Page 266 - Handbook of Civil Engineering Calculations, Second Edition

PRESTRESSED CONCRETE 2.51

Case 2: surcharge extending to H—p 2370 500 2870 lb/sq.ft.(137.4 kPa); V
6.5[2870 /2(2474 828)] 7920 lb (35,228.1 N) < V allow ; M 12(6.5) [ /2 2870
1
2 1
1 /6(2474 2 828)] 379,000 in.·lb (42,819.4 N·m); A s 2.12(383/538) 1.51 sq.in.
2
(9.742 cm ).
1
To maintain uniform bar spacing throughout the member, use no. 8 bars 5 /2 in. (139.7
mm) on centers. In the heel, tension occurs at the top of the slab, and A s 1.72 sq.in.
2
(11.097 cm ); o 6.9 in. (175.26 mm); u 91 lb/sq.in. (627.4 kPa); u allow 186
lb/sq.in. (1282.5 kPa). This is acceptable.
6. Design the toe
For this purpose, assume the absence of backfill on the toe, but disregard the minor modi-
fication in the soil pressure that results. Let V and M denote the shear and bending mo-
ment, respectively, at section C (Fig. 29). The downward pressure p 1.5(150) 225
lb/sq.ft.(10.8 kPa).
Case 1: surcharge extending to G (Fig. 29)—V 3[ /2(3680 2723) 225] 8930
1
2
1
lb (39,720.6 N); M 12(3) [( /6)(2723 2 3680) /2(225)] 169,300 in.·lb
1
(19,127.5 N·m).
Case 2: surcharge extending to H (Fig. 29)—V 9020 lb (40,121.0 N) < V allow ; M
2
169,300 in.·lb (19,127.5 N·m); A s 2.12(169,300/538,000) 0.67 sq.in. (4.323 cm ).
Use no. 5 bars 5 /2 in. (139.7 mm) on centers. Then A s 0.68 sq.in. (4.387 cm ); o
2
1
4.3 in. (109.22 mm); u 166 lb/sq.in. (1144.4 kPa); u allow 422 lb/sq.in. (2909.7 kPa).
This is acceptable.
The stresses in the key are not amenable to precise evaluation. Reinforcement is
achieved by extending the dowels and short bars into the key and bending them.
In addition to the foregoing reinforcement, no. 4 bars are supplied to act as tempera-
ture reinforcement and spacers for the main bars, as shown in Fig. 30.

PART 2
PRESTRESSED CONCRETE

Prestressed-concrete construction is designed to enhance the suitability of concrete as a
structural material by inducing prestresses opposite in character to the stresses resulting
from gravity loads. These prestresses are created by the use of steel wires or strands,
called tendons, that are incorporated in the member and subjected to externally applied
tensile forces. This prestressing of the steel may be performed either before or after pour-
ing of the concrete. Thus, two methods of prestressing a concrete beam are available: pre-
tensioning and posttensioning.
In pretensioning, the tendons are prestressed to the required amount by means of hy-
draulic jacks, their ends are tied to fixed abutments, and the concrete is poured around the
tendons. When hardening of the concrete has advanced to the required state, the tendons
are released. The tendons now tend to contract longitudinally to their original length and
to expand laterally to their original diameter, both these tendencies being opposed by the
surrounding concrete. As a result of the longitudinal restraint, the concrete exerts a tensile
force on the steel and the steel exerts a compressive force on the concrete. As a result of