The size ifftct on the nominal strength if quasibrittle structures failing at crack initiation, and particularly on the modulus if rupture if plain concrete beams, is analyzed. First, an improved deterministic formula is derived from the energy release due to a boundary layer if cracking (initiatingfracture process zone) whose thickness is not negligible compared to beam depth. To fit the test data, a rapidly converging iterative nonlinear optimization algorithm is developed. The formula is shown to give an excellent agreement with the existing test data on the size ifftct on the modulus if rupture if plain concrete beams. The data range, however, is much too limited; it does not cover the extreme sizes encountered in arch dams,foundations, and retaining walls. Therifore, it becomes necessary to extrapolate on the basis if a theory. For extreme sizes, the Weibull type statistical ifftct if random material strength must be incorporated into the theory. Based on structural analysis with the recently developed statistical nonlocal model, a generalized energetic-statistical size ifftct formula is developed. The formula represents asymptotic matching between the deterministic-energetic formula, which is approached for small sizes, and the power law size ifftct if the classical Weibull theory, which is approached for large sizes. In the limit if irifinite Weibull modulus, the deterministic-energetic formula is recovered. Data fitting with the new formula reveals that, for concrete and mortar, the Weibull modulus m z 24 rather than 12, the value widely accepted so far. This means that,for extreme sizes, the nominal strength (modulus ifrupture) decreases,for two-dimensional similarity, as the-1/12 power if the structure size, and for three-dimensional similarity, as the-1 /8 power (whereas the-1/4 power has been assumed thusfar). The coifficient if variation characterizing the scatter if many test results for one shape and one size is shown not to give the correct value if l/1!ibull modulus because the energetic size ifftct inevitably intervenes. The results imply that the size ifftct at fracture Initiation must have been a signiji"cant contributingfactor in many disasters (for example,