Page 284 - Handbook of Civil Engineering Calculations, Second Edition

PRESTRESSED CONCRETE 2.69

3. Determine whether the section moduli are excessive
Do this by setting f bf and f ti equal to their allowable values and computing the corresponding
values of f bi and f tf . Thus, f bf 0.85f bp 2334 425; therefore, f bp 2246 lb/sq.in.
( 15,486.2 kPa); f ti f tp 190 lb/sq.in. ( 1310.1 kPa); f bi f bp 2246 < 2400
lb/sq.in.( 16,548.0 kPa). This is acceptable. Also, f tf 0.85( 190) 1067 905 < 2250
lb/sq.in. ( 15,513.8 kPa); this is acceptable. The section moduli are therefore excessive.
4. Find the minimum prestressing
force and its eccentricity
Refer to Fig. 40. Thus, f bp 2246
lb/sq.in. ( 15,486.2 kPa); f tp 190
lb/sq.in. ( 1310.1 kPa); slope of AB
2246 ( 190)/16 152.3 lb/(sq.in.·in.)
(41.33 MPa/m); F i /A CD 2246
10.98 (152.3) 574 lb/sq.in. (3957.7
kPa); F i 574(316) 181,400 lb
(806,867.2 N); slope of AB F i e/I
152.3; e 152.3(7240)/181,400 6.07
in. (154.178 mm).
5. Determine the number of FIGURE 40. Prestress diagram.
strands required, and establish
their disposition
In accordance with the ACI Code, allowable initial force per strand 0.1089
(0.70)(248,000) 18,900 lb (84,067.2 N); number required 181,400/18,900 9.6.
Therefore, use 10 strands (5 in each web) stressed to 18,140 lb (80,686.7 N) each.
Referring to the ACI Code for the minimum clear distance between the strands, we
3
7
find the allowable center-to-center spacing 4( /16) 1 /4 in. (44.45 mm). Use a 2-in.
(50.8-mm) spacing. In Fig. 41, locate the centroid of the steel, or y (2 2 1 4)/5
1.60 in. (40.64 mm); v 10.98 6.07 1.60 3.31 in. (84.074 mm); set v 3 /16 in.
5
(84.138 mm).
6. Calculate the allowable ultimate moment of the member
in accordance with the ACI Code
2
Thus, A s 10(0.1089) 1.089 sq.in. (7.0262 cm ); d y t e 5.02 6.07 11.09
in. (281.686 mm); p A s /(bd) 1.089/[72(11.09)] 0.00137.

FIGURE 41. Location of tendons.