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NOMINAL CROSS NOMINAL NOMINAL

SECTION AREA WEIGHT DIAMETER PERIMETER

(sq. in.) (lb/ft) (in.) (in.)

# 3 0.11 0.376 0.375 1.18

# 4 0.20 0.668 0.500 1.57

# 5 0.31 1.043 0.625 1.96

# 6 0.44 1.502 0.750 2.36

# 7 0.60 2.044 0.875 2.75

# 8 0.79 2.670 1.000 3.14

# 9 1.00 3.400 1.128 3.54

# 10 1.27 4.303 1.270 3.99

# 11 1.56 5.313 1.410 4.43

# 14 2.25 7.650 1.693 5.32

# 18 4.00 13.600 2.257 7.09

Note: The nominal dimensions of deformed bars are equivalent to those of a plain bar having

the same mass per foot as the deformed bars.

REINFORCEMENT 1 - Nominal cross section area, weight, and nominal

diameter of ASTM standard reinforcing bars

BAR

SIZE

DESIGNATION

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0 5 1 2 3 4 5

1 0.20 1.20 0.31 0.42 0.53 0.64 0.75

2 0.40 1.40 0.51 0.62 0.73 0.84 0.95

#4 3 #4 0.60 1.60 #3 0.71 0.82 0.93 1.04 1.15

4 0.20 0.80 1.80 0.11 0.91 1.02 1.13 1.24 1.35

5 1.00 2.00 1.11 1.22 1.33 1.44 1.55 1 2 3 4 5

1 0.31 1.86 0.51 0.71 0.91 1.11 1.31 0.42 0.53 0.64 0.75 0.86

2 0.62 2.17 0.82 1.02 1.22 1.42 1.62 0.73 0.84 0.95 1.06 1.17

#5 3 #5 0.93 2.48 #4 1.13 1.33 1.53 1.73 1.93 #3 1.04 1.15 1.26 1.37 1.48

4 0.31 1.24 2.79 0.20 1.44 1.64 1.84 2.04 2.24 0.11 1.35 1.46 1.57 1.68 1.79

5 1.55 3.10 1.75 1.95 2.15 2.35 2.55 1.66 1.77 1.88 1.99 2.10 1 2 3

1 0.44 2.64 0.75 1.06 1.37 1.68 1.99 0.64 0.84 1.04 1.24 1.44 0.55 0.66 0.77

2 0.88 3.08 1.19 1.50 1.81 2.12 2.43 1.08 1.28 1.48 1.68 1.88 0.99 1.10 1.21

#6 3 #6 1.32 3.52 #5 1.63 1.94 2.25 2.56 2.87 #4 1.52 1.72 1.92 2.12 2.32 #3 1.43 1.54 1.65

4 0.44 1.76 3.96 0.31 2.07 2.38 2.69 3.00 3.31 0.20 1.96 2.16 2.36 2.56 2.76 0.11 1.87 1.98 2.095 2.20 4.40 2.51 2.82 3.13 3.44 3.75 2.40 2.60 2.80 3.00 3.20 2.31 2.42 2.53

1 0.60 3.60 1.04 1.48 1.92 2.36 2.80 0.91 1.22 1.53 1.84 2.15 0.80 1.00 1.20

2 1.20 4.20 1.64 2.08 2.52 2.96 3.40 1.51 1.82 2.13 2.44 2.75 1.40 1.60 1.80

#7 3 #7 1.80 4.80 #6 2.24 2.68 3.12 3.56 4.00 #5 2.11 2.42 2.73 3.04 3.35 #4 2.00 2.20 2.40

4 0.60 2.40 5.40 0.44 2.84 3.28 3.72 4.16 4.60 0.31 2.71 3.02 3.33 3.64 3.95 0.20 2.60 2.80 3.00

5 3.00 6.00 3.44 3.88 4.32 4.76 5.20 3.31 3.62 3.93 4.24 4.55 3.20 3.40 3.60

1 0.79 4.74 1.39 1.99 2.59 3.19 3.79 1.23 1.67 2.11 2.55 2.99 1.10 1.41 1.72

2 1.58 5.53 2.18 2.78 3.38 3.98 4.58 2.02 2.46 2.90 3.34 3.78 1.89 2.20 2.51

#8 3 #8 2.37 6.32 #7 2.97 3.57 4.17 4.77 5.37 #6 2.81 3.25 3.69 4.13 4.57 #5 2.68 2.99 3.30

4 0.79 3.16 7.11 0.60 3.76 4.36 4.96 5.56 6.16 0.44 3.60 4.04 4.48 4.92 5.36 0.31 3.47 3.78 4.09

5 3.95 7.90 4.55 5.15 5.75 6.35 6.95 4.39 4.83 5.27 5.71 6.15 4.26 4.57 4.88

1 1.00 6.00 1.79 2.58 3.37 4.16 4.95 1.60 2.20 2.80 3.40 4.00 1.44 1.88 2.32

2 2.00 7.00 2.79 3.58 4.37 5.16 5.95 2.60 3.20 3.80 4.40 5.00 2.44 2.88 3.32

#9 3 #9 3.00 8.00 #8 3.79 4.58 5.37 6.16 6.95 #7 3.60 4.20 4.80 5.40 6.00 #6 3.44 3.88 4.32

4 1.00 4.00 9.00 0.79 4.79 5.58 6.37 7.16 7.95 0.60 4.60 5.20 5.80 6.40 7.00 0.44 4.44 4.88 5.32

5 5.00 10.00 5.79 6.58 7.37 8.16 8.95 5.60 6.20 6.80 7.40 8.00 5.44 5.88 6.32

1 1.27 7.62 2.27 3.27 4.27 5.27 6.27 2.06 2.85 3.64 4.43 5.22 1.87 2.47 3.07

2 2.54 8.89 3.54 4.54 5.54 6.54 7.54 3.33 4.12 4.91 5.70 6.49 3.14 3.74 4.34

#10 3 #10 3.81 10.16 #9 4.81 5.81 6.81 7.81 8.81 #8 4.60 5.39 6.18 6.97 7.76 #7 4.41 5.01 5.61

4 1.27 5.08 11.43 1.00 6.08 7.08 8.08 9.08 10.08 0.79 5.87 6.66 7.45 8.24 9.03 0.60 5.68 6.28 6.88

5 6.35 12.70 7.35 8.35 9.35 10.35 11.35 7.14 7.93 8.72 9.51 10.30 6.95 7.55 8.15

1 1.56 9.36 2.83 4.10 5.37 6.64 7.91 2.56 3.56 4.56 5.56 6.56 2.35 3.14 3.93

2 3.12 10.92 4.39 5.66 6.93 8.20 9.47 4.12 5.12 6.12 7.12 8.12 3.91 4.70 5.49

#11 3 #11 4.68 12.48 #10 5.95 7.22 8.49 9.76 11.03 #9 5.68 6.68 7.68 8.68 9.68 #8 5.47 6.26 7.05

4 1.56 6.24 14.04 1.27 7.51 8.78 10.05 11.32 12.59 1.00 7.24 8.24 9.24 10.24 11.24 0.79 7.03 7.82 8.61

5 7.80 15.60 9.07 10.34 11.61 12.88 14.15 8.80 9.80 10.80 11.80 12.80 8.59 9.38 10.17

1 2.25 13.50 3.81 5.37 6.93 8.49 10.05 3.52 4.79 6.06 7.33 8.60 3.25 4.25 5.25

2 4.50 15.75 6.06 7.62 9.18 10.74 12.30 5.77 7.04 8.31 9.58 10.85 5.50 6.50 7.50

#14 3 #14 6.75 18.00 #11 8.31 9.87 11.43 12.99 14.55 #10 8.02 9.29 10.56 11.83 13.10 #9 7.75 8.75 9.75

4 2.25 9.00 20.25 1.56 10.56 12.12 13.68 15.24 16.80 1.27 10.27 11.54 12.81 14.08 15.35 1.00 10.00 11.00 12.00

5 11.25 22.50 12.81 14.37 15.93 17.49 19.05 12.52 13.79 15.06 16.33 17.60 12.25 13.25 14.25

1 4.00 24.00 6.25 8.50 10.75 13.00 15.25 5.56 7.12 8.68 10.24 11.80 5.27 6.54 7.812 8.00 28.00 10.25 12.50 14.75 17.00 19.25 9.56 11.12 12.68 14.24 15.80 9.27 10.54 11.81

#18 3 #18 12.00 32.00 #14 14.25 16.50 18.75 21.00 23.25 #11 13.56 15.12 16.68 18.24 19.80 #10 13.27 14.54 15.81

Columns headed 1, 2, 3, 4,5 con

data for bars of two sizes with

one to five of each size

REINFORCEMENT 2 - Cross section areas for various combination of bars

Areas As (or A's), sq in.

Columns headed 0, 5 contain

data for bars of one size in

groups of one to ten

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Spacing, in. #3 #4 #5 #6 #7 #8 #9 #10 #11 #14 #18 Spacing, in.

4.0 0.330 0.600 0.930 1.320 1.800 2.370 3.000 3.810 4.680 4.0

4.5 0.293 0.533 0.827 1.173 1.600 2.107 2.667 3.387 4.160 6.000 4.5

5.0 0.264 0.480 0.744 1.056 1.440 1.896 2.400 3.048 3.744 5.400 9.600 5.05.5 0.240 0.436 0.676 0.960 1.309 1.724 2.182 2.771 3.404 4.909 8.727 5.5

6.0 0.220 0.400 0.620 0.880 1.200 1.580 2.000 2.540 3.120 4.500 8.000 6.0

6.5 0.203 0.369 0.572 0.812 1.108 1.458 1.846 2.345 2.880 4.154 7.385 6.5

7.0 0.189 0.343 0.531 0.754 1.029 1.354 1.714 2.177 2.674 3.857 6.857 7.0

7.5 0.176 0.320 0.496 0.704 0.960 1.264 1.600 2.032 2.496 3.600 6.400 7.5

8.0 0.165 0.300 0.465 0.660 0.900 1.185 1.500 1.905 2.340 3.375 6.000 8.0

8.5 0.155 0.282 0.438 0.621 0.847 1.115 1.412 1.793 2.202 3.176 5.647 8.5

9.0 0.147 0.267 0.413 0.587 0.800 1.053 1.333 1.693 2.080 3.000 5.333 9.0

9.5 0.139 0.253 0.392 0.556 0.758 0.998 1.263 1.604 1.971 2.842 5.053 9.5

10.0 0.132 0.240 0.372 0.528 0.720 0.948 1.200 1.524 1.872 2.700 4.800 10.010.5 0.126 0.229 0.354 0.503 0.686 0.903 1.143 1.451 1.783 2.571 4.571 10.5

11.0 0.120 0.218 0.338 0.480 0.655 0.862 1.091 1.385 1.702 2.455 4.364 11.0

11.5 0.115 0.209 0.323 0.459 0.626 0.824 1.043 1.325 1.628 2.348 4.174 11.5

12.0 0.110 0.200 0.310 0.440 0.600 0.790 1.000 1.270 1.560 2.250 4.000 12.0

12.5 0.106 0.192 0.298 0.422 0.576 0.758 0.960 1.219 1.498 2.160 3.840 12.5

13.0 0.102 0.185 0.286 0.406 0.554 0.729 0.923 1.172 1.440 2.077 3.692 13.0

13.5 0.098 0.178 0.276 0.391 0.533 0.702 0.889 1.129 1.387 2.000 3.556 13.5

14.0 0.094 0.171 0.266 0.377 0.514 0.677 0.857 1.089 1.337 1.929 3.429 14.0

14.5 0.091 0.166 0.257 0.364 0.497 0.654 0.828 1.051 1.291 1.862 3.310 14.5

15.0 0.088 0.160 0.248 0.352 0.480 0.632 0.800 1.016 1.248 1.800 3.200 15.0

15.5 0.085 0.155 0.240 0.341 0.465 0.612 0.774 0.983 1.208 1.742 3.097 15.5

16.0 0.083 0.150 0.233 0.330 0.450 0.593 0.750 0.953 1.170 1.688 3.000 16.0

16.5 0.080 0.145 0.225 0.320 0.436 0.575 0.727 0.924 1.135 1.636 2.909 16.5

17.0 0.078 0.141 0.219 0.311 0.424 0.558 0.706 0.896 1.101 1.588 2.824 17.0

17.5 0.075 0.137 0.213 0.302 0.411 0.542 0.686 0.871 1.070 1.543 2.743 17.5

18.0 0.073 0.133 0.207 0.293 0.400 0.527 0.667 0.847 1.040 1.500 2.667 18.0

REINFORCEMENT 15 - Areas of bars in a section 1 ft wide

For use of this Design Aid, see Flexure Examples 3, and 4.

Cross section area of bar, As (or A's), sq. in.

