Civil Engineering Reference
In-Depth Information
TABLE 2.2
Selection of Factors
α
and
β
1
f
c
, psi
≤4000
5000
6000
7000
≥8000
0.72
0.68
0.64
0.60
0.56
α
0.425
0.400
0.375
0.350
0.325
β
0.85
0.80
0.75
0.70
0.65
β
1
= 2 β
0.85
0.85
0.85
0.86
0.86
γ = α/ β
1
Source:
Kaar, Hanson, and Capell (1978).
2.2.4.2 Behavior of Concrete in Tension
Concrete experiences very little hardening or nonlinear plasticity, if any, prior to crack-
ing or fracture. The ultimate strength of concrete in tension is relatively low, and cracked
member behavior is significantly different, which is why the prediction of cracking
strength is critical. Three distinct tests estimate concrete tensile strength: direct tension
test, split-cylinder test, and flexure test. In direct tension test, stress concentration at the
grips and load axis misalignment yield lower strength. The split-cylinder test uses a
6 × 12 in. (150 × 300 mm) standard cylinder on its side subjected to vertical compression
generating splitting tensile stresses of
≠
d
2
. More reasonable estimates of tensile strength
are generated by the split-cylinder test. A flexure test is the most widely used test to
measure the modulus of rupture (
f
r
). This test assumes that concrete is elastic at frac-
ture, and the bending stress is known to be localized at the tension face. Accordingly,
results are expected to slightly overestimate tensile strength. According to ACI 318-11,
the modulus of rupture (
f
r
) is
f
=λ
7.5
f
in psi
(2.22)
r
c
f
=λ
0.62
f
in MPa
(2.23)
r
c
For normal weight concrete, λ = 1.0 (Section 8.6.1, ACI 318-11)
For sand-lightweight concrete, λ = 0.85
For all lightweight concrete, λ = 0.75
If
f
ct
is given for lightweight concrete, λ=
f
≤
1.0
ct
'
6.7
f
c
The value of λ can be determined from ACI 318-11 based on two alternative approaches
presented in commentary R8.6.1. Typical values for direct tensile strength
f
()
for normal weight concrete are
35
−
f
c
in psi and for light weight concrete are
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