Vibration Plancher Beton

7/23/2019 Vibration Plancher Beton

1/13

Design of PostDesign of Post--TensionedTensioned

or an a am

President,

ADAPT

Corporation

VIBRATION DESIGN OF CONCRETE

FLOORS

Part 1 Basic information and pract ical approachWhy are we concerned about vibration;

What are the causes of vibration;

What are the allowable limits of vibration;

How to evaluate the vibration acceptability of a

floor Numerical Example

Why are we concerned about vibration ?

Vibrations may be considered as annoying by

occu ants

Threshold of perceptionThreshold of annoyance

Vibrations may interfere with the functions of

,

Each lab/instrument has its own specific limits o

acceptable vibration


FLOORS

a are e causes o v ra on

Most common cause is foot drop (heel drop)

occupants;

Dynamic impact from rolling object.

What are the allowable limits of vibration?

Perception of vibration depends on:

Frequency (cycles per second, Hz); and Peak acceleration (expressed as percentage of

Consensus is that humans are most sensitive to

vibration for fre uencies between 4 to 8 Hz.

Higher accelerations can be tolerated at higher

or lower frequencies.

PERCEPTION OF VIBRATION


Frequency (Hz); and

Peak acceleration

1.50

ion(%g

)

0.50

.

Office, residence,assembly hall

kAcce

lera

0.25

1 2 4 8 12 20

rooms

Pe

ATC = A lied Technolo Council

Threshold of Human Sensitivity to Vertical Vibration

(ATC)


2/13


FLOORS

How to evaluate the vibration acceptability of a

floor?

6 steps for complete evaluation

Step 1 - Determine natural frequencies (Hz)

ep e ec exc ng orce o v ra on

Step 3 - Select floor type

Step 4 Calculate the weight of vibrating panel

Step 6 - Evaluate the floor

Numerical example

NATURAL FREQUENCIES

Step 1 - Determine natural frequencies (Hz)

Use Finite Element Method with plate elements, or

empirical formulas

For specific areas, such as a lab or operating roomdetermine the dominant frequencies of the

location of interest.

Observe vibration modes of the above floor system

EXITING FORCE OF VIBRATION

Step 2 - Select exciting force of vibration

Use the following graph to determine the exciting

force

1.0

actor(DLF)

0.6

0.8

namicL

oad

0.4

D

0 1.0 2.0 3.00

.

Dynamic Load Factor for First Harmonic of

Walking Force

Exciting force = DLF * (Weight of Person)

TRANSMISSION PATH OF VIBRATION


Refer to the table to select damping factor ();

in most cases 0.03 applies

The recommended values vary from 2-3% for bare

concrete floors to 5-8% for furnished rooms with

artitions extendin full hei ht.

RECOMMENDED DAMPING

FACTORS FOR VARIOUS OCCUPANCIES

OccupancyDamping factor

are concrete oor .

Furnished, low partition 0.03

Furnished, full height partition 0.05

Shopping malls 0.02


3/13

PEAK ACCELERATION

Step 4 Calculate weight of target panel (W)Include superimposed load that follows the vibration

stones; tiles

Step 5 Calculate Peak Acceleration (ap/g)Use an empirical relationship, such as the one below for

1

0.35fnp 0

a P e

a = eak acceleration

g W

g = gravitational acceleration [32.2 ft/sec2; 9.81 m/sec2 ];

Po = constant force representing the walking force (fromStep 2 and weight of walking person);

= modal damping ratio, from previous table

W = effective weight of the panel and the superimposedload; and

n .

PERCEPTIBILITY OF MOTION

Step 6 Evaluate the floor Use natural frequency from Step 1; and

Peak ground acceleration (ao/g) from Step 5; and

Chart below from ATC to determine acceptability

1.50

n(%g

)1.00


Acceleratio

0.25

.

1 2 4 8 12 20

Operatingrooms

Peak

Threshold of Human Sensitivity to Vertical

Vibration ATC

Frequency (Hz)

NUMERICAL EXAMPLE

Numerical Example

ven Concrete floor system

Slab thickness 8 (203 mm)

Superimposed DL 20 psf (1 kN/m2)

oncre e c ps . a

Modulus of Elasticity 1.2 Ec

Required

identified under foot drop

NUMERICAL EXAMPLE

TNO_123

Slab thickness8'' (200mm)

(a) Floor plan Column18'' x 24''(460mm x 610mm)

26'-3''(8.00m)

30'-0'' (9.14m)

Identification of Panel for Vibration Evaluation

(b) Panel plan


4/13


FLOORS

Step 1Determine natural frequencies (Hz) Generate model of the entire floor Use modulus of elasticity 1.2Ec

Include weight of objects attached to floor

Obtain first few natural frequencies

Discretization of the Floor for a


FLOORS

.

.

