Preliminary Structural Design and Criterion Prediction of Steel Beams Using the Deflection Governance Ratio

1) A closed-form Deflection Governance Ratio was developed as the ratio of deflection-limited load capacity to strength-limited load capacity. Under the assumptions stated in the paper, it also equals the ratio of strength utilization to deflection utilization. The critical span-to-depth ratio is λcr = Φ·E/(2αnσs) and is independent of section size for the doubly symmetric sections considered. 2) The load distribution and support conditions have a substantial influence on the critical ratio. A central point load increases λcr by 25% for a simply supported beam, while it decreases the ratio for the restrained-beam and cantilever cases examined. 3) Higher-strength steel can become deflection-governed at a lower span-to-depth ratio because the elastic modulus changes little as yield strength increases. For a simply supported beam under UDL, the tabulated ratio falls from 21.1 for E250 to 11.7 for E450. 4) The balanced-depth procedure selected ISMB 400 for the 7 m floor-beam example. Selecting a section based on deflection alone would have led to ISMB 350, which did not satisfy the strength check in the example. 5) Support restraint can significantly reduce deflection. For a UDL, the fixed–fixed case reduces the maximum deflection by 80% compared with the simply supported case. The ISMB 300 study also showed a larger usable span when end restraint was increased. 6) Macaulay’s method, the unit load method, and the finite element model produced the same reported mid-span deflection of 22.57 mm for the worked example. The reinforced-concrete example also showed that the estimated deflection depends strongly on the effective stiffness adopted. Future work could extend the criterion to combined load cases, unsymmetrical and composite sections, and lateral-torsional buckling, and could validate its predictions against laboratory load tests.

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