Q 2 max = 5.42(40,000) = 216,800 Ib
(964,326.4 N); smax = 216,800/(10(255O)]
= 8.50 in (215.9 mm).- Compute the ultimate-
moment capacity
Thus, MMmax = 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
INA TBEAM 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/,' = 3000 lb/in^2 (20,685 kPa) and/J, =
40,000 lb/in^2 (275,800 kPa).Calculation Procedure:- 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 11 by the capacity-reduction factor to obtain a moment MJ that is not subject to reduc-
tion. Thus M'u = 3,960,000/0.9 = 4,400,000 in-lb (497,112 N-m). - Compute the value of s associated with the given moment
From step 2 in the previous calculation procedure, MJ 1 = 1,300,000 in-lb (146,874 N-m).
Then MJ 2 = 4,400,000 - 1,300,000 = 3,100,000 in-lb (350,238 N-m). But MJ 2 =
2550(10^(19.5-5/2), so s = 7.79 in (197.866 mm). - Compute the area of reinforcement
Thus, Cu2 = MJ 2 AW-^1 As) = 3,100,0007(19.5 - 3.90) = 198,700 Ib (883,817.6 N). From
step 1 of the previous calculation procedure, C 111 = 76,500 Ib (340,272 N); Tu = 76,500 +
198,700 = 275,200 Ib (1,224,089.6 N); As = 275,200/40,000 = 6.88 in^2 (174.752 mm). - Verify the solution
To verify the solution, compute the ultimate-moment capacity of the member. Use the no-
tational system given in earlier calculation procedures. Thus, Cuf = 16(5)(2550) =
204,000 Ib (907,392 N); Cuw = 275,200 - 204,000 = 71,200 Ib (316,697.6 N); m =
71,200/[2550(1O)] = 2.79 in (70.866 mm); MM = 0.90 [204,000 (19.5 - 2.5) + 71,200(19.5
- 5 - 1.4O)] = 3,960,000 in-lb (447,400.8 N-m). Thus, the result is verified because the
computed moment equals the given moment.
REINFORCEMENTAREA FORA 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 ft = 5000 lb/in^2 and
fy = 50,000 lb/in^2 (344,750 kPa), determine the area of reinforcement.