compatibility of ultra high performance concrete as repair material

From the equilibrium of forces of Figure 2.10, τ n and σ n can be expressed in terms ofcompressive force, P, cross section, A, and the angle between the interface and thehorizontal, α, as:σ n = P A ∗ cos2 (α) Equation 2.2τ n = P A ∗ sin(α) ∗ cos(α) Equation 2.3Figure 2.10 Equilibrium of stresses in the slant shear test and Mohr circle. Modified from Austin et al. (1999).From Equation 2.1, Equation 2.2 and Equation 2.3, the applied compressive forcerequired to produce shear failure along the interface is:σ 0 = P A = c ∗ 1 + tan2 (α)tan(α) − µ Equation 2.4The most critical interface angle corresponding to a minimum applied stress, σ 0 , iscalculated by means of the derivative of the previous equation respected α.34