# Comfort criteria for footbridges

The comfort criteria is defined in terms of a maximum acceptable acceleration of any part of the deck.

## EN 1990:2002+A1:2005 Cl A2.4.3.2 Pedestrian comfort criteria (for serviceability)

The accelerations are deemed to be acceptable if the natural frequency of the deck is greater than:

• $$5.0\textrm{ Hz}$$ for vertical vibrations,
• $$2.5\textrm{ Hz}$$ for horizontal (lateral) and torsional vibrations.

If the above is not satisfied, further checks should be undertaken to ensure accelerations are not greater than:

• $$0.7\textrm{ m/s}^{2}$$ for vertical vibrations,
• $$0.2\textrm{ m/s}^{2}$$ for horizontal vibrations due to normal use,
• $$0.4\textrm{ m/s}^{2}$$ for exceptional crowd conditions.

## LRFD Guide Specifications for the Design of Pedestrian Bridges

### Vertical

The accelerations are deemed to be acceptable if the frequency of the first vertical mode is greater than 3.0 Hz.

If the above is not satisfied, a further check (see derivation) should be undertaken to ensure:

$f_{n} \geq 2.86 \ln (\frac{180}{W})$

Symbol Description
$$f_{n}$$ Frequency of first vertical mode of structure
$$W$$ Total dead load in kips

This formula incorporates an acceleration limit of $$0.05g$$.

### Horizontal

The accelerations are acceptable if the frequency of the first horizontal mode is greater than $$1.3\textrm{ Hz}$$.

## BD 37/01 Appendix B

Accelerations are deemed acceptable if the fundamental natural frequency of vibration exceeds 5 Hz for the unloaded bridge in the vertical direction and 1.5 Hz for the loaded bridge in the horizontal direction.

For superstructures where the natural frequency in the vertical direction is equal to or less than 5 Hz, the maximum vertical acceleration of any part of the superstructure shall be limited to $$0.5\sqrt{f_{0}\textrm{ [Hz]}} \textrm{ m s}^{-2}$$.

## ISO 10137:2012 C.1.2 Walkways

Note that ISO 10137 lists maximum root mean square accelerations rather than peak. To convert from r.m.s. to peak, you multiply by the crest factor. Allen estimates a crest factor for typical walking vibration of $$1.7$$.

### Vertical

Frequency Max allowable r.m.s. acceleration ($$\textrm{m/s}^{2}$$))
$$1\textrm{ Hz} \leq f \leq 4\textrm{ Hz}$$ $$0.6f^{-0.5}$$
$$4\textrm{ Hz} \leq f \leq 8\textrm{ Hz}$$ $$0.3$$
$$8\textrm{ Hz} \leq f \leq 80\textrm{ Hz}$$ $$0.0375f$$

### Horizontal

Frequency Max allowable r.m.s. acceleration ($$\textrm{m/s}^{2}$$)
$$1\textrm{ Hz} \leq f \leq 2\textrm{ Hz}$$ $$0.216$$
$$2\textrm{ Hz} \leq f \leq 80\textrm{ Hz}$$ $$0.108f$$