Analytical moment-curvature solutions for generalized textile-reinforced concrete sections

A piecewise linear parametric constitutive model of elastic-plastic-hardening in tension and elastic-plastic in compression is used to develop closed-form solutions for flexural moment-curvature of generalized sections. Brittle matrix composite such as Textile Reinforced Concrete (TRC) is homogenized using three zones of elastic, distributed cracking, and tension stiffening up to the maximum tensile strength. Linear segments of the tensile and compressive constitutive responses are integrated for various states of strain and extended to geometrical structural shapes such as steel W-, T-, and C- sections. The closed-form moment-curvature response is obtained using two independent variables of strain distribution and neutral axis location and extended to obtain the stress distribution, curvature, rotation, and deflection profile of statically determinate load cases using an input strain. The solutions for serviceability-based criteria and limit state parameters such as curvature, rotation, and deflection distribution as a function of the applied load can be obtained. The generalized parametric solutions are applied to the elastic-plastic flexural response of quasi-brittle or ductile beams of structural steel with unique cross-sectional geometries. Case studies of the correlation of tensile and flexural tests of TRC with variables such as types and direction of the weave, number of textile layers, and section geometry are validated. The parametric nature of the formulation offers computational efficiency for applications that address material and shape optimization, as well as serviceability-based flexural design using different limit states.