Dynamic Analysis for Frame Structure Rev00_NM

DYNAMIC ANALYSIS FOR FRAME STRUCTURE

Mr. Nuttaphon Magteppong

1

Thammasat UniversityCIVIL Engineering Department

Frame structure

2

Frame structure

XYZ

X

Y2nd Plan

Frame structure

XYZ

X

YRoof Plan

Frame structure

Section properties

2nd beam section

roof beam section

All col section

All slab section

Frame structure

6

XYZ

X

Z

U1

U2K2

K1

M2

M1

Frame structure

7

U1

U2

K2

K1

M2

M1

X-direction

2

100m

mM

22

221kkkkk

K

021 KMNatural frequency and Modeshape

0det 21 KM

Frame structure

U1

U2

K2

K1

M2

M1

Mass matrix

2

100m

mM

List b(m) h(m) L(m) N Q'ty unit Weight per unit total weight (kg)Roof

roof 9.00 1.0036.0

0 1 324.00m2 40 12,960beam B2 0.20 0.40 189 1 15.12m3 2400 36,288col 0.35 0.35 1.50 18 3.31m3 2400 7,938

sum roof 57,1862nd Floor

slab+sdl 9.00 0.1536.0

0 1 48.60m3 2400 116,640beam B1 0.30 0.60 189 1 34.02m3 2400 81,648col 0.35 0.35 3 18 6.62m3 2400 15,876sum 2nd floor 214,164

180,5700164,214

M kg

Frame structure

U1

U2

K2

K1

M2

M1

Stiffness matrix

Assume: shear mode E= 20 Gpa 001251.0121 3 bdI C m4

8321 100016.21812 HEIKK N/m

22

221kkkkk

K

0016.20016.20016.20032.4108K N/m

Frame structure

Dynamic properties

Natural Frequency

669,40071.7002

n

875.1000213.4

21 2nnf Hz.Modeshape

000.1000.1334.0800.0

Mode 1 Mode 2U1U2 U1

U2

K2

K1

M2

M1

Frame structure

U1

U2K2

K1

M2

M1=

Peff2

Peff1

q1

K*1

M*1 P*1q2

K*2

M*2 P*2

tqtq

tutu

tqtu21

22121211

21)()(

Mode1 Mode1

tqtqtqtq

222112212111

1211

2212

+

Mode1 Mode2

Modal analysis

Frame structure

Input ground acceleration

geff UMP

U1

U2

K2

K1

M2

M1)2sin(4.0 tfU ugg G

)2sin(374,224

)2sin(380,840)2sin(81.94.0180,57)2sin(81.94.0164,214

tftf

tftf

Pug

ug

ug

ugeff

)2sin(374,224)2sin(380,840

000.1000.1334.0800.0* *2

*1tftf

PP

PPug

ugT

effT

N05.0 00.5ugf

)2sin(313,56

)2sin(678,896*tftf

Pug

ug

NModal analysis

Frame structure

U1

U2

K2

K1

M2

M1

Modal analysis

000.1000.1334.0800.0

180,5700164,214

000.1000.1334.0800.0* TTMM

044,8100186,194

00

*2

*1*m

mM

8*2

*1* 107840.3003607.1

00

kk

K

8* 10000.1000.1334.0800.0

0016.20016.20016.20032.4

000.1000.1334.0800.0

T

T KK

Kg

N

Frame structure

Modal analysis

tDtCtBtAetq ugnugnnnnntn n cossinsincos)(

222 211

nn

nDMF

22**0 1 nnn

nn DMFK

PC

nnnn

nn DMFK

PD 22**0

n

ugn

DUA nn 0 d

ugnnnnn

CAB

21 nd00 nU 00 nU

Frame structure

mode1 2fn (Hz) 4.213 10.875wn 26.47 68.33m*n (Kg) 194,186 81,044k*n (N) 1.3607E+08 3.7839E+08Damping 0.05 0.05beta_n 1.187 0.460P*n0 (N) 896,678 -56,313DMF 2.351 1.266wd 26.44 68.24U0n 0 0U'0n 0 0Cn -1.4876E-02 -1.8808E-04Dn -4.3219E-03 1.0965E-05An 4.3219E-03 -1.0965E-05Bn 1.7894E-02 8.6031E-05

tt

tte t

10cos10322.410sin104876.147.26sin10789.147.26cos10322.4

32233235.1

tDtCtBtAetq ugnugnnnnntn n cossinsincos)(

)(1 tq

tt

tte t

10cos10097.110sin108808.133.68sin10603.833.68cos10097.1

54554165.3

)(2 tq

tqtqtqtq

tqtq

tqtutu

tu2121

21

21 *00.100.1

*334.08.0000.1000.1334.0800.0)()(

Frame structure

U1

U2

2e5 KN/m

2e5 KN/m

57 T

214=

224 KN

840 KN

q1

1.36e5 KN/m

194 T 897 KNq2

3.78e5 KN/m

81 T -56 KN

tqtq

tutu

tqtu21

22121211

21)()(

Mode1 Mode1

tqtqtqtq

222112212111

00.180.0

00.1

33.0+

Mode1 Mode2

Modal analysis

Frame structure

U1

U2

K2

K1

M2

M1

tqtqtqtq

tqtq

tqtutu

tu2121

21

21 *00.100.1

*334.08.0000.1000.1334.0800.0)()(

0 1 2 3 4 5-0.025-0.02

-0.015-0.01

-0.0050

0.0050.01

0.0150.02

X: 0.54Y: 0.02397

Time (sec)

U 2(t) (m

)

X: 5.14Y: 0.01564

Modal AnalysisSAP2000

Modal Analysis SAP2000


1

2


1


1


1

2

3

4


1

=2400x9.81

2


=0

2



1

2

3

4


Define other section


1


Get model from template

No column


1. 2.3.

4. select all col in XZ plane (Y=6) and node and delete



Assign beam section

1.2.


Set show beam section

1.

2.


Select all beam in 2nd floor


assign beam section for 2nd floor to B1

1.2.

3.


Move to XY plane at Z=6.00

Assign all beam to section B2


Define slab


Define Area section


1.

2.

3.

Define Area section


1.

2.

3.

Define Area section


Assign slab

1.

3.

4.


Assign all slab at Z=6 to Roof


Assign all slab at Z=3 to S1


Select all slab to assign auto mesh


Select all slab to assign auto mesh


Assign auto mesh for slab






Assign fix support

Select all support

1. 2.3.

4.


Assign fix support


Define Load patterns


Define function of ground acceleration



0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4-0.4-0.3-0.2-0.1

00.10.20.30.4

Func01

Time(s)



1/fug = 1/5 =0.2

1 cycle

Total time x fug=10sec x 5Hz = 50 cycle

tfgU ug2sin4.0Hzfug 5;

Acceleration in G unit (1G = 9.81 m/s2)

G


Define Load case


Define Load case (DEAD LOAD)


Define Load case (Modal)


Define Load case (SDL)


Define Load case (ground)

Value of g in length unite/s^2

=Total time/output time step=10sec/0.01sec=1000


Select roof slab to assign load


Select roof slab to assign load


Assign roof load to roof slab


Define Mass source



Set parameter to analysis (2D analysis in XZ plane)


Set Load Cast to Run


Run


Result for natural frequency

1.



1.

Natural freq.; f1=4.128

875.100

0213.421 2nnf



Select mode

Natural freq; f2=10.63

875.100

0213.421 2nnf


Result for modeshape

Select node for obtaine output

node9

node8



mode1 mode2

node8 0.797 -0.325

node9 1 1

000.1000.1334.0800.0

Mode 1 Mode 2U1U2-0.0571 / -0.07166

0.036 / -0.1104


Result for Ground motion excitation

Select node for output




Result to Grund motionResult for Ground motion excitation




Time step (sec)

Ux



Result to Ground motion

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-0.025-0.02

-0.015-0.01

-0.0050

0.0050.01

0.0150.02

0.025

Time (sec)

U(t) (m

)

Modal analysisSAP2000


WORKSHOP

Obtain Disp. of 2nd floor due to ground acceleration in X direction

tfgyU ug2sin4.0 G Hzfug 0.2;

Dynamic Analysis for Frame Structure

Documents

Dynamic Analysis for Frame Structure Rev00_NM