A flexural design methodology for composite heterogeneous and homogeneous UHPC bridge beams prestressed with bonded strands

Abstract

A non-iterative flexural design methodology for composite, heterogeneous, and homogeneous ultra-high performance concrete (UHPC) bridge beams prestressed with bonded strands is presented. One key feature of the proposed methodology is the development of closed-form equations for calculating strain in concrete at the most extreme compression fiber at the ultimate limit state, εc, as a function of various parameters. Separate formulations for predicting εc are provided for homogeneous and composite cross-sections. The predicted concrete strain, together with the maximum usable tensile strain for UHPC, εtu, at the most extreme tension fiber are used to calculate cross-sectional curvature and the distribution of strains and stresses. Force equilibrium is then used to determine the depth to the neutral axis and the nominal moment capacity of the beam. The flexural failure mode for the majority of beams considered is a fiber tension controlled failure. From a beam flexural strength perspective, the compressive strength of the deck or top flange for composite and heterogeneous beams, respectively, does not need to exceed 28 MPa. Any excess compressive strength will remain either unutilized or will result in marginal or negligible increases in moment capacities. The magnitude of the cracking strength of UHPC plays an important role in the contribution of UHPC to the moment capacity of the beam and determines whether this contribution is higher or smaller than that provided by the prestressing strands. The strand stress at the ultimate limit state, fps, varied from 1688 MPa to 1743 MPa and was past the linear elastic branch of the assumed stress-strain curve. The parameter that had the highest influence on fps was εtu. The proposed methodology is validated using test data as well as results from validated nonlinear finite element models and strain compatibility analysis.