SCI P354 – Coefficients and Phase Angles

One of the available options in the Footfall Coefficients dialog under the Design Method setting is SCI P354, which is based on the publication Design of Floors for Vibration: A New Approach (Revised Edition, February 2009) [1]. This standard provides predefined amplitude coefficients and phase angles for various activity types and excitation sources.

The excitation frequency range is set directly in the Footfall load case.

The following activity types and sources are supported under SCI P354:

Walking activity

SCI P354 - Table 3.1
Manual input

Staircases

ISO 10137
Manual input

Each of these activities is described in detail in the following sections, including tables of harmonic coefficients and phase angles. The order of the chapters follows the list above.

Walking activities

For walking activities, two types of sources are available. The first is SCI P354 – Table 3.1, which provides predefined amplitude coefficients and phase angles based on the standard. The second option is Manual input, which allows the user to specify custom values.

Source = SCI P354 - Table 3.1

The coefficients for this activity are defined in the SCI P354 standard, specifically in Table 3.1, which provides amplitude coefficients and phase angles for each harmonic term within specified excitation frequency ranges.

Harmonic - h	Excitation frequency range - h f_p [Hz]	Design value of coefficient - α_h	Phase angle - Φ_h [rad]
1	1.8 - 2.2	0.436 ( h f_p - 0.95)	0
2	3.6 - 4.4	0.006 ( h f_p + 12.3)	- π/2
3	5.4 - 6.6	0.007 ( h f_p + 5.2)	π
4	7.2 - 8.8	0.007 ( h f_p + 2.0)	π/2

As shown in the table, the amplitude coefficients depend on the excitation frequency and vary within the specified frequency ranges for each harmonic term. In the Footfall Coefficients dialog, only the coefficients for the lowest excitation frequency within each range are displayed, specifically for 1.8 Hz, 3.6 Hz, 5.4 Hz, and 7.2 Hz.

Although values for other frequencies within the ranges are not explicitly shown in the Footfall Coefficients , the frequency dependency of the coefficients is fully respected in the calculation.

Example of coefficient calculation for the displayed values:

For the 1st harmonic term (h f_p = 1×1.8 = 1.8 Hz):

α_h = 0.436 ( h f_p - 0.95) = 0.436 (1.8 - 0.95) = 0.3706
For the 2nd harmonic term (h f_p = 2×1.8 = 3.6 Hz):

α_h = 0.006 ( h f_p + 12.3) = 0.006 (3.6 + 12.3) = 0.0954
For the 3rd harmonic term (h f_p = 3×1.8 = 5.4 Hz):

α_h = 0.007 ( h f_p + 5.2) = 0.007 (5.4 + 5.2) = 0.0742
For the 4th harmonic term (h f_p = 4×1.8 = 7.2 Hz):

α_h = 0.007 ( h f_p + 2.0) = 0.007 (7.2 + 2.0) = 0.0644

The phase angles are constant for each harmonic term and do not depend on the excitation frequency.

Source = Manual input

When Manual input is selected, the user can specify individual values for both the amplitude coefficients α_h and phase angles Φ_h for all four harmonic terms.

In this mode, the coefficient values are considered constant and no longer depend on the excitation frequency.

Staircases

For the Staircase activity type, the SCI P354 standard refers to the table published in ISO 10137 [2]. This is also reflected in the settings, where the Source selection offers two options: ISO 10137 and Manual input.

Source = ISO 10137

The amplitude coefficients and phase angles are directly taken from ISO 10137, which provides the following values:

Harmonic - h	Excitation frequency range -h f_p [Hz]	Design value of coefficient - α_h	Phase angle - Φ_h [rad]
1	1.2 - 4.5	1.1	0
2	2.4 - 9.0	0.22	0

Both harmonic terms use constant values for the amplitude coefficient and the phase angle, regardless of the excitation frequency within the specified range.

Source = Manual input

When the Manual input option is selected, the user can define both the amplitude coefficient α_h and the phase angle Φ_h for each of the two harmonic terms manually. Similar to the ISO 10137 source, these values are constant and do not vary with excitation frequency.

References

[1] Smith, A.L., Hicks, S.J. and Devine, P.J. (2009), Design of Floors for Vibration: A New Approach (Revised Edition, February 2009), The Steel Construction Institute, Silwood Park, Ascot, Berkshire, England.

[2] International Organization for Standardization (2007), ISO 10137: Bases for Design of Structures – Serviceability of Buildings and Walkways Against Vibrations, ISO, Geneva, Switzerland.

[3] Ellis, B.R., Ji, T. and Littler, J. (2000), “The Response of Grandstands to Dynamic Crowd Loads,” Proceedings of The Institution of Civil Engineers – Structures and Buildings, Vol. 140, No. 4, pp. 355–365.