Vibration of floors and footfall analysis - Autodesk … 20, 2016 · Vibration of floors and footfall analysis 20/04/2016 Artur Kosakowski ... AISC DG 11 : Acceptance criteria for

Webinar Autodesk Robot Structural Analysis Professional

Vibration of floors and footfall analysis

20/04/2016

Artur Kosakowski

Rafał Gawęda

© 2016 | Global Customer Support & Operations

Webinar summary

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In this webinar we will focus on the theoretical

background and present floor vibrations and footfall

analysis in Robot.


This webinar: Vibration of floors and footfall analysis

Dynamic analysis of structures

Modal analysis definition

Dynamic mass definition

Forced harmonic analysis in the frequency domain (FRF)

Footfall analysis

Frequent mistakes

Tips & tricks

Next webinar: Time History Analysis

Topics covered in this Webinar and what we

plan for the next one:

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Basis of dynamic analysis

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M * a(t) + C * v(t) + K * d(t) = F(t)

where:

M - mass matrix

K - stiffness matrix

C - damping matrix

d - displacement vector

v - velocity vector

a - acceleration vector

F - load vector

t - time


Dynamic modal analysis

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For this type of analysis the previous general equation simplifies to the following form:

M * a(t) + K * d(t) = 0

This equation defines the eigenvalue problem and by solving it we can obtain natural

frequencies (eigenfrequencies) and determine associated shapes (modes, eigenvectors) of

free vibrations of a structure.

Mind that the mass matrix M Robot can be influenced by defined added masses or load to mass

conversion.


Harmonic analysis in the frequency domain

(FRF)

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This analysis is intended for specific type of forced vibrations. It treats all loads defined in

the associated load case as amplitudes of harmonic force from some range of

frequencies.

The obtained results (displacements, accelerations, forces, moments, etc.) are also

amplitudes corresponding to steady-state sinusoidal harmonic vibrations.



(FRF)

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Peaks on this diagram correspond

to resonance observed for natural

frequencies of the structure. In case

of no damping these peaks would

go to the infinity.

In case of a model with many dynamic degrees of freedom and with non-zero damping the

typical diagram of response in the function of frequency may look as on the picture below:



(FRF)

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The same type of diagram from

FRF analysis in Robot obtained

for the slab with using 1%

damping declared.



(FRF)

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Inflence of damping value on the reduction of the resonace peaks

1% damping 3% damping


The Steel Construction Institute

SCI P354, Design of Floors for Vibration, 2007 rev. 2009

SCI AD 253

SCI AD 254

SCI AD 254

The Concrete Centre, A design Guide for Footfall Induced Vibration of

Structures, 2006

AISC DG11, Floor Vibrations Due to Human Activities, 2003

Footfall analysis

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The implementation of the footfall analysis in Robot is based on:

SCI and Concrete Center publications additionally refer to BS 6399-1, BS 6472,

BS 6841, EN 1990:2002, ISO 2631, ISO 10137


Footfall analysis

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Footfall analysis is to some extent similar to harmonic FRF analysis – it is also based on harmonic

sinusoidal force input but instead of single harmonic a complex continuous founction is used instead.

This function „can be broken down into a series of sine waves, each of which has a frequency at

an integer multiple (or harmonic) of the forcing frequency. Each harmonic will have an

associated amplitude and phase shift, and the set of harmonics are known as a Fourier series.”

The first harmonic, with the lowest frequency, corresponds to the frequency of footsteps. This

frequency for floors in various methods is in the following range:

1.8 to 2.2 Hz for SCI P354

1.0 to 2.8 Hz for Concrete Centre

1.6 to 2.2 Hz for AISC DG11

In all these methods 4 harmonics are used.

In case of footfall analysis for stairs (SCI P354) the range of footstep frequency is higher (1.2 to 4.5 Hz)

and only 2 harmonics are used


Footfall analysis

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The example of representing low

impact aerobics as Fourier series

Walking activity on floors is

approximated in SCI P354 by 4

harmonics with amplitudes Fh and

frequencies and phase angles

given in this formula and table


Footfall analysis

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Response of a structure to footfall depends both on the

frequency of force function (footfall) and eigenfrequencies

of the floor.

Types of responses:

resonant – when the response for the consecutive

footsteps „builds up” (cumulates), especially for these

harmonics of footsteps which have the same

frequencies as the natural frequencies of the floor.

impulsive (transient) – significant mainly for high

frequency floors (having the fundamental frequency

higher than the 4th harmonic of walking). In such

situation the response from one footstep will fade away

before the next one starts.


Footfall analysis

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The resonant response is calculated in the way similar to harmonic FRF analysis by

composing the response from different harmonics

The impulsive (transient) response is calculated as for the time history analysis for single

footfall impulse

It is observed that:

the resonant response is dominating for low frequency floors

the impulsive (transient) response is dominating for high frequency floors.