Bar size

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clear spacing, sc>db AND

clear cover, cc>db AND

Minimum stirrups or ties along ld per

ACI 11.5.5 (stirrups) or 7.10.5 (ties)

OR

clear spacing, sc>2db AND

clear cover, cc>db AND

Bar fy, ksi B

Size f'c, ksi 3 4 5 6 3 4 5 6 3 4 5 6 Si

#3 0.375 10.95 9.49 8.49 7.75 13.69 11.86 10.61 9.68 16.43 14.23 12.73 11.62 #

#4 0.500 14.61 12.65 11.31 10.33 18.26 15.81 14.14 12.91 21.91 18.97 16.97 15.49 #

#5 0.625 18.26 15.81 14.14 12.91 22.82 19.76 17.68 16.14 27.39 23.72 21.21 19.36 #

#6 0.750 21.91 18.97 16.97 15.49 27.39 23.72 21.21 19.36 32.86 28.46 25.46 23.24 #

#7 0.875 31.95 27.67 24.75 22.59 39.94 34.59 30.94 28.24 47.93 41.50 37.12 33.89 #

#8 1.000 36.51 31.62 28.28 25.82 45.64 39.53 35.36 32.27 54.77 47.43 42.43 38.73 #

#9 1.128 41.19 35.67 31.90 29.12 51.49 44.59 39.88 36.41 61.78 53.51 47.86 43.69 #

#10 1.270 46.37 40.16 35.92 32.79 57.97 50.20 44.90 40.99 69.56 60.24 53.88 49.19 #

#11 1.410 51.49 44.59 39.88 36.41 64.36 55.74 49.85 45.51 77.23 66.88 59.82 54.61 #

#14 1.693 61.82 53.54 47.89 43.71 77.27 66.92 59.86 54.64 92.73 80.31 71.83 65.57 #

#18 2.257 82.41 71.37 63.84 58.28 103.02 89.22 79.80 72.84 123.62 107.06 95.76 87.41 #

all other cases (other than CASE 1)

Bar fy, ksi B

Size f'c, ksi 3 4 5 6 3 4 5 6 3 4 5 6 Si

#3 0.375 16.43 14.23 12.73 11.62 20.54 17.79 15.91 14.52 24.65 21.35 19.09 17.43 #

#4 0.500 21.91 18.97 16.97 15.49 27.39 23.72 21.21 19.36 32.86 28.46 25.46 23.24 #

#5 0.625 27.39 23.72 21.21 19.36 34.23 29.65 26.52 24.21 41.08 35.58 31.82 29.05 #

#6 0.750 32.86 28.46 25.46 23.24 41.08 35.58 31.82 29.05 49.30 42.69 38.18 34.86 #

#7 0.875 47.93 41.50 37.12 33.89 59.91 51.88 46.40 42.36 71.89 62.26 55.68 50.83 #

#8 1.000 54.77 47.43 42.43 38.73 68.47 59.29 53.03 48.41 82.16 71.15 63.64 58.09 #

#9 1.128 61.78 53.51 47.86 43.69 77.23 66.88 59.82 54.61 92.67 80.26 71.79 65.53 #

#10 1.270 69.56 60.24 53.88 49.19 86.95 75.30 67.35 61.48 104.34 90.36 80.82 73.78 #

#11 1.410 77.23 66.88 59.82 54.61 96.54 83.60 74.78 68.26 115.84 100.32 89.73 81.91 #

#14 1.693 92.73 80.31 71.83 65.57 115.91 100.38 89.78 81.96 139.09 120.46 107.74 98.35 #

#18 2.257 123.62 107.06 95.76 87.41 154.53 133.82 119.70 109.27 185.43 160.59 143.63 131.12 #

REINFORCEMENT 17.1 - Development length ld of bars in tension (12.2.2)

Development length ld, in., of bars in tension

CASE 2:

a, b & l (modifiers, see Notes, REINFORCEMENT 17.2)

Reference: ACI 318-95 Sections 12.2.2, 12.2.4 and 12.2.5

CASE 1:

40 50 60

Development length, ld = a x b x l x ld > 12in

40 50 60

Development length ld, in., of bars in tension

25smallerand#6

y

b

d fdl a=

20largerand#7

y

b

df

d

l ab=

'50

3smallerand#6

c

y

b

d

f

f

d

l abl=

40

3largerand#7

y

b

d

f

f

d

l ab=

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c = minimum of c1, c2 & c3,

where from CASE 2, REINFORCEMENT 17.1

Atr=Area of transverse reinforcement which crosses the plane of splitting, in2

fyt=Yeild strength of transverse reinforcement, psi

s=maximum spacing of transvesre reinforcement within ld, in.

n=number of bars being developed along the plane of splitting

fyt # & Bar Atr

ksi size in.2

2 4 6 8 10 12 14 16 18 20 22 2

1-#3 0.11 1.467 0.733 0.489 0.367 0.293 0.244 0.210 0.183 0.163 0.147 0.133 0.1

2-#3 0.22 2.933 1.467 0.978 0.733 0.587 0.489 0.419 0.367 0.326 0.293 0.267 0.2

3-#3 0.33 4.400 2.200 1.467 1.100 0.880 0.733 0.629 0.550 0.489 0.440 0.400 0.3

4-#3 0.44 5.867 2.933 1.956 1.467 1.173 0.978 0.838 0.733 0.652 0.587 0.533 0.4

1-#4 0.20 2.667 1.333 0.889 0.667 0.533 0.444 0.381 0.333 0.296 0.267 0.242 0.2

2-#4 0.40 5.333 2.667 1.778 1.333 1.067 0.889 0.762 0.667 0.593 0.533 0.485 0.4

3-#4 0.60 8.000 4.000 2.667 2.000 1.600 1.333 1.143 1.000 0.889 0.800 0.727 0.6

4-#4 0.80 10.667 5.333 3.556 2.667 2.133 1.778 1.524 1.333 1.185 1.067 0.970 0.8

1-#5 0.31 4.133 2.067 1.378 1.033 0.827 0.689 0.590 0.517 0.459 0.413 0.376 0.3

2-#5 0.62 8.267 4.133 2.756 2.067 1.653 1.378 1.181 1.033 0.919 0.827 0.752 0.6

3-#5 0.93 12.400 6.200 4.133 3.100 2.480 2.067 1.771 1.550 1.378 1.240 1.127 1.04-#5 1.24 16.533 8.267 5.511 4.133 3.307 2.756 2.362 2.067 1.837 1.653 1.503 1.3

1-#3 0.11 2.200 1.100 0.733 0.550 0.440 0.367 0.314 0.275 0.244 0.220 0.200 0.1

2-#3 0.22 4.400 2.200 1.467 1.100 0.880 0.733 0.629 0.550 0.489 0.440 0.400 0.3

3-#3 0.33 6.600 3.300 2.200 1.650 1.320 1.100 0.943 0.825 0.733 0.660 0.600 0.5

4-#3 0.44 8.800 4.400 2.933 2.200 1.760 1.467 1.257 1.100 0.978 0.880 0.800 0.7

1-#4 0.20 4.000 2.000 1.333 1.000 0.800 0.667 0.571 0.500 0.444 0.400 0.364 0.3

2-#4 0.40 8.000 4.000 2.667 2.000 1.600 1.333 1.143 1.000 0.889 0.800 0.727 0.6

3-#4 0.60 12.000 6.000 4.000 3.000 2.400 2.000 1.714 1.500 1.333 1.200 1.091 1.0

4-#4 0.80 16.000 8.000 5.333 4.000 3.200 2.667 2.286 2.000 1.778 1.600 1.455 1.3

1-#5 0.31 6.200 3.100 2.067 1.550 1.240 1.033 0.886 0.775 0.689 0.620 0.564 0.5

2-#5 0.62 12.400 6.200 4.133 3.100 2.480 2.067 1.771 1.550 1.378 1.240 1.127 1.0

3-#5 0.93 18.600 9.300 6.200 4.650 3.720 3.100 2.657 2.325 2.067 1.860 1.691 1.5

4-#5 1.24 24.800 12.400 8.267 6.200 4.960 4.133 3.543 3.100 2.756 2.480 2.255 2.0

1.3 (top bars, minimum of 12'' of concrete below) Reinforcement size factor g = 0.8 #6 & smaller

1.0 (all others) 1.0 #7 & larger

1.5 (clear cover < 3db or clear spacing < 6db) Lightweight aggregate concrete factor l = 1.3 (fct not specified)

1.2 (other epoxy coated bars)

1.0 (all others)

1.0 (normal weight concrete

values of Ktr1 for computing Ktr

4

0

0

0

0

REINFORCEMENT 17.2 - Development length ld of bars in tension (12.2.3)

a, b & l (modifiers, see Notes below)

Reference: ACI 318-95 Sections 12.2.3, 12.2.4 and 12.2.5

Development length, ld = a x b x g x l x ld > 12in

Except a x b < 1.7

Epoxy coating factor b =

spacing s, in.

6

0

0

0

0

Note 1: To compute development length ld for a bar in tension, multiply ld from CASE 2, REINFORCEMENT 17.1 by applicable mofication factors

Reinforcement location factor a =

+=

b

tr

c

y

b

d

d

Kcf

f

d

l

'

40

3#

abgl

'b

tr

40

3and2.5

d

Kc

c

y

f

f g

+

nK

snfA tryttr 1tr1500

K ==

0.17.6

'

ct

c

ff

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fy

f'c

db in. 3 4 5 6 3 4 5 6 3 4 5 6

#3 0.375 5.48 4.74 4.50 4.50 6.85 5.93 5.63 5.63 8.22 7.12 6.75 6.75

#4 0.500 7.30 6.32 6.00 6.00 9.13 7.91 7.50 7.50 10.95 9.49 9.00 9.00

#5 0.625 9.13 7.91 7.50 7.50 11.41 9.88 9.38 9.38 13.69 11.86 11.25 11.25

#6 0.750 10.95 9.49 9.00 9.00 13.69 11.86 11.25 11.25 16.43 14.23 13.50 13.50

#7 0.875 12.78 11.07 10.50 10.50 15.98 13.83 13.13 13.13 19.17 16.60 15.75 15.75

#8 1.000 14.61 12.65 12.00 12.00 18.26 15.81 15.00 15.00 21.91 18.97 18.00 18.00

#9 1.128 16.48 14.27 13.54 13.54 20.59 17.84 16.92 16.92 24.71 21.40 20.30 20.30

#10 1.270 18.55 16.06 15.24 15.24 23.19 20.08 19.05 19.05 27.82 24.10 22.86 22.86

#11 1.410 20.59 17.84 16.92 16.92 25.74 22.29 21.15 21.15 30.89 26.75 25.38 25.38

#14 1.693 24.73 21.41 20.32 20.32 30.91 26.77 25.40 25.40 37.09 32.12 30.47 30.47#18 2.2570 32.97 28.55 27.08 27.08 41.21 35.69 33.86 33.86 49.45 42.82 40.63 40.63

Note 1:

a =

a =

a =

Note 2:

As required / As provided

1.0 for all other cases

Values of basic development length ldb above the heavy line are less than the minimum development length of 8 in. Development length ld (basic

development length ldb multiplied by the applicable modifications factors) shall be not less than 8 in.

60

Basic development length ldb, in.,of bars in compression

To compute development length ld for a bar in compression, multiply basic development length ldb from table above by applicable mofication

factors:

0.75 for reinforcement enclosed in spirals not less than 1/4 in. diameter and not more than 4 in. ptich or within #4 ties in accordance

with Section 7.10.5 and spaced not more than 4 in. on center

50

a (modifier, see Notes below)

ldb (basic development length, see table below)

Development length, ld = a x ldb > 8in

REINFORCEMENT 17.4 - Basic development length ldb of bars in compression

Reference: ACI 318-95 Section 12.3

Bar

size

40

= yb

c

ybfd

f

fd0003.0,02.0max

'

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fy

f'c 8 db

db in. 3 4 5 6 3 4 5 6 3 4 5 6 in.

#3 0.375 5.48 4.74 4.24 3.87 6.85 5.93 5.30 4.84 8.22 7.12 6.36 5.81 3.0

#4 0.500 7.30 6.32 5.66 5.16 9.13 7.91 7.07 6.45 10.95 9.49 8.49 7.75 4.0

#5 0.625 9.13 7.91 7.07 6.45 11.41 9.88 8.84 8.07 13.69 11.86 10.61 9.68 5.0

#6 0.750 10.95 9.49 8.49 7.75 13.69 11.86 10.61 9.68 16.43 14.23 12.73 11.62 6.0

#7 0.875 12.78 11.07 9.90 9.04 15.98 13.83 12.37 11.30 19.17 16.60 14.85 13.56 7.0

#8 1.000 14.61 12.65 11.31 10.33 18.26 15.81 14.14 12.91 21.91 18.97 16.97 15.49 8.0

#9 1.128 16.48 14.27 12.76 11.65 20.59 17.84 15.95 14.56 24.71 21.40 19.14 17.47 9.0

#10 1.270 18.55 16.06 14.37 13.12 23.19 20.08 17.96 16.40 27.82 24.10 21.55 19.67 10.2#11 1.410 20.59 17.84 15.95 14.56 25.74 22.29 19.94 18.20 30.89 26.75 23.93 21.84 11.3

#14 1.693 24.73 21.41 19.15 17.49 30.91 26.77 23.94 21.86 37.09 32.12 28.73 26.23 13.5#18 2.2570 32.97 28.55 25.54 23.31 41.21 35.69 31.92 29.14 49.45 42.82 38.30 34.97 18.1

Note 1:

a =

a =

a =

a =

a =

a =

b =

b =

l =

l =

Note 2: Values of basic development length lhb above the heavy line are less than the minimum development length of 6 in. Development length ldh (basic development

length lhb multiplied by the applicable modifications factors) shall be not less than 8 db, nor less than 6 in., whichever is greater.


1.2 for epoxy-coated reinforcement

1.3 for lightweight aggregate concrete

Basic development length lhb, in.,of standard hooks in tension


0.8 for 90 deg hooks of #11 and smaller bars that are either enclosed within ties or stirrups perpendicular to the bar being developed, spaced not

greater than 3db along the development length ldh of the hook; or enclosed within ties or stirrups parallel to the bar being developed, spaced not

greater than 3db along the length of the tail extension of the hook plus the bend

60

0.75 for reinforcement enclosed in spirals not less than 1/4 in. diameter and not more than 4 in. ptich or within #4 ties in accordance with

Section 7.10.5 and spaced not more than 4 in. on center

50

0.8 for 180 deg hooks of #11 and smaller bars that are either enclosed within ties or stirrups perpendicular to the bar being developed, spaced not

greater than 3db along the development length ldh of the hook

As required / As provided


Development length, ldh = a x b x l lhb > 8db > 6 in.

Where a, b and l represent modifiers fron Note 1

below and lhb is the basic development length of

standard hook in tension

REINFORCEMENT 18.1 - Basic development length lhb of standard hook in tension

Reference: ACI 318-95 Sections 7.1 and 12.5.1-12.5.3

To compute development length ldh for a standard hook in tension, multiply basic development length lhb from table above by applicable mofication factors:

0.7 for #11 and smaller hools with side cover (normal to plane of hook) not less then 2 1/2 in. and for 90 deg hook cover on bar exttension beyond

hook not less than 2 in.

