Page 304 - Handbook of Civil Engineering Calculations, Second Edition

PRESTRESSED CONCRETE 2.89

TABLE 5. Calculations for Two-Span Continuous Beam: Part b
Section 1 2 3 4 B
e con , in. (mm) 21.12 26.88 17.28 7.68 48.00
(536.4) ( 682.8) ( 438.9) ( 195.1) ( 1,219.2)
f bp , lb/sq.in. (kPa) 2,116 2,503 1,857 178 2,535
( 14,588) ( 17,256) ( 12,802) ( 1,227) ( 17,476)
f tp , lb/sq.in. (kPa) 37 142 157 933 2188
( 255) ( 979) ( 1,082) ( 6,660) ( 15,084)
0.85f bp , lb/sq.in. (kPa) 1,799 2,128 1,578 151 2,155
( 12,402) ( 14,670) ( 10,879) ( 1,041) ( 14,857)
0.85f tp , lb/sq.in. (kPa) 31 121 133 793 1,860
( 214) ( 834) ( 917) ( 5,467) ( 12,823)
f bi , lb/sq.in. (kPa) 1,157 1,282 1,072 527 355
( 7,976) ( 8,838) ( 7,390) ( 3,633) ( 2,447)
f bf , lb/sq.in. (kPa) 149 65 51 193 1,305
( 1,027) ( 448) ( 352) ( 1,331) ( 8,997)
f ti , lb/sq.in. (kPa) 481 423 520 772 1,180
( 3,316) ( 2,916) ( 3,585) ( 5,322) ( 8,135)
f tf , lb/sq.in. (kPa) 794 894 886 774 260
( 5,474) ( 6,163) ( 6108) ( 5,336) ( 1,792)

final stress at 2 and the allowable value of 60 lb/sq.in. ( 413.7 kPa) arises from the de-
gree of precision in the calculations.)
With the exception of f bi at B, all stresses at the boundary sections lie within the allow-
able range.
19. Locate the section at which f bi = –60 lb/sq.in. (–413.7 kPa)
Since f bp and f bw vary parabolically across the span, their sum f bi also varies in this manner.
Let x denote the distance from the interior support to a given section. Apply Eq. 66 to find the
equation for f bi using the initial-stress values at sections B, 3, and 1. Or, 355 2 1072
1157 1342 ( 9253.1 kPa); 3( 355) 4(1072) 1157 4196 ( 28,931.4 kPa); f bi
2
2684(x/96) 4196x/96 355. When f bi 60 ( 413.7), x 7.08 ft (2.15 m). The
tensile stress at transfer is therefore excessive in an interval of only 14.16 ft (4.32 m).
20. Design the nonprestressed reinforcement over the
interior support
As in the preceding procedures, the member must be investigated for ultimate-strength
capacity. The calculation pertaining to any quantity that varies parabolically across the
span may be readily checked by verifying that the values at uniformly spaced sections
have equal “second differences.” For example, with respect to the values of f bi recorded in
Table 5, the verification is:
1157 1282 1072 527 355
125 210 545 882
335 335 337

The values on the second and third lines represent the differences between successive val-
ues on the preceding line.