Prediction of Fatigue Strength in Plain and Reinforced Concrete Beams

ACI Structural Journal, Sep/Oct 2007 by Sain, Trisha, Kishen, J M Chandra

Figures 4 and 5 show the fatigue crack propagation curves for the experimental results reported by Slowik et al. (1996) for their compact tension specimens together with the proposed fatigue law, considering the variable amplitude loading. Two sets of experimental results having different fatigue load cycles are validated herein under the same fatigue loading as reported by Slowik et al. (1996) in their experiments. One set is represented by G05 and the other set is represented by G06, G07, G13, G15, and G17 by Slowik et al. (1996). For Specimen G05, it is seen from Fig. 4 that at 1800 cycles and 3700 cycles, there is a sudden increase in crack length. This is due to the presence of spikes/overload in the load spectrum at 1800 cycles and 3700 cycles. For the second set of specimens, two spikes were introduced in the experiments at 1800 cycles and 2700 cycles and a sudden increase in crack length is predicted at these load cycles by the proposed analytical model as seen in Fig. 5.

Hence, under variable amplitude loading, a sudden increase in load magnitude causes a rapid propagation of the effective crack. A good agreement is seen between the experimental results and the proposed model validating the same.

RESIDUAL STRENGTH ASSESSMENT OF PLAIN CONCRETE BEAMS

In this study, an analytical procedure is developed to assess the residual strength in terms of load/moment carrying capacity of plain and reinforced concrete beams by considering damage in the form of a dominant discrete crack. Failure of the member takes place when a dominant discrete crack propagates and becomes unstable at some critical crack size. To determine the critical crack length, the energy criteria is used according to which unstable crack propagation takes place when the energy release rate GI reaches the critical energy release rate GIC.

Strength of cracked plain concrete beams

According to linear elastic fracture mechanics, the basic equation that relates the stress intensity factor with the applied load, specimen geometry, and crack size are given by (Bazant and Kangming 1991)

... (6)

where α is the relative crack depth equal to a/d, a is the crack length, d is the characteristic dimension of the structure such as depth of beam, b is the specimen thickness, P is the applied load, and f(α) is a function depending on specimen geometry and for a three-point bend beam is given by

... (7)

The value Cn is a coefficient chosen for convenience to generalize the stress expression. For a three-point bend beam specimen having an initial notch length a0, Cn = 3L/{2(d - a0)}.

In terms of energy release rate, Eq. (6) can be written as

... (8)

where E is the elastic modulus. Equations (6) and (8) are used to determine the load carrying capacity of a cracked plain concrete member characterized by the critical energy release rate GIC for a given size.

Procedure for computing residual life of plain concrete

At the beginning of this paper, a model for computing the rate of crack propagation with respect to the number of cycles of fatigue load is discussed. This model, explained by Eq. (1) and (4) is used to determine the number of load cycles required for a dominant crack to reach a critical size. In addition, the strength or the load carrying capacity at a particular crack length can be determined using Eq. (6). These three equations are used in this study to assess the residual strength of a plain concrete beam using the following procedure: