Design Interaction Diagrams for Shear Adequacy Using MCFT-Based Strength of AS 5100.5—Advantages of Using Monte Carlo Simulation

This paper presents three different approaches for generating points along the interaction diagram corresponding to design load effects—shear, bending moment, and axial force—to achieve optimal shear strength adequacy with the Australian bridge design standard AS 5100.5. The methodology targets the optimal shear condition by matching the design shear V* with the capacity ϕVu, which represents achieving a load rating factor of unity within the specified tolerance limits. The first typical approach for generating points for two load effects is by increasing the moment–shear ratio ηm in small increments from zero to a large value (theoretically infinity), and for each increment, to goal-seek the condition. The other approaches investigated are the use of increasing factored moment M* and the use of Monte Carlo simulation. A pretensioned bridge I-girder section reported in the literature was used in the study. The Monte Carlo simulation method was found to be the simplest to program. It allows an interaction surface for the influence of three load effects for optimal shear adequacy to be obtained with minimal program coding and outperforms the goal–seeking approaches for multi-variable interactions. It can create 2-D interaction lines for various levels of shear adequacy for the interaction of M* and V*, and 3-D interaction surfaces for M*, V*, and N*. The potential use of interaction diagrams was explored, and the advantages and limitations of using each method are presented. The interaction curves of two typical pretensioned concrete sections of a plank girder, one next to an end support and the other close to mid-span, were created to show the distinguishing features resulting from their reinforcement.