nilson book-appendix a

APPENDIX

DESIGN AIDS

TABLE A.1

Designations, diameters, areas, and weights of standard bars

Bar No. Cross-Sectional Nominal Weight,Inch-Pound" Sib Diameter, in. Area, in2 Ib/ft

3 10 i '" 0.375 0.11 0.376\3 t=0.500 . 0.20 0.668

5 16 ~=0.625 0.31 1.0436 19 ~=0.750 0.44 1.5027 22 ~=0.875 0.60 2.0448 25 I = 1.000 0.79 2.670

9 29 I~= 1.128< 1.00 3.40010 )2 Ii = 1.270< 1.27 4.303II 36 I~ = 1.410< 1.56 5.31314 43 I~ = 1.693" 2.25 7.65018 57 2i = 2.257< 4.00 13.600

"Ba""d on the number of eighths of an inch included in the nominal diameter of the bars. The nominal

diameter of a deformed bar is equivalent to the diameter of a plain bar having the same weight per foot a.sthedeformed bar.

"Bar number approximates the number of millimelers included in the nominal diameler of the bar. Bars are

marked with this desig~ation.

("Approximate 10 nearest ~ in.

736 DESIGNOF CONCRETESTRUCTURES AppendixA

TABLE A.2

Areas of groups of standard bars, in2

Bar No.Number of Bars

Inch.Pound 51 1 2 3 4 '( 6 7 8 9 10 11 12-

4 13 0.20 0.40 MO 0.80 1.00 1:20 1.40 1.60 1.80 2.00 2.20 2.405 16 0.31 0.62 0.93 1.24 1.55 1.86 2.17 2.48 2.79 3.10 3.41 3.726 19 0.44 . 0.88 1.32 1.76 2.20 2.64 3.08 3.52 3.96 4.40 4.84 5.287 22 0.60 1.20 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00 6.60 7.208 25 0.79 1.58 2.37 3.16 3.95 4.74 5.53 6.32 7.11 7.90 8.69 9.489 29 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00

10 32 1.27 2.54 3.81 5.08 6.35 7.62 8.89 10.16 11.43 12.70 13.97 15.24i1 36 1.56 3.12 4.68 6.24 7.80 9.36 10.92 12.48 14.04 15.60 17.16 18.72... 43 2.25 4.50 6.75 9.00 11.25 13.50 15.75 18.00 20.25 22.50 24.75 27.0018 57 4.00 8.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00 44.00 48.00

TABLE A.3

Areas of bars in slabs, in2/ft

Inch- Bar No.

Spacing, Pound: 3 4 5 6 7 8 9 10 11in. 51: 10 13 16 19 22 25 29 32 36

3 0.44 0.78 1.23 1.77 2.40 3.14 4.00 5.06 . 6.253 0.38 0.67 1.05 1.51 2.06 2.69 3.43 4.34 5.364 0.33 0.59 0.92 1.32 1.80 2.36. 3.00 3.80 4.684 0.29 0.52 0.82 1.18 1.60 2.09 2.67 3.37 4.175 0.26 0.47 0.74 1.06 1.44 1.88 2.40 3.04 3.755! 0.24 0.43 0.67 0.96 1.31 1.71 2.18 2.76 3.41f, 0.::2 0.39. 0.61 0.88 1.20 1.57 2.00 2.53 3.126 lJ.:a 0,36 0.57 0.82 1.11 1.45 1.85 2.34 2.897 u.19 0.34 0.53 0.76 1.03 1.35 1.71 2.17 2.687; 0.18 0.31 0.49 0.71 0.96 1.26 1.60 2.02 2.508 0.17 0.29 0.46 0.66 0.90 1.18 1.50 1.89 2.349 0.15 0.26 0.41 0.59 0.80 1.05 1.33 1.69 2.08

10 0.13 0.24 0.37 0.53 0.72 0.94 1.20 1.52 1.8712 0.1I 0.20 0.31 0.44 0.60 0.78 1.00 1.27 1.56

DESIGNAIDS 737

TABLEA.4

Limiting steel reinforcement ratios for tension-controlled membersp. P.....

.

3\1'1;200'1' psi f;' psi p, t =0.005 t =0.004 Pmitt= T PmiII= -y-T T

40.000 3000 0.85 0.0203 0.0232 0.0050 0.00414000 0.85 0.0271 0.0310 0.0050 0.00475000 0.80 0.0319 0.0364 0.0050 0.00536000 0.75 0.0359 0.0410 0.0050 0.00587000 0.70 0.0390 0.0446 0.0050 0.00638000 0.65 0.0414 0.0474 0.0050 0,(10679000 0.65 0.0466 0.0533 0.0050 0.0071

50,000 3000 0.85 0.0163 0.0]86 0.0040 0.00334000 0.85 0.0217 0.0248 0.0040 0.00385000 0.80 0.0255 0.029] 0.0040 0.00426000 0.75 0.0287 0.0328 0.0040 0.00467000 0.70 0.0312 0.0357 0.0040 0.00508000 0.65 0.0332 0.0379 0.0040 0.00549000 0.65 0.0373 0.0426 0.0040 OJ1057

60,000 3000 0.85 0.0135 0.0155 0.0033 0.00274000 0.85 0.0]81 0.0206 00033 0.00325000 0.80 0.0213 0.0243 0.0033 0.00356000 0.75 0.0239 0.0273 0.0033 0.00397000 0.70 0.0260 0.0298 o.(xm 0.00428000 0.65 0.0276 0.0316 0.0033 0.0045.

