Control of cracking - Concrete Structures: Stresses and Deformations - page 390

N - graph (Fig. 11.3) will exhibit a large drop in the value of N at the forma-

tion of the

ε

N r1 ). Subsequent increase in N will
occur, at a relatively low rate, to reach a limiting value equal to N y

fi rst crack (at ε = ε 1 and N =

A s f y <
N r1 ; where f y is the yield strength. At this point, the mean crack width w m

=

=

s rm ζ f y / E s . Any further increase of the imposed displacement, D will be accom-

panied by an increase of the same magnitude in the crack width, while the
value of N remains constant equal to N y and no further cracks develop. Thus,
when the steel ratio ρ min, y a single, usually excessively wide, crack occurs.

Equations will be derived in Section 11.5 for

ρ ≤

ρ min, y in reinforced concrete

sections with or without prestressing.

Experimental veri cation

Jaccoud 4 conducted experiments on reinforced concrete prisms subjected to
an imposed axial end displacement (Fig. 11.4). The geometrical and material
data are given in the

fi

gure; all parameters have values approximately equal to
the values employed in the above example, with the exception of A s which is
reduced, but is still su

fi

cient to avoid yielding. Fig. 11.4 compares the graphs

of =

constant (as observed for this specimen) and using Equations (11.12) to
(11.18).

σ c ( = N/A 1 ) versus ε obtained by experiment and by analysis setting f ct i

Figure 11.4 Comparison of analysis with experimental results of Jaccoud (see Note 2,
page 406). A prism subjected to imposed end displacement.