Bar

size

40

'

02.0

c

yb

bh

f

fdl abl=

7/31/2019 SP-17(05)

8/35

where Mn is in kip-ft and d in in.

taking (which is a typical value) =>

preferred r = 0.5rmax

3000 4000 5000 6000

0.85 0.85 0.8 0.75

fy (psi) 40000

an 2.967 2.967 2.967 2.967

rmin 0.00500 0.00500 0.00530 0.00581

preferred r 0.01392 0.01856 0.02184 0.02457

rmax 0.02784 0.03712 0.04367 0.04913

preferred r @et=0.01 0.01250 0.01667 0.01962 0.02207

preferred r @et=0.005 0.02032 0.02709 0.03188 0.03586

rmax @ et=0.004 0.02322 0.03096 0.03643 0.04098

rbal 0.03712 0.04949 0.05823 0.06551

fy (psi) 60000

an 4.450 4.450 4.450 4.450

rmin 0.00333 0.00333 0.00354 0.00387

preferred r 0.00802 0.01069 0.01258 0.01415

rmax 0.01604 0.02138 0.02515 0.02830

preferred r @et=0.01 0.00834 0.01112 0.01308 0.01471

preferred r @et=0.005 0.01355 0.01806 0.02125 0.02391

rmax @ et=0.004 0.01548 0.02064 0.02429 0.02732

rbal 0.02138 0.02851 0.03354 0.03773

fy (psi) 75000

an 5.563 5.563 5.563 5.563

rmin 0.00267 0.00267 0.00283 0.00310

preferred r 0.00582 0.00776 0.00913 0.01027rmax 0.01164 0.01552 0.01826 0.02054

preferred r @et=0.01 0.00667 0.00889 0.01046 0.01177

preferred r @et=0.005 0.01084 0.01445 0.01700 0.01913

rmax @ et=0.004 0.01239 0.01651 0.01943 0.02186

rbal 0.01552 0.02069 0.02435 0.02739

For use of this Design Aid, see Flexure Example 1

f'c (psi)

b1

FLEXURE 1 - Reinforcement ratios and an for quick approximation design of

rectangular beams with no compression reinforcement

Reference: ACI 318-95 Sections 9.3.2, 10.2, 10.3.1-10.3.3, and 10.5.1 and ACI 318R-95 Section 10.3.1

da

M

An

n

s =

12000

21

-

=d

af

ay

n f

u

n

MM

89.02

1 =

-

d

a

12000

89.0y

n

fa =

( )

+=

yy

c

ff

f

000,87

000,8785.075.0'

1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

9/35

f'c = 3000 psi

b1 = 0.85

f'c = 3000 psi

fy = 40000 fy = 60000 fy = 75000 psi

Kn an an an c/d a/d jn t0.01 29.8 0.00075 3.314 0.900 0.00050 4.971 0.900 0.00040 6.213 0.900 0.0138 0.0118 0.9941 0.2138

0.02 59.3 0.00150 3.294 0.900 0.00100 4.941 0.900 0.00080 6.176 0.900 0.0277 0.0235 0.9882 0.1054

0.03 88.4 0.00225 3.275 0.900 0.00150 4.912 0.900 0.00120 6.140 0.900 0.0415 0.0353 0.9824 0.0693

0.04 117.2 0.00300 3.255 0.900 0.00200 4.882 0.900 0.00160 6.103 0.900 0.0554 0.0471 0.9765 0.0512

0.05 145.6 0.00375 3.235 0.900 0.00250 4.853 0.900 0.00200 6.066 0.900 0.0692 0.0588 0.9706 0.04040.06 173.6 0.00450 3.216 0.900 0.00300 4.824 0.900 0.00240 6.029 0.900 0.0830 0.0706 0.9647 0.0331

0.0667 192.2 0.00500 3.203 0.900 0.00333 4.804 0.900 0.00267 6.005 0.900 0.0923 0.0784 0.9608 0.0295

0.07 201.4 0.00525 3.196 0.900 0.00350 4.794 0.900 0.00280 5.993 0.900 0.0969 0.0824 0.9588 0.0280

0.08 228.7 0.00600 3.176 0.900 0.00400 4.765 0.900 0.00320 5.956 0.900 0.1107 0.0941 0.9529 0.0241

0.09 255.7 0.00675 3.157 0.900 0.00450 4.735 0.900 0.00360 5.919 0.900 0.1246 0.1059 0.9471 0.0211

0.1 282.4 0.00750 3.137 0.900 0.00500 4.706 0.900 0.00400 5.882 0.900 0.1384 0.1176 0.9412 0.0187

0.11 308.6 0.00825 3.118 0.900 0.00550 4.676 0.900 0.00440 5.846 0.900 0.1522 0.1294 0.9353 0.0167

0.12 334.6 0.00900 3.098 0.900 0.00600 4.647 0.900 0.00480 5.809 0.900 0.1661 0.1412 0.9294 0.0151

0.13 360.2 0.00975 3.078 0.900 0.00650 4.618 0.900 0.00520 5.772 0.900 0.1799 0.1529 0.9235 0.0137

0.14 385.4 0.01050 3.059 0.900 0.00700 4.588 0.900 0.00560 5.735 0.900 0.1938 0.1647 0.9176 0.0125

0.15 410.3 0.01125 3.039 0.900 0.00750 4.559 0.900 0.00600 5.699 0.900 0.2076 0.1765 0.9118 0.01150.16 434.8 0.01200 3.020 0.900 0.00800 4.529 0.900 0.00640 5.662 0.900 0.2215 0.1882 0.9059 0.0105

0.1667 451.1 0.01250 3.006 0.900 0.00834 4.510 0.900 0.00667 5.637 0.900 0.2308 0.1962 0.9019 0.0100

0.17 459.0 0.01275 3.000 0.900 0.00850 4.500 0.900 0.00680 5.625 0.900 0.2353 0.2000 0.9000 0.0098

0.18 482.8 0.01350 2.980 0.900 0.00900 4.471 0.900 0.00720 5.588 0.900 0.2491 0.2118 0.8941 0.0090

0.19 506.3 0.01425 2.961 0.900 0.00950 4.441 0.900 0.00760 5.551 0.900 0.2630 0.2235 0.8882 0.0084

0.2 529.4 0.01500 2.941 0.900 0.01000 4.412 0.900 0.00800 5.515 0.900 0.2768 0.2353 0.8824 0.0078

0.21 552.2 0.01575 2.922 0.900 0.01050 4.382 0.900 0.00840 5.478 0.900 0.2907 0.2471 0.8765 0.0073

0.22 574.6 0.01650 2.902 0.900 0.01100 4.353 0.900 0.00880 5.441 0.900 0.3045 0.2588 0.8706 0.0069

0.23 596.6 0.01725 2.882 0.900 0.01150 4.324 0.900 0.00920 5.404 0.900 0.3183 0.2706 0.8647 0.0064

0.24 618.4 0.01800 2.863 0.900 0.01200 4.294 0.900 0.00960 5.368 0.900 0.3322 0.2824 0.8588 0.0060

0.25 639.7 0.01875 2.843 0.900 0.01250 4.265 0.900 0.01000 5.331 0.900 0.3460 0.2941 0.8529 0.0057

0.26 660.7 0.01950 2.824 0.900 0.01300 4.235 0.900 0.01040 5.294 0.900 0.3599 0.3059 0.8471 0.00530.27 681.4 0.02025 2.804 0.900 0.01350 4.206 0.900 0.01080 5.257 0.900 0.3737 0.3176 0.8412 0.0050

0.2709 683.3 0.02032 2.802 0.900 0.01355 4.203 0.900 0.01084 5.254 0.900 0.3750 0.3188 0.8406 0.0050

0.28 701.6 0.02100 2.784 0.882 0.01400 4.176 0.878 0.01120 5.221 0.873 0.3875 0.3294 0.8353 0.0047

0.29 721.6 0.02175 2.765 0.864 0.01450 4.147 0.855 0.01160 5.184 0.846 0.4014 0.3412 0.8294 0.0045

0.2910 723.6 0.01164 5.180 0.843 0.4028 0.3424 0.8288 0.00440.3 741.2 0.02250 2.745 0.846 0.01500 4.118 0.834 0.01200 5.147 0.820 0.4152 0.3529 0.8235 0.0042

0.3096 759.7 0.02322 2.726 0.831 0.01548 4.089 0.815 0.01239 5.112 0.796 0.4286 0.3643 0.8179 0.0040

0.31 760.4 0.02325 2.725 0.830 0.01550 4.088 0.814 0.4291 0.3647 0.8176 0.00400.32 779.3 0.02400 2.706 0.815 0.01600 4.059 0.795 0.4429 0.3765 0.8118 0.0038

0.3207 780.6 0.01604 4.057 0.794 0.4439 0.3773 0.8114 0.0038

0.33 797.8 0.02475 2.686 0.801 0.4567 0.3882 0.8059 0.0036

0.34 816.0 0.02550 2.667 0.788 0.4706 0.4000 0.8000 0.0034

0.35 833.8 0.02625 2.647 0.775 0.4844 0.4118 0.7941 0.0032

0.36 851.3 0.02700 2.627 0.763 0.4983 0.4235 0.7882 0.0030

0.37 868.4 0.02775 2.608 0.752 0.5121 0.4353 0.7824 0.0029

0.3712 870.5 0.02784 2.605 0.751 0.5138 0.4367 0.7816 0.0028

bal bal 0.03712 0.0014 0.02138 0.0021 0.01552 0.0026

Mn = KnF, ft-kips

and F = bd2/12,000 (from FLEXURE 5)

w = rfy/f'c

For use of this Design Aid, see Flexure Examples 1, 2, 3 and 4

where an = fyjn/12,000

*Values ofr above light rule are less than rmin: as provided in Section 10.5.1 of ACI 318-95

c/d = (1/0.85)(w/b1)Mn > Mu/f

FLEXURE 2.1 - Nominal strength coefficients for design of rectangular beams with tension reinforcement only

max=0.75 bal

where Kn = f'cwjn

a/d = b1(c/d)

jn = 1 - (a/2d)

jn = 1 - w/1.7

Reference: ACI 318-95 Sections 9.3.2, 10.2, and 10.3.1-10.3.3 and ACI 318R-95 Section 10.3.1

Also, Mn = Asdan (As in in.2)

yy

c

fff 2003

'

min =r

7/31/2019 SP-17(05)

10/35

f'c = 4000 psi

b1

= 0.85

f'c = 4000 psi

fy = 40000 fy = 60000 fy = 75000 psi


0.02 79.1 0.00200 3.294 0.900 0.00133 4.941 0.900 0.00107 6.176 0.900 0.0277 0.0235 0.9882 0.1054

0.03 117.9 0.00300 3.275 0.900 0.00200 4.912 0.900 0.00160 6.140 0.900 0.0415 0.0353 0.9824 0.06930.04 156.2 0.00400 3.255 0.900 0.00267 4.882 0.900 0.00213 6.103 0.900 0.0554 0.0471 0.9765 0.0512

0.0500 194.1 0.00500 3.235 0.900 0.00333 4.853 0.900 0.00267 6.066 0.900 0.0692 0.0588 0.9706 0.0404

0.06 231.5 0.00600 3.216 0.900 0.00400 4.824 0.900 0.00320 6.029 0.900 0.0830 0.0706 0.9647 0.03310.07 268.5 0.00700 3.196 0.900 0.00467 4.794 0.900 0.00373 5.993 0.900 0.0969 0.0824 0.9588 0.0280

0.08 304.9 0.00800 3.176 0.900 0.00533 4.765 0.900 0.00427 5.956 0.900 0.1107 0.0941 0.9529 0.0241

0.09 340.9 0.00900 3.157 0.900 0.00600 4.735 0.900 0.00480 5.919 0.900 0.1246 0.1059 0.9471 0.0211

0.1 376.5 0.01000 3.137 0.900 0.00667 4.706 0.900 0.00533 5.882 0.900 0.1384 0.1176 0.9412 0.0187

0.11 411.5 0.01100 3.118 0.900 0.00733 4.676 0.900 0.00587 5.846 0.900 0.1522 0.1294 0.9353 0.0167

0.12 446.1 0.01200 3.098 0.900 0.00800 4.647 0.900 0.00640 5.809 0.900 0.1661 0.1412 0.9294 0.0151

0.13 480.2 0.01300 3.078 0.900 0.00867 4.618 0.900 0.00693 5.772 0.900 0.1799 0.1529 0.9235 0.0137

0.14 513.9 0.01400 3.059 0.900 0.00933 4.588 0.900 0.00747 5.735 0.900 0.1938 0.1647 0.9176 0.0125

0.15 547.1 0.01500 3.039 0.900 0.01000 4.559 0.900 0.00800 5.699 0.900 0.2076 0.1765 0.9118 0.01150.16 579.8 0.01600 3.020 0.900 0.01067 4.529 0.900 0.00853 5.662 0.900 0.2215 0.1882 0.9059 0.0105

0.1667 601.5 0.01667 3.006 0.900 0.01112 4.510 0.900 0.00889 5.637 0.900 0.2308 0.1962 0.9019 0.0100

0.17 612.0 0.01700 3.000 0.900 0.01133 4.500 0.900 0.00907 5.625 0.900 0.2353 0.2000 0.9000 0.0098

0.18 643.8 0.01800 2.980 0.900 0.01200 4.471 0.900 0.00960 5.588 0.900 0.2491 0.2118 0.8941 0.0090

0.19 675.1 0.01900 2.961 0.900 0.01267 4.441 0.900 0.01013 5.551 0.900 0.2630 0.2235 0.8882 0.0084

0.2 705.9 0.02000 2.941 0.900 0.01333 4.412 0.900 0.01067 5.515 0.900 0.2768 0.2353 0.8824 0.00780.21 736.2 0.02100 2.922 0.900 0.01400 4.382 0.900 0.01120 5.478 0.900 0.2907 0.2471 0.8765 0.0073

0.22 766.1 0.02200 2.902 0.900 0.01467 4.353 0.900 0.01173 5.441 0.900 0.3045 0.2588 0.8706 0.0069

0.23 795.5 0.02300 2.882 0.900 0.01533 4.324 0.900 0.01227 5.404 0.900 0.3183 0.2706 0.8647 0.0064

