SINGLE DEGREE OF FREEDOM SYSTEM (SDOF)

Prof.Dr.Ir.Bambang Budiono, M.E.

SDOF

SDOF

SDOF

Due to no external force p(t)= 0

STIFFNESS AND FUNDAMENTAL PERIOD

STIFFNESS AND FUNDAMENTAL PERIOD

= angular velocity [radial/second]m= mass of structure [Weight/gravity]k = stiffness [Spring Force/displacement]f = frequency (Hertz)T = fundamental period (second)

UNDAMPED (FREE) VIBRATION

UNDAMPED (FREE) VIBRATION

EXAMPLE

EXAMPLE

EXAMPLE

EXAMPLE

DAMPED VIBRATION

Amplitude of motion (p)

DAMPED VIBRATION

Order of fraction of critical damping for structures = 3 % to 5%, then d can be considered as

RESPONSE OF SDOF USING STEP BY STEP INTEGRATION METHOD

RESPONSE OF SDOF USING STEP BY STEP INTEGRATION METHOD

RESPONSE OF SDOF USING STEP BY STEP INTEGRATION METHOD

RESPONSE OF SDOF USING STEP BY STEP INTEGRATION METHOD

RESPONSE OF SDOF USING STEP BY STEP INTEGRATION METHOD

RESPONSE OF SDOF USING STEP BY STEP INTEGRATION METHOD

RESPONSE OF SDOF USING STEP BY STEP INTEGRATION METHOD

Response Spectra

Maximum Displacement is Sd (spectral displacement)

Response Spectra

Response Spectra

Maximum Pseudo Velocity is Sv

(pseudo spectral velocity)

Maximum Pseudo Acceleration is Sa

(spectral displacement)-see Eq.4-37

Tripartite Log Response Spectra

Design Response Spectra

Design Response Spectra

Design Response Spectra

Design Response Spectra

Design Response Spectra

Design Response Spectra

Koefisien Gempa C = Sa/g (UBC 1997-SNI 2002)

21 Agustus, 2008 Jakarta, HAKI08 32