floor vibration analysis

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STAAD.Pro 2005 Release Report

AD.2005.2.1 Floor Vibration Analysis

Purpose

The adequacy of a floor system from the standpoint of its vibration serviceability due to humanactivity, specifically walking excitation, can now be assessed using STAAD.Pro. Theprocedures of Chapters 3 and 4 of the AISC Steel Design Guide Series No. 11 - FloorVibrations due to Human Activity - have been implemented.

Description

To utilize this feature, the floor system must be defined as a composite deck. The compositedeck modeling feature of the program was introduced in the second edition of STAAD.Pro2004, and is explained in the Software Release report for that edition. An example of itsapplication is discussed later in this section.

The vibration calculation is done for

a. beam or the joist modeb. girder mode

The two modes are then combined to obtain the system frequency and other results of thecombined mode using the Dunkerley relationship described in chapter 3 of the AISC DesignGuide. Results for the 2 basic modes and the combined mode are provided in a tabular form.

The output for the combined mode consists of

a. the peak acceleration for walking excitationb. allowable acceleration (known in the code as the acceleration limit)

The design criterion as stated in the code in the third paragraph in Chapter 4 is that a floor system is satisfactory if the peak acceleration does not exceed the acceleration limit.

Theoretical Basis

The fundamental natural frequency of the joist mode and the girder mode can be determinedfrom equation 3.3 on page 11 of the design guide:

f j / g = 0.18 ( g / delta ) ½ ------ ( 1 )

f j / g

= fundamental natural frequency of the joist or the girder mode. g = acceleration due to gravity delta = midspan deflection of the member due to the weight supported.

For the combined mode, the fundamental natural frequency can be determined from equation3.4 on page 11 of the design guide:

f = 0.18 / delta + delta ½ ----- 2

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f n

= fundamental natural frequency for the combined mode

g = acceleration due to gravity

delta j

= joist deflection due to the weight supported delta

g= girder deflection due to the weight supported.

deltag

and delta j

are the local deflection of the joist and the girder determined from a

secondary operation after the analysis. The sti ffness analysis will yield the global deflectionvalues for the girder beams. A line joining the start and the end nodes of the girder beam in itsdeflected position is created as a base line. Relative to this base line, the deflection values arezero for the start and end nodes. The local deflection values of the intermediate points of thegirder beam are evaluated from the global deflection values relative to this base l ine.

It is this local deflection that is used in calculating the fundamental natural frequency asshown in the earlier equations. Further, the local deflection is also used in calculating theequivalent uniform loading on the joist and the girder, w

jand w

g, as shown in the equation on

page 21 of the AISC Design Guide:

384 Es

Ij / g

delta j / g

w

j / g= ---------------------- --------- ( 3 )

5 Lj / g

4

I j / g

= moment of inertia of the effective joist or girder section. L

j / g= joist or girder span

Es

= modulus of elasticity of steel.

In addition to the terms f j, delta

j, w

jshown above , the following additional terms - D

s, D

j, B

jand W

j- which are explained below, are also reported for the joist mode.

Ds

is the transformed slab moment of inertia per unit width and is determined from the

equation at the bottom right corner of page 17 of the AISC Design Guide:

de

3 D

s= --------------

12n

where de

= effective depth of the concrete slab, usually taken as the depth of the concreteabove the form deck plus one-half the depth of the form deck.

N = dynamic modular ratio = Es / 1.35 E

c

Ec

= modulus of elasticity of concrete

D j

is the joist or the or beam transformed moment of inertia per unit width, and is determinedfrom the equation shown at the top left of page 18 of the AISC Design Guide:

I j

D j

= --------------S

S = joist or beam spacing.

B is the effective width for the beam or joist panel mode and is determined from equation 4.3a





on page 17 of the AISC Design Guide:

B j

= C j

(Ds / D

j) ¼ L

j<= 2 / 3 x floor width

C j

= 1.0 for interior panels= 2.0 for edge panels

W j is the weight of the beam panel and is calculated from equation 4.2 on page 17 of the AISCDesign Guide and page 21 left side:

W j

= w j

B j

L j

( x 1.5 if continuous )

For the girder mode, the terms reported include f g

, deltag, w

gwhich were explained earlier,

and, Dg

, Bg

and Wg

which are described below.

