## 1564Concrete Tensile Strength

Tensile strength is an important parameter used to calculate cracking loads and to determine the required minimum amounts of reinforcement. ACI 318-02 uses the modulus of rupture f to determine the flexural cracking moment from the following expressions:

ACI Committee 363 [78] reported the following relationships for fr, which was recommended by Carrasquillo et al. [77], for concrete having a compressive strength between 3,000 and 12,000 psi (20 to 80 MPa):

NZS 3101-95 adopted the following expression for the modulus of rupture:

EC2-02 uses the direct tensile strength as the basic parameter to categorize the tensile strength of the concrete. In the absence of direct tensile tests, which are very difficult to perform correctly, EC2-02 provides the following expressions for the mean tensile strength for the concrete fctm.

fctm = 0.30/c2k/3 MPa, for fk < 50 MPa fctm = 2.12lnf 1 + f^) MPa, for fk > 50 MPa (159)

where fcm is the mean compressive strength taken as fck + 8 MPa. One interesting aspect of EC2-02 is that it makes a clear distinction in applying the different values of tensile strengths. A lower-bound characteristic tensile strength, | fractile value (f^.^ = 0.7f-tm), is used when accounting for tensile stresses contributing to strength (e.g., shear). An average or mean value is used when computing deflections and crack widths. An upper-bound characteristic tensile strength, 95% fractile value (/ctk,0.95 = 1.3ftm), is also provided for the designer and can be used to estimate the upper bound of cracking loads to check minimum reinforcement requirements.

It is a well-known fact in fracture mechanics that for brittle materials, as the member size increases, the tensile strength decreases. Some codes account for this so-called "size effect'' when determining the cracking stress. For the data examined in this article for the modulus of rupture, it is concluded that the equation proposed by Carasquillo et al. [77] provides a reasonable estimate of the average modulus of rupture. For this same data set, the ACI 318-02 equation for the modulus of rupture provides a reasonable estimate of the minimum values.

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