Design for serviceability of prestressed concrete - Concrete Structures: Stresses and Deformations - page 419

12.7 Residual opening of cracks
Consider a prestressed concrete member containing non-prestressed re-
inforcement. While the sustained stress,

bre of a cross-
section is compressive, assume that the member is subjected to cyclic loads
producing cyclic stress change at the same

σ perm at extreme fi

fi bre. Assume that the maximum

value, ect of live load and/or tem-

perature variation. It is assumed here that the value

∆ σ represents in practice the transient e ff

is calculated for a
noncracked section. Experiments and observations have shown that in each
load cycle the crack opens and closes and the width varies between w max and
w res ; where the former is the maximum width and the latter is a residual crack
width , caused by a permanent damage of the bond between the concrete and
the reinforcement.
Experiments 5 on a prestressed member subjected to axial tension produced
by a displacement controlled actuator show that the residual crack width,
w res is highly dependent upon the sustained compressive stress,

∆ σ

σ perm . Figure

12.6 shows the results of a series of tests in which σ perm is varied between 0

and σ perm is varied from

zero (reinforced non-prestressed member) to 3.5 MPa, w res varies from
0.12 mm to almost zero. The ordinates plotted in the graph are crack widths
measured after 9000 cycles; the widths measured after one cycle are not sub-
stantially di

− 3.5 MPa. It can be seen that as the absolute value of

ff erent. The experiments repeated with di ff erent non-prestressed

steel ratio ρ ns ( = A ns /gross concrete cross-sectional area) show that w res is

slightly in ρ ns . This is contrary to what is generally observed for

reinforced non-prestressed elements.
The speci

fl uenced by

ed concrete strength and the diameter of the non-prestressed
bars (for a given

fi

ect on the maximum width of
crack at the peak of the transient stress; however, the same two parameters
have negligible in

ρ ns value) have an important e ff

uence on the residual crack width w res .
The residual crack width may be considered an important parameter in
design, because it is closely related to the durability of the structure. Charac-
teristic limit values, w k res

fl

0.2 to 0.05 mm are recommended or required by
some codes in the design of prestressed concrete structure; the lower value is
for the case when water-tightness is required, as for example the deck slab of
a bridge. The characteristic value w k res is assumed to be equal to 1.5 times the
mean value obtained in experiments or by analysis.

=

12.8 Water-tightness
Avoiding or limiting leakage is one of the reasons of controlling cracking in
structural members that are permanently or occasionally in contact with
water. Examples of such structures are water tanks, tunnels, parking

fl oors

and bridge decks. The repeated ow of contaminated water, often with

de-icing salts has negative impact on the structures' durability.

fl