Predictions of the ultimate tensile strength of 3-dimensional fiber-reinforced composites as a function of the fiber statistical strength distribution and fiber geometry (square vs. hexagonal packing) are presented for materials in which the load transfer from broken to unbroken fibers is very localized. The predictions are obtained using a previously-developed simulation model adapted here for hexagonal fiber arrays. The model includes (1) the Hedgepeth and Van Dyke load transfer model to determine in-plane load transfer and (2) fiber slip in the longitudinal direction via a shear-lag model. Results show that, although the load transfer does depend on fiber geometry, the average composite tensile strength and the statistical distribution of strengths do not depend strongly on the fiber geometry. The size scaling of strength is then also shown to be nearly-independent of local fiber geometry. These results are physically reasonable since the critical clusters of fiber damage causing failure are observed to be larger than 15-20 fibers, so that the detailed local geometry at smaller length scales is not crucial to failure. Hence, analytic models developed previously for square fiber arrangements can be used with reasonable accuracy independent of fiber arrangements. Applications of the model to polymer matrix composites are discussed in a companion paper (Part II).