Page 297 - Handbook of Civil Engineering Calculations, Second Edition

2.82 REINFORCED AND PRESTRESSED CONCRETE ENGINEERING AND DESIGN

2. Analyze the eccentricities
All eccentricities have thus been altered by an amount directly proportional to the dis-
tance from the adjacent end support to the given section, and the trajectory has undergone
a linear transformation. The advantage accruing from plotting a concordant trajectory is
shown in the next calculation procedure.

DESIGN OF TRAJECTORY TO OBTAIN
ASSIGNED PRESTRESS MOMENTS

The prestress moments shown in Fig. 52 are to be obtained by applying an initial pre-
stressing force of 72 kips (320.3 kN) with an eccentricity of 2 in. ( 50.8 mm) at B. De-
sign the trajectory.

Calculation Procedure:
1. Plot a concordant trajectory
Set e M p /F i , or e a 3200(12)772,000 0.533 in. ( 13.5382 mm); e d 0.784
in. (19.9136 mm); e b 1.632 in. ( 41.4528 mm); e e 0.837 in. (21.2598 mm); e c
0.800 in. ( 20.32 mm).
2. Set e b = desired eccentricity, and transform the trajectory
linearly
Thus, e a 0.533 in. ( 13.5382 mm); e c 0.800 in. ( 20.32 mm); e d 0.784
1 /2(2.000 1.632) 0.600 in. ( 15.24 mm); e e 0.837 0.184 0.653 in.
( 16.5862 mm).

EFFECT OF VARYING ECCENTRICITY
AT END SUPPORT

For the beam in Fig. 50, consider that the parabolic trajectory in span AB is displaced
thus: e b is held constant as e a is changed to 0.72 in. ( 18.288 mm), the eccentricity at
every intermediate section being decreased algebraically by an amount directly propor-
tional to the distance from that section to B. Compute the prestress moment at the sup-
ports and at midspan caused by a prestressing force of 96 kips (427.0 kN).

Calculation Procedure:

1. Apply the revised value of e a ; repeat the calculations
of the earlier procedure
Thus, M pa 5760 ft·lb (7810.6 N·m); M pd 3680 ft·lb ( 4990.1 N·m); M pb 9280
ft·lb (12,583.7 N·m); M pe 5280 ft·lb ( 7159.7 N·m); M pc 4800 ft·lb (6508.8 N·m).
The change in prestress moment caused by the displacement of the trajectory varies
linearly across each span. Figure 54 compares the original and revised moments along
AB. This constitutes method 1.