0.24 824.5 0.02400 2.863 0.900 0.01600 4.294 0.900 0.01280 5.368 0.900 0.3322 0.2824 0.8588 0.0060

0.25 852.9 0.02500 2.843 0.900 0.01667 4.265 0.900 0.01333 5.331 0.900 0.3460 0.2941 0.8529 0.0057

0.26 880.9 0.02600 2.824 0.900 0.01733 4.235 0.900 0.01387 5.294 0.900 0.3599 0.3059 0.8471 0.00530.27 908.5 0.02700 2.804 0.900 0.01800 4.206 0.900 0.01440 5.257 0.900 0.3737 0.3176 0.8412 0.0050

0.2709 911.0 0.02709 2.802 0.900 0.01806 4.203 0.900 0.01445 5.254 0.900 0.3750 0.3188 0.8406 0.0050

0.28 935.5 0.02800 2.784 0.882 0.01867 4.176 0.878 0.01493 5.221 0.873 0.3875 0.3294 0.8353 0.0047

0.29 962.1 0.02900 2.765 0.864 0.01933 4.147 0.855 0.01547 5.184 0.846 0.4014 0.3412 0.8294 0.0045

0.2910 964.8 0.01552 5.180 0.843 0.4028 0.3424 0.8288 0.00440.3 988.2 0.03000 2.745 0.846 0.02000 4.118 0.834 0.01600 5.147 0.820 0.4152 0.3529 0.8235 0.0042

0.3096 1013.0 0.03096 2.726 0.831 0.02064 4.089 0.815 0.01651 5.112 0.796 0.4286 0.3643 0.8179 0.0040

0.31 1013.9 0.03100 2.725 0.830 0.02067 4.088 0.814 0.4291 0.3647 0.8176 0.00400.32 1039.1 0.03200 2.706 0.815 0.02133 4.059 0.795 0.4429 0.3765 0.8118 0.0038

0.3207 1040.8 0.02138 4.057 0.794 0.4439 0.3773 0.8114 0.0038

0.33 1063.8 0.03300 2.686 0.801 0.4567 0.3882 0.8059 0.0036

0.34 1088.0 0.03400 2.667 0.788 0.4706 0.4000 0.8000 0.0034

0.35 1111.8 0.03500 2.647 0.775 0.4844 0.4118 0.7941 0.0032

0.36 1135.1 0.03600 2.627 0.763 0.4983 0.4235 0.7882 0.0030

0.37 1157.9 0.03700 2.608 0.752 0.5121 0.4353 0.7824 0.0029

0.3712 1160.6 0.03712 2.605 0.751 0.5138 0.4367 0.7816 0.0028

bal bal 0.04949 0.0014 0.02851 0.0021 0.02069 0.0026




Mn = KnF, ft-kips


w = rfy/f'c

c/d = (1/0.85)(w/b1)




max =0.75 bal

Mn > Mu/f

where Kn

= f'cwj

n

a/d = b1(c/d)

jn = 1 - (a/2d)

jn = 1 - w/1.7

yy

c

fff 2003

'

min =r

7/31/2019 SP-17(05)

11/35

f'c = 5000 psi

b1 = 0.8

f'c = 5000 psi

fy = 40000 fy = 60000 fy = 75000 psi


0.02 98.8 0.00250 3.294 0.900 0.00167 4.941 0.900 0.00133 6.176 0.900 0.0294 0.0235 0.9882 0.0990

0.03 147.4 0.00375 3.275 0.900 0.00250 4.912 0.900 0.00200 6.140 0.900 0.0441 0.0353 0.9824 0.06500.04 195.3 0.00500 3.255 0.900 0.00333 4.882 0.900 0.002 7 .103 0.900 0.0588 0.0471 0.97 5 0.0480

0.0424 206.8 0.00530 3.250 0.900 0.00354 4.875 0.900 0.00283 6.094 0.900 0.0624 0.0499 0.9750 0.0451

0.05 242.6 0.00625 3.235 0.900 0.00417 4.853 0.900 0.00333 6.066 0.900 0.0735 0.0588 0.9706 0.03780.06 289.4 0.00750 3.216 0.900 0.00500 4.824 0.900 0.00400 6.029 0.900 0.0882 0.0706 0.9647 0.0310

0.07 335.6 0.00875 3.196 0.900 0.00583 4.794 0.900 0.00467 5.993 0.900 0.1029 0.0824 0.9588 0.0261

0.08 381.2 0.01000 3.176 0.900 0.00667 4.765 0.900 0.00533 5.956 0.900 0.1176 0.0941 0.9529 0.0225

0.09 426.2 0.01125 3.157 0.900 0.00750 4.735 0.900 0.00600 5.919 0.900 0.1324 0.1059 0.9471 0.0197

0.1 470.6 0.01250 3.137 0.900 0.00833 4.706 0.900 0.00667 5.882 0.900 0.1471 0.1176 0.9412 0.0174

0.11 514.4 0.01375 3.118 0.900 0.00917 4.676 0.900 0.00733 5.846 0.900 0.1618 0.1294 0.9353 0.0155

0.12 557.6 0.01500 3.098 0.900 0.01000 4.647 0.900 0.00800 5.809 0.900 0.1765 0.1412 0.9294 0.0140

0.13 600.3 0.01625 3.078 0.900 0.01083 4.618 0.900 0.00867 5.772 0.900 0.1912 0.1529 0.9235 0.0127

0.14 642.4 0.01750 3.059 0.900 0.01167 4.588 0.900 0.00933 5.735 0.900 0.2059 0.1647 0.9176 0.01160.15 683.8 0.01875 3.039 0.900 0.01250 4.559 0.900 0.01000 5.699 0.900 0.2206 0.1765 0.9118 0.0106

0.1569 712.2 0.01962 3.026 0.900 0.01308 4.538 0.900 0.01046 5.673 0.900 0.2308 0.1846 0.9077 0.0100

0.16 724.7 0.02000 3.020 0.900 0.01333 4.529 0.900 0.01067 5.662 0.900 0.2353 0.1882 0.9059 0.0098

0.17 765.0 0.02125 3.000 0.900 0.01417 4.500 0.900 0.01133 5.625 0.900 0.2500 0.2000 0.9000 0.0090

0.18 804.7 0.02250 2.980 0.900 0.01500 4.471 0.900 0.01200 5.588 0.900 0.2647 0.2118 0.8941 0.0083

0.19 843.8 0.02375 2.961 0.900 0.01583 4.441 0.900 0.01267 5.551 0.900 0.2794 0.2235 0.8882 0.0077

0.2 882.4 0.02500 2.941 0.900 0.01667 4.412 0.900 0.01333 5.515 0.900 0.2941 0.2353 0.8824 0.0072

0.21 920.3 0.02625 2.922 0.900 0.01750 4.382 0.900 0.01400 5.478 0.900 0.3088 0.2471 0.8765 0.0067

0.22 957.6 0.02750 2.902 0.900 0.01833 4.353 0.900 0.01467 5.441 0.900 0.3235 0.2588 0.8706 0.0063

0.23 994.4 0.02875 2.882 0.900 0.01917 4.324 0.900 0.01533 5.404 0.900 0.3382 0.2706 0.8647 0.0059

0.24 1030.6 0.03000 2.863 0.900 0.02000 4.294 0.900 0.01600 5.368 0.900 0.3529 0.2824 0.8588 0.00550.25 10 .2 0.03125 2.843 0.900 0.02083 4.2 5 0.900 0.01 7 5.331 0.900 0.3 7 0.2941 0.8529 0.0052

0.2550 1083.8 0.03188 2.833 0.900 0.02125 4.250 0.900 0.01700 5.313 0.900 0.3750 0.3000 0.8500 0.0050

0.26 1101.2 0.03250 2.824 0.889 0.02167 4.235 0.887 0.01733 5.294 0.884 0.3824 0.3059 0.8471 0.0048

0.27 1135.6 0.03375 2.804 0.869 0.02250 4.206 0.862 0.01800 5.257 0.854 0.3971 0.3176 0.8412 0.0046

0.2739 1148.8 0.01826 5.243 0.843 0.4028 0.3222 0.8389 0.0044

0.28 1169.4 0.03500 2.784 0.851 0.02333 4.176 0.839 0.01867 5.221 0.826 0.4118 0.3294 0.8353 0.00430.29 1202.6 0.03625 2.765 0.833 0.02417 4.147 0.818 0.01933 5.184 0.800 0.4265 0.3412 0.8294 0.0040

0.2914 1207.3 0.03643 2.762 0.831 0.02429 4.143 0.815 0.01943 5.179 0.796 0.4286 0.3429 0.8286 0.0040

0.3 1235.3 0.03750 2.745 0.817 0.02500 4.118 0.798 0.4412 0.3529 0.8235 0.0038

0.3018 1241.2 0.02515 4.112 0.794 0.4439 0.3551 0.8224 0.0038

0.31 1267.4 0.03875 2.725 0.802 0.4559 0.3647 0.8176 0.0036

0.32 1298.8 0.04000 2.706 0.788 0.4706 0.3765 0.8118 0.0034

0.33 1329.7 0.04125 2.686 0.774 0.4853 0.3882 0.8059 0.0032

0.34 1360.0 0.04250 2.667 0.762 0.5000 0.4000 0.8000 0.0030

0.3494 1387.9 0.04367 2.648 0.751 0.5138 0.4110 0.7945 0.0028

bal bal 0.05823 0.0014 0.03354 0.0021 0.02435 0.0026

Mn = KnF, ft-kips


w = rfy/f'c




c/d = (1/0.85)(w/b1)Mn > Mu/f


max =0.75 bal

where Kn = f'cwjn

a/d = b1(c/d)

jn = 1 - (a/2d)

jn = 1 - w/1.7



yy

c

fff 2003

'

min =r

7/31/2019 SP-17(05)

12/35

f'c = 6000 psi

b1 = 0.75

f'c = 6000 psi

fy = 40000 fy = 60000 fy = 75000 psi


0.02 118.6 0.00300 3.294 0.900 0.00200 4.941 0.900 0.00160 6.176 0.900 0.0314 0.0235 0.9882 0.09260.03 17 .8 0.00450 3.275 0.900 0.00300 4.912 0.900 0.00240 .140 0.900 0.0471 0.0353 0.9824 0.0 08

0.0387 227.1 0.00581 3.257 0.900 0.00387 4.886 0.900 0.00310 6.108 0.900 0.0608 0.0456 0.9772 0.0464

0.04 234.4 0.00600 3.255 0.900 0.00400 4.882 0.900 0.00320 6.103 0.900 0.0627 0.0471 0.9765 0.0448

0.05 291.2 0.00750 3.235 0.900 0.00500 4.853 0.900 0.00400 6.066 0.900 0.0784 0.0588 0.9706 0.03530.06 347.3 0.00900 3.216 0.900 0.00600 4.824 0.900 0.00480 6.029 0.900 0.0941 0.0706 0.9647 0.0289

0.07 402.7 0.01050 3.196 0.900 0.00700 4.794 0.900 0.00560 5.993 0.900 0.1098 0.0824 0.9588 0.0243

0.08 457.4 0.01200 3.176 0.900 0.00800 4.765 0.900 0.00640 5.956 0.900 0.1255 0.0941 0.9529 0.0209

0.09 511.4 0.01350 3.157 0.900 0.00900 4.735 0.900 0.00720 5.919 0.900 0.1412 0.1059 0.9471 0.0183

0.1 564.7 0.01500 3.137 0.900 0.01000 4.706 0.900 0.00800 5.882 0.900 0.1569 0.1176 0.9412 0.0161

0.11 617.3 0.01650 3.118 0.900 0.01100 4.676 0.900 0.00880 5.846 0.900 0.1725 0.1294 0.9353 0.0144

0.12 669.2 0.01800 3.098 0.900 0.01200 4.647 0.900 0.00960 5.809 0.900 0.1882 0.1412 0.9294 0.0129

0.13 720.4 0.01950 3.078 0.900 0.01300 4.618 0.900 0.01040 5.772 0.900 0.2039 0.1529 0.9235 0.01170.14 770.8 0.02100 3.059 0.900 0.01400 4.588 0.900 0.01120 5.735 0.900 0.2196 0.1647 0.9176 0.0107

0.1471 806.3 0.02207 3.045 0.900 0.01471 4.567 0.900 0.01177 5.709 0.900 0.2308 0.1731 0.9135 0.0100

0.15 820.6 0.02250 3.039 0.900 0.01500 4.559 0.900 0.01200 5.699 0.900 0.2353 0.1765 0.9118 0.0098

0.16 869.6 0.02400 3.020 0.900 0.01600 4.529 0.900 0.01280 5.662 0.900 0.2510 0.1882 0.9059 0.0090

0.17 918.0 0.02550 3.000 0.900 0.01700 4.500 0.900 0.01360 5.625 0.900 0.2667 0.2000 0.9000 0.0083

0.18 965.6 0.02700 2.980 0.900 0.01800 4.471 0.900 0.01440 5.588 0.900 0.2824 0.2118 0.8941 0.0076

0.19 1012.6 0.02850 2.961 0.900 0.01900 4.441 0.900 0.01520 5.551 0.900 0.2980 0.2235 0.8882 0.0071

0.2 1058.8 0.03000 2.941 0.900 0.02000 4.412 0.900 0.01600 5.515 0.900 0.3137 0.2353 0.8824 0.0066

0.21 1104.4 0.03150 2.922 0.900 0.02100 4.382 0.900 0.01680 5.478 0.900 0.3294 0.2471 0.8765 0.0061

0.22 1149.2 0.03300 2.902 0.900 0.02200 4.353 0.900 0.01760 5.441 0.900 0.3451 0.2588 0.8706 0.00570.23 1193.3 0.03450 2.882 0.900 0.02300 4.324 0.900 0.01840 5.404 0.900 0.3608 0.2706 0.8647 0.0053

0.2391 1232.7 0.03586 2.865 0.900 0.02391 4.297 0.900 0.01913 5.371 0.900 0.3750 0.2813 0.8594 0.0050

0.24 1236.7 0.03600 2.863 0.898 0.02400 4.294 0.897 0.01920 5.368 0.897 0.3765 0.2824 0.8588 0.0050

