Page 224 - Handbook of Civil Engineering Calculations, Second Edition

REINFORCED CONCRETE 2.9

C u2,max 5.42(40,000) 216,800 lb
(964,326.4 N); s max 216,800/[10(2550)]
8.50 in. (215.9 mm).
2. Compute the ultimate-
moment capacity
Thus, M u,max 0.90[(76,500(19.5 5/2)
216,800(19.5 8.50/2)] 4,145,000
in.·lb (468,300 N·m).
FIGURE 5
DESIGN OF REINFORCEMENT
IN A T BEAM OF GIVEN SIZE

The T beam in Fig. 5 is to resist an ultimate moment of 3,960,000 in.·lb (447,400.8 N·m).
Determine the required area of reinforcement, using f c
3000 lb/sq.in. (20,685 kPa) and
f y 40,000 lb/sq.in. (275,800 kPa).

Calculation Procedure:

1. Obtain a moment not subject to reduction
From the previous calculation procedure, the ultimate-moment capacity of this member is
4,145,000 in.·lb (468,300 N·m). To facilitate the design, divide the given ultimate moment
M u by the capacity-reduction factor to obtain a moment M u
that is not subject to reduction.
Thus M u
3,960,000/0.9 4,400,000 in.·lb (497,112 N·m).
2. Compute the value of s associated with the given moment
From step 2 in the previous calculation procedure, M u1
1,300,000 in.·lb (146,874 N·m).
Then M u2
4,400,000 1,300,000 3,100,000 in.·lb (350,238 N·m). But M u2
2550(10s)(19.5 s/2), so s 7.79 in. (197.866 mm).
3. Compute the area of reinforcement
1
Thus, C u2 M u2
/(d /2s) (19.5 3.90) 198,700 lb (883,817.6 N). From step 1 of
the previous calculation procedure, C u1 76,500 lb (340,272 N); T u 76,500 198,700
275,200 lb (1,224,089.6 N); A s 275,200/40,000 6.88 sq.in. (174.752 mm).
4. Verify the solution
To verify the solution, compute the ultimate-moment capacity of the member. Use the
notational system given in earlier calculation procedures. Thus, C uf 16(5)(2550)
204,000 lb (907,392 N); C uw 275,200 204,000 71,200 lb (316,697.6 N); m 71,200/
[2550(10)] 2.79 in. (70.866 mm); M u 0.90 [204,000(19.5 2.5) 71,200(19.5 5
1.40)] 3,960,000 in.·lb (447,400.8 N·m). Thus, the result is verified because the com-
puted moment equals the given moment.

REINFORCEMENT AREA FOR A DOUBLY
REINFORCED RECTANGULAR BEAM

A beam that is to resist an ultimate moment of 690 ft·kips (935.6 kN·m) is restricted to a
14-in. (355.6-mm) width and 24-in. (609.6-mm) total depth. Using f c
5000 lb/sq.in. and
f y 50,000 lb/sq.in. (344,750 kPa), determine the area of reinforcement.