0.00479000 0.65 0.0311 0.0355 0.0033

75.000 3000 0.85 0.0108 0.0]24 0.0027 0.00224000 0.85 0.0145 0.0165 0.0027 0.00255000 0.80 0.0170 0.0194 0.0027 0.00286000 0.75 0.0191 0.0219 0.0027 0.003]7000 0.70 0.0208 0.0238 0.0027 0.00338000 0.65 0.0221 0.0253 0.0027 0.00369000 0.65 0.0249 0.0284 0.0027 0.0038

'p = 0.85P.f 0.003t.0.003 + E,

738 DF.5IGN OF CONCRETE STRUCTURES Appendix A

TABLE A.Sa

(pi

)Flexuralresistancefactor: R = pfy 1 - 0.588 ft psify =40,000 psi fy =60,000 psi

f;, psi f;, psi .

p 3000 4000 5000 6000 3000 4000 5000 6000

(J.OOO5 20 20 20 20 30 30 30 300.0010 4(J 40 40 40 59 59 60 600.0015 59 59 60 60 88 89 89 89o.Oo:W 79 79 79 79 117 118 118 119(J.(J025 98 99 99 99 146 ]47 147 148

0.(1()30 1]7 118 118 119 174 175 176 1770.0035 136 ]37 138 138 201 204 205 206O.OO-W 155 156 157 157 229 232 233 2340.0045 174 175 176 ]77 256 259 261 2630.0050 192 194 195 ]96 282 287 289 291

0.0055 211 . 213 214 215 309 314 311 319O.1J060 229 232 233 234 335 341 345 3470.0065 247 250 252 253 360 368 371 3750.0070 265 268 271 272 385 394 399 4030.0075 282 287 289 291 410 420 426 430

o ()(ISO 300 305 308 310 ';35 446 453 4570.00"5 317 323 326 329 459 471 479 4850.11090 .\35 341 345 347 483 497 506 51100095 352 359 363 366 506 522 532 5380.0100 369 376 81 384 529 547 558 565

0.0105 385 394 \99 403 552 572 583 591o.QIIO 4p2 412 417 421 575 596 609 6170.01]5

I

419 429 435 439 . 597 620 634 643. .OO!20 435 446 453 457 618 644 659 6690.0125 451 463 471 476 640 667 684 695

('11130 467 480 488 494 661 691 708 7100.OD5 483 497 506 511 681 714 733 74600140 499 514 523 529 702 736 757 7710014'; 514 51, 540 547 712 759 7111 796( )150 I 529 547 558 565 741 7bl 1105 821

i(.0 "'5 i 545 563 575 582 760 80.1 828 845O()IW

I560 580 592 600 825 852 870

I ):(). I 575 596 609 -617 846 875 8941"1"'0 i

589 6' ) 626 635 867 898 918. I ,-(\ OJ-'5 I 004 o2h 642 652 888 920 942

!C.o180 fil8 644 659 669 909 943 966O.fJIS5 633 660 676 686 929 965 \/89()() I') 647 (,75 6112 703 949 9117 1013O.U''I5 661 691 708 710 %9 1009 1036o.o:wo

,

675 IIJIJ 715 737 988 1031 1059

I>ESIGN AIDS 739

TABLEA.5b

(pf

)Flexural resistance factor: R = pfy 1 - 0.588 ft psi

ff. :: 40,000 psi fy.:: 60,000 psi.. --.._-f;. psi f;. psi

p 3000 4000 5000 6000 3000 4000 5000 6000..

0.003 117 118 1111 119 174 175 176 1770.004

I

155 15f> 157 157 I.} J -,3 jJ0.005 192 194 195 196 2!\ 87 1I9 (jl

o.(J(J6 I 21.) , \3 2-'4 -'35 341 345 '470.(J07 265 68 271 27 -'1<5 3I.J4 399 4030.(J08 300 305 308 310 435 446 453 4570.009 335 341 345 347 483 497 506 5110.010 361.} 376 381 384 51.} 547 551\ 565

0.011 402 412 417 41 575 596 605 6170.012 435 446 453 457 61X 644 059 6090.013 467 480 488 494 I 661 691 708 7200.014 499 514 523 51.} 70 736 757 771(W15 529 547 551\ 505 741 7111 805 !l21

0.016 560 580 592 600 779 1I5 85 8700'<117 589 612 626 635 867 898 9180.018 618 644 659 069 909 943 9(,60.019 647 675 692 703 949 987 IOJ<0.020 675 706 725 i37 988 1031 1059

0.021 702 736 757 771 1073 1 i040.022 728 766 789 8()4 1115 I! 440.023 754 796 820 837 1156 i ili30.024 1\25 852 870 111.}6 i 23 7O.O5 853 882 902 12!\()

0.026 881 913 934 I ;_ '0.027 909 943 966 1,'"0.028 936 972 I.}Q70.029 %2 1002 10180.030

,

%1) 1031 1059

0.031 1014 lOW 101190.032 10117 11190.033 I I 15 11490.034 1142 11790.035 1170 1208

0.036 1196 12370.037 12650.038 12940.039 1322(J.040 13490.041 1376

740 DESIGN OF CONCRETE STRUCTURES Appendix A

TABLE A.6

Parameters k and j for elastic, cracked section beam analysis, wherek = V2pn -I- (pn)2 - pn; j = 1 - i k

n=7 n=8 n=9 n = 10

p k j k j k j k j

0.0010 0.112 0.963 0.119 0.960 0.125 0.958 0.132 0.9560.0020 0.154 0.949 0.164 0.945 0.173 0.942 0.180 0.940. 0.0030 0.185 0.938 0.196 0.935 0.207 0.931 0.217 0.928

