Beam (structure)

Engineering

Statistics

Geotechnical engineering

Materials science

Bending

Ultimate tensile strength

Geology

Mathematics

Cracking

Slippage

Composite material

Parametric statistics

Structural engineering

Fracture (geology)

Brittleness

Fracture mechanics

Magazine of Concrete Research

In the present work, cohesive and overlapping crack models are integrated in a comprehensive numerical algorithm in order to investigate both tensile and compressive failures in plain or steel-bar reinforced concrete (RC) structural elements. These two fracture mechanics models offer a high capability in the investigation of non-linear phenomena occurring in the loading process of plain concrete or RC beams subjected to bending. Based on the crack-length control scheme, these non-linear models are able to describe snap-back and snap-through instabilities, crack formation/propagation, steel yielding/slippage, concrete crushing and scale effects on the structural brittleness. In the present work, some parametric studies are carried out on plain concrete or RC beams in order to highlight how the abovementioned structural phenomena, which are observed in engineering practice, can be effectively captured by means of a non-linear fracture mechanics approach. Moreover, dimensional analysis is adopted to confirm how the behaviour of lightly reinforced concrete beams can be effectively described by means of two non-dimensional brittleness numbers, leading to a scale effect on the minimum reinforcement percentage, ρ min , proportional to beam depth raised to −0.15.

The cohesive/overlapping crack model for plain and RC beams: scale effects on cracking and crushing failures