Floor and span
- Beam span (simply supported)
- Tributary width carried by the beam
- Permanent area load (incl. services)
- Imposed area load (office)
Structural · worked example · 4 pages
Steel floor beam: strength and deflection
A simply supported steel beam carries a strip of office floor. The area loads become a line load, then bending strength and deflection are checked and two candidate sections compared. Scope: bending and deflection of a fully restrained, compact section — shear, bearing and lateral-torsional buckling are separate checks outside this example.
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What this calculation covers
Line loads on the beam
- Permanent line load
- Imposed line load
- Factored load, 1.2G + 1.5Q (AS/NZS 1170.0)
- Serviceability load, short term (ψs = 0.7)
Design actions
The Beams panel's simply-supported case: M = wL²/8 at midspan, V = wL/2 at the supports, δ = 5wL⁴/384EI.
- Design bending moment
- Design shear at the support
Trial section
Example properties for a 310UB-class universal beam — copy exact values for your section from the Sections panel or a catalogue, so the sheet stands alone.
- Second moment of area
- Effective section modulus (compact)
- Yield stress (example)
- Elastic modulus of steel
- Capacity reduction factor
Strength check
- Design bending capacity φM
- Bending strength adequate
- Bending utilisation
Deflection check
Deflection utilisation (0.90) exceeds bending utilisation (0.64): serviceability governs this beam, as it often does at ordinary office spans.
- Midspan deflection under w_s
- Deflection limit L/360
- Deflection within limit
- Deflection utilisation
A lighter section for comparison
The same checks as functions of the section properties, then a 250UB-class trial (example values I = 44.5×10⁶ mm⁴, Z = 354×10³ mm³):
- Deflection for a section with second moment I
- Bending utilisation for modulus Z
- 250UB-class deflection
- Lighter section passes deflection?
- 250UB-class bending utilisation
Results summary
- The 310UB-class section carries the 6 m bay at 64% bending and 90% deflection utilisation — deflection governs. The 250UB-class alternative deflects 29 mm against a 16.7 mm limit and is over strength capacity too, so the heavier beam stands.
Try changing…
- Stretch the span to 7 m — deflection grows with L⁴ and fails long before strength does.
- Halve the tributary width — both utilisations halve; a lighter section then passes.
- Tighten the limit to L/500 (brittle finishes) — the chosen section now fails serviceability.