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Seismic Analysis of Seismic Analysis of StructuresStructures
lumped MDOF-sytem with rigid base translation (horizontal case)
Earthquake Loading
From Clough, Penzien (3)
0tm v c v k v
where direction cosine, for buildings typicall "1"
tgv v j v
j
eff tm v c v k v p
eff gt tp m j vhysteresis law
ground acc.
Earthquake EngineeringEarthquake EngineeringProf. Dr.-Ing. Uwe E. DorkaProf. Dr.-Ing. Uwe E. Dorka Stand: 11.07.2006
33Stahlbau Grundlagen – EinführungProf. Dr.-Ing. Uwe E. Dorka 3
Reference peak-ground acceleration at Udine: 2.75 m/s2
viscously damped SDOF oscillator
where: Eigenfrequency:
Damping ratio:
solving this equation for various and butonly for one specific earthquake, the maximum absolute acceleration of this solution gives us the diagram above
Response Spectra
From Petersen (2)
From Meskouris (5)
simplified response spectrum
Earthquake EngineeringEarthquake EngineeringProf. Dr.-Ing. Uwe E. DorkaProf. Dr.-Ing. Uwe E. Dorka Stand: 11.07.2006
55
Example:• School building with
steel frames or Hyde system
Hyde System
Static Systems
IPE 500IPE 500
IPE 500IPE 500
IPE 500IPE 500
IPE 500IPE 500
IPE 500IPE 500
M2=12450KgM2=12450Kg
3.2
03
.20
8.00m8.00m
3.2
03
.20
3.2
03
.20
3.2
03
.20
3.2
03
.20
HE
B 4
00
HE
B 4
00
HE
B 4
00
HE
B 4
00
HE
B
HE
B
40
04
00
HE
B
HE
B
40
04
00
HE
B 4
00
HE
B 4
00
HE
B 4
00
HE
B 4
00
HE
B
HE
B
40
04
00
HE
B
HE
B
40
04
00
HE
B 4
00
HE
B 4
00
HE
B 4
00
HE
B 4
00
M1=16185KgM1=16185Kg
M1=16185KgM1=16185Kg
M1=16185KgM1=16185Kg
M1=16185KgM1=16185Kg
mmmm
mmmm
mm
Frame
IPE 500IPE 500
IPE 500IPE 500
IPE 500IPE 500
IPE 500IPE 500
IPE 500IPE 500
3.2
03
.20
8.00m8.00m
3.2
03
.20
3.2
03
.20
3.2
03
.20
3.2
03
.20
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
HE
B
HE
B
20
02
00
mmmm
mmmm
mm
Earthquake EngineeringEarthquake EngineeringProf. Dr.-Ing. Uwe E. DorkaProf. Dr.-Ing. Uwe E. Dorka Stand: 11.07.2006
77
Frame Hyde System
Earthquake EngineeringEarthquake EngineeringProf. Dr.-Ing. Uwe E. DorkaProf. Dr.-Ing. Uwe E. Dorka Stand: 11.07.2006
88
Frame Hyde System
Earthquake EngineeringEarthquake EngineeringProf. Dr.-Ing. Uwe E. DorkaProf. Dr.-Ing. Uwe E. Dorka Stand: 11.07.2006
99
Frame
Earthquake EngineeringEarthquake EngineeringProf. Dr.-Ing. Uwe E. DorkaProf. Dr.-Ing. Uwe E. Dorka Stand: 11.07.2006
1010
Frame details
Earthquake EngineeringEarthquake EngineeringProf. Dr.-Ing. Uwe E. DorkaProf. Dr.-Ing. Uwe E. Dorka Stand: 11.07.2006
1111
Hyde System
Earthquake EngineeringEarthquake EngineeringProf. Dr.-Ing. Uwe E. DorkaProf. Dr.-Ing. Uwe E. Dorka Stand: 11.07.2006
1212Hyde System details
