Handbook of Civil Engineering Calculations

2. Replace the prestressing
   system with two hypothetical
   systems that jointly induce
   eccentricity moments identical
   with those of the true system
   This constitutes method 2. For this pur-
   pose, consider the beam to be subjected to
   two prestressing forces of 96 kips (427.0
   kN) each. One has the parabolic trajectory
   described in the earlier procedure; the oth-
   er has a trajectory that is linear in each FIGURE 54 Prestress.moment ^.
   span, the eccentricities being ea = -0.72 - grams
   (-0.40) = -0.32 in (-8.128 mm), eb, = 0,^8
   and ec = O.


3. Evaluate the prestress
   moments induced by the
   hypothetical system having the
   linear trajectory
   The tendons exert a force on the concrete at A 9 B, and C, but only the force at A causes
   bending moment.
   Thus, Mpa = -Ff 0 = -96,000(-0.32)/12 = 2560 ft-lb (3471.4 N-m). Also, Mp 0 L 1 +
   2Mp 13 (L 1 + L 2 ) + MpcL 2 = O. But Mpc = O; therefore, Mpb = -512 ft-lb (-694.3 N-m); Mpd =
   /2(2560 - 512) = 1024 ft-lb (1388.5 N-m); Mpe = y 2 (-5l2) = -256 ft-lb (-347.1 N-m).


4. Find the true prestress moments by superposing the two
   hypothetical systems
   Thus Mpa = 3200 + 2560 = 5760 ft-lb (7810.6 N-m); Mpd = 4704 + 1024 = 3680 ft-lb
   (-4990.1 N-m); Mpb = 9792 - 512 - 9280 ft-lb (12,583.7 N-m); Mpe = 5024 - 256 - -5280
   ft-lb (-7159.7 N-m); Mpc = 4800 ft-lb (6508.8 N-m).

DESIGN OF TRAJECTORY FOR A TWO-SPAN
CONTINUOUS BEAM

A T beam that is continuous across two spans of 120 ft (36.6 m) each is to carry a uni-
formly distributed live load of 880 Ib/lin ft (12,842.6 N/m). The cross section has these
properties: A = 1440 in^2 (9290.8 cm^2 ); / = 752,000 in^4 (3130.05 dm^4 ); yb = 50.6 in
(1285.24 mm); yt = 23.4 in (594.36 mm). The allowable stresses are: initial, +2400 and

• 60 lb/in^2 (+16,548.0 and -413.7 kPa); final, +2250 and -60 lb/in^2 (+15,513.8 and
  413.7 kPa). Assume that the minimum possible distance from the extremity of the sec-
  tion to the centroidal axis of the prestressing steel is 9 in (228.6 mm). Determine the
  magnitude of the prestressing force, and design the parabolic trajectory (a) using solely
  prestressed reinforcement; (b) using a combination of prestressed and non-prestressed
  reinforcement.

Calculation Procedure:

1. Compute the section moduli, kern distances, and beam weight
   For part a, an exact design method consists of these steps: First, write equations for the

•Original moments

Revised moments