0.0040 0.210 0.930 0.223 0.926 0.235 0.922 0.246 0.918

0.0050 0.232 0.923 0.246 0.918 0.258 0.914 0.270 0.9]0

0.0054 0.240 0.920 0.254 0.915 0.267 0.911 0.279 0.907

0.0058 0.247 0.918 0.262 0.913 0.275 0.908 0.287 0.904

0.0062 0.254 0.915 0.269 0.910 0.283 0.906 0.296 0.901

0.0066 0.261 0.913 0.276 0.908 0.290 0.903 0.303 0.899

0.0070 0.268 0.911 0.283 0.906 0.298 0.901 0.3\1 0.896

0.0072 0.27\ 0.910 0.287 0.904 0.30\ 0.900 0.314 0.895

0.0074 0.274 0.909 0.290 0.903 0.304 0.899 0.318 0.894

0.0076 0.277 0.908 0.293 0.902 0.308 0.897 0.32\ 0.893

0.0078 0.280 0.907 0.296 0.90\ 0.3\\ 0.896 0.325 0.892

0.0080 0.283 0.906 0.299 0.900 0.314 0.895 0.328 0.891

0.0082 0.286 0.905 0.303 0.899 0.317 0.894 0.33\ 0.890

0.0084 0.289 0.904 0.306 0.898 0.32\ 0.893 0.334 0.889

0.0086 0.292 0.903 0.308 0.897 0.324 0.892 0.338 0.887

0.0088 0.295 0.902 0.311 0.896 0.327 0.89\ 0.341 0.886

0.0090 0.298 0.90\ 0.314 0.895 0.330 O.a90 0.344 0.885

0.0092 0.300 0.900 0.317 0.894 0.332 0.889 0.347 0.884

0.0094 0.303 0.899 0.320 0.893 0.335 0.888 0.350 0.883

0.0096 0.306 0.898 0.323 0.892 0.338 0.887 0.353 0.882

0.0098 0.308 0.897 0.325 0.892 0.341 0.886 0.355 0.882

0.0100 0.311 0.896 0.328 0.891 0.344 0.885 0.358 0.88\

0.0104 0.316 0.895 0.333 0.889 0.349 0.884 0.364 0.879

0.0108 0.321 0.893 0.338 0.887 0.354 0.882 0.369 0.877

0.0112 0.325 0.892 0.343 0.886 0.359 0.880 0.374 0.875

0.0116 0.330 0.890 0.348 0.884 0.364 0.879 0.379 0.874

0.0120 0.334 0.889 0.353 0.882 0.369 0.877 0.384 0.871

0.0124 0.339 0.887 0.357 0.881 0.374 0.875 0.389 0.870

0.0128 0.343 0.886 0.362 0.879 0.378 0.874 0.394 0.867

0.0132 0.347 0.884 0.366 0.878 0.383 0.872 0.398 0.867

0.0136 0.351 0.883 0.370 0.877 0.387 0.871 0.403 0.866

0.0140 0.355 0.882 0.374 0.875 0.392 0.869 0.407 0.864

0:0144 0.359 0.880 0.378 0.874 0.396 0.868 0.412 0.863

0.0148 0.363 0.879 0.382 0.873 0.400 0.867 0.4\6 0.861

0.0\52 0.367 0.878 0.386 0.87\ 0.404 0.&65 0.420 0.860

0.0156 0.371 0.876 0.390 0.870 0.408 0.864 0.424 0.859

0.0160 0.374 0.875 0.394 0.869 0.412 0.863 0.428 0.857

0.0170 0.383 0.872 0.403 0.867 0.421 0.860 0.437 0.854

0.0180 0.392 0.869 0.412 0.863 0.430 0.857 0.446 0.851

0.0190 0.400 0.867 0.420 0.860 0.438 0.854 0.455 0.848

0.0200 0.407 0.864 0.428 0.857 0,446 0.851 0.463 0.846

DESIGNAIDS 741

TABLEA.7..

Maximum number of bars as a single layer in' beam stems

1in. MaximumSizeAggregate,No.4 (No.13)Stirrups.BarNo. Beam Width bW'in.

Inch- .Pound 51 8 10 12 14 16 18 20 22 24 26 28 30

5 16 2 4 5 6 7 8 10 II 12 13 15 166 19 2 3 4 6 7 8 9 10 II 12 14 IS7 22 2 3 4 5 6 7 8 9 10 II 12 138 25 2 3 4 5. 6 7 8 9 10 II 12 139 29 I 2 3 4 5 6 7 8 9 9 10 II

10 32 I 2 3 4 5 6 6 7 8 9 )() 10II 36 I 2 3 3 4 5 5 6 7 8 8 914 43 I 2 2 3 3 4 5 5 6 6 7 I>18 57 I 1 2 2 3 3 4 4 4 5 5 6

1 in. Maximum Size Aggregate;o. 4 (No. 13) Stirrups.

Bar No. Beam Width bW' in.Inch-

Pound 51 8 10 12 14 16 18 20 22 24 26 28 30

5 16 2 3 4 5 6 7 8 9 10 11 12 136 19 2 3 4 5 6 7 8 9 9 10 II 127 22 1 2 3 4 5 6 7 8 9 10 10 1.18 25 I 2 3 4 5 6 7 7 8 9 10 II9 29 I 2 3 4 5 (; 7 7 8 9 9 10

10 32 I 2 3 4 5 6 6 7 7 8 9 10

"Minimumconcretecoverassumed10be Ii in.10theNo.4 (No.13)sunup.SoUfC: Adapted from Ref. 3.8. Used by pennission of American Conc:reteInstitule..

742 DESIGN OF ~ONCREl'E STRUCTURES Appendix A

TABLEA.'

Minimumnumber of bars as a single layer in beam stems governed by crack controlrequirements of the ACICode(a) 2 in. &tar cover, sides and bottom

Minimum Number of Bars as a Single Layer of a Beam StemBar No. Beam Stem Width b... in.

Inch.Pound 51 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

3-14 10-43 I I 2 2 3 3 3 3 3 4 4 4 4 4 518 57 I I 2 2 2 3 3 3 3 3 4 4 4 4 4

(b) 1 in. clear c;over, sides and bottom

Minimum Number of Bars as a Single Layer of a Beam StemBar No. Beam Stem Width b... in.

Inch.Pound 51 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36

3-4 10-13 1 I 2 2 3 3 3 3 3 4 4 4 4 4 45-14 16-43 I 1 2 2 3 3 3 3 3 3 4 4 4 4 4

18 57 1 I 2 2 2 3 3 3 3 j 4 4 4 4

DESIGNAIDS 743

TABLE A.9

Design strength Mn for slab sections 12 in. wide, ft-kips; fy =60 ksi;4>Mn= pfybd2(1 - 0.59pfy/fJ

Effective Depth d, in.

f;. psi p 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 8.0 9.0 10.0 12.0..

