• No results found

Modelling of Floor Slabs in Dynamic Analysis

N/A
N/A
Protected

Academic year: 2020

Share "Modelling of Floor Slabs in Dynamic Analysis"

Copied!
8
0
0

Loading.... (view fulltext now)

Full text

(1)

Modelling Of Floor Slabs In Dynamic Analysis

K V Subramanian l) R P Sudarasan 2)

1) TCE Consulting Engineers Limited., Mumbai, India

2) Nuclear Power Corporation of India Limited, Mumbai, India ABSTRACT

This paper discusses various approaches to modelling of floor slabs in R.C.C flamed structures of auxiliary b.uildings in Nuclear Power Plants. While stiffness of floor slabs for horizontal excitation depends on the in-plane stiffness, response in the vertical direction is governed by the flexural behaviour of the floor slabs modelled appropriately. For the various approaches to modelling, responses are evaluated and compared. Floor response spectra generated using the modelling approaches are compared to recommend an appropriate model for modelling of floor slabs.

I N T R O D U C T I O N & SCOPE

Auxiliary buildings in Nuclear Power Plants are RCC framed structures with floor slabs at various elevations. Shear walls, columns and beams form part of the framing system. Main beams or secondary beams form the edges of the floor slabs. While the stiffness of the floor slabs for horizontal excitation depends on the in-plane stiffness, the response to vertical excitation is governed by the flexural behaviour with the masses lumped appropriately. The distribution of lumped masses in plan at each floor level influences the vertical frequencies and the system response. Different approaches to modelling are considered and the responses studied with reference to a given seismic excitation. The generated floor response spectra, an important input for the design of the secondary systems, are also examined to evaluate the appropriateness of the model. TYPES OF F L O O R M O D E L S :

For three-dimensional framed structural systems, three approaches to modelling of floor slab panels are examined: 1. Model 1: In this model, the secondary beams in the structural slab are not considered. Floor slabs are modelled

as a single panel bounded by main beams and masses are lumped at beam-column junctions only. Masses are lumped at main beam column junctions only. Masses of the secondary beams are proportionately lumped at the nearest node.

2. Model 2.: As in model 1, in this case the secondary beams are not modelled. However, addition to the stiffness to the slab panel due to the presence of the secondary beams is considered. The equivalent thickness is worked out based on the principle of stiffness equivalence. The equivalent thickness is derived by equating the deflection at the centre of the slab panel obtained by finite element analysis of the slab panel with fixed boundary conditions to the deflection of a slab panel with equivalent thickness. Lumped masses are calculated based on the actual floor thickness and other superimposed loads. Masses are lumped at all main beam column junctions, midpoints of main beams, mid-panel points. Masses of the secondary beams have been proportionately lumped at the nearest node. The slab panels are modelled as four plate and shell elements between the main beams.

3. Model 3:This is the closest finite element representation of the floor with all main beams, secondary beams, openings truly modelled. Masses are lumped at beam column junctions, main beams and secondary beam junctions, mid points of main beams where no secondary beam intersects, and midpoints of secondary beams. Any points on the beams where equipment are located are appropriately considered. Masses of the slabs are propo~ionately lumped at the appropriate panel nodes.

Using the models defined above, the response of a chosen structure is evaluated to draw conclusions.

P R O B L E M C H O S E N

A single storeyed structure is adopted for this study. The structure consists of four bays in the X- direction spaced at 7.3m and six bays in the Y- direction at 7.0m spacing. All the columns originate at EL 0.0m and are fixed at this level. The first floor is at EL 8.00m. Alternate panels have one or two secondary beams shown in Fig 1. Some cut-outs exists in the slab as indicated in the figure. The sectional properties and material properties adopted are indicated under Fig 1. For this model, the structure is modelled using the three models described above.

SMiRT 16, Washington DC, August 2001

Paper # 1458

(2)

7 3 0 0 7 3 0 0 7 3 0 0 7 3 0 0 _

E] ] [

E] ] [

@ E] ] [] SECT ON AXIS @

E] ] [ ]

AS

[ ] ] [ ]

E] ] [ ]

Y BEA

©

®

Fig.1

Model 1" (M1) (Figure 2)

Single plate element thickness 175 m m L u m p e d mass nodes

B e a m elements Column elements Plate elements

Model 2: (M2) (Figure 3) L u m p e d mass nodes Column elements B e a m elements Plate elements

Model 3" (M3) (Figure 4) L u m p e d mass nodes Column elements

B e a m elements (main & sec)

D a t a : -

Column: - 1.0m x 1.0m Main beams: - 0.45m x 1.2m Secondary beams: - 0.35m x 0.8m Poisson's ratio: - 0.2

Modulus of elasticity:- 2.85 E6 t/m 2 t - s e c / m

Mass density: - 0.24 2

Live load: - 1 t/m 2 Slab thickness :-0.175m

35 58 35 22

115 35 115 86

142 35

199

O - - - - N O D E S

[~:~----COLUMN NOS/Gn LEVEL NODE NOS I-"-I----BE.AM NOS

* * * ----SLAB NOS.