(c) Third mode frequency 6.44 Hz

Demonstrate live


FLOORSStep 2 - Select exciting force of vibration

Weight of person 150 lb (667 N)

From the chart:

DLF = 0.53

Po = 0.53 * 150 = 79.5 lb (354 N)

) 0.8

1.0

dFactor

(DLF

0.6

DynamicLoa

0.2

0.4

Frequency Hz

0 1.0 2.0 3.00

Dynamic Load Factor for First Harmonic of

Walking Force


FLOORS


From below select () = 0.03 From table

Office furnished; low partitions

OccupancyDamping factor

Bare concrete floor 0.02

Furnished low artition .

Furnished, full height partition 0.05

Shopping malls 0.02


5/13


FLOORS

Step 4Calculate weight of target panel (W)

Dimensions of panel as shown below

Mortar, stone, firmly attached to floor 20 psf (1 kN/m2)

Concrete weight: 150 pcf; (25 kN/m3)

The total weight of the panel W is :

W = = 94.5 k (421 kN) 830 26.25 0.15 0.0212

TNO_123

Slabthickness8'' (200mm)

(a) Floor plan Column18'' x 24''(460mm x 610mm)

26'-3''(8.00m)

30'-0'' (9.14m)

(b) Panel plan


FLOORS

Step 5 Calculate Peak Acceleration (ap/g) Use an empirical relationship, such as the one below for

footfall.

p 0a e

g W

ap = peak acceleration;

g = gravitational acceleration [32.2 ft/sec2; 9.81 m/sec2

Po = 0.53 * 150 = 79.7 lb (0.354 kN) (step 2)

= damping ratio 0.03 (step 3)

W = 94.5 k ( 421 kN ) (step 4)

fn = first natural frequency (Hz) = 5.79 Hz (step 1).

= = 0.00367 ; 0.37%

0.35 5.9779.5 e

0.03 94.5 1000

pa

Peak ground acceleration ( ap) is calculated to be

0.37% of gravitational acceleration (g)


FLOORSStep 6 Evaluate the floor Use natural frequency from Step 1; 5.79 Hz; and

Peak ground acceleration from Step 5; 0.37% g; and

Chart below from ATC to determine acceptability

1.50

ion(%g

)

0.50

.


kAcce

lera

0.25 Panelstatus

1 2 4 8 12 20

rooms

Pe

Threshold of Human Sensitivity to Vertical

Vibration (ATC)

The target panel is acceptable for office and residential

occupancies, but not for hospital operating room


FLOORSEliminate the noise (disturbance) from non-

targeted floor regionsTNO 123

Floor plan showing

the target panel

_

First mode frequency 5.79 Hz

Note that the first mode is primarily due to

excitation of a non-tar eted re ion of floor


6/13


FLOORS

Isolate the target area for vibration analysis

The response of the isolated region is greatly

influenced by the boundary conditions specified

aroun e cu If the cut does not extend adequately beyond the

target panel, the results may not be reflective of the

prototype

Note: first frequency of the entire

floor is 5.79 Hz


FLOORS

(a) Selection of an extended region

(b) First mode of vibration Frequency 6.07 Hz

Note: first frequency of the entire

floor is 5.79 Hz


FLOORSHow can we bring the vibration of a given floor

to compliance?

Increase in weight reduces the frequencies

Increase in frequency, increases the peak acceleration

Increase in weight reduces the peak acceleration

ncrease n restra nt o oun ary con t ons,

reduction in span increases frequency

For the given example, increase slab thickness from 8

(203 mm) to 10 (250 mm)

Frequency fn = 7.72 Hz

W = 115.3 k (514 kN) 1.00

1.50

Peak acceleration(ap/g) = 0.154 %

ation(%g

)

0.50

Office,residence,assembly hall

Operatingrooms

eakAccele

0.25

1

2 4 8 12 20P

Frequency (Hz)Panelstatus


FLOORS

Part 2 Past pract ice; alternative methods

vibration evaluation Numerical Example

Estimate the natural frequencies

using empirical relationships

Make a good engineering judgment on the

probable shape of the first natural

frequency


7/13

FORMULAS FOR NATURAL FREQUENCIES

CaseBoundary

Constant

FIRST NATURAL FREQUENCY CONSTANT

1 2 1.57 1

a

b

2 2 4 1.57 1 2.5 5.14

2 41.57 5.14 2.92 2.44

4 2 4 1.57 1 2.33 2.44

5 2 4 1.57 2.44 2.72 2.44

2 4 . . . .

rigidly supported, rotationally free

rigidly supported, rotationally fixed

a span length in x-direction

b span l length in y-direction

a/b

DETERMINATION OF NATURAL

FREQUENCIES

The parameters for the Table are:

Where2

cf

a

3

2

Eh gc =

q12 1-

f = first natural frequency [Hz];a = span length in X-direction;

= .

in psi; MPa];

h = slab thickness [in; mm];

= Poissons ratio [0.2];

g = gravitational acceleration [32.2 ft/sec2 ; 9810

mm/sec2]; andq = weight per unit surface area of the slab.


