Dynamic Analysis for Frame Structure Rev00_NM

CIVIL Engineering Department Thammasat University

DYNAMIC ANALYSIS FOR FRAME STRUCTURE Mr. Nuttaphon Magteppong

Frame structure

2

1

Frame structure

Z

Y X

Y

2nd Plan

X

Frame structure

Z

Y X

Roof Plan

Y X

Frame structure Section properties

All col section All slab section

2nd beam section

roof beam section

Frame structure

Z

Y X

U2

M2 K2

U1

M1 K1

Z X 6

Frame structure X-direction

m M  1 0

U2

M2

k  k K  1 2   k2

0 m2 

 k2  k 2 

K2

Natural frequency and Modeshape U1

M1

M

1



K 2   0





det M 1 K   2  0

K1

7

Frame structure Mass matrix

List

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

Roof

U2

M2 K2

U1

M1 K1

roof beam B2 col sum roof 2nd Floor slab+sdl beam B1 col sum 2nd floor

36.0 9.00 1.00 0 1 324.00m2 0.20 0.40 189 1 15.12m3 0.35 0.35 1.50 18 3.31m3

40 2400 2400

12,960 36,288 7,938 57,186

36.0 9.00 0.15 0 1 48.60m3 0.30 0.60 189 1 34.02m3 0.35 0.35 3 18 6.62m3

2400 2400 2400

116,640 81,648 15,876 214,164

m M  1 0

0 m2 

0  214,164 M  57,180  0

kg

Frame structure Stiffness matrix Assume: shear mode

E= 20 Gpa

I C

1 bd 3  0.001251 m4 12

U2

M2 K2

U1

M1 K1

K 1 K 2 

k  k K  1 2   k2

12 EI  18  2.0016  108 N/m 3 H  k2  k 2 

 4.0032  2.0016 K  108     2.0016 2.0016 

N/m

Frame structure Dynamic properties Natural Frequency 0  700.71 4,669  0

n2  

fn 

Modeshape

0  4.213 1 n2   10.875 2  0

Hz. U2

M2

Mode 1 Mode 2 0.800  0.334 U1  1.000 1.000  U2

K2



U1

M1

K1

Frame structure Mode1 Mode1

Modal analysis

   q t   u t   u (t )  q (t )   1    11 12   1  u2 t  12 22  q2 t 

M2

Mode1

U2 Peff2 K2

M1

  q t   12  q2 t    11 1  12  q1 t   22  q2 t 

=

U1 Peff1

11      12 

M*1

Mode2 q1 P*1

+

12      22 

K*1

K1

M*2

q2 P*2

K*2

Frame structure Input ground acceleration Peff   MUg

K2

Ug  0.4  sin( 2f ug t ) G

214,164  0.4  9.81 sin( 2f ug t ) 840,380  sin( 2f ug t )  Peff      57,180  0.4  9.81 sin( 2f ug t )  224,374  sin( 2f ug t )

Modal analysis

U2

M2

  0.05

 896,678  sin(2f ug t )  P*     56,313  sin(2f ug t )

K1

f ug  5.00

 P1*  0.800  0.334 P*   Peff   *      P2  1.000 1.000  T

N

T

840,380  sin( 2f ug t )  224,374  sin( 2f t ) ug  

U1

M1

N

Frame structure Modal analysis 0  0.800  0.334 0.800  0.334 214,164 M   M     57,180 1.000 1.000  1.000 1.000   0 T

*

U2

M2

T

m* M*   1 0

0  0  194,186  * 81,044 m2   0

Kg

K2 U1

M1

K1

0.800  0.334 K   K    1.000 1.000  *

T

k1* K  0 *

T

 4.0032  2.0016 0.800  0.334 8  2.0016 2.0016  1.000 1.000   10   

0  0  1.3607   108  * 3.7840 k2   0

N

Frame structure Modal analysis qn (t )  e  nt An cos nt  Bn sin nt   Cn sin ug t  Dn cos ug t

DMFn 

U 0n  0

1

1     2  2 2 n

2

n 

n

ug n

d  n 1   2

U 0 n  0





P0*n Cn  *  DMFn2  1   n2 Kn P* Dn  0 n*  DMFn2   2 n  n  Kn An  U 0 n  D

Bn 

A   n

n

n

 Cnug

d



Frame structure mode 1 2 4.213 10.875 26.47 68.33 194,186 81,044 1.3607E+08 3.7839E+08 0.05 0.05 1.187 0.460 896,678 -56,313 2.351 1.266 26.44 68.24 0 0 0 0 -1.4876E-02 -1.8808E-04 -4.3219E-03 1.0965E-05 4.3219E-03 -1.0965E-05 1.7894E-02 8.6031E-05

fn (Hz) wn m*n (Kg) k*n (N) Damping beta_n P*n0 (N) DMF wd U0n U'0n Cn Dn An Bn

qn (t )  e  nt An cos nt  Bn sin nt   Cn sin ug t  Dn cos ug t

q1 (t )  e 1.3235t 4.322 10 3 cos 26.47t  1.789 10 2 sin 26.47t 









  1.4876 10  2 sin 10t   4.322 10 3 cos10t

q2 (t )  e 3.4165t  1.097 10 5 cos 68.33t  8.603 10 5 sin 68.33t 









  1.8808 10  4 sin 10t  1.097 10 5 cos10t

 u t  0.800  0.334  q1 t  0.8  q1 t   0.334 * q2 t  u (t )   1   q (t )    q t   1.00  q t   1.00 * q t    u t 1 . 000 1 . 000  2    1 2  2  