The code defined limit can be different e.g.: the 4th harmonic of walking frequency; 8 Hz;

4.2 times the maximum walking frequency; 10 Hz

Mind that Robot for Concrete Centre and for SCI provisions provides results for both responses as

especially that for irregular floors resonant response may dominate in some parts of the floor while

impulsive (transient) response may dominate in other parts.


Footfall analysis

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Presentation of variable acceleration (response):

Peek value

root-mean-square (rms) value

In case of sinusoidal signal the rms value is √2 times less than the peak value.

root-mean-quad (rmq) value:

It gives more emphasis to higher values


Footfall analysis

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Acceptance criteria for human comfort

Human perception of vibrations depends on their frequency.

This diagram shows the „base curve” for human perception of

continuous vertical vibration according to BS 6472. It uses rms

acceleration and logarithmic scale.

In the most sensitive frequency range, between 4 and 8 Hz, the

criterion is constant acceleration. Above 8 Hz it is linearly

increasing acceleration which corresponds to constant velocity.

Such base curve is directly used by Concrete Centre and

refered to in SCI P354 and AISC DG11.


Footfall analysis

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The basic value, calculated by footfall analysis for SCI P354 and for Concrete Centre

provisions, is the response factor (R). It is a multiplier for the level of vibration compared

to the average threshold of human perception.

Mind that the response factor of 1 corresponds to the magnitude of vibration just perceptible by

typical human while R=2 corresponds to vibration twice stronger, R=4 corresponds to vibration 4

times stronger than perceptible and so on.

In case of the resonant response R is calculated for each harmonic and then combined

as SRSS (square root of the sum of squares) combination.

In case of impulsive (transient) response R is based on RMS values calculated from

time histories using 1-second averaging period.

Acceptance criteria for human comfort


Footfall analysis

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SCI P354, based on BS 6472: AISC DG 11 :

Acceptance criteria for human comfort – code defined limits:


Footfall analysis

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Recommendations from references: Using the dynamic value of the modulus of elasticity for the concrete, 38 GPa for normal

weight concrete, 22 GPa for lightweight concrete

Recommended values of relative damping:

Load to mass conversion:

unfactored self weight and other dead loads

live loads: it is recommended to convert to masses only 10% of nominal imposed load

(EN 1990 mentions 30% but it is considered as conservative)


Footfall analysis

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Footfall analysis parameters:


Frequent mistakes

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Not all required loads are converted to masses

Doubled self weight due to unchecked Ignore/Disregard density switch

while converting to mass the load case containing the self weight load

Comparing eigenfrequencies obtained for Footfall analysis with only

mass in the Z direction active with modal analysis case where all

directions are active.


Tips & tricks

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The default maximum frequency limit of 15 Hz in Footfall analysis may

result in having no results for a structure with vibration frequencies higher

than this limit.

Depending on the method some results of footfall analysis such as e.g.:

velocities for SCI P354, RMS acceleration for Concrete Centre provisions,

transient/impulsive results, velocities and RMS acceleration for AISC

DG11) may be not available.

In case of large number of modes below

15 Hz limit running Footfall analysis may

take long time. Starting from RSA 2016

SP3 it is possible to speed up analysis

several times by setting the Lanczos

Method in Job Preferences.


Tips & tricks

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The Self excitation method in Footfall analysis calculates and stores the

response only for the same nodes where excitation forces were applied.

For the Full excitation method in Footfall analysis the solver can

calculate results for selected nodes which are not the ones where

excitation forces are applied. These results are available in „Footfall

analysis – tables” and „Footfall analysis – maps...”.

„Footfall analysis – diagrams...” are calculated „on line” and can be used

to access results for all nodes for both above methods regardless of

their original node selection.


Tips & tricks

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The footstep excitation forces are applied independently for each of the

nodes and there is no interaction between them.

In Harmonic FRF analysis excitation forces can be aplied simultaneously

in different locations but they are limited to the same frequency in all

these locations with no phase angles among them.

Footfall analysis is limited to standard walking activities. In this type of

analysis it is not possible to calculate e.g. the influence of crowd

movement or aerobics activities or interaction between footstep

excitation forces.

In case you need more use Time History Analysis


Useful links

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Robot webinars

Robot discussion forum

Robot troubleshooting articles on AKN

https://www.youtube.com/watch?v=3G5NwyDSzxs&feature=youtu.be&list=PLY-ggSrSwbZqow_60fiqJwS69mg1nQMzk

http://forums.autodesk.com/t5/robot-structural-analysis/bd-p/351

http://knowledge.autodesk.com/support/robot-structural-analysis-products/troubleshooting


Questions ?

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We may not be able to answer all questions during the webinar. Please post them on the Robot

forum after the presentation.

Please feel free to ask questions using « GoToMeeting » Questions tab now

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errors that may appear in this document.

© 2016 Autodesk. All rights reserved | Global Customer Support & Operations

Next webinar session on 25/05/2015 on the following topic :

Time history analysis

Documents

Vibration of floors and footfall analysis - Autodesk … 20, 2016 · Vibration of floors and footfall analysis 20/04/2016 Artur Kosakowski ... AISC DG 11 : Acceptance criteria for