FREQUENCIES

Shape of first Natural Frequency Mode

The first mode of vibration is affine to that of a

s ng e pane s mp y suppor e p a e. e s ape s

not analogous to the deflected profile under

selfweight

(a) Simple support (b) Fixed

(c) Continuous spans

First Mode Shapes and Deflection of

(d) Deflection self weight


FREQUENCY

Shape of first Natural Frequency

Use a simply supported boundary conditions along

the four sides of an interior anel

Where columns are on a regular orthogonal grid,

the first mode is likely to be in form of a one-way

slab deflecting in a cylindrical form.

Panels bounded by smaller spans, may

vibrate analogous to a rotationally fixed plate

c on nuous spans

First Mode Shapes and Deflectionof Simple and Continuous Spans

(d) Deflection self weight


8/13


FLOORS

Numerical Example

below, for foot drop having the same details in

former example, using empirical formulas

View of the Floor System


FLOORS

Step 1Envisage the probable shape of the first mode of

.

A column supported slab, such as the floor system

under consideration is likely to vibrate in form of a

cylinder(one-way system)

Probable Shape of First Mode


FLOORSStep 2Select from the Table of frequency formulas, the case

that can best simulate the envisaged shape of first

mode of vibrationTNO_123

Find the First Natural Frequency

Using the parameters of frequency table:

g 9.81 m/sec2 ;32.2 ft/sec2

First natural frequency, fn:

fn =

=

2

c

a

3dynE h g

Est = 29,000 MPa

= 4287 ksi , using ACI-318

2 q12 1

Assume Edyn = 1.2 Est = 1.2* Est

CALCULATE NATURAL FREQUENCY

FIRST NATURAL FREQUENCY CONSTANT

Boundary

Conditions

1 2 1.57 1 b

rigidly supported, rotationally free

a span length in x-direction

b span l length in y-direction

a/b

c = 2

D Eh g

m q12 1

21.57 1

fn = ( c / a2 ) (frequency of first mode)


9/13


Consider a region as shown in

the figure

b

a

a = 3*90*12 = 1080 in (42.5 m)

= 1.57(1+2) = = 20.03

290

1.57 126.25

3

2D Eh gm q12 1

c

=

*dyn . st . ,


h = 8 inch (203 mm)

q = weight/unit area =150 * 8 20

*

35144 * 1000 * 8 32.2 * 12

= 0.833 lb/ in2 ( 5.74 *10-3 MPa )

2.

0.83312 1 0.2

c = = 325,653

(2.1*108 mm2/sec

in2/sec

n = = 5.59 Hz2

* 20.031080

0.35fnp 0

g W

= = 0.004 ; 0.4 %

. .. e

0.03 94.5 1000

pa

g

Note that the weight of one panel is used for W


FLOORS

Check the Results for

ccep a y

First natural frequency (5. 59 Hz)

Peak response acceleration relative to

gravitational acceleration (0.4 %)

) 1.00

1.50

ration(%g

0.50


Operatingroomse

akAccel

0.25

Panel

status

1

2 4 8 12 20

Frequency (Hz)

,for operating rooms


FLOORS

Part 3 Impact of secondary factors

Post-tensioning

Post-tensioned slabs are generally thinner

than their conventionally reinforced

counterparts; hence, they have lower

frequencies Precompression from post-tensioning inhibits,

or reduces crack formation. Post-tensioned

slabs are stifferthan RC slabs of the same

thickness

Add picture of a PT slab???


10/13


FLOORS


Cracking of concrete

Cracking of concrete, in particular in

conventionally reinforced concrete, where hair

cracks under service condition are common

and numerous in number result in reduction of

local stiffness.

Concentration of local cracks over the supports

and at midspan can result in a change in the


FLOORS



Neutral axis

Reinforcement

(a) Cracked beam elevation

(b) Applied moment

Crackingmoment

le

Loss of stiffness due to cracking results

in shorter fre uencies


FLOORS

Part 3Impact of secondary factors


Extent of cracking under dead load. Max local

reduction in stiffness 69%

EXTENT OF CRACKING SHOWN THROUGH REDUCTION

IN STIFFNESS FOR MOMENTS ABOUT Y-Y AXIS


FLOORS


Crackin of concreteExtent of cracking under dead load. Max local

reduction in stiffness 67%

EXTENT OF CRACKING SHOWN THROUGH

REDUCTION IN STIFFNESS FOR MOMENTS

ABOUT X-X AXIS


11/13


FLOORS

art Impact of secondary factors

Floor covers; tiles; stones

Equipment that is fixed to the floor

The weight of the objects that are attached to a

floor and follow its motion in harmony should

be included in the analysis. These include tiles,

an equ pmen xe o a oor. Objects attached to a floor will add weight, but

not necessarily stiffness. Addition of weight

reduces the frequency Depending on the method of fixity of an object

to a floor, analysis software allow users to

define a fraction of the mass of each

e ui ment to be active for motion in each of the

three principal directions.

