Footbridge Deflection and the Contractor's Web-Thickness Proposal
A 12 m simply supported steel footbridge over a drainage channel carries pedestrians between a car park and a hospital entrance. The deck is formed by two 356×171×51 kg/m universal beams at 1.8 m centres with a 120 mm concrete slab on permanent formwork. Under a service load of 4.5 kN/m the measured midspan deflection is 42 mm. The design basis states a deflection limit of span/360. The contractor has proposed reducing the web thickness from 10 mm to 8 mm, arguing that the resulting lower self-weight will bring deflection within the limit and save steel. The client has asked for a technical review before approving the change. The bridge also shows noticeable sway when groups of people walk across it, which has not been assessed. No dynamic testing has been carried out, and the measured deflection does not distinguish between the slab's construction camber and the live-load component.
1. Calculate the deflection limit and determine whether the measured 42 mm establishes non-compliance. State what additional information you need before making that judgement.
Read the worked answer
The limit is L/360 = 12,000/360 = 33.3 mm. The measured 42 mm exceeds this by 8.7 mm, or about 26%, so the deflection is a genuine flag.
It does not, however, establish non-compliance on its own, because the comparison is only valid if the measured value and the limit refer to the same load case. Many bridge criteria apply the limit to the live-load deflection, sometimes to the total deflection after erection, and sometimes to a load case that excludes construction camber. The setup says only that the reading was taken "under a service load of 4.5 kN/m" and that camber was not separated.
Before concluding, require:
- Whether 42 mm is total deflection from a survey datum or the live-load increment only.
- The exact load at measurement: is 4.5 kN/m total, imposed, or a factored combination?
- As-built section properties and span, plus support settlement and temperature at the time of survey.
- A statement of which deflection criterion the design basis intends: live load, total load, or a percentage of span.
If 42 mm is live-load-only, the bridge is clearly over the limit. If it is total including dead load and camber, the dead-load component must be removed analytically or by measurement before any verdict.
2. Evaluate the contractor's proposal using section properties and state whether it can achieve the required reduction.
Read the worked answer
The proposal fails on mechanics, not just on cost.
For an I-section, the second moment of area is approximately the sum of the flange contribution, 2·b·t_f·(d/2)², and the web contribution, t_w·h_w³/12. The web term is small because the web is thin and its material lies close to the neutral axis. Reducing t_w from 10 mm to 8 mm is a 20% reduction in the web term, which may reduce the total I by only about 2–4%.
Deflection under a given load is inversely proportional to EI. A 2–4% loss of stiffness gives roughly a 2–4% increase in deflection for the same load, not a reduction.
The self-weight saving is also small. The web area removed is about 2 mm × 300 mm = 600 mm² per beam. At 7,850 kg/m³ that is about 4.7 kg/m per beam, or roughly 9 kg/m over two beams, against a total dead load that includes the slab and finishes. Even if dead load were 40% of the deflection, the saving would be well under 2 mm.
So the proposal cannot recover 8.7 mm. It also reduces shear capacity and local buckling resistance. A credible fix would increase effective depth, add flange cover plates, or reduce dead load; otherwise accept a revised limit only if a proper assessment supports it.
3. The sway complaint: explain the dynamic check required and why the static deflection limit does not cover it.
Read the worked answer
Static deflection and pedestrian-induced vibration are different serviceability issues. A bridge can satisfy L/360 and still be uncomfortable or potentially resonant.
For a simply supported beam the fundamental vertical frequency is approximately f₁ = (π/2)·√(EI/(m·L⁴)), where m is mass per unit length. Walking pacing is about 2 Hz and its second harmonic about 4 Hz. If f₁ falls near 2 Hz or 4 Hz, resonant build-up is possible; design guidance commonly seeks f₁ above about 5 Hz for footbridges, or requires a forced-vibration check with damping and crowd loading if it does not.
The required work is:
- Compute f₁ from as-built stiffness and mass, including the slab and any finishes.
- Measure the actual frequency and damping by a heel-drop or modal test.
- If f₁ is in a sensitive range, perform a response analysis for a pedestrian stream and compare acceleration with comfort criteria.
- Check lateral sway separately, since synchronous walking can excite horizontal modes that the vertical deflection limit ignores.
The 42 mm static reading gives no information about frequency, damping, or acceleration, so it cannot clear the sway complaint.