Sectional analysis for design of ultra-high performance fiber reinforced concrete beams with passive reinforcement

Sectional flexural analysis, as performed in normal strength concrete design, requires uniaxial constitutive models. For ultra-high performance fiber reinforced concrete (UHPFRC), the constitutive model tensile backbone varies with section heights for different flexural members, due to the size-dependent stress-crack opening relation used to derive it. In this paper, several simplified size-independent constitutive models were investigated. For unreinforced sections with heights between 51 mm and 1067 mm, the elastic-perfectly-plastic tension model leads to conservative ultimate moment prediction (or results within 5%) when compared to that obtained by the size-dependent model. For reinforced sections, the difference between the two models is affected by the reinforcing condition and is even smaller than the unreinforced cases. By assuming an elastic-perfectly-plastic tension model, the flexural strength of rectangular or T section UHPFRC beams was estimated analytically. The flexural strengths are greatly influenced by the reinforcement ratio and yielding strength of the longitudinal reinforcement. Including shear strength predictive equations from past research, the load capacity and failure mode for rectangular and T beams are presented in a design chart. The impact of several factors on UHPFRC beam flexural responses were investigated, such as different compressive strength, curing conditions, and anisotropic fiber orientation distributions. The load-deflection relationships generated from beam flexural analysis were compared to experimental results for both unreinforced and reinforced beams, with or without fiber alignment. Factors affecting the first crack strength in tension (i.e., fiber orientation distribution) had greater impact on the flexural strength of UHPFRC beams than the effect of using a size-dependent model.