0.25 1279.4 0.03750 2.843 0.876 0.02500 4.265 0.870 0.02000 5.331 0.864 0.3922 0.2941 0.8529 0.0047

0.2568 1307.9 0.02054 5.306 0.843 0.4028 0.3021 0.8490 0.0044

0.26 1321.4 0.03900 2.824 0.856 0.02600 4.235 0.845 0.02080 5.294 0.833 0.4078 0.3059 0.8471 0.00440.27 13 2.7 0.04050 2.804 0.837 0.02700 4.20 0.822 0.021 0 5.257 0.805 0.4235 0.317 0.8412 0.0041

0.2732 1375.8 0.04098 2.798 0.831 0.02732 4.196 0.815 0.02186 5.246 0.796 0.4286 0.3214 0.8393 0.0040

0.28 1403.3 0.04200 2.784 0.819 0.02800 4.176 0.800 0.4392 0.3294 0.8353 0.0038

0.2830 1415.2 0.02830 4.168 0.794 0.4439 0.3329 0.8335 0.0038

0.29 1443.2 0.04350 2.765 0.803 0.4549 0.3412 0.8294 0.0036

0.3 1482.4 0.04500 2.745 0.788 0.4706 0.3529 0.8235 0.0034

0.31 1520.8 0.04650 2.725 0.774 0.4863 0.3647 0.8176 0.0032

0.32 1558.6 0.04800 2.706 0.760 0.5020 0.3765 0.8118 0.0030

0.3275 1586.6 0.04913 2.691 0.751 0.5138 0.3853 0.8073 0.0028

bal bal 0.06551 0.0014 0.03773 0.0021 0.02739 0.0026

jn = 1 - w/1.7

Mn > Mu/f

w = rfy/f'cwhere Kn = f'cwjn

a/d = b1(c/d)

jn = 1 - (a/2d)

c/d = (1/0.85)(w/b1)



max =0.75 bal





Mn = KnF, ft-kips


yy

c

ff

f 2003'

min=r

7/31/2019 SP-17(05)

13/35

f'c = 3000 & 4000 psi

b1 = 0.85 b1 = 0.85

f'c

fy

d'/d ' a'n or anf ' a'n or anf ' a'n or anf ' a'n or anf ' a'n or anf ' a'n or anf hf/d j

0.01 0.0010 3.300 0.0012 4.950 0.0021 6.188 0.0013 3.300 0.0016 4.950 0.0028 6.188 0.02 0.9

0.02 0.0020 3.267 0.0023 4.900 0.0042 6.125 0.0027 3.267 0.0031 4.900 0.0056 6.125 0.04 0.9

0.03 0.0030 3.233 0.0035 4.850 0.0063 6.063 0.0040 3.233 0.0047 4.850 0.0084 6.063 0.06 0.9

0.04 0.0040 3.200 0.0047 4.800 0.0084 6.000 0.0053 3.200 0.0062 4.800 0.0112 6.000 0.08 0.9

0.05 0.0050 3.167 0.0058 4.750 0.0105 5.938 0.0067 3.167 0.0078 4.750 0.0140 5.938 0.1 0.9

0.06 0.0060 3.133 0.0070 4.700 0.0126 5.875 0.0080 3.133 0.0093 4.700 0.0168 5.875 0.12 0.9

0.07 0.0070 3.100 0.0081 4.650 0.0147 5.813 0.0094 3.100 0.0109 4.650 0.0196 5.813 0.14 0.9

0.08 0.0080 3.067 0.0093 4.600 5.750 0.0107 3.067 0.0124 4.600 5.750 0.16 0.9

0.09 0.0090 3.033 0.0105 4.550 5.688 0.0120 3.033 0.0140 4.550 5.688 0.18 0.9

0.1 0.0100 3.000 0.0116 4.500 5.625 0.0134 3.000 0.0155 4.500 5.625 0.2 0.9

0.11 0.0110 2.967 0.0128 4.450 5.563 0.0147 2.967 0.0171 4.450 5.563 0.22 0.8

0.12 0.0120 2.933 0.0140 4.400 5.500 0.0160 2.933 0.0186 4.400 5.500 0.24 0.8

0.13 0.0130 2.900 0.0151 4.350 5.438 0.0174 2.900 0.0202 4.350 5.438 0.26 0.8

0.14 0.0140 2.867 0.0163 4.300 5.375 0.0187 2.867 0.0217 4.300 5.375 0.28 0.8

0.15 0.0150 2.833 0.0175 4.250 5.313 0.0201 2.833 0.0233 4.250 5.313 0.3 0.8

0.16 0.0160 2.800 0.0186 4.200 5.250 0.0214 2.800 0.0248 4.200 5.250 0.32 0.8

0.17 0.0171 2.767 0.0198 4.150 5.188 0.0227 2.767 0.0264 4.150 5.188 0.34 0.8

0.18 0.0181 2.733 0.0210 4.100 5.125 0.0241 2.733 0.0279 4.100 5.125 0.36 0.8

0.19 0.0191 2.700 4.050 5.063 0.0254 2.700 4.050 5.063 0.38 0.8

0.2 0.0201 2.667 4.000 5.000 0.0267 2.667 4.000 5.000 0.4 0.8

0.21 0.0211 2.633 3.950 4.938 0.0281 2.633 3.950 4.938 0.42 0.7

0.22 0.0221 2.600 3.900 4.875 0.0294 2.600 3.900 4.875 0.44 0.7

0.23 0.0231 2.567 3.850 4.813 0.0308 2.567 3.850 4.813 0.46 0.7

0.24 0.0241 2.533 3.800 4.750 0.0321 2.533 3.800 4.750 0.48 0.7

0.25 0.0251 2.500 3.750 4.688 0.0334 2.500 3.750 4.688 0.5 0.7

0.26 0.0261 2.467 3.700 4.625 0.0348 2.467 3.700 4.625 0.52 0.7

0.27 0.0271 2.433 3.650 4.563 0.0361 2.433 3.650 4.563 0.54 0.7

0.28 0.0281 2.400 3.600 4.500 0.0374 2.400 3.600 4.500 0.56 0.70.29 0.0291 2.367 3.550 4.438 0.0388 2.367 3.550 4.438 0.58 0.7

0.3 0.0301 2.333 3.500 4.375 0.0401 2.333 3.500 4.375 0.6 0.7

0.31 0.0311 2.300 3.450 4.313 0.0415 2.300 3.450 4.313 0.62 0.6

0.32 0.0321 2.267 3.400 4.250 0.0428 2.267 3.400 4.250 0.64 0.6

0.33 0.0331 2.233 3.350 4.188 0.0441 2.233 3.350 4.188 0.66 0.6

0.34 0.0341 2.200 3.300 4.125 0.0455 2.200 3.300 4.125 0.68 0.6

0.35 0.0351 2.167 3.250 4.063 0.0468 2.167 3.250 4.063 0.7 0.6

0.36 0.0361 2.133 3.200 4.000 0.0481 2.133 3.200 4.000 0.72 0.6

0.37 0.0371 2.100 3.150 3.938 0.0495 2.100 3.150 3.938 0.74 0.6


FLEXURE 3.1 - Nominal strength coefficients rectangular beams with compression reinforcement

As = Asw + Asf

75000

jf= 1 -hf/2d

75000

4000

40000 60000

in which f's = fy and for flanged sections with hf< a;

where Asf= Knfjfbwhf/anf, in.2

(Knffrom FLEXURE 3.3)

which f's = fy:

and Mn2 = As2da'n, kip-ft

Reference: ACI 318-95 Sections 9.3.2, 10.2, and 10.3.1-10.3.4 and ACI 318R-95 Section 10.3.1-10.3.3

For a rectangular beam with

compression reinforcement in

For a flanged section with hf< a

Mn2 = Asfdanf, kip-ft

where

40000 60000

3000

r = As/bd, Mn > Mu/f

As = As1 + As2

yy

c

fd

d

f

f

--

000,87

000,87'85.0'

'

1brr

-=

d

dfa

y

n

'1

000,12

'

-= 1

000,12

85.0 '

w

cnf

b

bfK

-=

d

hfa

fy

nf2

1000,12

7/31/2019 SP-17(05)

14/35

f'c = 5000 & 6000 psi

b1 = 0.8 b1 = 0.75

f'c

fy

d'/d ' a'n or anf ' a'n or anf ' a'n or anf ' a'n or anf ' a'n or anf ' a'n or anf hf/d j

0.01 0.0016 3.300 0.0018 4.950 0.0033 6.188 0.0018 3.300 0.0021 4.950 0.0037 6.188 0.02 0.9

0.02 0.0031 3.267 0.0037 4.900 0.0066 6.125 0.0035 3.267 0.0041 4.900 0.0074 6.125 0.04 0.9

0.03 0.0047 3.233 0.0055 4.850 0.0099 6.063 0.0053 3.233 0.0062 4.850 0.0111 6.063 0.06 0.9

0.04 0.0063 3.200 0.0073 4.800 0.0131 6.000 0.0071 3.200 0.0082 4.800 0.0148 6.000 0.08 0.9

0.05 0.0079 3.167 0.0091 4.750 0.0164 5.938 0.0089 3.167 0.0103 4.750 0.0185 5.938 0.1 0.9

0.06 0.0094 3.133 0.0110 4.700 0.0197 5.875 0.0106 3.133 0.0123 4.700 0.0222 5.875 0.12 0.9

0.07 0.0110 3.100 0.0128 4.650 0.0230 5.813 0.0124 3.100 0.0144 4.650 0.0259 5.813 0.14 0.9

0.08 0.0126 3.067 0.0146 4.600 5.750 0.0142 3.067 0.0164 4.600 5.750 0.16 0.9

0.09 0.0142 3.033 0.0164 4.550 5.688 0.0159 3.033 0.0185 4.550 5.688 0.18 0.9

0.1 0.0157 3.000 0.0183 4.500 5.625 0.0177 3.000 0.0205 4.500 5.625 0.2 0.9

0.11 0.0173 2.967 0.0201 4.450 5.563 0.0195 2.967 0.0226 4.450 5.563 0.22 0.8

0.12 0.0189 2.933 0.0219 4.400 5.500 0.0212 2.933 0.0247 4.400 5.500 0.24 0.8

0.13 0.0205 2.900 0.0237 4.350 5.438 0.0230 2.900 0.0267 4.350 5.438 0.26 0.8

0.14 0.0220 2.867 0.0256 4.300 5.375 0.0248 2.867 0.0288 4.300 5.375 0.28 0.8

0.15 0.0236 2.833 0.0274 4.250 5.313 0.0266 2.833 0.0308 4.250 5.313 0.3 0.8

0.16 0.0252 2.800 0.0292 4.200 5.250 0.0283 2.800 0.0329 4.200 5.250 0.32 0.8

0.17 0.0267 2.767 0.0310 4.150 5.188 0.0301 2.767 0.0349 4.150 5.188 0.34 0.8

0.18 0.0283 2.733 0.0329 4.100 5.125 0.0319 2.733 0.0370 4.100 5.125 0.36 0.8

0.19 0.0299 2.700 4.050 5.063 0.0336 2.700 4.050 5.063 0.38 0.8

0.2 0.0315 2.667 4.000 5.000 0.0354 2.667 4.000 5.000 0.4 0.8

0.21 0.0330 2.633 3.950 4.938 0.0372 2.633 3.950 4.938 0.42 0.7

0.22 0.0346 2.600 3.900 4.875 0.0389 2.600 3.900 4.875 0.44 0.7

0.23 0.0362 2.567 3.850 4.813 0.0407 2.567 3.850 4.813 0.46 0.7

0.24 0.0378 2.533 3.800 4.750 0.0425 2.533 3.800 4.750 0.48 0.7

0.25 0.0393 2.500 3.750 4.688 0.0443 2.500 3.750 4.688 0.5 0.7

0.26 0.0409 2.467 3.700 4.625 0.0460 2.467 3.700 4.625 0.52 0.7

0.27 0.0425 2.433 3.650 4.563 0.0478 2.433 3.650 4.563 0.54 0.7

0.28 0.0441 2.400 3.600 4.500 0.0496 2.400 3.600 4.500 0.56 0.70.29 0.0456 2.367 3.550 4.438 0.0513 2.367 3.550 4.438 0.58 0.7

0.3 0.0472 2.333 3.500 4.375 0.0531 2.333 3.500 4.375 0.6 0.7

0.31 0.0488 2.300 3.450 4.313 0.0549 2.300 3.450 4.313 0.62 0.6

0.32 0.0503 2.267 3.400 4.250 0.0566 2.267 3.400 4.250 0.64 0.6

0.33 0.0519 2.233 3.350 4.188 0.0584 2.233 3.350 4.188 0.66 0.6

0.34 0.0535 2.200 3.300 4.125 0.0602 2.200 3.300 4.125 0.68 0.6

0.35 0.0551 2.167 3.250 4.063 0.0620 2.167 3.250 4.063 0.7 0.6

0.36 0.0566 2.133 3.200 4.000 0.0637 2.133 3.200 4.000 0.72 0.6

0.37 0.0582 2.100 3.150 3.938 0.0655 2.100 3.150 3.938 0.74 0.6

(Knffrom FLEXURE 3.3)

which f's = fy:

and Mn2 = As2da'n, kip-ft

where

40000 60000

5000

r = As/bd, Mn > Mu/f

As = As1 + As2


For a rectangular beam with

compression reinforcement in

For a flanged section with hf< a

Mn2 = Asfdanf, kip-ft

where Asf= Knfjfbwhf/anf, in.2


FLEXURE 3.2 - Nominal strength coefficients rectangular beams with compression reinforcement

As = Asw + Asf

75000

jf= 1 -hf/2d

75000

6000

40000 60000

in which f's = fy and for flanged sections with hf< a;

yy

c

fd

d

f

f

--

000,87

000,87'85.0'

'

1brr

-=

d

dfa

y

n

'1

000,12

'

-= 1

000,12

85.0 '

w

cnf

b

bfK

-=

d

hfa

fy

nf2

1000,12

7/31/2019 SP-17(05)

