Earth 0205-response spectrum

2.5. Response 2.5. Response SpectrumSpectrum

EARTHQUAKEEARTHQUAKE ENGINEERINGENGINEERING

2.5.1. Definition and Construction 2.5.1. Definition and Construction of Response Spectrumof Response Spectrum

2.5.2. Analysis Procedure 2.5.2. Analysis Procedure Using Response SpectrumUsing Response Spectrum

2.5.1. Definition and Construction of Response Spectrum

Prof.Dr. Osman Shaalan Earthquake Engineering Dr. Tharwat Sakr2

Response Spectrum is a Plot of the Maximum Peak Response of Single Degree of Freedom System as a Function of its Natural Period (Frequency) For a Specific Dynamic Force (or Earthquake)

DefinitionDefinition



ExampleExample

NorthBridge Earthquake



Damping EffectsDamping Effects



BenefitsBenefitsCharacterization of Ground Motions

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

5

10

15

Response Spectrum

Period [sec]

Acc

eler

atio

n

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

2

4

6

8

10

12

14

16

18

20

Response Spectrum

Period [sec]

Acc

eler

atio

n

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.50

1000

2000

3000

4000

5000

6000

7000

8000

9000

Response Spectrum

Period [sec]

Acc

eler

atio

n



BenefitsBenefitsEarthquake Resistance Design

Almost all Codes of Practice recommends the Response Spectrum as the Main Method for Earthquake Resistance Design



Generation of Response SpectrumGeneration of Response SpectrumSelect the Required excitation & Damping Ration

Choose SDOF System

Change the Period of the System in the practical range

For each Period make a Time History and Get the Maximum Required Response (Displacement – Velocity – Acceleration)

Plot The Response Vs Period

REFER TO THE MATLAB SEGMENT ATTACHED

2.5.2. Analysis Procedure Using Response Spectrum


SDOF Structures (Procedure)SDOF Structures (Procedure)Calculate the Structure dynamic parameters (K, M, , T)

Select the Appropriate Value of Damping Ratio

From the Response Spectrum Chart get the Spectral Value of the required response (Sa, Sv or Sd) Commonly Sa

The Maximum Displacement

The Maximum Base Shear

The Maximum Base Moment



SDOF ExampleSDOF ExampleDetermine The Maximum Displacement, Base Shear and Overturning moment of the following Frame for 5% damping (Response Spectrum Chart is Given)

Stiffness= 100000 kN.m2 - Mass = 100 t - Height = 4 m

0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Response Spectrum

Period [sec]

Acc

eler

atio

n



SDOF Example (Solution)SDOF Example (Solution) = 31.6278 rad /s T = 0.1988 s

From the ChartSa = 0.25 m/s

Umax = Sa/2 =0.00025 m =0.25 mmVmax = Sam =25.00 kN =2.50 tMmax = Vmax h = 100 kN.m =10.0 t.m



MDOF Structures (Procedure)MDOF Structures (Procedure)

For each degree of freedom (Mode)

From the Response Spectrum Chart get the value of Sa corresponding to the mode i frequency i

The Max. Displacement at DOF number j

The Max. Story Force at Story j

The Max. Inter-Story Drift Story j

Calculate the Structure dynamic parameters (I and I) Corresponding to each DOF

Based on the Story Force, Story Shear, Moment and Base moment can be computed

Combine all modes by the SRSS formula

2.5. Response Spectrum


MDOF ExampleMDOF ExampleInvestigate the inter-story drift and story shear for the given multistory building using the attached response spectrum chart

No of Stories = 2Story Height = 4 mStory Mass = 60 tStory Stiffness = 240000 kN/mDamping Ratio = 5%



MDOF ExampleMDOF Example

0 0.5 1 1.5 2 2.5 3 3.5 40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

Period [sec]

Acc

eler

atio

n [g

]

= 39.09 T =0.1607 102.30 0.0614s

= -0.0679 -0.1098 -0.1098 0.0679



MDOF Example (Solution)MDOF Example (Solution)

From the SpectrumSa1 = 0.45Sa2 = 0.315

Participation Factor = -10.66

-2.517

Displacements (Mode1 2 SRSS E-4u1 = 2.1 0.0832 2.13 mU2 = 3.44 -0.0514 3.45 m



MDOF Example (Solution)MDOF Example (Solution)

Forces (Mode1 2 SRSS)f1 = 19.54 5.22 20.23 kNf2 = 31.6 -3.23 31.77 kN

Inter-Story Drift (Mode1 2SRSS) E-41 = 2.1 0.0832 0.053%0

2 = 1.31 -0.134 0.033%0

Overturning MomentM = 335.05 kN.m

Technology

Earth 0205-response spectrum