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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
Modal Analysis SAP2000
1
2
Modal Analysis SAP2000
1
Modal Analysis SAP2000
1
Modal Analysis SAP2000
1
2
3
4
Modal Analysis SAP2000
1
=2400x9.81
2
Modal Analysis SAP2000
=0
2
Modal Analysis SAP2000
Modal Analysis SAP2000
1
2
3
4
Modal Analysis SAP2000
Define other section
Modal Analysis SAP2000
1
Modal Analysis SAP2000
Get model from template
No column
Modal Analysis SAP2000
1. 2.3.
4. select all col in XZ plane (Y=6) and node and delete
Modal Analysis SAP2000
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
Modal Analysis SAP2000
1.
2.
3.
Define Area section
Modal Analysis SAP2000
1.
2.
3.
Define Area section
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 auto mesh for slab
Modal Analysis SAP2000
Assign auto mesh for slab
Modal Analysis SAP2000
Assign fix support
Select all support
1. 2.3.
4.
Modal Analysis SAP2000
Assign fix support
Modal Analysis SAP2000
Define Load patterns
Modal Analysis SAP2000
Define function of ground acceleration
Modal Analysis SAP2000
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)
Modal Analysis SAP2000
Define function of ground acceleration
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
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
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.
Modal Analysis SAP2000
Result for natural frequency
1.
Natural freq.; f1=4.128
875.100
0213.421 2nnf
Modal Analysis SAP2000
Result for natural frequency
Select mode
Natural freq; f2=10.63
875.100
0213.421 2nnf
Modal Analysis SAP2000
Result for modeshape
Select node for obtaine output
node9
node8
Modal Analysis SAP2000
Result for modeshape
Modal Analysis SAP2000
Result for modeshape
Modal Analysis SAP2000
Result for modeshape
Modal Analysis SAP2000
Result for modeshape
Modal Analysis SAP2000
Result for modeshape
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
Modal Analysis SAP2000
Result for Ground motion excitation
Select node for output
Modal Analysis SAP2000
Result for Ground motion excitation
Modal Analysis SAP2000
Result to Grund motionResult for Ground motion excitation
Modal Analysis SAP2000
Result for Ground motion excitation
Modal Analysis SAP2000
Result for Ground motion excitation
Modal Analysis SAP2000
Result for Ground motion excitation
Modal Analysis SAP2000
Result for Ground motion excitation
Modal Analysis SAP2000
Result for Ground motion excitation
Modal Analysis SAP2000
Time step (sec)
Ux
Result for Ground motion excitation
Modal Analysis SAP2000
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
Modal Analysis SAP2000
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