Compound Size Effect in Composite Beams with Softening Connectors. I: Energy Approach

Abstract

The size effect on the nominal strength of steel-concrete composite beams caused by shear failures of connectors such as welded studs is analyzed by two different approaches: (1) In this paper (Part I) by a fracture type analysis of the energy release caused by propagation of the zone of failed connectors along the beam; and (2) in a companion paper (Part II) by a direct solution of the load-deflection diagrams from the differential equations of beam bending theory. The former can capture the large size asymptotic size effect and yields simple formulas suitable for design, whereas the latter can provide the solution for small beam sizes for which the connector failure zone is not much shorter than the span. The force-slip diagram of the connectors exhibits postpeak softening, which engenders an energetic size effect on the nominal strength of the connector. If the connectors are geometrically scaled with the beam, the size effect in the shear failure of connectors (mesoscale) is superimposed on the size effect due to propagation of the zone of connector failures along the beam (macroscale), producing in the beam as a whole a compound size effect that is stronger than in linear elastic failure mechanics. If the connector sizes and the interface area per connector are not scaled with the overall dimensions of the composite beam, the size effect law proposed by Bažant in 1984 is applicable. Comparisons with available test results are presented in Part II.