.9.2.1 405
146 14.3.6 269, 280, 326, 18.9.3 405 13.6.4 185,204,207 328 18.9.3.2 406 13.6.4.1 89, 127, 179, 14.4 269,271,324, 18.9.3.3 406
185,204,205, 326,327, 18.10.4 388 207 328,334,335 18.11.2.1 389
13.6.4.2 81,89 14.5 324, 327, 328, 18.12 389 13.6.4.4 89, 127, 179, 389 18.19.3 17
185,204,205, 14.5.1 271,324 19.1.2 327 207 14.5.2 328 19.1.3 327
13.6.4.5 110, 190 14.5.3.1 328,334 19.5.1 436 13.6.5 1I0, 185,207 14.6 334,389 20.0 440 13.6.5.1 127,185, 195, 14.6.1 328,330 20.1 14
205,206,207, 15.2.2 336 20.1.2 437 213 15.4.2 338,349,363 20.1.3 437,440
13.6.5.3 183,193, 195, 15.4.4 347 20.2.5 439 198 15.5.3 337 20.3.1 439
13.6.6 185 15.5.3.3 349 20.3.3 437 13.6.7 28,79,81, 15.6.3 340 20.4.3 440
120 15.7 337 20.5.2 440 13.6.8 110,183 15.8.1.2 356 20.5.3 438 13.6.8.1 123,209 15.8.2 342 20.5.4 438 13.6.8.2 188, 194, 197 15.8.2.1 342,348,358 20.5.5 438 13.6.8.3 122, 187, 194 15.8.2.3 343,376,378 20.6 433,438 13.6.8.4 197 15.10.2 349 21.6 324 13.6.9.2 88, Ill, 147, 16.3 324 22.1.1.1 423
190,235 16.4.2 324 22.1.1.2 423 13.7 94, 155,202, 18.0 395 22.2.1 324
307,349 18.1.1 388 22.2.2 423 13.7.3.3 121,158 18.1.3 324,327 22.2.3 423 13.7.4 154, 155 18.2.2 398 22.2.4 423 13.7.4.1 121, 156 18.2.3 398 22.3.1 424 13.7.4.2 156 18.2.4 398 22.4.3 266 13.7.4.3 121, 157 18.2.5 398 22.4.4 424 13.7.5 110 18.3.1 393 22.4.8 337,338,424, 13.7.5.1 20,159,200 18.3.2 398 429 13.7.6.2 95,103 18.4.1 398 22.5.1 424 13.7.6.3 160, 164, 170 18.4.2 398,407,41I 22.5.2 424 13.7.6.4 160 18.4.3 398 22.5.3 334,425 13.7.7.2 119,120 18.5 398 22.5.4 424 13.8.5 77 18.5.1 408 22.5.5 425
466 / Code Section Index
Code Code Code Section Pages Section Pages Section Pages
22.6 324,334 22.7.2 426 ASS 68 22.6.1 425 22.7.3 337,426 A6 15 22.6.2 425 22.7.4 337,426 A6.2 267 22.6.3 425 22.7.5 426 A.7 15 22.6.5 324,425 22.7.6 426 B.8.4.1 31 22.6.5.1 324 22.8.2 426 8.8.8.4 34 22.6.6.2 425 A.3 15 B.9.2 31 22.6.6.3 425 A4 15 B.9.3 31 22.6.6.5 426 AS 15 22.7.1 426 A.5.4 420
