Size Effect in Flexure of Prestressed Concrete Beams Failing by Compression Softening

The typical cause of flexural failure of prestressed beams is compression crushing of concrete, which is a progressive softening damage. Therefore, according to the amply validated theory of deterministic (or energetic) size effect in quasi-brittle materials, a size effect must be expected. A commercial finite-element code, ATENA, with embedded constitutive equations for softening damage and a localization limiter in the form of the crack band model, is calibrated by the existing data on the load-deflection curves and failure modes of prestressed beams of one size. Then this code is applied to beams scaled up and down by factors of 4 and $1/2$. It is found that the size effect indeed takes place. Within the size range of beam depths of approximately 152–1,220 mm, the size effect represents a nominal strength reduction of about 30% to 35%. In the interest of design economy and efficiency, a size effect correction factor could be introduced easily into the current code design equation. However, this is not really necessary for safety since the safety margin required by the code is exceeded for the normal practical size range if the hidden safety margins are taken into account. The mildness of the size effect in the normal size range is explained by the fact that the compression softening zone occupies a large portion of the beam and that, at peak load, the normal stress profiles across the softening zone exhibit only a minor stress reduction below the strength limit. Fitting the type 2 size effect law to the data can provide a simple extrapolation to much deeper beams, for which a stronger size effect is expected. But the extrapolation has some degree of uncertainty because of higher scatter of the test data used for calibrations.