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Despite decades of study, an understanding of how the peptidoglycan network is assembled with a robustly maintained micron-scale shape and size has remained elusive. In this work, we introduce a model of rod-shaped cell growth that we use to investigate the roles of spatial regulation of peptidoglycan synthesis, biochemical properties of glycan strands, and mechanical stretching during insertion. Our studies reveal that rod shape maintenance requires insertion to be insensitive to fluctuations in cell-wall density and stress, and that a helical pattern of insertion is sufficient for elongation without significant loss of shape. In addition, we present evidence that left-handed chirality of the cytoskeleton in Escherichia coli gives rise to a global, right-handed chiral ordering of the cell wall. Local, MreB-guided insertion of material into the peptidoglycan network naturally orders the glycan strands and causes cells to twist left-handedly during elongational growth. Through comparison with the right-handed twisting of Bacillus subtilis cells, our work supports a common mechanism linking helical insertion and chiral cell-wall ordering in rod-shaped bacteria. Finally, we use molecular dynamics simulations to support a hydrolysis-dependent curvature-based model of FtsZ force generation. Upon integration of this force generation into our cell-wall model, we find that cleavage of misaligned glycan strands is likely to be a critical element of robust constriction during cell division. These physical principles of cell growth link the molecular structure of the bacterial cytoskeleton, mechanisms of wall synthesis and the coordination of cell-wall architecture.