Multicriteria Capacity Envelopes for Biaxial Bending of Concrete Hydraulic Structures

Envelopes for biaxial bending capacity of reinforced concrete elements are used extensively in design or in structural safety evaluation to verify the adequacy of internal force resultants from series of axial $P$ and bending moments $M_x$ and $M_y$ loading pairs computed for prescribed load combinations. However, existing methods to construct $P\text{-}{M}_x\text{-}{M}_y$ (PMM) interaction curves are not appropriate for concrete hydraulic structures because (1) pressurized water could penetrate in cracks leading to a coupled hydromechanical problem and (2) the structural performance is assessed using several criteria related to the allowable cracked area as well as allowable compressive (tensile) stresses for usual, unusual, and extreme load combinations. This paper presents a methodology to construct PMM interaction curves for arbitrary cross sections of hydraulic structures considering multiperformance criteria, water penetration in cracks, as well as the presence of reinforcing steel. The computations are based on a robust and efficient isogonic approach based on strength of materials where the position of the neutral axis is systematically varied over the cross section to find PMM equilibrium solutions. Four application examples of the proposed approach are presented (1) to illustrate its versatility, (2) to validate the results, and (3) to show its convergence properties. In some cases, PMM capacity envelopes are formed by distinct closed surfaces where equilibrium solutions are possible. This type of PMM capacity envelope, which the proposed algorithm is able to construct, is not found for classical reinforced concrete elements.