Let ψ μ,ν (z) = (1-2 cos νe iμ z + e 2iμ z 2)-1 , μ, ν ∈ [0, 2π) and p be an analytic mapping with Re p > 0 on the open unit disk. We consider the sense-preserving planar harmonic mappings f = h + g, which are shears of the mapping z 0 ψ μ,ν (ξ)p(ξ) dξ in the direction μ. These mappings include the harmonic right half-plan mappings, vertical strip mappings, and their rotations. For various choices of dilatations g /h of f , sufficient conditions are found for the convex combinations of these mappings to be univalent and convex in the direction μ.