DESIGN OF A DOUBLE-T ROOF BEAM
The beam in Fig. 39 was selected for use on a simple span of 40 ft (12.2 m) to carry the
following loads: roofing, 12 lb/ft^2 (574.5 N/m^2 ) snow, 40 lb/ft^2 (1915.1 N/m^2 ); total, 52
lb/ft^2 (2489.6 N/m^2 ). The member will be pretensioned with straight seven-wire strands,
Yi6 in (11.11 mm) diameter, having an area of 0.1089 in^2 (0.70262 cm^2 ) each and an ulti-
mate strength of 248,000 lb/in^2 (1,709,960.0 kPa). The concrete strengths are/c' = 5000
lb/in^2 (34,475.0 kPa) and/c; = 4000 lb/in^2 (27,580.0 kPa). The allowable stresses are: ini-
tial, +2400 and -190 lb/in^2 (+16,548.0 and - 1310.1 kPa); final, +2250 and -425 lb/in^2
(+15,513.8 and -2930.4 kPa). Investigate the adequacy of this section, and design the ten-
dons. Compute the camber of the beam after the concrete has hardened and all dead loads
are present. For this calculation, assume that the final value of E 0 is one-third of that at
transfer.
Calculation Procedure:- Compute the properties of the cross section
Let fbfandftf denote the respective stresses at midspan andfbi and/, denote the respective
stresses at the support Previous calculation procedures demonstrated that where the sec-
tion moduli are excessive, the minimum prestressing force is obtained by setting fbf and fti
equal to their allowable values.
Thus,4 = 316 in^2 (2038.8 cm^2 ); /= 7240 in^4 (30.14 dm^4 );^ = 10.98 in (278.892 mm);
yt = 5.02 in (127.508 mm); Sb = 659 in^3 (10,801.0 cm^3 ); St = 1442 in^3 (23,614 cm^3 ); ww =
(316/144)150 = 329 Ib/lin ft (4801.4 N/m). - Calculate the total midspan moment due to gravity loads
and the corresponding stresses
Thus ws = 52(6) = 312 Ib/lin ft (4553.3 N/m); ww, = 329 Ib/lin ft (4801.4 N/m); and Mw +
Ms = (^1 / 8 )(641)(40^2 )(12) = 1,538,000 in-lb (173,763.2 N-m);/^ +fbs = -1,538,000/659 =
-2334 lb/in^2 (-16,092.9 kPa);/^ +fta = +1,538,000/1442 - +1067 lb/in^2 (+7357.0 kPa).
FIGURE 39. Double-T roof beam.