Longtudnal Cross Secton of A Flud Damper he dfference of the pressure between each sde of the pston head results n the dampng force. he dampng constant of the damper can be determned by adustng the confguraton of the orfce of the pston head.
Force-Velocty Relatonshp of Vscous Dampers F D C u& sgn ( u& ) Lne : F D C N V, Nonlnear Damper wth < Lne : F D C L V, Lnear Damper Lnear Vscous Dampers Lne 3: F D C N V, Nonlnear Damper wth > Damper Force, F D < < Nonlnear Vscous Dampers Lne Lne Lne 3 Velocty, V Mechancal Propertes of Flud Vscous Dampers Hysteress Loops of Vscous Dampers (Snusodal Moton) Force Nonlnear Damper Dsplacement No storage stffness! Lnear Damper Vscous dampers won t change the natural frequency of the prmary structure. Mechancal Propertes of Flud Vscous Dampers
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he Equvalent Dampng Rato of Structures wth Lnear Vscous Dampers
Lnear Vscous Dampng Rato k Vscous Damper u u sn t P P sn( t δ) Force d D 4 s D s Dsplacement MDOF System wth Lnear Vscous Dampers eff d nherent dampng rato dampng rato attrbuted to added dampers V F βeff β 4k MDOF System wth Lnear Vscous Dampers
MDOF System wth Lnear Vscous Dampers SDOF eff d d d MDOF D 4 s D all dampers 4 S MDOF System wth Lnear Vscous Dampers Energy Dsspated by Lnear Vscous Dampers ( n one cycle of snusodal vbraton ) P(t) U(t) u u sn t ( t ) Cu& P P sn δ D F C u D C u du Cudu & cos t d( t) Cu& dt V MDOF System wth Lnear Vscous Dampers C δ r
MDOF System wth Lnear Vscous Dampers S d Consderng the Frst Mode of Vbraton r C C u cos [ ] [ ] Φ Φ Φ Φ s m m m K 4 r k u F Effectve Dampng Rato of A Structure wth Lnear Vscous Dampers (FEMA73) r r eff m C m C 4 cos 4 cos F r eff F u u C β β cos
he Effectve Dampng Rato of Structures wth Nonlnear Vscous Dampers SDOF System wth Nonlnear Vscous Dampers Velocty me Hstory Damper Force u& u snt F D Cu& Nonlnear vscous damper wth dampng constant, C K M Snusodal Moton SDOF System wth Nonlnear Vscous Dampers
Dampng Rato Contrbuted by Nonlnear Vscous Dampers M X& C X& C & & d X KX MX g Nonlnear Approxmated by M X& C C ) X& ( KX M & eq X g Equvalent Lnear Dampng Rato Contrbuted by Nonlnear Vscous Dampers Equal Energy work done by nonlnear damper eff ( ) d 4 k
Energy Dsspated by Nonlnear Vscous Dampers Beta Functon D F C D du Cu& dt F udt & ( u ) sn t dt D F D C u& SDOF System wth Nonlnear Vscous Dampers u& u snt D C( u ) sn d D λc u Let t dt ( ) d C u sn cos Γ C u Γ ( ) λ Γ( ) Γ m n / B(, ) sn m cos nd Γ( a) Γ( b) B( a, b) Γ( a b) ( ) d Values of Parameter Exponent..5..5.3.35.4.45.5.55.6.65.7.75.8.85.9.95 Calculated 3.88 3.83 3.77 3.7 3.67 3.63 3.58 3.54 3.5 3.46 3.4 3.38 3.34 3.3 3.7 3.4 3. 3.7 3.4 FEMA 3.9 3.8 3.8 3.7 3.7 3.6 3.6 3.5 3.5 3.5 3.4 3.4 3.3 3.3 3.3 3. 3. 3. 3.
MDOF System wth Lnear Vscous Dampers S d Consderng the Frst Mode of Vbraton (Lnear Damper) r C C u cos [ ] [ ] Φ Φ Φ Φ s m m m K 4 r MDOF System wth Nonlnear Vscous Dampers Effectve Dampng Rato of A Structure wth Nonlnear Vscous Dampers r eff m A C cos λ Dsplacement Dependent A
A Γ S d.5 D ( ) S d Z IC C m.5 C D.5 4 eff S ad I / B Effectve Dampng Rato of A Structure wth Nonlnear Vscous Dampers eff λc A r cos m Dsplacement Dependent MDOF System wth Nonlnear Vscous Dampers
he loadng combnaton factors CF and CF Responses at the nstant of maxmum acceleraton Responses at the nstant of maxmum dsplacement CF CF Responses at the nstant of maxmum velocty B F C A -u K u cosδ u u Loadng Combnaton Factors
u u me at max. acc. t* δ/n /n t B F C A u. -u -u K u cosδ u u t -u n [ tan ( )] CF cos eff [ ( )] CF sn tan eff
A Desgn Example of A Structure wth Lnear Vscous Dampers Propertes of the Desgned Structure Mass 855 kg cos.87 Frst Mode r.95 9378 kg 9378 kg.87.83.85.494.3.494.33 sec C r cos nherent dampng rato of d Assume the prmary frame of the structure the structure % Desgn 4of Lnear m Vscous Dampng System Assume all dampers have the same dampng constant remans elastc dampng rato attrbuted to.33 (.87.95.87.3.83.494 ).8 Each floor C d C contans 4 ( ( kn two lnear s m) dampers vscous damper d 8% 855 9378.85 9378.494 ) A Desgn Example
.., NCREE-5-xxx, 5.., NCREE-5-xxx, 5. RC., NCREE-4-, 4. NCREE-4-9, 4. (I)., NCREE-3-, 3..., NCREE-3-, 3.. LRB FVD., NCREE--3, 3.., NCREE--,. NCREE- FEMA 73/74 (997) FEMA 356 () FEMA 368/369 () MCEER-9-3 (99) MCEER-97-4 (997) MCEER-- ()