3000 0.<X12 0.9 1.3 1.7 2.1 2.6 3.2 . 3.8 4.5 5.2 5.7 8.5 10.5 15.20.003 U 1.9 2.5 3.2 3.9 4.7 5.6 6.6 7.7 10.0 12.7 15::) 22.50.001 I) 2.5 .3 4.2 5.1 6.2 7.4 8.7 10.1 13.2 16.7 20.6 29.60005 2.:1 3 I 4.1 5.1 6.4 7.7 9.1 10.7 12.4 16.3 20.6 23.4 36.6ll.<X16 2.7 3.7 4.8 6.1 7.5 9.1 10.8 12.7 14.8 19.3 24.4 30.1 4.l40.<X17 3.1 4. 5.5 7.0 8.7 10.5 12.5 14.7 17.0 22.2 28.1 34.7 49.90.0011 3.5 4.8 6.3 7.9 9.8 11.8 14.1 16.5 192 25.0 31.7 39.1 56.3O.or" 3.9 5.3 7.0 8.8 10.9 13.1 I " 18.4 21.3 27.8 35.2 43.4 62.60.010 4.3 5.8 7.6 9.6 11.9 14.4 17.1 20.1 23.3 30.5 38.6 47.6 68.60.011 4.7 6.3 8.3 10.5 12.9 15.6 18.6 21.8 25.3 33.1 41.9 51.7 74.4

WOO 0.002 1.0 1.3 1.7 2.1 2.7 3.2 3.8 4.5 5.2 6.8 8.6 10.6 15.30.003 1.4 1.9 2.5 3.2 3.'1 4.1S 5.7 6.7 7.7 10.1 12.8 15.8 22.70.004 1.9 2.6 3.3 4.2 5.2 6.3 7.5 8.8 10.2 13.3 16.9 20.8 30.00.005 2.3 3.2 4.1 5.2 6.5 7.8 9.3 10.9 12.6 16.5 20.9 25.8 37.20.006 2.8 3.8 4.9 6.2 7.7 9.3 11.0 13.0 15.0 19.6 24.9 30.7 44.20.007 3.2 4.3 5.7 7.2 8.9 10.7 12.8 15.0 17.4 22.7 28.7 35.5 51.10.<X18 3.6 4.9 6.4 8.1 10.0 12.1 14.5 17.0 19.7 25.7 32.5 40.1 57.1!0.009 4.0 5.5 7.2 9.1 11.2 13.5 16.1 18.9 21.9 28.6 36.2 447 64.40.010 4.4 6.0 7.9 10.0 12.3 14.9 17.7 20.8 24.1 31.5 39.9 49.2 70.9O.oJI 4.8 6.6 8.6 10.9 13.4 16.2 19.3 22.7 26.,3 34.3 43.4 536 77.20.012 5.2 7.1 9.3 11.7 14.5 17.5 20.9 24.5 28.4 37.1 46.9 57.9 83.40.013 5.6 7.6 9.9 12.6 15.5 18.8 22.4 26.2 30.4 39.8 50.3 62.1 89.50.014 6.0 8.1 10.6 13.4 16.6 20.0 23.8 28.0 32.5 42.4 53.6 66.2 95.40.015 6.3 8.6 11.2 14.2 17.6 21.2 25.3 29.7 34.4 45.0 56.9 70.2 101.2

SOOO 0.002 1.0 1.3 1.7 2.2 2.7 3.2 3.8 4.5 5.2 6.8 8.6 10.6 15.30.003 \.4 \.9 2.5 3.2 4.0 4.8 5.7 6.7 7.8 10.1 12.8 15.9 22.80.004 \.9 2.6 3.4 4.3 5.2 6.3 7.6 8.9 10.3 13.4 17.0 21.0 30.20.005 2.3 3.2 4.2 5.3 6.5 7.9 9.4 11.0 12.8 16.7 21.1 26.0 37.50.006 2.8 3.8 5.0 6.3 7.8 9.4 11.2 13.1 15.2 19.9 25.1 31.0 44.70.007 3.2 4.4 5.7 7.3 9.0 10.9 12.9 15.2 17.6 23.0 29.1 35.9 51.70.008 3.7 5.0 6.5 8.3 10.2 12.3 14.7 17.2 20.0 26.1 33.0 40.8 58.70.009 4.1 5.6 7.3 9.2 11.4 13.8 16.4 19.2 22.3 29.1 36.9 45.5 65.50.010 4.5 6.1 8.0 10.2 12.5 15.2 18.1 2\.2 24.6 32.1 40.6 50.2 72.30.011 4.9 6.7 8.8 ILl 13.7 16.6 19.7 23.1 26.8 35.1 44.4 54.8 78.90.0\2 5.3 7.3 9.5 12.0 14.8 17.9 21.3 25.1 29.1 37.9 48.0 59.3 85.40.013 5.7 7.8 10.2 12.9 15.9 19.3 22.9 26.9 3\.2 40.8 5\.6 63.7 91.80.014 6.1 8.3 10.9 13.8 17.0 20.6 24.5 28.8 33.4 43.6 55.2 61!.1 98.10.015 6.5 8.9 I\.6 14.7 18.1 21.9 26.1 30.6 35.5 46.3 58.6 72.4 104.30.016 6.9 9.4 12.3 15.5 19.2 23.2 27.6 32.4 37.5 49.0 62.1 76.6 110.30.IH7 7.3 9.9 12.9 16.4 20.2 24.4 29.1 34.1 39.6 51.7 65.4 80.8 116.3

Case a: Clear spacing of bars being developed or spliced O!:db' clear cover O!:d". and stirrups or ties throughoul/~ not less thanthe Code minimum.

Case b: Clear spacing of bars being developed or spliced O!:211".and clear cover not less than d".

