5 D. Steel required for reinforcement:

Select Rebar Table 7.2 page 38 Leet

# 10 1.27 sq in

# 10 1.27 sq in

# 9 1.00 sq in

Total 3.54 sq in

As actual = 3.54 sq in > 3.37 in As required

O. K.

If we add

h = d + radius rebar + concrete coverage

h = 15.6 in + 0.635 in + 2 in

h = 18.235 in

Although a depth of 18 in will result in a slightly

smaller d if 2 in of coverage is maintained, the

moment capacity will still be adequate since

As supplied is greater than the As required.

Normally the designer can neglect small differences of this magnitude.

The built-in safety factor of the design process

will take care of it.

5 E. Check z for control of crack width

As a reinforced concrete beam deflects, the tension side of the beam cracks wherever the low tensile strength of the concrete is exceeded.

The maximum crack width the designer should allow depends on exposuure conditions:

Exposure Max. Crack Width

seawater or

wet dry cyles 0.006 in (0.15 mm)

= exposed 0.008 in (0.20 mm) max

protected 0.016 in (0.41 mm)

are permitted by ACI code but may not be

acceptable for the architect who desires a

smooth monolithic concrete surface.

for steel with a yield point up to 40 kips/in

use Gergely-Lutz Eq. 3.28 p. 81 Leet

w = maximum width of crack in 1000th/in

For steel with a yield point over 40 kips/in

use modified Gergely-Lutz Eq. 3.29 p. 81 Leet

z = w / 0.091

fs = stress in steel due to service load

fs = 0.6 x fy

fy = yield strength of rebar

fs = 0.6 x 50 kips/sq in

fs = 30 kips/sq in

dc = distance from tension surface to center

of the row of reinforcing bars closest

to the outside surface

2.4 in was assume

2 in + radius 0.635in = 2.635 in

A = effective tension area of concrete divided

by the number of reinforcing bars

A = AREA OF CONCRETE IN TENSION

NUMBER OF BARS

A = (COVERAGE +RADIUS)x 2 x b

As / cross sectional area of bar

A = (2.4 in) (2) (12 in)

3.53 in / 1.27 in

A = 20.7 sq in

z = 110 kips/in

ACI code (p. 81 Leet) specifies that z not to exceed

exterior exposure 145 kips/in

0.013 in (0.33mm) crack

interior exposure 175 kips/in

0.016 in (0.41mm) crack

z = 110 kips/in <145 kips/in OK

5 F. Check Rebar spacing:

Spacing between bars must not be less than

1 inch or 1 bar diameter .

Allowing 2 inch of side cover on each side.

The available spacing between bars equals.

b - ( side cover (2) + n rebar diameters) = s

n - 1

12 - (2 in (2) + 2 (10/8) + 1(9/8) = 2.2 in

2 spaces

s = 2.2 in > 10/8 > 1 inch OK