Sensitive use analysis DG11

The vibration check calculations can be performed for sensitive equipment & occupancy if required.

These calculations make use of Chapter 6 of DG11 2nd Edition (2016) with revisions and errata of 27 July 2018. They only cover ⅓ octave spectral velocity and acceleration.

For these calculations the mode shape factors ɸ_E and ɸ_W are taken as 1.0. i.e. it is conservatively assumed that the walker and sensitive equipment or sensitive occupant are both at mid-bay.


Use Case - Sensitive Equipment If walking speed = Very Slow ,
f_step	=	1.25 Hz	[Table 6-1]
V_1/3	=	(250 * 10⁶) / (β * W) * (f_step^2.43 / f_n^1.8) * (1 - e^{-2πβ*fn / fstep})	[Eqn 6-3a]
A_1/3/g	=	(100 * 4.2) / (β * W) * (f_step^2.43 / f_n^0.8) * (1 - e^{-2πβ*fn / fstep})	[Eqn 6-8a]
Else if walking speed = Slow , or Moderate or Fast
f_step , f_L , f_U and γ as appropriate to selected walking speed			[Table 6-1]
If f_n ≤ f_L
V_1/3	=	(175 * 10⁶) / (β * W * f_n^0.5) * (e^-γ*fn)	[Eqn 6-3b]¹
A_1/3/g	=	(100 * 6.4) / (β * W) * (e^-γ*fn)	[Eqn 6-8b]¹
If f_n ≥ f_U
V_1/3	=	(250 * 10⁶) / (β * W) * (f_step^2.43 / f_n^1.8) * (1 - e^{-2πβ*fn / fstep})	[Eqn 6-3b]²
A_1/3/g	=	(100 * 4.2) / (β * W) * (f_step^2.43 / f_n^0.8) * (1 - e^{-2πβ*fn / fstep})	[Eqn 6-8b]²

Else if f_L < f_n < f_U For V_1/3 evaluate [Eqn 6-3b]¹ with f_n = f_L , then evaluate [Eqn 6-3b]² with f_n = f_U , then linear interpolate for actual f_n For A_1/3/ g evaluate [Eqn 6-8b]¹ with f_n = f_L , then evaluate [Eqn 6-8b]² with f_n = f_U , then linear interpolate for actual f_n


Use Case - Sensitive Occupancy DG11 2nd Edn does not provide explicit ⅓ octave spectral Acceleration equations for Sensitive Occupancy, so in Tekla Structural Designer these equations have been derived from the ⅓ octave spectral Acceleration equations for Sensitive Equipment by ‘modifying’ them by factors 200/250 (for very slow walking) and 120/175 (for other walking speeds). These modification factors are derived from consideration of the differences between ⅓ octave spectral Velocity equations for Sensitive Equipment and Sensitive Occupancy, which are given explicitly in DG11 2nd Edn.
If walking speed = Very Slow ,
f_step	=	1.25 Hz	[Table 6-1]
V_1/3	=	(200 * 10⁶) / (β * W) * (f_step^2.43 / f_n^1.8) * (1 - e^{-2πβ*fn / fstep})	[Eqn 6-9a]
A_1/3/g	=	(200/250)(100 4.2) / (β * W) * (f_step^2.43 / f_n^0.8) * (1 - e^{-2πβ*fn / fstep})	[Eqn 6-8a] modified


Else if walking speed = Slow , or Moderate or Fast
f_step , f_L , f_U and γ as appropriate to selected walking speed [Table 6-1]
If f_n ≤ f_L
V_1/3	=	(120 * 10⁶) / (β * W * f_n^0.5) * (e^-γ*fn)	[Eqn 6-9b]¹
A_1/3/g	=	(120/175)(100 6.4) / (β * W) * (e^-γ*fn)	[Eqn 6-8b]¹ modified
If f_n ≥ f_U
V_1/3	=	(200 * 10⁶) / (β * W) * (f_step^2.43 / f_n^1.8) * (1 - e^{-2πβ*fn / fstep})	[Eqn 6-9b]²
A_1/3/g	=	(200/250)(100 4.2) / (β * W) * (f_step^2.43 / f_n^0.8) * (1 - e^{-2πβ*fn / fstep})	[Eqn 6-8b]² modified


Else if f_L < f_n < f_U For V_1/3 evaluate [Eqn 6-9b]¹ with f_n = f_L, then evaluate [Eqn 6-9b]² with f_n = f_U , then linear interpolate for actual f_n For A_1/3/ g evaluate [Eqn 6-8b]¹ modified with f_n = f_L , then evaluate [Eqn 6-8b]² modified with _n = f_U , then linear interpolate for actual f_n