design spectra

Design of Earthquake-resistant Reinforced Concrete Buildings DESIGN SPECTRA

• Concepts of Dynamic Response Analysis (SDOF and MDOF systems, Natural Period, Damping, Response Spectra, Application of Response Spectra to the Analysis of SDOF and MDOF systems, Smoothed Design Spectra)

• Ductility Modified Spectra (Definition of Ductility, Effect of Ductility on Structural Response, Ductility Modified Spectra, Applications)

• Code Design Spectra (Relation between Elastic Spectra and Code Design Spectra, UBC / Eurocode 8 / Japanese / EAK Design Spectra)

Costas Georgopoulos 24/02/05


Structure corresponding to a SDOF system

SDOF (position described completely by one parameter)



Two storey frame building = 2 DOF system

Natural Period (time for one complete oscillation)

km2T π= (seconds)

Damping (decrease of oscillations with time due to aerodynamic drag forces, friction in connections, soil & foundations, bond slip & cracking of concrete or yield) Structures have damping levels = 0.5 to 5% of critical



Mode shapes of a multi-storey frame building



Acceleration Response Spectrum of the El Centro Earthquake (1940) Response Spectrum is the peak response of a SDOF system to an E/Q motion as a function of its natural period and damping If T<0.2s very stiff structure i.e. it moves together with the ground, 0.2s<T<1.0s resonance i.e. amplification 2 to 8 and 1.0s<T<3s flexible i.e. structure acts as an isolator



Application of Response Spectra to the Analysis of Linear SDOF systems Data (Mass, Stiffness & Response Spectrum) Unknowns (Forces and Displacements)

km2Tnatural π= a

trumsponseSpecRe SDamping, →

amSF =

dkSF =

2

2a

2ad 4TS

m4TmS

kFS

π=

π==



Modal Response Spectrum Analysis of a MDOF system Each Mode is a SDOF system Effective Mass or Mass Participation Factor (0.75, 013, 0.05, etc.) Combination of Responses (max do not occur simultaneously – SRSS)



Tripartite Response Spectrum from Newmark & Hall



Smoothed Design Spectrum Peaks and troughs are determined by a number of uncertain factors such as the location of the E/Q therefore the spectrum is an envelop of a range of E/Q’s.



Quantifying Deflection Ductility in a Simple System Ductility is the ability to withstand repeated cycles of loading into the post elastic range without significant loss of strength (local curvature ductility or global structural ductility) EFFECTS OF DUCTILITY Plastic hinges form in one direction but close in the other After yielding accelerations are limited and therefore the forces Damping can dissipate up to 64% of the E/Q energy Yielding increases the natural period i.e. reduced acceleration in the response spectrum



Construction of Ductility Modified Spectrum Displacements for ductile structures are the same with the elastic ones but accelerations are smaller and therefore the forces. Ductility benefits flexible structures because there is no gain in accelerations for very stiff ones.



Comparison of Deflections and Forces in the Ductile and Elastic response of a typical 10-storey building Instead of carrying out a time-history non-linear analysis (full line on the graphs) we can analyse the structure elastically using a ductility modified response spectrum and then multiply the displacements with the ductility factor µ Most Codes specify a behaviour factor q that takes into account the ductility as well as the degree of redundancy of the structure, the strain hardening properties of its elements, the code used, the contribution of non-structural elements to the strength, the nature of E/Q ground motion and anything else we do not understand….



Lateral Force Requirements of UBC 94



Comparison of shape of UBC 94 response spectrum with lateral force requirements



Eurocode 8 lateral force design spectra



Comparison of shapes of EC8 design and elastic ground spectra



Comparison of Japanese, EC8 and UBC lateral force requirements for regular, ductile frames (hard soil sites)

Comparison of Japanese, EC8 and UBC lateral force requirements for regular, ductile frames (soft soil sites)


design spectra

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