Calculation Procedure:- Compute the properties of the cross section
Since the tendons will be curved, the initial stresses at midspan may be equated to the al-
lowable values. The properties of the cross section are A = 856 in
2
(5522.9 cm
2
); / =
394,800 in
4
(1643 dm
4
); yb = 34.6 in (878.84 mm); yt = 21A in (695.96 mm); Sb = 11,410
in
3
(187,010 cm
3
); St = 14,410 in
3
(236,180 cm
3
); ww = 892 Ib/lin ft (13,017.8 N/m). - Calculate the stresses at midspan caused by gravity loads
Thus/^ = -950 lb/in
2
(-6550.3 kPa);/fe = -2300 lb/in
2
(-15,858.5 kPa);/^ = +752 lb/in
2
(+5185.0 kPa);.4 = + 1820 lb/in^2 (+12,548.9 kPa). - Test the section adequacy
To do this, equate^and fti to their allowable values and compute the corresponding val-
ues of/k andftf. Thusfbf = 0.85/^ - 950 - 2300 = -425;/, =ftp + 752 = -190; therefore,
fbp = +3324 lb/in
2
(+22,919.0 kPa) andftp = -942 lb/in
2
(-6495.1 kPa);/w = +3324 - 950
= +2374 < 2400 lb/in
2
(16,548.0 kPa). This is acceptable. And^-= 0.85(-942) + 752 +
1820 = + 1771 < 2250 lb/in^2 (15,513.8 kPa). This is acceptable. The section is therefore
adequate. - Find the minimum prestressing force and its eccentricity
at midspan
Do this by applying the prestresses found in step 3. Refer to Fig. 43. Slope of AB = [3324
- (-942)]/62 = 68.8 Ib/(in^2 -in) (18.68 kPa/mm); F 1 IA = CD = 3324 - 34.6(68.8) = 944
lb/in^2 (6508.9 kPa); F 1 = 944(856) = 808,100 Ib (3,594,428.8 N); slope of AB = F 1 ClI =
68.8; e = 68.8(394,800)/808,100 = 33.6 in (853.44 mm). Sinceyb = 34.6 in (878.84 mm),
this eccentricity is excessive.
- Select the maximum feasible eccentricity; determine the
minimum prestressing force associated with this value
Trye = 34.6 - 3.0 = 31.6 in (802.64 mm). To obtain the minimum value OfF 1 , equate/6/to
its allowable value. Check the remaining stresses. As before,/^ = +3324 lb/in^2 (+22,919
kPa). But fa, = F,-/856 + 31.6F 1 Vl 1,410 = +3324; therefore F 1 = 844,000 Ib (3754.1 kN).
Also,/0, = -865 lb/in^2 (-5964.2 kPa);/w = +2374 lb/in^2 (+16,368.7 kPa);/, = -113 lb/in^2
(-779.1 kPa);/^ = + 1837 lb/in^2 (+12,666.1 kPa). - Design the tendons, and establish their pattern at midspan
Refer to a table of the properties of Freyssinet cables, and select 12/0.276 cables. The des-
ignation indicates that each cable consists of 12 wires of 0.276-in (7.0104-mm) diameter.
FIGURE 43. Prestress diagram.