15/35

where

jf= 1 - hf/2d

and

3000 4000 5000 6000

0.2125 0.2833 0.3542 0.4250

0.2550 0.3400 0.4250 0.5100

0.2975 0.3967 0.4958 0.5950

0.3400 0.4533 0.5667 0.6800

0.3825 0.5100 0.6375 0.7650

0.4250 0.5667 0.7083 0.8500

0.4675 0.6233 0.7792 0.9350

0.5100 0.6800 0.8500 1.0200

0.5525 0.7367 0.9208 1.1050

0.5950 0.7933 0.9917 1.1900

0.6375 0.8500 1.0625 1.2750

0.6800 0.9067 1.1333 1.3600

0.7225 0.9633 1.2042 1.4450

0.7650 1.0200 1.2750 1.5300

0.8075 1.0767 1.3458 1.6150

0.8500 1.1333 1.4167 1.7000

0.8925 1.1900 1.4875 1.7850

0.9350 1.2467 1.5583 1.8700

0.9775 1.3033 1.6292 1.9550

1.0200 1.3600 1.7000 2.0400

1.0625 1.4167 1.7708 2.1250

1.1050 1.4733 1.8417 2.2100

1.1475 1.5300 1.9125 2.2950

1.1900 1.5867 1.9833 2.3800

1.2325 1.6433 2.0542 2.4650

1.2750 1.7000 2.1250 2.5500

1.3175 1.7567 2.1958 2.6350

1.3600 1.8133 2.2667 2.7200

1.4025 1.8700 2.3375 2.80501.4450 1.9267 2.4083 2.8900

1.4875 1.9833 2.4792 2.9750

1.5300 2.0400 2.5500 3.0600

1.5725 2.0967 2.6208 3.1450

1.6150 2.1533 2.6917 3.2300

1.6575 2.2100 2.7625 3.3150

1.7000 2.2667 2.8333 3.4000

1.7425 2.3233 2.9042 3.4850

1.7850 2.3800 2.9750 3.5700

1.8275 2.4367 3.0458 3.6550

1.8700 2.4933 3.1167 3.7400

1.9125 2.5500 3.1875 3.8250

b/bw

FLEXURE 3.3 - Coefficient Knffor use in computing Asffor a flanged section with hf< a


(jfand anffrom FLEXURE 3.1 and 3.2)

Knf

f'c , psi

2.8

3.03.23.4

2.02.22.42.6

4.44.64.8

5.0

3.63.8

4.04.2

6.06.26.46.6

5.25.45.65.8

7.67.8

8.08.2

.8

7.07.27.4

10.0

9.29.49.69.8

8.48.68.8

9.0

( )2in.,

nf

fwfnf

sf

a

hbjKA =

-=

d

hfa

fy

nf2

112000

f

u

n

MM

-= 1

000,12

85.0 '

w

c

nf

b

bfK

7/31/2019 SP-17(05)

16/35

FLEXURE 6.1.2 - Nominal strength Mn for slab sections 12 in. wide

Reference: ACI 318-95 Sections 7.12, 8.4.1, 8.4.3, 9.3.2, 10.2, 10.3.1-10.3.3, 10.5.1 and 10.5.3

and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 3.3333 Asd - 2.1786 As2

,k-ft

fy = psi

b1 = 0.85 Shrinkage & Temperature reinforcement = 0.0020 bh h=d+1

1 2 3 4 5 6 7 8 9 10 11 12

Ast&s 0.0480 0.0720 0.0960 0.1200 0.1440 0.1680 0.1920 0.2160 0.2400 0.2640 0.2880 0.3120

Asmin 0.0600 0.1200 0.1800 0.2400 0.3000 0.3600 0.4200 0.4800 0.5400 0.6000 0.6600 0.7200

Asmax 0.3341 0.6682 1.0023 1.3363 1.6704 2.0045 2.3386 2.6727 3.0068 3.3409 3.6749 4.0090

As0.120 0.369 0.769 0.882 1.182

0.240 0.675 1.475 2.275 3.075 2.929 3.529 4.129 4.729 5.329

0.360 2.118 3.318 4.518 5.718 6.918 6.141 7.041 7.941 8.841 9.741 10.641

0.480 2.698 4.298 5.898 7.498 9.098 10.698 12.298 10.518 11.718 12.918 14.118

0.600 3.216 5.216 7.216 9.216 11.216 13.216 15.216 17.216 19.216 16.059 17.559

0.720 6.071 8.471 10.871 13.271 15.671 18.071 20.471 22.871 25.271 27.671

0.840 6.863 9.663 12.463 15.263 18.063 20.863 23.663 26.463 29.263 32.063

0.960 7.592 10.792 13.992 17.192 20.392 23.592 26.792 29.992 33.192 36.392

1.080 11.859 15.459 19.059 22.659 26.259 29.859 33.459 37.059 40.659

1.200 12.863 16.863 20.863 24.863 28.863 32.863 36.863 40.863 44.863

1.320 13.804 18.204 22.604 27.004 31.404 35.804 40.204 44.604 49.004

1.440 19.482 24.282 29.082 33.882 38.682 43.482 48.282 53.082

1.560 20.698 25.898 31.098 36.298 41.498 46.698 51.898 57.0981.680 27.451 33.051 38.651 44.251 49.851 55.451 61.051

1.800 28.941 34.941 40.941 46.941 52.941 58.941 64.941

1.920 30.369 36.769 43.169 49.569 55.969 62.369 68.769

2.040 38.533 45.333 52.133 58.933 65.733 72.533

2.160 40.235 47.435 54.635 61.835 69.035 76.235

2.280 41.875 49.475 57.075 64.675 72.275 79.875

2.400 51.451 59.451 67.451 75.451 83.451

2.520 53.365 61.765 70.165 78.565 86.965

2.640 55.216 64.016 72.816 81.616 90.416

2.760 66.204 75.404 84.604 93.804

2.880 68.329 77.929 87.529 97.129

3.000 70.392 80.392 90.392 100.392

3.120 82.792 93.192 103.5923.240 85.129 95.929 106.729

3.360 98.604 109.804

3.480 101.216 112.816

3.600 103.765 115.765

3.720 118.651

3.840 121.475

3.960 124.2354.080

Mn (Nominal Moment, k-ft) vs. d

Mn > Mu/f

3000

40,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

17/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 5.0000 Asd - 4.9020 As2

,k-ft

fy = psi


1 2 3 4 5 6 7 8 9 10 11 12

Ast&s 0.0432 0.0648 0.0864 0.1080 0.1296 0.1512 0.1728 0.1944 0.2160 0.2376 0.2592 0.2808

Asmin 0.0400 0.0800 0.1200 0.1600 0.2000 0.2400 0.2800 0.3200 0.3600 0.4000 0.4400 0.4800

Asmax 0.1924 0.3848 0.5773 0.7697 0.9621 1.1545 1.3469 1.5394 1.7318 1.9242 2.1166 2.3091

As0.070 0.326 0.511

0.140 0.604 1.304 2.004 2.046 2.571

0.210 1.884 2.934 3.984 5.034 4.603 5.391 6.178

0.280 2.416 3.816 5.216 6.616 8.016 9.416 8.184 9.234 10.284 11.334

0.350 2.900 4.650 6.400 8.150 9.900 11.650 13.400 11.475 12.787 14.100 15.412

0.420 5.435 7.535 9.635 11.735 13.835 15.935 18.035 20.135 16.839 18.414

0.490 6.173 8.623 11.073 13.523 15.973 18.423 20.873 23.323 25.773 28.223

0.560 6.863 9.663 12.463 15.263 18.063 20.863 23.663 26.463 29.263 32.063

0.630 10.654 13.804 16.954 20.104 23.254 26.404 29.554 32.704 35.854

0.700 11.598 15.098 18.598 22.098 25.598 29.098 32.598 36.098 39.598

0.770 16.344 20.194 24.044 27.894 31.744 35.594 39.444 43.294

0.840 17.541 21.741 25.941 30.141 34.341 38.541 42.741 46.941

0.910 18.691 23.241 27.791 32.341 36.891 41.441 45.991 50.5410.980 24.692 29.592 34.492 39.392 44.292 49.192 54.092

1.050 26.096 31.346 36.596 41.846 47.096 52.346 57.596

1.120 27.451 33.051 38.651 44.251 49.851 55.451 61.051

1.190 34.708 40.658 46.608 52.558 58.508 64.458

1.260 36.318 42.618 48.918 55.218 61.518 67.818

1.330 37.879 44.529 51.179 57.829 64.479 71.129

1.400 46.392 53.392 60.392 67.392 74.392

1.470 48.207 55.557 62.907 70.257 77.607

1.540 57.675 65.375 73.075 80.775

1.610 59.744 67.794 75.844 83.894

1.680 61.765 70.165 78.565 86.965

1.750 72.488 81.238 89.988

1.820 74.763 83.863 92.9631.890 76.990 86.440 95.890

1.960 88.969 98.769

2.030 91.450 101.600

2.100 93.882 104.382

2.170 107.117

2.240 109.804

2.3102.380


Mn > Mu/f

3000

60,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

18/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 3.3333 Asd - 1.6340 As2

,k-ft

fy = psi


1 2 3 4 5 6 7 8 9 10 11 12

Ast&s 0.0480 0.0720 0.0960 0.1200 0.1440 0.1680 0.1920 0.2160 0.2400 0.2640 0.2880 0.3120

Asmin 0.0600 0.1200 0.1800 0.2400 0.3000 0.3600 0.4200 0.4800 0.5400 0.6000 0.6600 0.7200

Asmax 0.4454 0.8909 1.3363 1.7818 2.2272 2.6727 3.1181 3.5636 4.0090 4.4545 4.8999 5.3454

As0.160 0.492 1.025 1.176 1.576 1.976

0.320 0.899 1.966 3.033 4.099 5.166 4.706 5.506 6.306 7.106 7.906 8.706 9.506

0.480 2.824 4.424 6.024 7.624 9.224 10.824 12.424 10.588 11.788 12.988 14.188

0.640 3.597 5.731 7.864 9.997 12.131 14.264 16.397 18.531 20.664 17.224 18.824

0.800 4.288 6.954 9.621 12.288 14.954 17.621 20.288 22.954 25.621 28.288 30.954

0.960 8.094 11.294 14.494 17.694 20.894 24.094 27.294 30.494 33.694 36.894

1.120 9.150 12.884 16.617 20.350 24.084 27.817 31.550 35.284 39.017 42.750

1.280 10.123 14.390 18.656 22.923 27.190 31.456 35.723 39.990 44.256 48.523

1.440 15.812 20.612 25.412 30.212 35.012 39.812 44.612 49.412 54.212

1.600 17.150 22.484 27.817 33.150 38.484 43.817 49.150 54.484 59.817

1.760 18.405 24.272 30.139 36.005 41.872 47.739 53.605 59.472 65.339

1.920 25.976 32.376 38.776 45.176 51.576 57.976 64.376 70.776

2.080 27.597 34.531 41.464 48.397 55.331 62.264 69.197 76.1312.240 36.601 44.068 51.535 59.001 66.468 73.935 81.401

2.400 38.588 46.588 54.588 62.588 70.588 78.588 86.588

2.560 40.492 49.025 57.558 66.092 74.625 83.158 91.692

2.720 51.378 60.444 69.511 78.578 87.644 96.711

2.880 53.647 63.247 72.847 82.447 92.047 101.647

3.040 55.833 65.966 76.099 86.233 96.366 106.499

3.200 68.601 79.268 89.935 100.601 111.268

3.360 71.153 82.353 93.553 104.753 115.953

3.520 73.621 85.354 97.088 108.821 120.554

3.680 88.272 100.539 112.805 125.072

3.840 91.106 103.906 116.706 129.506

4.000 93.856 107.190 120.523 133.856

4.160 110.390 124.256 138.1234.320 113.506 127.906 142.306

4.480 131.472 146.405

4.640 134.954 150.421

4.800 138.353 154.353

4.960 158.201

5.120 161.966

5.280 165.6475.440


Mn > Mu/f

4000

40,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

19/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 5.0000 Asd - 3.6765 As2

,k-ft

fy = psi


1 2 3 4 5 6 7 8 9 10 11 12

Ast&s 0.0432 0.0648 0.0864 0.1080 0.1296 0.1512 0.1728 0.1944 0.2160 0.2376 0.2592 0.2808

Asmin 0.0400 0.0800 0.1200 0.1600 0.2000 0.2400 0.2800 0.3200 0.3600 0.4000 0.4400 0.4800

Asmax 0.2566 0.5131 0.7697 1.0262 1.2828 1.5394 1.7959 2.0525 2.3091 2.5656 2.8222 3.0787

As0.095 0.442 0.917 1.050

0.190 0.817 1.767 2.717 3.667 3.488 4.200 4.913

0.285 2.551 3.976 5.401 6.826 8.251 9.676 8.382 9.451 10.520 11.588 12.657

0.380 3.269 5.169 7.069 8.969 10.869 12.769 14.669 16.569 13.951 15.376 16.801

0.475 3.920 6.295 8.670 11.045 13.420 15.795 18.170 20.545 22.920 25.295 20.908

0.570 7.356 10.206 13.056 15.906 18.756 21.606 24.456 27.306 30.156 33.006

0.665 8.349 11.674 14.999 18.324 21.649 24.974 28.299 31.624 34.949 38.274

0.760 9.276 13.076 16.876 20.676 24.476 28.276 32.076 35.876 39.676 43.476

0.855 14.412 18.687 22.962 27.237 31.512 35.787 40.062 44.337 48.612

0.950 15.682 20.432 25.182 29.932 34.682 39.432 44.182 48.932 53.682

1.045 22.110 27.335 32.560 37.785 43.010 48.235 53.460 58.685

1.140 23.722 29.422 35.122 40.822 46.522 52.222 57.922 63.622

1.235 25.268 31.443 37.618 43.793 49.968 56.143 62.318 68.4931.330 33.397 40.047 46.697 53.347 59.997 66.647 73.297