Frame structure Mode1 Mode1

Modal analysis

   q t   u t   u (t )  q (t )   1    11 12   1  u2 t  12 22  q2 t 

  q t   12  q2 t    11 1  12  q1 t   22  q2 t 

U2 57 T

Mode1

224 KN 2e5 KN/m U1 214

Mode2 q1

=

194 T 0.80 897 KN 1.00    

+

 0.33  1.00    

81 T

q2 -56 KN

840 KN

1.36e5 KN/m 2e5 KN/m

3.78e5 KN/m

Frame structure  u t  0.800  0.334  q1 t  0.8  q1 t   0.334 * q2 t  u (t )   1   q (t )      1.000 1.000  q2 t  1.00  q1 t   1.00 * q2 t  u2 t  X: 0.54 Y: 0.02397

0.02

X: 5.14 Y: 0.01564

U2

M2

0.015 0.01

K2

U2(t) (m)

0.005 0

U1

M1

-0.005 -0.01

K1

-0.015 -0.02 -0.025

0

1

2

3 Time (sec)

Modal Analysis SAP2000

4

5



1

2


1


1


1

4

2 3


1

2

=2400x9.81


2

=0


Modal Analysis SAP2000 1

2 3

4

Modal Analysis SAP2000 Define other section


1

Modal Analysis SAP2000 Get model from template

No column


3.

1.

2.

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


Modal Analysis SAP2000 Assign beam section

1.

2.

Modal Analysis SAP2000 Set show beam section

1.

2.

Modal Analysis SAP2000 Select all beam in 2nd floor

Modal Analysis SAP2000 assign beam section for 2nd floor to B1

1. 2.

3.

Modal Analysis SAP2000 Move to XY plane at Z=6.00 Assign all beam to section B2

Modal Analysis SAP2000 Define slab

Modal Analysis SAP2000 Define Area section


3.

1. 2.


3.

1. 2.

Modal Analysis SAP2000 Assign slab 1.

3.

4.

Modal Analysis SAP2000 Assign all slab at Z=6 to Roof

Modal Analysis SAP2000 Assign all slab at Z=3 to S1

Modal Analysis SAP2000 Select all slab to assign auto mesh

Modal Analysis SAP2000 Select all slab to assign auto mesh

Modal Analysis SAP2000 Assign auto mesh for slab



Modal Analysis SAP2000 Assign fix support Select all support

3.

1.

2.

4.

Modal Analysis SAP2000 Assign fix support

Modal Analysis SAP2000 Define Load patterns

Modal Analysis SAP2000 Define function of ground acceleration



Ug  0.4 sin 2f ug t  G ; f ug  5 Hz

1/fug = 1/5 =0.2

0.4 0.3 0.2

Func01

0.1 0

1 cycle

-0.1 -0.2 -0.3 -0.4 0

0.05

0.1

0.15

0.2 Time(s)

0.25

0.3

0.35

0.4

Total time x fug=10sec x 5Hz = 50 cycle Acceleration in G unit (1G = 9.81 m/s2)

Modal Analysis SAP2000 Define Load case

Modal Analysis SAP2000 Define Load case (DEAD LOAD)

Modal Analysis SAP2000 Define Load case (Modal)

Modal Analysis SAP2000 Define Load case (SDL)

Modal Analysis SAP2000 Define Load case (ground)

Value of g in length unite/s^2

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

Modal Analysis SAP2000 Select roof slab to assign load

Modal Analysis SAP2000 Select roof slab to assign load

Modal Analysis SAP2000 Assign roof load to roof slab

Modal Analysis SAP2000 Define Mass source


Modal Analysis SAP2000 Set parameter to analysis (2D analysis in XZ plane)

Modal Analysis SAP2000 Set Load Cast to Run…

Modal Analysis SAP2000 Run…

Modal Analysis SAP2000 Result for natural frequency

1.


1. Natural freq.; f1=4.128

fn 

0  4.213 1 n2   10.875 2  0


Natural freq; f2=10.63

fn 

0  4.213 1 n2   10.875 2  0

Select mode

Modal Analysis SAP2000 Result for modeshape Select node for obtaine output

node9 node8

Modal Analysis SAP2000 Result for modeshape





mode1

mode2

node8

0.797

-0.325

node9

1

1

-0.0571 / -0.07166

Mode 1 Mode 2 0.800  0.334 U1  1.000 1.000  U2



0.036 / -0.1104

Modal Analysis SAP2000 Result for Ground motion excitation

Select node for output


Modal Analysis SAP2000 Result for to Grund Ground motion motion excitation







Time step (sec) Ux

Modal Analysis SAP2000 Result to Ground motion 0.025

Modal analysis SAP2000

0.02 0.015 0.01

U(t) (m)

0.005 0 -0.005 -0.01 -0.015 -0.02 -0.025

0

0.5

1

1.5

2

2.5 Time (sec)

3

3.5

Modal Analysis SAP2000 WORKSHOP Obtain Disp. of 2nd floor due to ground acceleration in X direction

Ugy  0.4 sin 2f ug t  G ; f ug  2.0 Hz

4

4.5

5

Dynamic Analysis for Frame Structure Rev00_NM

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