(3)

r-~ r - ~ r-~ r,m r~q 258

@

°

~ ][

,- iN

@

- L U M P E D MASS NODES 115 O -NODES

L_.~-COL NOS/Gn LEVEL NODE NOS I"-"1-BEAM NOS.

* * * Sba~B NOS.

Fig. 3 MODEL 2

oo oo5oo oo

I

-

~ [ ~ T ~

~ %T~ ~

~ % ~

- ~ ,

9 ~ ' ~ D ~

~'~'D~ ' ~ D ~

~ E

r~

®.~

r~

E ~

[ , r ~ ¸

250 7

2.51 252 255 ~ 254- 256 257

• - - - - L U M P E D MASS NODES(TOTAL 14-2) O - - - - N O D E S

I---1 - - - - B E A M S

- - - - C O L N O S / G n L E V E L S A M E AS M O D E L 2.

Fig. 4 MODEL 3

@

E]

F

(4)

The study was performed on ANSYS. For all the three structural models free vibration response was determined. The number of modes extracted were such that mass participation was close to 1.0 in all the three directions. To achieve this, for the vertical direction, 27 modes were extracted for model 1, 107 modes for model 2, 134 modes for model 3. Table 1 tabulates the results for free vibration analysis.

SSE spectra with 7 % damping was used as the input to evaluate the member forces in the three models. The analysis was performed in the global X, Y and Z 0.6

directions with the spectral input applied in the three 0.55 directions separately. The grouping method was used for combination of modal responses. Table 2 compares the 0.5 axial forces in the columns due to horizontal excitation 0.45 and vertical excitation. Table 3 compares the vertical shear and bending moments along two beams located AC 0.4

on grid 28 and grid Ez. NC~o.35

The mode superposition method was used to obtain the relative acceleration response histories of 0.3 nodes at EL 8000. The absolute acceleration time 0.25 history was obtained and the response spectra derived for the nodes at EL 8000. Figure 5 plots the vertical FRS for 0.2 nodes 58 & 43 for model 1. Figure 6 plots the vertical o.15 FRS for nodes 127, 1 2 1 , 1 0 4 and 142 of model 2. Figure 7 plots the vertical FRS for nodes 128,121,104 and 142 o.1 for model 3. Figures 8, 9, 10, 11 compares the FRS at a node as determined for the different models.

f

t

0 20 40

FREQUENCY(Hz)

Fig. 5 COMPARISON OF FRS FOR DIFFERENT NODES AT FIRST FLOOR L E V E L - M O D E L 1

2_8 2.6

2 4

2_2 2 1.8 1.6 5 o 1.4

o <

1.2 1

0.8

0.6

0.4 0.2 0

104

i i

0 2O 4O

FRECtEI',CY(Hz)

Fig. 6 COMPARISON OF FRS FOR DIFFERENT NODES AT FIRST FLOOR L E V E L - M O D E L 2

2 . 2 . . .

2.1- 2~

1.9 -'

1.8

1.7 1.6 -~

1.5 4 Node 104

1.4 ,:,, 1.3 5 1 2

~1.1

< 1

o.~ ~,~_~, ~ , _ _ ~

0.8 0.7 0.6

0.5

0.4 -~

o2 t

0.1 i i

2O 4O

~ ( e z )

(5)

0.60 ...

0.55

0.50

0.45

O.4O

Z ._1

o 0.35 o <

030

0.25

0.23

0.15

0.10

N

~.,,~ M o d e l 3

i ! , / / - ~ / - - M o d el 2

[ - ~_ \\ \ A ' / - - - M o d e l l

f !

i i

2O 40

~ Y ( I - I z )

Fig. 8 C O M P A R I S O N OF FRS F O R N O D E A T G R I D Ey-28 F O R D I F F E R E N T M O D E L S

0 . 6 . . .

0.55 .

0.45

z ~" 0.4

O 0.35 M o d e l 1

0.25. ""~...~.~ M o d e l 2

0.2.

0.15.

0.1 , ,

6O

0 2O 4O

~ ( H ~ )

Fig. 9 C O M P A R I S O N OF FRS F O R N O D E A T G R I D G-28 F O R D I F F E R E N T M O D E L S

2 6 . . .

2_4

2_2

2-

1.8-

1.6-

~ 1.4 o d e l 2

...i

o

~ 1.2

1

0.8

0.6- ~ ' ~ "

0.4

0.2

0 ~ ,

0 20 40 60

FFr:Ct.e'~He_)

Fig. 1 0 C O M P A R I S O N OF FRS F O R N O D E 1 0 4 - M O D E L 2 A N D M O D E L 3

..~0.9

Z

"0.8 o o

<0.7

0

1 . 6 . . .

