Page 300 - Handbook of Civil Engineering Calculations, Second Edition

PRESTRESSED CONCRETE 2.85

TABLE 4. Calculations for Two-Span Beam: Part a
Section 1 2 3 4 B
0.0675 0.0950 0.0825 0.0300 0.0625
1 C 1
0.0125 0.0250 0.0375 0.0500 0.0625
2 C 2
0.0550 0.0700 0.0450 0.0200 0.1250
3 C 3
4 f bw , lb/sq.in. 959 1,221 785 349 2,180
(kPa) ( 6,611) ( 8,418) ( 5,412) ( 2406) ( 15,029)
5 f bs1 , lb/ 691 972 844 307 640
sq.in. (kPa) ( 4,764) ( 6,701) 5,819) ( 2,116) ( 4,412)
6 f bs2 , lb/ 128 256 384 512 640
sq.in. (kPa) ( 882) ( 1,765) ( 2,647) ( 3,530) ( 4,412)
7 f tw , lb/sq.in. 444 565 363 161 1,008
(kPa) ( 3,060) ( 3895) ( 2,503) ( 1,110) ( 6,949)
8 f ts1 , lb/sq.in. 319 450 390 142 296
(kPa) ( 2,199) ( 3,102) ( 2689) ( 979) ( 2,041)
9 f ts2 , lb/sq.in. 59 118 177 237 296
(kPa) ( 407) ( 813) ( 1,220) ( 1,634) ( 2,041)
10 e con , in. 17.19 21.87 14.06 6.25 39.05
(mm) ( 436.6) ( 555.5) ( 357.1) ( 158.8) ( 991.9)
11 f bp , lb/sq.in. 2,148 2,513 1,903 318 2,243
(kPa) ( 14,808) ( 17,325) ( 13,119) ( 2,192) ( 15,463)
12 f tp , lb/sq.in. 185 16 298 1,031 2,215
(kPa) ( 128) ( 110) ( 2,054) ( 7,108) ( 15,270)
0.85f bp
13 lb/sq.in. 1,826 2,136 1,618 270 1,906
(kPa) ( 12,588) ( 14,726) ( 11,154) ( 1,861) ( 13,140)
0.85f tp
14 lb/sq.in. 157 14 253 876 1,883
(kPa) ( 1,082) ( 97) ( 1,744) ( 6,039) ( 12,981)
At midspan: C 3 0.0625 and e con 19.53 in. (496.1 mm)

Since the gravity loads induce the maximum positive moment at section 2 and the
maximum negative moment at section B, the prestressing force and its trajectory will be
designed to satisfy the stress requirements at these two sections. (However, the stresses at
all boundary sections will be checked.) The Magnel diagram for section 2 is similar to
that in Fig. 37, but that for section B is much different.
3. Compute the value of C 3 at midspan
Thus, C 3 0.0625.
4. Apply the moment coefficients to find the gravity-load stresses
2
Record the results in Table 4. Thus M w C 3 (1500)(120) (12) 259,200,000C 3 in.·lb
(29.3C 3 kN·m); f bw 259,200,000C 3 /14,860 17,440C 3 ; f bs1 10,230C 1 ; f bs2
10,230C 2 ; f tw 8065C 3 ; f ts1 4731C 1 ; f ts2 4731C 2 .
Since S t far exceeds S b , it is manifest that the prestressing force must be designed to
confine the bottom-fiber stresses to the allowable range.