Dg

is the girder transformed moment of inertia per unit width described on page 18 of theAISC Design Guide:

Dg

= Ig

/ L j

for all but edge girders= I

g / 2L

jfor edge girders.

Bg

is the effective width for the girder panel mode and is determined by equation 4.3b on page18:

For the interior panel- Bg

= Cg

(Dg / D

j) ¼ L

g<= 2 / 3 x floor width

For edge panel, Bg

= 2 / 3 L j

Cg

is defined on page 18 as:

Cg

= 1.6 for girders supporting joists connected to girder flange (e.g., joist seats )

= 1.8 for girders supporting beams connected to the girder web.

Wg

is the weight of the girder panel and is calculated by equation 4.2 on page 17 and describedon page 21:

Wg

= wg

Bg

Lg

( x 1.5 if continuous )

For the combined mode of vibration the parameters reported are f n

, W , beta , Peak Acceleration and Acceleration Limit.

f n

is calculated from equation 2 shown above .

W is the equivalent panel weight in the combined mode and is calculated from the equationshown on page 21 of the AISC Design Guide:

delta j

deltag

W = ------------------- W j

+ --------------------- Wg

delta j

+ deltag

delta j

+ deltag

Beta is the value of the damping ratio as per Table 4.1 on page 18 of AISC Design Guide.





The peak acceleration due to walking excitation is then determined from the equation 4.1 onpage 17 and on page 21 of the AISC Design Guide:

ap

P0

exp ( - 0.35 Fn

)----------- = ----------------------------

g beta x W

ap = peak acceleration value due to walking excitationP

0= a constant force representing excitation and is determined as per Table 4.1 of the Design

Guide.f n

= fundamental natural frequency in combined mode.

The acceleration limit is determined from Table 4.1 on page 18 of the Design Guide.

Tutorial problem

A composite deck is system composed of a concrete slab lying over a steel deck with orwithout ribs. The steel deck in turn is supported by steel beams or joists and they span thedistance between girders and are supported by those gi rders. The slab may or may not beconnected to the joists by shear studs.

To model this system in STAAD, one has to go to Geometry > Composite Deck from the leftside of the screen as shown in the next figure:

Figure 70





A box titled Composite Deck opens up on the right side of the screen as shown in the nextfigure.

Figure 71

When you click on the “Create New Deck” tab, you will see the mouse cursor change to look like an icon of a colored composite deck. To define the periphery of the composite deck, click the corner nodes in clockwise or counter-clockwise sequence using this mouse cursor. The lastclick must be on the starting node to close the periphery. In the figure shown, the sequenceused is A-B-C-D-A.

Figure 72

Immediately upon closing the periphery, a box titled “New Composite Deck” will appear asshown in the next figure. Specify any name with which to identify the deck, and click on OK.





Figure 73

The name of the composite deck will appear in the “Composite Deck” box. Click on that nameand then dialog box will display several additional contents as shown in the next f igure.

Figure 74

In the main view, the composite deck will appear in hatched lines. An arrow mark will indicatethe direction along which the composite deck spans. This arrow will appear by default. Tochange the span direction, select two beams whose X axis is perpendicular to the intended spandirection, and click on the tab “Create Direction”.Define the concrete properties, rib properties and connectivity details in the appropriate fields





of the “Composite Deck” dialog box. To save the properties, click on the tab “Update Deck Property” (see previous figure). A sample data set is shown in the next figure.