1.5

1.4

1.3

1.2

1.1

1

d e l 3

0.5

0.4

0.3

0.2 0.1

i i

0 20 40

FREQUEN3Y(Hz)

(6)

DISCUSSIONS

Free Response Analysis

For all the three models, the frequency response analysis results in the horizontal direction compare well with one other. This indicates all the three models are satisfactory. Thus the dynamic characteristics in the horizontal direction are well represented by the Models 1, 2 & 3. Comparison of vertical frequencies indicates a reasonable agreement between the models 2 & 3. Model 1 does not reflect the frequencies of the slab panel. It can therefore be concluded from the results that model 1 is unsuitable for vertical direction response. Models 2 & 3 can be adopted for the same.

Response Spectrum Analysis

Table 2 (a) compares the axial forces in the columns due to vertical excitation. The axial forces depicted by Models 2 & 3 show a very close agreement where as Model 1 shows a different pattern of distribution. Comparison of horizontal forces due to transverse excitation indicates all the models are in good agreement in terms of the horizontal forces. Hence all the models though adequate for horizontal direction response only models 2 & 3 can be adopted for vertical excitation.

Table 3 compares the forces in the beam members along axis 28 and Ez with respect to beam shear and moment. It is evident the forces predicted are reasonably in agreement in all the three models.

Floor Response Spectra

Plots of the FRS 5,6,7 do indicate how the location of the node influences the Floor response spectra in the vertical direction. Compare Node no.104 located in a slab panel to node 121 located at beam column junction. Comparison of FRS between the models indicate with the model 3 being the closest to reality, model 2 follows closely model 3. Here model 2 is a viable alternative for modelling and determination of FRS.

C O N C L U S I O N S

,

The following conclusions can be drawn from the results of the study

For translational direction, the response is practically not influenced by the model as the floor rigidity are well represented.

For FRS, all the models are adequate as far as horizontal excitation is concerned. However for FRS in the vertical direction model 2 is recommended.

A C K N O W L E D G E M E N T

(7)

Table- 1 Free Vibration Analysis- Comparison of Frequencies (a) Vertical Direction- Z

Model 1 Mode n o 1 5 10 11 14 16 19 24 27 Frequency(cps) 33.10 33.78 36.49 36.57 40.45 41.89 42.30 42.72 43.09 Model 2

Mode Frequency

No

1 15.34

2 15.49

11 16.54

16 17.52

21 17.76

45 30.06

75 36.64

92 65.54

107 70.89

Mode No 1 3 11 14 22 48 54 61 81 84 86 91 115 123 128 130 134

Model 3 Frequency 14.91 15.02 16.37 16.63 17.15 29.64 30.69 31.99 36.75 37.68 38.44 40.86 72.31 76.92 79.93 80.23 82.43

(b) Horizontal Frequencies- X direction

Mode no

Model 1 Model 2 Model 3

Frequency(cps) 4.077 4.515

Mode No Frequency

4.133 4.636

Mode No Frequency

4.133 4.644

(c) Horizontal Frequencies- Y direction

Mode no

Model 1 Model 2 Model 3

Frequency(cps) 4.143

Mode No Frequency

4.192

Mode No Frequency

4.151

Table-2

(a) Axial Forces in columns due to vertical excitation

Column No Model 1 Model 2 Model 3

1 2 3 4 5 11 12 13 14 15 31 32 33 34 35 Total Vert Force

(8)

(b) Horizontal Forces in the columns in X direction due to X excitation

Column No Model 1 Model 2 Model 3

1 5 15 25 35 Total Horz force 30.78 25.59 37.81 34.43 22.11 1082.05 30.414 26.19 37.04 34.31 22.48 1084.01 29.75 26.65 36.13 34.49 23.16 1085.55

(c) Horizontal Forces in the columns in Y direction due to Y excitation

Column No Model 1 Model 2 Model 3

1 5 15 25 35 Total Horz force 26.445 32.581 26.94 33.11 26.411 1095.0 26.479 32.228 27.31 33.11 26.44 1095.8 26.316 32.029 26.82 32.81 26.30 1088.30 Table-3 Beam Forces - Grid 28

Beam

No 80 ne 8 2 f e 8 5 f e

Model 1 Vert Shear 29.23 16.44 21.19 Moment 83.08 57.40 82.75 Beam No 120 ne

125 fe 131fe Model 2 Vert Shear 18.74 14.41 19.07 Moment 74.03 50.04 74.57 Beam No 126 ne 132 fe 140 fe

Model 3 Vert Shear 20.96 16.32 20.98 Moment 82.46 56.94 82.38

Beam Forces - Grid Ez

Beam

No 48 ne

4 9 f e 5 1 f e

Model 1 Vert Shear 21.47 16.13 21.47 Moment 87.45 60.32 87.45 Beam No 56 ne 5 9 f e 63 fe

Model 2 Vert Shear 18.82 14.00 18.33 Moment 77.57 52.55 77.57

B e a m

No 56 ne

5 9 f e 63 fe

Figure

Fig. 3 MODEL 2  oo oo5oo oo
Fig. 5 COMPARISON OF FRS FOR DIFFERENT NODES AT FIRST FLOOR LEVEL-MODEL 1
Fig. 8 COMPARISON OF FRS FOR NODE AT GRID Ey-28 FOR DIFFERENT MODELS

References

Related documents