Control of cracking - Concrete Structures: Stresses and Deformations - page 381

variation, volumetric change or settlement of supports, a reduction of sti -

ness occurs and the magnitude of the internal forces drops from the values
existing before cracking. Cracking in the

ff

rst and second cases will be
referred to as force-induced and displacement-induced cracking and analysis
of the two types of cracking will be discussed.
Provision of bonded reinforcement of su

fi

cient magnitude and appropri-

ate detailing can e ed value.

The amount of reinforcement required for crack control is discussed below.
The equations presented include two parameters which have to be predicted
by empirical expressions. The two parameters are the mean crack spacing s rm
and the coe

ff ectively limit the mean crack width to any speci fi

ness which con-
crete in tension provides to the state of full cracking where concrete in tension
is ignored (see Equation 8.48). The empirical expressions used here for

cient ζ used to account for the additional sti ff

and
s rm are adopted from codes (see Equation 8.45 and Appendix E); the accuracy
of the predicted crack width depends upon these empirical expressions.
Concrete of very high strength reaching 80-100 MPa (12 000-15 000 psi) is
increasingly used in practice. The increase in f ct can prevent cracking. But if
cracking takes place the crack width will generally be smaller because of the
improved bond between the concrete and the reinforcing bars. Cracking of
high-strength concrete members will be discussed.

ζ

11.2 Variation of tensile strength of concrete
The value of the normal force, N r and/or the bending moment M r at which
cracking of a section occurs, is directly proportional to the tensile strength of
concrete, f ct . It is important to use an appropriate value of f ct to predict
whether or not cracking will occur and to account for the e ff ect of cracking in

the calculations of the probable de ections. The minimum reinforcement

required for control of cracking also depends upon the value f ct , which will be
further discussed in Section 11.5.
The values of f ct determined in tests for a given concrete composition can

fl

di er from the average value f ctm by plus or minus 30 per cent. The value of f ct

in a member varies from section to section; as a result, cracks do not all form
at the same load level. Furthermore, in a structure, the value of f ct is generally
smaller than the value measured by the testing of cylinders made out of the
same concrete; the di

ff

erence between the two values is larger in members of
larger size. This can be attributed to microcracking and to surface shrinkage
cracking resulting from the rapid loss of moisture in freshly placed concrete.
Appendix A includes equations for f ct according to codes and technical
committee reports.

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