. ACI CommitlCC 408 recommends that the \-aJues indicated for bar sizes No. 7 (No. 22) and larger be used for all bar sizes.


TABLE A.10

Simplified tension development length in bar diameters I,Jdb foruncoated bars and normal-weight concrete

No.6 (No. 19) and Smalle.... No. 7 (No. 22) a.,d Larger

f;. psi f;, psi

t ksi 4000 SOOO 6000 4000 SOOO 6000

(1) Bottom bars

Spacing. cover 40 25 23 21 32 28 26and ties as per 50 32 28 26' 40 35 32Case a or b 60 38 34 31 47 42 39

Other cases 40 38 34 31 47 42 3950 47 42 39 59 53 4860 57 51 46 71 64 58

(2) Top bars

Spacing. cover 40 33 29 27 41 37 4

and ties as per 50 41 37 34 51 46 42Case a or b 60 49 44 40 62 55 50

Other cases 40 49 44 40 62 55 5050 62 S5 50 77 69 6360 74 66 6(j 92 83 76

DESIGN AIDS 745

TABLE A.11

Development length in compression, in.'de = greater of (O.02fy/)db or O.0003fydb (Minimum length 8 in. in all cases.)

f;, psiBar No. 3000 4000 5000 6000

Inch- fy. Basic Basic Basic BasicPound 51 ksi 'db Confined '<It- Confined 'db Confined 'db Confined

3 10 40 8 8 8 8 8 8 8 850 8 P 8 8 8 8 8 860 8 8 8 8 8 8 8 8

.4 13 40 8 8 8 8 8 8 8 8

50 9 8 8 8 8 8 8 860 11 8 9 8 9 8 9 8

5 16 40 9 8 8 8 8 8 8 850 II 9 10 8 9 8 9 860 14 10 12 9 11 8 11 8

6 19 40 II 8 9 8 9 8 9 850 14 10 12 9 11 8 11 860 16 12 14 11 14 10 14 10

7 22 40 13 10 11 8 11 8 11 850 16 12 14 10 13 10 13 1060 19 14 17 ]2 16 12 16 12

8 25 40 15 11 13 9 12 9 12 950 18 14 16 12 15 11 15 1160 22 16 19 14 18 14 18 14.

9 29 40 16 12 14 11 14 10 14 1050 2] IS 18 13 17 13 17 ]360 25 19 21 16 20 IS 20 IS

10 32 40 19 14 16 12 IS 11 IS 11SO 23 17 20 15 19 14 19 1460 28 21 24 18 23 17 23 17

11 36 40 21 IS 18 13 17 13 17 ]350 26 19 22 17 21 16 21 1660 31 23 27 20 25 19 25 19

14 43 40 25 19 21 16 20 IS 20 IS50 31 23 27 20 25 19 25 1960 37 28 32 24 30 23 30 23

18 57 40 33 2S 29 21 27 20 27 2050 41 31 36 27 34 25 34 2S60 49 37 43 32 41 30 41 30

746 CESIGN OF CONCRETE STRUCTURES Appendix A

TABLEA.12

Common stock styles of welded wire reinforcement (WWR)

Steel Area, in2jft Weigh~.(Approximate),

Ib per 100 ft2

1927395429415982

39547582

"1be designation W indicate. smooth wire: WWR is a'so available as defonned wire. designated with a D.

Steel Designay,on' Longitudinal Transverse

Rolls

6 x 6-W1.4x W1.4 0.02!! 0.0286 x 6-W2.0 x W2.0 0.040 0.0406 x 6-W2.9 x W2.9 0.058 OJJ586 x 6-W4.0 x W4.0 0.080 0.0804 x 4-W1.4 x WI.4 0.(J42 0.0424 x 4-W2.0 x W2.0 0.060 0.0604 x 4-W2.9 x W2.9 0.087 0.0874 x 4-W4.0 x W4.0 0.120 0.120

Sheets

6 x 6-W2.9 x W2.9 0.058 0.0586 x 6-W4.0 x W4.0 0.080 0.0806 x 6-W5.5 x W5.5 0.110 0.1104 x 4-W4.0 X W4.0 0.120 0.120

.Applicable when c,l/, = c:ll:. For ocher relationships between Ihcsc ratios.1hc c:onstanIs will be slightly in CITOr.

· Stiffness is KAJl=k,..E(I:h:/12/,) and KM = kME(/zh:/I21,).

"Applicable when c,/I, = ('Jlz. For other relationships between these ratios. the constants will be slighlly in error.

"Stiffness is KAB= kAsE(I,JrilI2/,) and K... =k...E(I~~/I2J,). .


TABLEA.13B

Coefficients for slabs with variable moment of inertiaa

CIA C,8

rI1 [2h,

OIL I

w .=rr1.25h,

i.-.G 2/, I,J, 6 3

I6 0

I I, ,IA

12in perpendiculardirectionB

Column Uniform Load Stiffness CarryoverDimension FEM = Coeff.(wlz/f> Factor b Factor

c,.//1 c,efl, MAS Mu kAS ku COFA8 COFBA0.00 0.00 0.088 0.088 4.78 4.78 0.541 0.541

0.05 0.087 0.089 4.80 4.82 0.545 0.5410.10 0.087 0.090 4.83 4.94 0.553 0.541

. 0.15 0.085 0.093 4.87 5.12 0.567 0.5400.20 0.084 0.096 4.93 5.36 0.585 0.5370.25 0.082 0.100 5.00 5.68 0.606 0.534

0.05 0.05 0.088 0.088 4.84 4.84 0.545 0.5450.10 0.087 0.090 4.87 4.95 0.553 0.5440.15 0.085 0.093 4.91 5.13 0.567 0.5430.20 0.084 0.096 4.97 5.38 0.584 0.5410.25 0.082 0.100 5.05 5.70 0.606 0.537

0.10 0.10 0.089 0.089 4.98 4.98 0.553 0.5530.15 0.088 0.092 5.03 5.16 0.566 0.5510.20 0.086 0.094 5.09 5.42 0.584 0.5490.25 0.084 0.099 5.17 5.74 0.606 0.546

0.15 0.15 0.090 0.090 5.22 5.22 0.565 0.5650.20 0.089 0.094 5.28 5.47 0.583 0.5630.25 0.087 0.097 5.37 5.80 0.604 0.559

0.20 0.20 0.092 0.()92 5.55 5.55 0.580 0.5800.25 0.090 0.096 5.64 5.88 0.602 0.577

0.25 0.25 0.094 0.094 5.98 5.98 0.598 0.598

TABLE A.13C

Stiffness factors for columns with variable moment of inertiaa

'Adapled from S. H. Simmonds and J. Misic, "Design Fact\otS for thcEquivaJenl Frame Method:' J. ACI. vol.

