Bond Shear Modulus and Equivalent Elastic Modulus in Thermally-Damaged RC Tension Members

Bond shear modulus and the equivalent elastic modulus are investigated in RC ties after a fire (residual conditions), based on eleven experimental campaigns well documented in the literature. Design-oriented laws are proposed for bond shear modulus kT [MPa/mm or ksi/in.], as a function of bar diameter, concrete residual strength in compression and temperature, in order to study tension stiffening in regularly-cracked RC ties in different thermal and restraint conditions, within the elastic domain. To tchis purpose, four approaches are adopted, the first based on a 1D analytical model and the other three on finite elements, with the bar modelled as a wire or as a 3D member. In all approaches, zero-thickness elastic springs take care of bond stiffness. The fitting of the not many test results available in the literature confirm the soundness of the proposed approach, and the effectiveness of the 1D analytical model. For a rather typical family of RC ties, the equivalent elastic modulus is shown to be larger – and even much larger - than the elastic modulus of naked bars, both at ambient temperature and in post-fire conditions. The results may contribute to the assessment of the residual stiffness of RC members fully or partly in tension (ties and beams), past a fire or a spell at high temperature, before taking steps to reuse, repair and/or stiffen the structure.