Page 269 - Handbook of Civil Engineering Calculations, Second Edition

2.54 REINFORCED AND PRESTRESSED CONCRETE ENGINEERING AND DESIGN

FIGURE 31

is in equilibrium, the left portion also induces compressive stresses on the concrete at C,
these stresses having a resultant that is numerically equal to and collinear with F i .
2. Express the prestress shear and moment in terms of F i
Using the sign convention described, express the prestress shear and moment in terms
of F i and . (The latter is positive if the slope of the trajectory is positive.) Thus V p
F i sin ; M p F i e cos .
3. Compute the prestress shear and moment
Since is minuscule, apply these approximations: sin tan , and cos 1. Then
V p F i tan (53)

Or, V p 300,000(0.014) 4200 lb ( 18,681.6 N).
Also,

M p F i e (54)
Or, M p 300,000(8) 2,400,000 in.·lb ( 271,152 N·m).

STRESSES IN A BEAM WITH
STRAIGHT TENDONS

A 12 18 in. (304.8 457.2 mm) rectangular beam is subjected to an initial prestressing
force of 230 kips (1023.0 kN) applied 3.3 in. (83.82 mm) below the center. The beam is
on a simple span of 30 ft (9.1 m) and carries a superimposed load of 840 lb/lin ft
(12,258.9 N/m). Determine the initial and final stresses at the supports and at midspan.
Construct diagrams to represent the initial and final stresses along the span.