Self-sensing concrete with nanomaterials - Nanotechnology in Eco-efficient Construction - page 71

subjected to the cracking load may therefore be calculated according to Eqs
[4.21]-[4.25]. The displacement of IGNA ( y 0 ) cr under the cracking load is
obtained from Eq. [4.19] and the degree of damage D of the concrete beam
under the cracking load can be evaluated according to Eq. [4.27].

4.6 Diphasic electrical conductive materials

Specimen BF28 is taken as an example for diphasic electric conductive
materials (the combination of NCB0.2% and CF0.8%). The beam dimen-
sions are given as follows: section width ( b ) = 100 mm, section depth (2 h )

= 300 mm. The loading history of the beam with

BF28 is illustrated in Fig. 4.4b. The elastic modulus ( E ) is 3.0

100 mm, beam length ( L ) =

× 10 4 N/mm 2 ;

the cracking load ( N cr ) is 14.5 kN; the parameters m ( = 13.45), n ( = 68.90)

and p ( -16.11) may be obtained from Table 4.7 before the beam is sub-

jected to loading N (at the beginning ( t

=

= 0 )), R 0 = 1190 Ω ; and ε

2

= 0, y 0 =

0, D 0. When the beam is subjected to load N , concrete damage occurs

and the resistance of the electric conduction concrete t R ( t ), can be mea-
sured at any time. The values of the degree of damage D , the stresses and
strains and the displacement of IGNA y 0 of diphasic electric conductive
concrete beam BF28 at different load times are calculated using Eqs [4.21]-
[4.27] and summarized in Table 4.8.
From Table 4.8 and Fig. 4.4, the following points may be observed:

=

• Prior to cracking in a fl exural beam, the electrical resistance ( R ) usually
declines with an increase in the loading magnitude and duration.
• The absolute value of the FCR in a fl exural beam increases with an
increase in the loading magnitude and duration.

• Both the degree of damage ( D ) and the strain of IGNA ( ε 2 ) increase

with an increase of the absolute value of FCR. At a time of 1655 seconds

￿ ￿ ￿ ￿ ￿ ￿

Table 4.8 Results of measured resistance, calculated degree of damage, and
the effective stress and strain of BF28

Variable factors Calculation results

Time t (s) 269 475 836

R ( Ω , measured) 1142 1119 1095

|FCR| (%) 4 6 8

D (%) 26.00 42.18 49.53

ε 2 (10 − 6 ) 7.23 19.67 34.86

y 0 (mm) − 2.38 − 4.12 − 4.91

˜ 1 (N/mm 2 )

σ − 4.35 − 6.58 − 8.08

˜ 3 (N/mm 2 )

σ 4.78 7.76 10.18

ε 1 (10 − 6 ) − 144.98 − 219.22 − 269.42

ε 3 (10 − 6 ) 159.47 258.59 339.17