68. no. II. 1971. pp. 825-831.

DESIGN AIDS 749

Slab Half-depth Stiffness Factor Slab Half-depth Stiffness Factor

c".!I, k,u C'A/I, k,u

0.00 4.00 0.14 9.430.02 4.43 0.16 11.010.04 4.94 0.18 13.010.060 5.54 0.20 15.560.08 6.25 0.22 18.870.10 7.11 0.24 23.260.12 8.15

TABLE A.14

Size and pitch of spirals, ACI Code

f;, psiDiameter of Out to OutColumn, in. of Spiral, in. 2SOO 3000 4000 SOOO

f.. = 40.000 psi14.IS 11,12 -2 Hi -2! Hi16 13 -2 Hi -2 -217-19 14-16 1-2* }-1} !-2! !-220-23 17-20 -2 ! Ij !-2! j-2.- .24-30 21-27 H* i-2 !-2 H

= 60,000 psiH 1-2i 1-2 !-2i14.15 11.12

16-23 13-20 H 1-2i i-2 !-324-29 21-26 H 1-3 -21 H30 27 H H -21 -3*

"Adapted from PCI Design Handbook. 5th cd.. Precast/Prestressed Concrete Institute. Chicago. IL. 1999.

"The ~in. special strand has a slightly larger actual diameter than the ~in. strand.

'Prestrcssing wires vary in diameter from 0.105 to 0.276 in. A full listing is given in the PCI Desigll Handbook.

"Fordesignpurposes.thefollowingassumptionsare satisfactoryfordeformedbars:E. = 29.000.000psiandf, = 0.95f...

750 DESIGN OF CONCRETE STRUCTURF.5 AppendixA

TABLE A.15

Properties of prestressing steels.

Seven-Wire Strand, fpu =270 ksi

NominalDiameter Area, Weight, O.7fpuApI' O.75fpu ApI' O.8fpu ApI' fpuApI'(in.) in2 plf kips kips kips kips

(0.375) 0.085 0.29 16.1 17.2 18.4 23.0

(O.500) 0.153 0.52 28.9 31.0 33.0 41.3

!S/' 0.167 0.53 31.6 33.8 36.1 45.1(0.6001 0.215 0.74 40.7 43.5 46.5 58.1

Prestressing Wirec

Area, Weight, fpu' O.7fpu ApI' O.8fpuAps' fpuApI'Diameter in2 plf ksi kips kips kips

0.192 0.0289 0.098 250 5.05 5.78 7.220.196 0.0302 .1).100 250 5.28 6.04 7.550.250 0.0491 0.170 240 8.25 942 11.780.276 0.0598 0.200 235 9.84 11.24 14.05

Deformed Prestressi:'lg Barsd

Nominal

Diameter Area, Weight, fpu' O.7fpuApI' O.8fpu ApI' fpuApI'(in.) in2 plf ksi kips kips kips

0.28 0.98 157 30.5 34.8 43.5

I 0.85 3.01 150 89.3 102.0 127.5I 0.85 3.01 160 95.2 108.8 136.0I 1.75 4.39 150 131.3 150.0 187.5I 1.25 4.39 160 140.0 160.0 200.0

1.58 5.56 150 165.9 159.6 237.0

GRAPH A.laMoment capacity ofrectangular sections.

DESIGN AIDS 751

752 DESIGN OF CONCRETE STRUCTURES AppendixA

GRAPHA.lbMOlllcnt capadty ofrectangular ~c"li()l1s.

600

500

-~.

I

'*'~-~

II

~..;:\,)< .r;

400

-

2C.v',i~

~l

o ':'A,

: i I'

II

it il i

---to

Ii~-l

I .I '

11-~i-~~. I I

I I tI I. -+--

-~-

- I I

:;f--+- _1I ,

IIi

0.012 0.016 0.018"iC08 C.010 0.014

DESIGN AIDS 753

100o 0.1 0.2 0.3 0.4 0.5

De~imals of span len.gth

GRAPH A.2 0ux:a!ion of points wherebar:; can be ben! up or CU!ofTfor simply supponed beams 10

uniformly loaded.

= 200'S0(5 30Q.:)c:

40Q).cQ).c>-'" 50Eiii-=Qj 60C)Cii'0

70c:Q)0

;f 80

90

T I I I I . I .---- ,-I"1 .1 I..Y- 00

7' I I II 1o I ,/ I I i

II . V. I

-,- .A' : II

I x /f 0- jq IiI J ! I I i I

I I .17 ! 0 I I J- 1----+----"-I . I!/

I I i !.' I :I

II II

) T I I; -IV ! T ! !

I ---:------1'-,/ . Ii I

· i I/ !I I I

: I II, I I IV . I I I - _00-___

J 'I,i/1 I I --

Ji : I i I. -lI . Ivr , I I . I


GRAPH A.3

Approximate locations of

points where bars can be bentup or down or cut off (orcontinuous beams uniformly

loaded and built integrdllywith their supports accordingto the coefficients in the ACICode.

10

20

30

o

-~

m0.2 0.3

oruo 0.1Decimals cf clear span lengl'1

0.4

I+

IIIJ'I

. I.