1.425 35.284 42.409 49.534 56.659 63.784 70.909 78.034

1.520 37.106 44.706 52.306 59.906 67.506 75.106 82.706

1.615 46.936 55.011 63.086 71.161 79.236 87.311

1.710 49.100 57.650 66.200 74.750 83.300 91.850

1.805 60.222 69.247 78.272 87.297 96.322

1.900 62.728 72.228 81.728 91.228 100.728

1.995 65.168 75.143 85.118 95.093 105.068

2.090 77.991 88.441 98.891 109.341

2.185 80.773 91.698 102.623 113.548

2.280 83.488 94.888 106.288 117.688

2.375 98.012 109.887 121.762

2.470 101.070 113.420 125.7702.565 104.062 116.887 129.712

2.660 120.287 133.587

2.755 123.620 137.395

2.850 141.138

2.945 144.814

3.040 148.424

3.1353.230


Mn > Mu/f

4000

60,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

20/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 3.3333 Asd - 1.3072 As2

,k-ft

fy = psi


1 2 3 4 5 6 7 8 9 10 11 12

Ast&s 0.0480 0.0720 0.0960 0.1200 0.1440 0.1680 0.1920 0.2160 0.2400 0.2640 0.2880 0.3120

Asmin 0.0636 0.1273 0.1909 0.2546 0.3182 0.3818 0.4455 0.5091 0.5728 0.6364 0.7000 0.7637

Asmax 0.5241 1.0481 1.5722 2.0962 2.6203 3.1443 3.6684 4.1924 4.7165 5.2406 5.7646 6.2887

As0.185 0.572 1.189 1.362 1.825 2.287 2.750

0.370 1.054 2.288 3.521 4.754 5.988 5.449 6.374 7.299 8.224 9.149 10.074 10.999

0.555 3.297 5.147 6.997 8.847 10.697 12.547 14.397 12.261 13.649 15.036 16.424

0.740 4.218 6.684 9.151 11.618 14.084 16.551 19.018 21.484 23.951 26.418 21.797

0.925 5.048 8.132 11.215 14.298 17.382 20.465 23.548 26.632 29.715 32.798 35.882

1.110 9.489 13.189 16.889 20.589 24.289 27.989 31.689 35.389 39.089 42.789

1.295 10.758 15.074 19.391 23.708 28.024 32.341 36.658 40.974 45.291 49.608

1.480 11.937 16.870 21.803 26.737 31.670 36.603 41.537 46.470 51.403 56.337

1.665 18.576 24.126 29.676 35.226 40.776 46.326 51.876 57.426 62.976

1.850 20.193 26.359 32.526 38.693 44.859 51.026 57.193 63.359 69.526

2.035 21.720 28.503 35.287 42.070 48.853 55.637 62.420 69.203 75.987

2.220 30.558 37.958 45.358 52.758 60.158 67.558 74.958 82.358

2.405 32.523 40.539 48.556 56.573 64.589 72.606 80.623 88.6392.590 34.398 43.031 51.665 60.298 68.931 77.565 86.198 94.831

2.775 45.434 54.684 63.934 73.184 82.434 91.684 100.934

2.960 47.747 57.614 67.480 77.347 87.214 97.080 106.947

3.145 60.454 70.937 81.421 91.904 102.387 112.871

3.330 63.205 74.305 85.405 96.505 107.605 118.705

3.515 65.866 77.583 89.299 101.016 112.733 124.449

3.700 80.771 93.105 105.438 117.771 130.105

3.885 83.870 96.820 109.770 122.720 135.670

4.070 86.880 100.447 114.013 127.580 141.147

4.255 103.983 118.167 132.350 146.533

4.440 107.431 122.231 137.031 151.831

4.625 110.788 126.205 141.622 157.038

4.810 130.090 146.123 162.1574.995 133.886 150.536 167.186

5.180 137.592 154.858 172.125

5.365 159.092 176.975

5.550 163.235 181.735

5.735 167.290 186.406

5.920 190.988

6.105 195.4806.290


Mn > Mu/f

5000

40,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

21/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 5.0000 Asd - 2.9412 As2

,k-ft

fy = psi


1 2 3 4 5 6 7 8 9 10 11 12

Ast&s 0.0432 0.0648 0.0864 0.1080 0.1296 0.1512 0.1728 0.1944 0.2160 0.2376 0.2592 0.2808

Asmin 0.0424 0.0849 0.1273 0.1697 0.2121 0.2546 0.2970 0.3394 0.3818 0.4243 0.4667 0.5091

Asmax 0.3018 0.6037 0.9055 1.2073 1.5092 1.8110 2.1129 2.4147 2.7165 3.0184 3.3202 3.6220

As0.110 0.514 1.064 1.217 1.630

0.220 0.958 2.058 3.158 4.258 5.358 4.870 5.695 6.520 7.345

0.330 2.980 4.630 6.280 7.930 9.580 11.230 9.720 10.957 12.195 13.432 14.670

0.440 3.831 6.031 8.231 10.431 12.631 14.831 17.031 19.231 21.431 17.830 19.480

0.550 4.610 7.360 10.110 12.860 15.610 18.360 21.110 23.860 26.610 29.360 32.110

0.660 8.619 11.919 15.219 18.519 21.819 25.119 28.419 31.719 35.019 38.319

0.770 9.806 13.656 17.506 21.356 25.206 29.056 32.906 36.756 40.606 44.456

0.880 10.922 15.322 19.722 24.122 28.522 32.922 37.322 41.722 46.122 50.522

0.990 16.917 21.867 26.817 31.767 36.717 41.667 46.617 51.567 56.517

1.100 18.441 23.941 29.441 34.941 40.441 45.941 51.441 56.941 62.441

1.210 25.944 31.994 38.044 44.094 50.144 56.194 62.244 68.294

1.320 27.875 34.475 41.075 47.675 54.275 60.875 67.475 74.075

1.430 29.736 36.886 44.036 51.186 58.336 65.486 72.636 79.7861.540 39.225 46.925 54.625 62.325 70.025 77.725 85.425

1.650 41.493 49.743 57.993 66.243 74.493 82.743 90.993

1.760 43.689 52.489 61.289 70.089 78.889 87.689 96.489

1.870 55.165 64.515 73.865 83.215 92.565 101.915

1.980 57.769 67.669 77.569 87.469 97.369 107.269

2.090 60.303 70.753 81.203 91.653 102.103 112.553

2.200 73.765 84.765 95.765 106.765 117.765

2.310 76.706 88.256 99.806 111.356 122.906

2.420 91.675 103.775 115.875 127.975

2.530 95.024 107.674 120.324 132.974

2.640 98.301 111.501 124.701 137.901

2.750 115.257 129.007 142.757

2.860 118.942 133.242 147.5422.970 122.556 137.406 152.256

3.080 141.499 156.899

3.190 145.520 161.470

3.300 149.471 165.971

3.410 170.400

3.520 174.758

3.6303.740


Mn > Mu/f

5000

60,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

22/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 3.3333 Asd - 1.0893 As2

,k-ft

fy = psi


1 2 3 4 5 6 7 8 9 10 11 12

Ast&s 0.0480 0.0720 0.0960 0.1200 0.1440 0.1680 0.1920 0.2160 0.2400 0.2640 0.2880 0.3120

Asmin 0.0697 0.1394 0.2091 0.2789 0.3486 0.4183 0.4880 0.5577 0.6274 0.6971 0.7669 0.8366

Asmax 0.5896 1.1791 1.7687 2.3582 2.9478 3.5374 4.1269 4.7165 5.3061 5.8956 6.4852 7.0747

As0.210 0.652 1.352 2.052 2.073 2.598 3.123 3.648

0.420 1.208 2.608 4.008 5.408 6.808 8.208 7.242 8.292 9.342 10.392 11.442 12.492

0.630 3.768 5.868 7.968 10.068 12.168 14.268 16.368 18.468 15.507 17.082 18.657

0.840 4.831 7.631 10.431 13.231 16.031 18.831 21.631 24.431 27.231 30.031 32.831

1.050 5.799 9.299 12.799 16.299 19.799 23.299 26.799 30.299 33.799 37.299 40.799

1.260 10.871 15.071 19.271 23.471 27.671 31.871 36.071 40.271 44.471 48.671

1.470 12.346 17.246 22.146 27.046 31.946 36.846 41.746 46.646 51.546 56.446

1.680 13.725 19.325 24.925 30.525 36.125 41.725 47.325 52.925 58.525 64.125

1.890 21.309 27.609 33.909 40.209 46.509 52.809 59.109 65.409 71.709

2.100 23.196 30.196 37.196 44.196 51.196 58.196 65.196 72.196 79.196

2.310 24.987 32.687 40.387 48.087 55.787 63.487 71.187 78.887 86.587

2.520 35.082 43.482 51.882 60.282 68.682 77.082 85.482 93.882

2.730 37.381 46.481 55.581 64.681 73.781 82.881 91.981 101.0812.940 39.584 49.384 59.184 68.984 78.784 88.584 98.384 108.184

3.150 52.191 62.691 73.191 83.691 94.191 104.691 115.191

3.360 54.902 66.102 77.302 88.502 99.702 110.902 122.102

3.570 69.417 81.317 93.217 105.117 117.017 128.917

3.780 72.635 85.235 97.835 110.435 123.035 135.635

3.990 75.758 89.058 102.358 115.658 128.958 142.258

4.200 92.784 106.784 120.784 134.784 148.784

4.410 96.415 111.115 125.815 140.515 155.215

4.620 99.949 115.349 130.749 146.149 161.549

4.830 119.487 135.587 151.687 167.787

5.040 123.529 140.329 157.129 173.929

5.250 127.475 144.975 162.475 179.975

5.460 149.525 167.725 185.9255.670 153.979 172.879 191.779

5.880 158.337 177.937 197.537

6.090 182.899 203.199

6.300 187.765 208.765

6.510 214.234

6.720 219.608

6.930 224.8857.140


Mn > Mu/f

6000

40,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

23/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 5.0000 Asd - 2.4510 As2

,k-ft

fy = psi


1 2 3 4 5 6 7 8 9 10 11 12

Ast&s 0.0432 0.0648 0.0864 0.1080 0.1296 0.1512 0.1728 0.1944 0.2160 0.2376 0.2592 0.2808

Asmin 0.0465 0.0930 0.1394 0.1859 0.2324 0.2789 0.3253 0.3718 0.4183 0.4648 0.5112 0.5577

Asmax 0.3396 0.6791 1.0187 1.3583 1.6978 2.0374 2.3770 2.7165 3.0561 3.3957 3.7352 4.0748

As0.120 0.565 1.165 1.330 1.780

0.240 1.059 2.259 3.459 4.659 5.859 5.321 6.221 7.121 8.021 8.921

0.360 3.282 5.082 6.882 8.682 10.482 12.282 10.621 11.971 13.321 14.671 16.021

0.480 4.235 6.635 9.035 11.435 13.835 16.235 18.635 21.035 23.435 19.482 21.282

0.600 5.118 8.118 11.118 14.118 17.118 20.118 23.118 26.118 29.118 32.118 35.118

0.720 9.529 13.129 16.729 20.329 23.929 27.529 31.129 34.729 38.329 41.929

0.840 10.871 15.071 19.271 23.471 27.671 31.871 36.071 40.271 44.471 48.671

0.960 12.141 16.941 21.741 26.541 31.341 36.141 40.941 45.741 50.541 55.341

1.080 18.741 24.141 29.541 34.941 40.341 45.741 51.141 56.541 61.941

1.200 20.471 26.471 32.471 38.471 44.471 50.471 56.471 62.471 68.471

1.320 22.129 28.729 35.329 41.929 48.529 55.129 61.729 68.329 74.929

1.440 30.918 38.118 45.318 52.518 59.718 66.918 74.118 81.318

1.560 33.035 40.835 48.635 56.435 64.235 72.035 79.835 87.6351.680 35.082 43.482 51.882 60.282 68.682 77.082 85.482 93.882

1.800 46.059 55.059 64.059 73.059 82.059 91.059 100.059

1.920 48.565 58.165 67.765 77.365 86.965 96.565 106.165

2.040 61.200 71.400 81.600 91.800 102.000 112.200

2.160 64.165 74.965 85.765 96.565 107.365 118.165

2.280 67.059 78.459 89.859 101.259 112.659 124.059

2.400 81.882 93.882 105.882 117.882 129.882

2.520 85.235 97.835 110.435 123.035 135.635

2.640 88.518 101.718 114.918 128.118 141.318

2.760 105.529 119.329 133.129 146.929

2.880 109.271 123.671 138.071 152.471

3.000 112.941 127.941 142.941 157.941

3.120 132.141 147.741 163.3413.240 136.271 152.471 168.671

3.360 140.329 157.129 173.929

3.480 161.718 179.118

3.600 166.235 184.235

3.720 170.682 189.282

3.840 194.259

3.960 199.1654.080


Mn > Mu/f

6000

60,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

24/35

FLEXURE 7.1.2 - Nominal strength Mn for beam sections 10 in. wide


and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 3.3333 Asd - 2.1786 As2

,k-ft

fy = psi


6 12 18 24 30 36 42 48 54 60 66 72

Ast&s 0.160 0.280 0.400 0.520 0.640 0.760 0.880 1.000 1.120 1.240 1.360 1.480

Asmin 0.300 0.600 0.900 1.200 1.500 1.800 2.100 2.400 2.700 3.000 3.300 3.600

Asmax 1.670 3.341 5.011 6.682 8.352 10.023 11.693 13.363 15.034 16.704 18.375 20.045

As0.600 11.22 23.22 26.56 35.56

1.200 20.86 44.86 68.86 92.86 88.24 106.24 124.24 142.24 160.24

1.800 64.94 100.94 136.94 172.94 208.94 185.03 212.03 239.03 266.03 293.03 320.03

2.400 83.45 131.45 179.45 227.45 275.45 323.45 371.45 316.94 352.94 388.94 424.94

3.000 100.39 160.39 220.39 280.39 340.39 400.39 460.39 520.39 580.39 483.97 528.97

