Non-linear analysis of pre-tensioned concrete planar beams

We have derived a one-dimensional mathematical model and a numerical procedure for the non-linear static analysis of pre-tensioned concrete planar beams, which intends to describe quantitatively the global behaviour as well as some local phenomena in the beam, such as the tangential slip and the traction between the tendon and concrete, with accuracy sufficient for engineering design. The advantage of such a model is its extreme computational efficiency compared to the two- and three-dimensional formulations. A shear-stiff, kinematically exact planar beam theory is used to model each component of the beam. The bending moment in the tendon is neglected. Cracking of concrete is accounted for using the smeared crack concept. Softening of material, and the related localisation of deformations, is in the numerical solution resolved by the combined use of the arc-length method and the constant strain crack band element, whose dimension is related to the fracture energy of concrete in tension. The tangential slip between the tendon and concrete is fully accounted for, yet the normal separation is not allowed. The model enables us to analyse the variation of slip and the tangential traction on tendons as well as softening of concrete in both tension and compression along the beam axis and in time. The validity of the present one-dimensional model is verified on two pre-stressed simply supported beams previously experimentally and computationally studied in literature (Rabczuk and Eibl, 2004 [2]; Rabczuk et al., 2005 [18]; Rabczuk and Belytschko, 2006 [20]). It is found out that the results of the present one-dimensional model are well in keeping with the experimental and numerical results from literature. Recalling the extreme computational efficiency of the present formulation compared to the 2D and 3D formulations it is concluded that the proposed method of analysis could be very convenient for engineering design.

► The mathematical model for analysis of pre-tensioned concrete beam is presented.
► Reissner’s planar beam theory is used to model the tendons and the concrete.
► The slip between the tendon and the concrete is accounted for.
► The smeared crack concept in combination with the crack-band model is adopted.
► The proposed method of analysis could be very convenient for engineering design.