Repository logo

Size effects in unreinforced and lightly reinforced concrete beams failing in flexure

Accepted version



Change log


Augusthus-Nelson, L 
Lees, JM 


Fracture-based models commonly use a characteristic length as the basis for determining size effects in concrete beams. The characteristic length is related to the concrete fracture process zone and defined in terms of the concrete fracture properties. Semi-empirical constants are then developed to accommodate any unidentified (geometric or crack bridging) parameters. However, a reliance on semi-empirical factors can limit the applicability to different systems, concretes and reinforcing materials. The aim of the current work is to formulate an analytical size effect model based solely on fundamental material and geometric properties. The particular focus is unreinforced and lightly reinforced concrete beams that fail in flexure due to unstable crack propagation. The proposed ’generalised’ characteristic length approach is based on the mode-I fracture behaviour of concrete and includes crack bridging forces due to the presence of longitudinal reinforcement. The theoretical expressions suggest that the geo-metric shape of a beam, the fracture properties of the concrete and the crack bridging forces (where present) significantly influence the characteristic length. Experimental investigations on geometrically similar unreinforced and lightly reinforced concrete beams in 2-D are undertaken as a means for initial validation. The validation is then extended to a wider dataset of existing experimental results in the literature. The generalised characteristic length approach is able to capture both the influence of the concrete strength and the size effect mitigation due to the inclusion of longitudinal reinforcement. This confirms that the generalised approach holds promise and could be expanded to other quasi-brittle materials and non-conventional reinforcing materials.



Characteristic length, Size effect, Reinforced concrete, Fracture mechanics

Journal Title

Engineering Fracture Mechanics

Conference Name

Journal ISSN


Volume Title


Elsevier BV
Engineering and Physical Sciences Research Council (EP/J002887/1)
Engineering and Physical Sciences Research Council (EP/N017668/1)
Cambridge Commonwealth Trust