Control of cracking - Concrete Structures: Stresses and Deformations - page 402

subjected to two symmetrically located equal forces. The results are given for
two load levels represented by the ratio σ s2 is steel stress at a

cracked section in the central part of the span (zone of constant bending) and
f y is the yield strength of the steel (460 MPa).
The empirical equations given in some codes to predict crack spacing or to
account for tension sti

σ s2 / f y ; where

ening do not accurately represent structures made of
HSC. This status will no doubt change because concrete strength higher than
50 MPa (7000 psi) and reaching up to 80 or 100 MPa (12 000 or 15 000 psi) is
increasingly used in modern structures.

ff

11.10 Examples worked out in British units

Example 11.2 Prestressed section: crack width calculation
Figure 11.9 shows the stress distribution in a prestressed concrete sec-
tion, at time t , after occurrence of creep, shrinkage and relaxation (the
same cross-section was analysed in Example 2.2, Fig. 2.6). Find the
crack width after application of live-load bending M 7000 kip-in.

(790 kN-m) about an axis through reference point O. Use the follow-
ing data:

=

σ cO ( t ) = − 0.360 ksi ( − 2.48 MPa); γ ( t ) = − 6.38 × 10 −3 ksi/in

( − 1.73 MPa/m); E s = 29 000 ksi (200 GPa), for all reinforcements, α ( t ) =

E s / E c ( t ) = 7; mean crack spacing s rm = 16 in (400 mm); interpolation

coe 0.9.

Properties of the transformed non-cracked section at time t :

cient, ζ =

Figure 11.9 Prestressed cross-section analysed to determine crack width after
application of live-load bending moment (Example 11.2).