Q5

= 400

'550

0Co

::I 60

] 70

Z 80E

90

c:CD 100ECDI:!,g 90coS!'0 80c:

If70

:s 60"5u6 50

o 40

30

20

10

GRAPH A.4Interpolation charts forlateral distribution of slabmoments.

DESIGN AIDS 755

100 100

I !cx'/211, = oj 80

: T-0.2

~.4

0.6J600.8

..1.0I '40

60

Interior negative moment40 .

100

80

Positive moment

40 1.0 .0.5

c100 100-.J , , . I I I , ,0

c I I I __O5Q)E0

cx'/2//' - 0 80 I. cQ:

E1.0 '0

. 60

0.2 :II

iii0.4. ---- E

c::0.6 60 1.5 .a

EExterior negativemoment

0.8 I g;;, 1 O

'0 400

40 .2.5

100. I1.0.. cx,/

8O§l'

0.60.40.2

60 0


0.00.00 C.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GR4.PH A.5

C..,lumnstrength interaction dIagram for rt"clangularsectiun will)bars on fuur faces and "y=0.60 (forinstructional useonly).

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2'".

Q.:> 1.1

II

Q."'"1.0

i--..UII 0.9':::c"

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

!? Interaction diagramf.' 4 ksi" 0 c

1/fy 60 ksi -=:l, ,'Y 0.60CI)

I . I

T ....., . I . I ·O' b . .0.08

l . I ·, , , .....0.07

30.06 O' L-.....,,

0.05 _0- II

,,(),Co ,0.04 (). ().

, ,

0.03

0'.02

Pg 0.01,

""\}.\s"

, ,/-,9Q

e'"''

t"-'O.002fs"-'fy I<'" - O'...

..::.:..o '. +-n--''''' t}'Q

, .I-i--t-H--+r..,.

. , -.-- +--

DESIGN AIDS 757

;: Interaction diagramo' f~ 4 ksi

~ fy 60ksi r-- h ~Qj 'Y 0.70 I r- ~h ---, I

~ r :. t..~ .0.08 b.: ·l . I ·..~..

0.07

~' e p.rn

0.06 <)f I

oII

0.05 '-"

~Q~ ~p .~v <).

. 0.03 '

io? ~

Pg 0.91

\ ~~ ~+s '

\~, e~~

_-lEt 0.002fs fy +

.~' ~,.."0

'l:f.;$0.0

0,00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GRAPH A.6

Columnstrengthinteractiondiagramfor rectangularsectionwith barson four facesand'Y= 0.70fforinstructionaluseonly).

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

O- 1.1

II

O-I1.0

II 0.9'::I:

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1


2.0

1.9

0.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GRAPH A.7Columnstrength interaction diagram for rectangular section with bars on four faces and 'V=0.80 (forinstructiunal use onl}).

,Interaction diagram$2

ci f.' 4 ksic/I

fy 60 ksi

I r-;h! '/q, 'Y 0.80r

..t..R I . .(:)' b

I

0.08 I : :l .. ..

0.07

0.06 1:)'(:)

It"- ,

0.05

I:)<-,0.04 ''-- ' 1:)'

0.03 ::;r-:...

0.02 . '-:..-. . --

+0.0 \

-+p \5

:-r

'\el

Et 0.002fs fy

""O.gas

1.8

1.7

1.6

1.5

1.4

1.3

1.21'«""

Q..:>I-u 1.1F$.II

Q..c:I1.0

,-..;II 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

DESIGN AIDS 759

2.0

1.9

1.8

1.7

1.6

0.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GRAPH A.S

Column strength interaction diagram for rectangular section with bars on four faces and 'Y= 0.90 (forinstructional use only).

, ,Interaction diagram0-

0 f' 4 ksiIt

c

fy 60 ksi t----- h --,<Ii Y 0.90 I r-yhil, I

, , r ..t... .O' bI

0.08. I .

L :..:0.07 '

'0.06<:) t§>

I; <:;).,..

' "'..

0.05

0.04 ,,<:;)<:;). <:;).

0.03

0.02'\

P 0.0\s".

\em'"

E,- 0.002fs ' fy

II /""0oo.. S

1.5

1.4

1.3

1.2

1.1

1/

a:lq:'"1.0

:0.."1/ 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

760 DESIGN OF CO:\CRETE STRUCT\jRES Appendix A

0.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

Pne PueHn= l 'A h = ""l' A hC 9 'YC 9

GRAPH A.9

Columnstrengthinteractiondiagramfor rectangularsectionwith barson endfacesand'Y= 0.60(for instructionaluseonly).

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

a.l 1.1re-II

0.0::1"(0)1.0

I11 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

c Interaction diagram-'0 f.' 4 ksiCI:

fy 60 ksi

I r-I'I:.:

CIJ . l' 0.60-'

1I

. .I . .

c' b . . .0.08

L : I

... 0.07

,.06 c'

0.05cq :P0.04 ", C' C'

0.03:

0'.02 .

Pg 0.01

"'s"'

00sit'''''\.

€,=:0.002 . ,'s=:fy

E(':

""0-'-:f-H'1;;.' POs .

DESIGN AIDS 761

0.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GRAPH A.tOColumn strength interaction diagram for rectangular section with ba"son end faces and 'Y= 0.70 (for instructionaluse only).

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

II

a::1

1.0

II 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

tSS: :H H -; .#-+0

-; . +-1 :rH' Interaction diagram0

.,.,. 4 ksi

R=-,--.. 1/ +. c

f+i+ 'f+. -+J-

fy 60 ksi ...- h--rQ) . y 0.70 yh-

.1-+ -f--'!' _ITI I

- r . , .--H- ---1'1

, I . .I., I . ..-. " c)' !

0.08-"-;''b . .

- - I '- -4--+ I . .. I . .

0.07- ! .

+-: , , _e--t-+-'

- . ,

0.06 .,

clrj L_____.,p::

0.05 6+- ,

// +' ,+ ,=i7=',..

