dynamic analysis for frame structure rev00_nm
DESCRIPTION
analysis buildingTRANSCRIPT
-
DYNAMIC ANALYSIS FOR FRAME STRUCTURE
Mr. Nuttaphon Magteppong
1
Thammasat UniversityCIVIL Engineering Department
Frame structure
2
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Frame structure
XYZ
X
Y2nd Plan
Frame structure
XYZ
X
YRoof Plan
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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
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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
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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
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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
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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
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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
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Modal Analysis SAP2000
Modal Analysis SAP2000
1
2
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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
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Modal Analysis SAP2000
1
Modal Analysis SAP2000
Get model from template
No column
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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
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Modal Analysis SAP2000
Define Area section
Modal Analysis SAP2000
1.
2.
3.
Define Area section
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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
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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
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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
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Modal Analysis SAP2000
Define Load case (DEAD LOAD)
Modal Analysis SAP2000
Define Load case (Modal)
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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
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Modal Analysis SAP2000
Modal Analysis SAP2000
Set parameter to analysis (2D analysis in XZ plane)
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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
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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