Page 244 - Handbook of Civil Engineering Calculations, Second Edition

REINFORCED CONCRETE 2.29

Calculation Procedure:

1. Identify the controlling stress
2
1
Thus, M ( /8)(4100)(22) (12) 2,977,000 in.·lb (336,341.5 N·m). From the previous
calculation procedure, M b 3,141,000 in.·lb (354,870.2 N·m). Since M b > M, the beam
size is slightly excessive with respect to balanced design, and the steel will therefore be
stressed to capacity under the stipulated load.
2. Compute the area of reinforcement
As an approximation, this area may be found by applying the value of jd associated with
balanced design, although it is actually slightly larger. From the previous calculation pro-
cedure, jd 14.61 in. (371.094 mm). Then A s 2,977,000/[20,000(14.61)] 10.19 sq.in.
2
(65.746 cm ).
3. Verify the design by computing the member capacity
Thus, nA s 101.9 sq.in. (657.46 cm ); kd (330 2.5 101.9 16.5)/(330 101.9)
2
5
5.80 in. (147.32 mm); z ( /3)(5.80 2 0.80)/(5.80 0.80) 1.87 in. (47.498 mm);
jd 14.63 in. (371.602 mm); M allow 10.19(20,000)(14.63) 2,982,000 in.·lb
(336,906.4 N·m). This is acceptable.

REINFORCEMENT FOR DOUBLY
REINFORCED RECTANGULAR BEAM

A beam of 4000-lb/sq.in. (27,580-kPa) concrete that will carry a bending moment of 230
ft·kips (311.9 kN·m) is restricted to a 15-in. (381-mm) width and a 24-in. (609.6-mm)
total depth. Design the reinforcement.

Calculation Procedure:

1. Record the pertinent beam data
In Fig. 18, where the imposed moment is substantially in excess of that corresponding to
balanced design, it is necessary to reinforce the member in compression as well as ten-
sion. The loss in concrete area caused by the presence of the compression reinforcement
may be disregarded.

FIGURE 18. Doubly reinforced beam.