:P0.04 C. C..

0..03' .

, ', , -+ .,4...

"". ,

0.02 ,. .

P 0.01 ,

ts",'!-,b;:;;,-L,+-1+

r

. ., 9(), a\l'

- -t Et 0.002. fs fy

j.+-L...j.

+-

II t

, fr""O.OO5,


0.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GRAPH A.lJ

Columnstrengthinteractiondiagramfor rectangular-sectionwith barson endfacesand'Y= 0.80(for instructionaluseonly).

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

II

I1.0

II 0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Interaction diagram

c:i t' 4 ksicII

fy 60 ksi

I'r-;hilCIi Y 0.80

r .I

.. . .O' b .

j

.0.08

l . .. .0.07

0.06 o'

-0.05 G

"''!o

.P0.04 o. o.

:9.03

0'.02

-nfjP -0.0

ts",,\ty

,90sit'''''

Et 0.002fs- fy

E 0.005

1m

DESIGN AIDS 763

0.4

0.3

0.2

0.110.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GRAPH A.12

lOhU)1!l strength interaction diagram for reclangular section with bars on end laces and 'Y = 0 <)0 qUi IIlstruClional

use onlY/.

2.0

1.9

1.8

1.7

,.-1.5I I I I I I 0.07 .'

1..1.3 0.051.2

,0.041.1

II tttI;;j:0.03

cl1.0

III=m=0.02

c0.9

0.8 Pg = 0.01

0.7

0.6

0.5

Interaction diagram- - '

C'.,_ .-f = 4 ksi

fy = 60 ksi r:- h ---;f./J3:tt;<: ,-' , ' ')' = 0.90 - ')'h- !t j&- .-

! . .. .O' I" r b . ., . , . .

I

L. .. .s5',"5 ,

. :

<:),1-

'....Q:::1:l-

<:).

, , ,---.I-

:t::

II' , ', .., I

'I "

.'-

=r:Ja:Il'l.:I::I:2Ll" , i I i ,,q' , ,

, .. .c<i.,el"' ,

Ii*=1=0.002

1mF11tmrtm1-t+-Hrl!1 !!+PJl-

III'ill111

'I I I I I I III I I I TTTTT"'T', E1=0.005

764 I>(':SIC;"Of CO'iCRETE STRUCTURES Appendix A

I""0.:,,'<:(

,o;Ui~II

0..<:.'<:(""I~

II

~<:.

1.4

~t0.05'1.3

~

;0.041.2

1.1 .0.03

1.0 1-0.02

0.9 ~p;= 0.01Ed~

0.8

0.7

0.6

0.5

0.4

0.3

0.2

--

.0II

,CoT

Hi

f.'c

fyY

Interaction diagram4 ksi60 ksi0.60 rh

I r yh l,

~ I... I. . I. .. ! ....

0.110.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

Et = 0.005

GR.\PH A.13Culumn stren~til interaction dia~ram for circular set.tion with y = O.hO (for mstructional use only).

~~lfII

_! Qc.:-I«~

II

~r::

2.0

f.'cfy'Y

Interaction diagram4 ksi60 ksi0.70

h1.9

It)oc::i"~

-

[}ESIG:\ AIDS 765

-yhI II~!I';.... I .. .. .. . .

.*<-,'V.~

'V~;-,- -i =H=

H;2

-

.

0.00.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

-

1.8

1.7 0.08

GRAPH A.14

Column ,uength intera,tion diagram for circular section with 'Y= 0.70 (for instructional use only).

1.6I,.

0.07

1.5 .0.06"

1.4<::III"

0.051.3

0.041.2

0.031.,1.0~

0.7

0.6

0.5

0.4 '-i- E,=0.002

0.3

0.2

.~Pl.. :-4-

0.1"'IN/rj~:t~

eE,= 0.005~ /-.-;-+Jl~1..;/+7~:= . ,


r+"tH'

1-+1+- +X2 . . $2 Interactiondiagram

~* 1="0 0 f~ 4ksi;:,:r.: I-j~ .:t:::-r.- _ fy 60 ksi r- h -

,. Cb' 'Y 0.80 i C ~h!!-l,

Q.Ib::i'0

,

.08 !:) I . .. ,

+i--h-' CV .. )~" ' :ft:t" ' - ' ' . O',TT' ., .. . .

f-i::+'O'.07'. r",,~ , . I .- . . ' .I'~ ' ' .~~.06,. "." ":+

,'~ ~,

e Pn0" " ~!:)

II , <)', 1p:::0.05. ,to , t-:-

I ' -+~." -<. I'

140.04H~" D

~ ',~ ''?~D' ~.'0.03 ' : '

J;Q.2 , ' . , ,

, , , "\,,' .o 0.01 q '1-.. 9 ,~

00e1tl"'\'

,00 2

~I==O.fs==fy

I

111m ~"'o '

E '00$0.0

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GRAPH A.ISColumnstrengthinteractiondiagramfor circularsectionwith 'Y= 0.80(for instructionaluseonly).

2.0

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2,'"

Q."0 1.1"$I

Q.<:"'{'"1.0

,,-"II 0.9<:

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

DESIGN AIDS 767

Interaction diagram

f~=4 ksi

fy =60 ksi'Y=0.90

(;)II"

H,

" .

~ II"EI",0.OO2

fs";'ty

01_" " <>,""0'JI.C-.,. " , " ' . !!oS:

0.0 '0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65

GRAPH A.16

Columnstrength interdctiondiagram for circular secli9n with)' =0.90 (for instructional u~eonly).

2.0IT:I. ,

.0'

1.911 i'I.: 1i :gII

181

17 008 .

1.6 ,0.07

1.5 0.06

1.4:0.05

1.3

1 'O.O4.2

1.1 bO.03II

cl1.0 OO2

II 0.9'"::t:.c

g- .01

0.8

0.7

0.6

0.5

0.4

0.3

0.2

nilson book-appendix a

Documents