Model-Detail Mismatch on a Continuous Floor Beam
A floor beam spans 7.2 m from an exterior wall to a girder and continues 4.8 m past the girder to a second bay. The analysis model uses the software default 'rigid' beam-to-girder connection, so the beam is analyzed as continuous over both spans. Factored load is 45 kN/m; service load is 20 kN/m; Fy = 345 MPa; E = 200,000 MPa. The model selected a section with Zx = 0.89×10⁶ mm³ and I = 127×10⁶ mm⁴. On the shop drawings the beam frames into the girder web with a single-row shear tab and three 20 mm bolts, a connection that transfers essentially no moment. The girder was sized using the reactions printed by the same model.
1. Compute the design moments under the continuity assumption and under the actual simply supported condition, and determine whether the selected section is adequate.
Read the worked answer
Continuity moment at the interior support (uniform load w on two spans, constant EI):
M_B = w(L₁³ + L₂³) / [8(L₁ + L₂)] = 45 × (7.2³ + 4.8³) / [8 × (7.2 + 4.8)] = 45 × (373.2 + 110.6) / 96 = 227 kN·m (hogging)
Positive moment, long span (as modeled): M = wL₁²/8 − M_B/2 = 45 × 51.84/8 − 227/2 = 291.6 − 113.4 = 178 kN·m
Positive moment, as detailed (simple span): M = wL₁²/8 = 292 kN·m, i.e. 64% higher than the model.
Capacity check:
- Required Zx (simple span) = 292×10⁶ / (0.9 × 345) = 0.94×10⁶ mm³
- Provided Zx = 0.89×10⁶ mm³ → φMn = 0.9 × 345 × 0.89×10⁶ = 275 kN·m < 292 kN·m → NG, about 6% short.
The section is adequate only if continuity is delivered. The shear tab cannot deliver it, so the beam is under-designed for the governing (simple-span) moment.
2. Trace the error into the girder and check serviceability.
Read the worked answer
Girder reaction at the interior support
- As modeled (continuous): R_B = (45×7.2/2 + 227/7.2) + (45×4.8/2 + 227/4.8) = (162 + 31.5) + (108 + 47.3) = 349 kN
- As detailed (both spans simply supported): R_B = 162 + 108 = 270 kN
The girder is carrying 29% more than it was designed for, and that error propagates into the column and foundation. The girder must be rechecked, not just the beam.
Deflection, long span, simply supported: δ = 5wL⁴/(384EI) = 5 × 20 × 7200⁴ / (384 × 200,000 × 127×10⁶) = 27.6 mm = L/261
Against a common L/360 limit (20 mm), the beam is over-deflected by about 38%. Under the continuity assumption it would have computed at roughly 11–12 mm, well inside the limit - which is exactly why the mismatch went unnoticed.
Takeaway: the error is not visible in the member check the model performed. It appears only when the demand is recomputed for the connection that is actually detailed, and it is worst where the model's numbers are used for the supporting members.
3. Recommend a resolution and a modeling control to prevent recurrence.
Read the worked answer
Option 1 (recommended) - make the analysis match the detail.
- Re-analyze both spans as simply supported.
- Select a section with Zx ≥ 0.94×10⁶ mm³ and I ≥ 175×10⁶ mm⁴ (I from δ = 5wL⁴/(384Eδ_allow) with δ_allow = 20 mm).
- Re-run the girder, column and foundation for the corrected reaction of 270 kN at the beam line, plus the increase in the adjacent spans.
- Verify the shear tab for the simple-span shear and the bolt bearing/tear-out with the revised demand.
Option 2 - deliver the continuity the model assumed.
- Provide a moment connection designed for M_B = 227 kN·m, and confirm the girder web and the girder's torsional/eccentricity capacity for that moment, and the column for the added moment.
- This is almost never economical for a shear-tab-scale detail, which is why Option 1 is preferred here.
Modeling control: in the analysis file, set the beam-to-girder connection default to 'pinned' and require an explicit release note on any member modeled as continuous. At the shop-drawing review, compare the connection schedule against the analysis assumptions for every member, and flag any member whose end release disagrees with its detail.