3.600 187.76 259.76 331.76 403.76 475.76 547.76 619.76 691.76 763.76 835.76

4.200 213.57 297.57 381.57 465.57 549.57 633.57 717.57 801.57 885.57 969.57

4.800 237.80 333.80 429.80 525.80 621.80 717.80 813.80 909.80 1005.80 1101.80

5.400 368.47 476.47 584.47 692.47 800.47 908.47 1016.47 1124.47 1232.47

6.000 401.57 521.57 641.57 761.57 881.57 1001.57 1121.57 1241.57 1361.57

6.600 433.10 565.10 697.10 829.10 961.10 1093.10 1225.10 1357.10 1489.10

7.200 607.06 751.06 895.06 1039.06 1183.06 1327.06 1471.06 1615.06

7.800 647.45 803.45 959.45 1115.45 1271.45 1427.45 1583.45 1739.458.400 854.27 1022.27 1190.27 1358.27 1526.27 1694.27 1862.27

9.000 903.53 1083.53 1263.53 1443.53 1623.53 1803.53 1983.53

9.600 951.22 1143.22 1335.22 1527.22 1719.22 1911.22 2103.22

10.200 1201.33 1405.33 1609.33 1813.33 2017.33 2221.33

10.800 1257.88 1473.88 1689.88 1905.88 2121.88 2337.88

11.400 1312.86 1540.86 1768.86 1996.86 2224.86 2452.86

12.000 1606.27 1846.27 2086.27 2326.27 2566.27

12.600 1670.12 1922.12 2174.12 2426.12 2678.12

13.200 1732.39 1996.39 2260.39 2524.39 2788.39

13.800 2069.10 2345.10 2621.10 2897.10

14.400 2140.24 2428.24 2716.24 3004.24

15.000 2209.80 2509.80 2809.80 3109.80

15.600 2589.80 2901.80 3213.8016.200 2668.24 2992.24 3316.24

16.800 3081.10 3417.10

17.400 3168.39 3516.39

18.000 3254.12 3614.12

18.600 3710.27

19.200 3804.86

19.800 3897.8820.400


Mn > Mu/f

3000

40,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

25/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 5.0000 Asd - 4.9020 As2

,k-ft

fy = psi


6 12 18 24 30 36 42 48 54 60 66 72

Ast&s 0.144 0.252 0.360 0.468 0.576 0.684 0.792 0.900 1.008 1.116 1.224 1.332

Asmin 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600 1.800 2.000 2.200 2.400

Asmax 0.962 1.924 2.886 3.848 4.811 5.773 6.735 7.697 8.659 9.621 10.583 11.545

As0.350 9.90 15.41

0.700 18.60 39.60 60.60 61.65 77.40 93.15

1.050 57.60 89.10 120.60 152.10 138.71 162.34 185.96 209.59

1.400 74.39 116.39 158.39 200.39 242.39 284.39 246.60 278.10 309.60 341.10 372.60

1.750 89.99 142.49 194.99 247.49 299.99 352.49 404.99 345.93 385.31 424.68 464.06

2.100 167.38 230.38 293.38 356.38 419.38 482.38 545.38 608.38 507.59 554.84

2.450 191.08 264.58 338.08 411.58 485.08 558.58 632.08 705.58 779.08 852.58

2.800 213.57 297.57 381.57 465.57 549.57 633.57 717.57 801.57 885.57 969.57

3.150 329.36 423.86 518.36 612.86 707.36 801.86 896.36 990.86 1085.36

3.500 359.95 464.95 569.95 674.95 779.95 884.95 989.95 1094.95 1199.95

3.850 504.84 620.34 735.84 851.34 966.84 1082.34 1197.84 1313.34

4.200 543.53 669.53 795.53 921.53 1047.53 1173.53 1299.53 1425.53

4.550 581.02 717.52 854.02 990.52 1127.02 1263.52 1400.02 1536.524.900 764.30 911.30 1058.30 1205.30 1352.30 1499.30 1646.30

5.250 809.89 967.39 1124.89 1282.39 1439.89 1597.39 1754.89

5.600 854.27 1022.27 1190.27 1358.27 1526.27 1694.27 1862.27

5.950 1075.96 1254.46 1432.96 1611.46 1789.96 1968.46

6.300 1128.44 1317.44 1506.44 1695.44 1884.44 2073.44

6.650 1179.72 1379.22 1578.72 1778.22 1977.72 2177.22

7.000 1439.80 1649.80 1859.80 2069.80 2279.80

7.350 1499.18 1719.68 1940.18 2160.68 2381.18

7.700 1788.36 2019.36 2250.36 2481.36

8.050 1855.84 2097.34 2338.84 2580.34

8.400 1922.12 2174.12 2426.12 2678.12

8.750 2249.69 2512.19 2774.69

9.100 2324.07 2597.07 2870.079.450 2397.24 2680.74 2964.24

9.800 2763.22 3057.22

10.150 2844.49 3148.99

10.500 2924.56 3239.56

10.850 3328.93

11.200 3417.10

11.55011.900


Mn > Mu/f

3000

60,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

26/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 3.3333 Asd - 1.6340 As2

,k-ft

fy = psi


6 12 18 24 30 36 42 48 54 60 66 72

Ast&s 0.160 0.280 0.400 0.520 0.640 0.760 0.880 1.000 1.120 1.240 1.360 1.480

Asmin 0.300 0.600 0.900 1.200 1.500 1.800 2.100 2.400 2.700 3.000 3.300 3.600

Asmax 2.227 4.454 6.682 8.909 11.136 13.363 15.591 17.818 20.045 22.272 24.500 26.727

As0.800 14.95 30.95 35.41 47.41 59.41 71.41

1.600 27.82 59.82 91.82 123.82 155.82 141.65 165.65 189.65 213.65 237.65 261.65 285.65

2.400 86.59 134.59 182.59 230.59 278.59 326.59 374.59 318.71 354.71 390.71 426.71

3.200 111.27 175.27 239.27 303.27 367.27 431.27 495.27 559.27 623.27 518.59 566.59

4.000 133.86 213.86 293.86 373.86 453.86 533.86 613.86 693.86 773.86 853.86 933.86

4.800 250.35 346.35 442.35 538.35 634.35 730.35 826.35 922.35 1018.35 1114.35

5.600 284.76 396.76 508.76 620.76 732.76 844.76 956.76 1068.76 1180.76 1292.76

6.400 317.07 445.07 573.07 701.07 829.07 957.07 1085.07 1213.07 1341.07 1469.07

7.200 491.29 635.29 779.29 923.29 1067.29 1211.29 1355.29 1499.29 1643.29

8.000 535.42 695.42 855.42 1015.42 1175.42 1335.42 1495.42 1655.42 1815.42

8.800 577.46 753.46 929.46 1105.46 1281.46 1457.46 1633.46 1809.46 1985.46

9.600 809.41 1001.41 1193.41 1385.41 1577.41 1769.41 1961.41 2153.41

10.400 863.27 1071.27 1279.27 1487.27 1695.27 1903.27 2111.27 2319.2711.200 1139.03 1363.03 1587.03 1811.03 2035.03 2259.03 2483.03

12.000 1204.71 1444.71 1684.71 1924.71 2164.71 2404.71 2644.71

12.800 1268.29 1524.29 1780.29 2036.29 2292.29 2548.29 2804.29

13.600 1601.78 1873.78 2145.78 2417.78 2689.78 2961.78

14.400 1677.18 1965.18 2253.18 2541.18 2829.18 3117.18

15.200 1750.48 2054.48 2358.48 2662.48 2966.48 3270.48

16.000 2141.70 2461.70 2781.70 3101.70 3421.70

16.800 2226.82 2562.82 2898.82 3234.82 3570.82

17.600 2309.86 2661.86 3013.86 3365.86 3717.86

18.400 2758.80 3126.80 3494.80 3862.80

19.200 2853.65 3237.65 3621.65 4005.65

20.000 2946.41 3346.41 3746.41 4146.41

20.800 3453.07 3869.07 4285.0721.600 3557.65 3989.65 4421.65

22.400 4108.13 4556.13

23.200 4224.52 4688.52

24.000 4338.82 4818.82

24.800 4947.03

25.600 5073.15

26.400 5197.1827.200


Mn > Mu/f

4000

40,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

27/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 5.0000 Asd - 3.6765 As2

,k-ft

fy = psi


6 12 18 24 30 36 42 48 54 60 66 72

Ast&s 0.144 0.252 0.360 0.468 0.576 0.684 0.792 0.900 1.008 1.116 1.224 1.332

Asmin 0.200 0.400 0.600 0.800 1.000 1.200 1.400 1.600 1.800 2.000 2.200 2.400

Asmax 1.283 2.566 3.848 5.131 6.414 7.697 8.980 10.262 11.545 12.828 14.111 15.394

As0.450 12.76 26.26 29.96

0.900 24.02 51.02 78.02 105.02 99.57 119.82 140.07 160.32

1.350 74.30 114.80 155.30 195.80 236.30 208.86 239.23 269.61 299.98 330.36 360.73

1.800 96.09 150.09 204.09 258.09 312.09 366.09 420.09 474.09 398.30 438.80 479.30

2.250 116.39 183.89 251.39 318.89 386.39 453.89 521.39 588.89 656.39 723.89 597.03

2.700 216.20 297.20 378.20 459.20 540.20 621.20 702.20 783.20 864.20 945.20

3.150 247.02 341.52 436.02 530.52 625.02 719.52 814.02 908.52 1003.02 1097.52

3.600 276.35 384.35 492.35 600.35 708.35 816.35 924.35 1032.35 1140.35 1248.35

4.050 425.70 547.20 668.70 790.20 911.70 1033.20 1154.70 1276.20 1397.70

4.500 465.55 600.55 735.55 870.55 1005.55 1140.55 1275.55 1410.55 1545.55

4.950 503.92 652.42 800.92 949.42 1097.92 1246.42 1394.92 1543.42 1691.92

5.400 702.79 864.79 1026.79 1188.79 1350.79 1512.79 1674.79 1836.79

5.850 751.68 927.18 1102.68 1278.18 1453.68 1629.18 1804.68 1980.186.300 799.08 988.08 1177.08 1366.08 1555.08 1744.08 1933.08 2122.08

6.750 1047.49 1249.99 1452.49 1654.99 1857.49 2059.99 2262.49

7.200 1105.41 1321.41 1537.41 1753.41 1969.41 2185.41 2401.41

7.650 1161.84 1391.34 1620.84 1850.34 2079.84 2309.34 2538.84

8.100 1459.79 1702.79 1945.79 2188.79 2431.79 2674.79

8.550 1526.74 1783.24 2039.74 2296.24 2552.74 2809.24

9.000 1862.21 2132.21 2402.21 2672.21 2942.21

9.450 1939.68 2223.18 2506.68 2790.18 3073.68

9.900 2015.67 2312.67 2609.67 2906.67 3203.67

10.350 2400.67 2711.17 3021.67 3332.17

10.800 2487.18 2811.18 3135.18 3459.18

11.250 2572.20 2909.70 3247.20 3584.70

11.700 3006.73 3357.73 3708.7312.150 3102.27 3466.77 3831.27

12.600 3196.32 3574.32 3952.32

13.050 3680.39 4071.89

13.500 3784.96 4189.96

13.950 3888.05 4306.55

14.400 4421.65

14.850 4535.2615.300 4647.38


Mn > Mu/f

4000

60,000

( )

+=

yy

c

ff

f

000,87

000,8785.075.0 '1max

br

yy

c

ff

f 2003'

min =r

7/31/2019 SP-17(05)

28/35



and ACI 318R-95 Section 10.3.1-10.3.2

f'c = psi Mn = 3.3333 Asd - 1.3072 As2

,k-ft

fy = psi


6 12 18 24 30 36 42 48 54 60 66 72

Ast&s 0.160 0.280 0.400 0.520 0.640 0.760 0.880 1.000 1.120 1.240 1.360 1.480

Asmin 0.318 0.636 0.955 1.273 1.591 1.909 2.227 2.546 2.864 3.182 3.500 3.818

Asmax 2.620 5.241 7.861 10.481 13.101 15.722 18.342 20.962 23.582 26.203 28.823 31.443

As0.950 17.82 36.82 42.09 56.34 70.59 84.84 99.09

1.900 33.28 71.28 109.28 147.28 185.28 168.35 196.85 225.35 253.85 282.35 310.85 339.35

2.850 103.38 160.38 217.38 274.38 331.38 388.38 445.38 378.78 421.53 464.28 507.03

3.800 133.12 209.12 285.12 361.12 437.12 513.12 589.12 665.12 741.12 817.12 673.38

4.750 160.51 255.51 350.51 445.51 540.51 635.51 730.51 825.51 920.51 1015.51 1110.51

5.700 299.53 413.53 527.53 641.53 755.53 869.53 983.53 1097.53 1211.53 1325.53

6.650 341.19 474.19 607.19 740.19 873.19 1006.19 1139.19 1272.19 1405.19 1538.19

7.600 380.50 532.50 684.50 836.50 988.50 1140.50 1292.50 1444.50 1596.50 1748.50

8.550 588.44 759.44 930.44 1101.44 1272.44 1443.44 1614.44 1785.44 1956.44

9.500 642.03 832.03 1022.03 1212.03 1402.03 1592.03 1782.03 1972.03 2162.03

10.450 693.25 902.25 1111.25 1320.25 1529.25 1738.25 1947.25 2156.25 2365.25

11.400 970.12 1198.12 1426.12 1654.12 1882.12 2110.12 2338.12 2566.12

12.350 1035.62 1282.62 1529.62 1776.62 2023.62 2270.62 2517.62 2764.6213.300 1364.77 1630.77 1896.77 2162.77 2428.77 2694.77 2960.77

14.250 1444.56 1729.56 2014.56 2299.56 2584.56 2869.56 3154.56

15.200 1521.99 1825.99 2129.99 2433.99 2737.99 3041.99 3345.99

16.150 1920.06 2243.06 2566.06 2889.06 3212.06 3535.06

17.100 2011.76 2353.76 2695.76 3037.76 3379.76 3721.76

18.050 2101.11 2462.11 2823.11 3184.11 3545.11 3906.11

19.000 2568.10 2948.10 3328.10 3708.10 4088.10

19.950 2671.74 3070.74 3469.74 3868.74 4267.74

20.900 2773.01 3191.01 3609.01 4027

Documents

SP-17(05)