Kinematics of layered reinforced-concrete planar beam finite elements with embedded transversal cracking

•We present an embedded-crack layered-beam finite element for analysis of reinforced-concrete beams.•Slippage between the reinforcement and the surrounding concrete is included.•A transversal crack in the beam element opens when the tensile strength in a layer has been reached.•Crack formation and development may be predicted without initial imperfections. In this work crack formation and development is addressed and implemented in a planar layered reinforced-concrete beam element. The crack initiation and growth is described using the strength criterion in conjunction with exact kinematics of the interlayer connection. In this way a novel embedded-discontinuity beam finite element is derived in which the tensile stresses in concrete at the crack position reaching the tensile strength will trigger a crack to open. Since the element is multi-layered, in this way the crack is allowed to propagate through the depth of the beam. The cracked layer(s) will involve discontinuity in the cross-sectional rotation equal to the crack-profile angle, as well as a discontinuity in the position vector of the layer’s reference line. A bond–slip relationship is superimposed onto this model in a kinematically consistent manner with reinforcement being treated as an additional layer of zero thickness with its own material parameters and a constitutive law implemented in the multi-layered beam element. Emphasis in this work is placed on the definition and finite-element implementation of kinematics of such a layered beam set-up with embedded cracking, rather than on constitutional details of the concrete, steel and interface between them. Several numerical examples are presented, in which the ability of the proposed procedure to predict crack occurrence and development is investigated.