Figure 75

Command in the STAAD input file

When the data is specified in the dialog boxes as we saw earlier, it is also simultaneouslystored in the STAAD input file in the appropriate command syntax. For the data we specifiedpreviously, the corresponding editor input will be as follows:

START DECK DEFINITION _DECK FLOOR1 PERIPHERY 1 TO 8 DIRECTION -1.000000 0.000000 0.000000 COMPOSITE 10 9 4 8 OUTER 1 4 8 5 DIA 0.000 HGT 0.000 CT 0.271

FC 576.000 RBW 2.000 RBH 0.167 SHR 0 VENDOR NONE CD 0.110





CMP 2.0 CW 10.000000 MEMB 10 CW 10.000000 MEMB 9 CW 5.000000 MEMB 4 CW 5.000000 MEMB 8 END DECK DEFINITION

Floor Vibration Report

In order to obtain the report, the finished model must be successfully analyzed. Go to the post-processing mode. From the Report menu on the top of the screen, select Floor Vibration Report as shown in the next figure.

Figure 76

A box titled “Floor Vibration Output” as shown in the next figure will appear. Select the deck

name, the load case, and click on Check to see the report.

Figure 77

An output similar to the one shown below will appear.





Figure 78

The terms displayed in the above box have been explained earlier.

Sample STAAD input file :

STAAD SPACE INPUT WIDTH 79 UNIT FEET KIP JOINT COORDINATES 1 0 0 0; 2 10 0 0; 3 20 0 0; 4 30 0 0; 5 0 0 35; 6 10 0 35; 7 20 0 35; 8 30 0 35; 9 0 -15 0; 10 30 -15 0; 11 0 -15 35; 12 30 -15 35; 13 0 15 0; 14 30 15 0; 15 0 15 35; 16 30 15 35; 17 10 15 0; 18 20 15 0; 19 20 15 35; 20 10 15 35; MEMBER INCIDENCES 1 1 2; 2 2 3; 3 3 4; 4 4 8; 5 8 7; 6 7 6; 7 6 5; 8 5 1; 9 2 6; 10 3 7; 11 1 9; 12 4 10; 13 5 11; 14 8 12; 15 1 13; 16 4 14; 17 5 15; 18 8 16; 19 13 17; 20 17 18; 21 18 14; 22 14 16; 23 16 19; 24 19 20; 25 20 15; 26 15 13; 27 17 20; 28 18 19; DEFINE MATERIAL START ISOTROPIC STEEL E 4.176e+006 POISSON 0.3 DENSITY 0.489024 ALPHA 6.5e-006 DAMP 0.03 END DEFINE MATERIAL MEMBER PROPERTY AMERICAN 4 8 TO 18 22 26 TO 28 TABLE ST W18X35 1 TO 3 5 TO 7 19 TO 21 23 TO 25 TABLE ST W21X50 START DECK DEFINITION _DECK C2 PERIPHERY 1 TO 8 DIRECTION -1.000000 0.000000 0.000000 COMPOSITE 10 9 4 8 OUTER 1 4 8 5 DIA 0.000000





HGT 0.000 CT 0.271 FC 576.000 RBW 2.000 RBH 0.167 SHR 0 VENDOR NONE CD 0.110 CMP 2.0 CW 10.000000 MEMB 10 CW 10.000000 MEMB 9 CW 5.000000 MEMB 4 CW 5.000000 MEMB 8 _DECK C3 PERIPHERY 19 TO 26 DIRECTION -1.000000 0.000000 0.000000 COMPOSITE 28 27 22 26 OUTER 13 14 16 15 DIA 0.000000 HGT 0.000 CT 0.800 FC 476.000 RBW 0.500 RBH 0.500 SHR 0 VENDOR NONE CD 0.150 CMP 2.0 CW 10.000000 MEMB 28 CW 10.000000 MEMB 27 CW 5.000000 MEMB 22 CW 5.000000 MEMB 26 END DECK DEFINITION CONSTANTS MATERIAL STEEL MEMB 1 TO 28 SUPPORTS 9 TO 12 FIXED LOAD 1 LOADTYPE None TITLE LOAD CASE 1 SELFWEIGHT Y -1 UNIT FEET POUND ONEWAY LOAD YRANGE 0 0 ONE -57 GY UNIT FEET KIP PERFORM ANALYSIS PRINT STATICS CHECK FINISH


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