FREQUENCIES

Floors mass

Factors affecting the natural frequencies:

Damping

Extent of cracking; post-tensioning

Expresses as (W/g), W is the weight of the objects that are

attached to the floor and faithfully follow its

displacement; the greaterthe weight the larger is

the period; the smaller is the frequency (Hz)

g is the gravitational acceleration taken as

32.2 ft/sec2 9.81 m/sec2 .

Modulus of Elasticity

The elastic modulus for vibration analysis is larger

t an t e stat c va ues, n partcu ar w en g

strength concrete is used. Recommended values are 25%

.

TRANSMISSION PATH OF VIBRATION

Extent of Cracking

Cracking reduces the stiffness of a floor and

consequently lowers its natural frequency.

For conventional RC allow for cracking

For RC flat slab construction; with span to

ept rat o or arger, a ow re uct on n

stiffness due to cracking

For post-tensioned floors designed using ACI

(IBC), no reduction in stiffness is due

For post-tensioned floors based on the

Euro ean code EC2 and most other ma or

non-US codes, reduction in stiffness may be

necessary


Peo le are most sensitive to vibration when

What i s considered unacceptable?

engaged in sedentary activity while seated or lying.

Much more is tolerated by people who are

standing, walking, or active in other ways

The response acceleration is sometimes compared

with the minimum acceptable value fn using theem irical formula develo ed for steel.

nKf 2.86lnW

K = a constant, given in [Table next slide];

W = weight of area of floor panel affected by

the point load (heel drop); and

f = minimum acceptable frequency.


12/13


The response acceleration is compared with the

minimum acceptable value fn .

nK

f 2.86lnW

CONSTANT K FOR MINIMUM ACCEPTABLE

FREQUENCY

Occu anciesK

ps

Offices, residences,

assembly halls13 58

Shopping malls.

Using the values of the previous example:

=

W = 94.5 kips (421 kN) (weight of panel)

= 0.03 (damping) 132.86ln

n . .. .5

RHYTHMIC MOTIONS

rhythmic motions; dance halls; gyms;

In each instance, the evaluation starts by

estimating the following:

Maximum number of individuals that are likely

to be in step harmony

Number of foot drops per second, assume 3,

in absence of information

Estimate oftotal wei ht of ersons in ste

harmony (P)

The remainder of the analysis and evaluation

follows exactly the same procedure outlined in

foregoing examples

PERCEPTION OF VIBRATION


Frequency (Hz); and

Peak acceleration

)15.0

eration(%

10.0

Rhythmic activitiesoutdoor footbridges

PeakA

ccel

0.0

5.0

1

2 4 8 12 20

Frequency (Hz)

Threshold of Human Sensitivity to Vertical Vibration

ATC = A lied Technolo Council

VIBRATION DESIGN OF CONCRETE FLOOR

References

ADAPT Technical Note TN290, 2010, Vibration Design of

, . . ,

pp., 2010

ADAPT Technical Note TN388, 2010, Vibration Evaluation

, . . , .,2010

AISC/CISC, (1997) ,Steel Design Guide Series 11, Floor

Vibrations Due to Human Activit American Institute of ,

Steel Construction, Chicago, IL, 1997.

ATC, (1999) ATC Design Guide 1, Minimizing FloorVibration, A lied Technolo Council, Redwood Cit , CA,

1999, 49 pp.

Bares, R., (1971), Tables for the Analysis of Plates, Slabs

and Diaphragms Based on the Elastic Theory, Bauverlag

GmbH, Wiesbaden und Berlin, 1971, pp. 626

Mast, F. R., (2001),Vibration of Precast Prestressed

Concrete Floors, PCI Journal, November-December 2001,

2001, pp. 76-86.


13/13

VIBRATION DESIGN OF CONCRETE FLOORS

References

, . ., , . .,

Criterion for Vibrations Due to Walking, Engineering

Journal, Fourth Quarter, American Institute of Steel

Construction, 1993, pp. 117-129.

TR43, (2005), Post-tensioned concrete floors: Design

Handbook, Second edition, The Concrete Society , Surrey

GU17 9AB, UK.

Szilard, R., (1974), Theory and Analysis of Plates-

Classical and Numerical Methods, Prentice-Hall, Inc., New

Jersey, 1974, 724 pp.

Thank you for listening

ANY QUESTIONS?

[email protected]

Documents

Vibration Plancher Beton