Adjust Zx to iterate toward an efficient beam — the trial log and utilization gauge update live.
Structural design is iterative. You guess a member size, check it against demands, and resize if needed. For a beam: pick a W-shape, compute φMn, compare to Mu. If overstressed, go bigger. If way under, go smaller to save weight. Each resize changes self-weight, which changes demands, which may change the answer. Convergence usually takes 2–3 iterations. The goal is a member that works with reasonable utilization (0.7–0.95 is efficient).
You can't design a beam without knowing its weight, but you can't know its weight until you've designed it. This circular dependency is why structural design is iterative. Start with an educated guess (rules of thumb: beam depth ≈ L/20 for steel). Check it against demands. If it fails, go bigger. If it's way overdesigned, go smaller. Each change affects self-weight, which changes the demand slightly. Usually converges in 2–3 iterations.
A utilization ratio of Mu/φMn = 1.0 means the member is exactly at capacity — no margin. In practice, you want 0.7 to 0.95. Below 0.7 is wasteful (heavier, more expensive, takes up more space). Above 0.95 is risky (no room for construction tolerances or future loads). The sweet spot depends on the project — a hospital might target 0.80 for conservatism; a warehouse might accept 0.95 for economy.