Respon Spektrum Gempa

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1 Mata Kuliah : Diamika Struktur & Pegatar Rekayasa Kegempaa Kode : TSP 302 SKS : 3 SKS Respo Spektrum Gempa Pertemua 10

2 TIU : Mahasiswa dapat mejelaska feomea-feomea diamik secara fisik. TIK : Mahasiswa dapat membuat spektrum respo utuk berbagai jeis eksitasi

3 Sub Pokok Bahasa : Respo Spektrum Peetua Spektrum Recaa

4 Respose Spectrum Cocept GW Houser was istrumetal i the widespread acceptace of the cocept of the earthquake respose spectrum itroduced by MA Biot i 1932 as a practical meas of characterizig groud motios ad their effects o structures. A plot of the peak value of a respose quatity as a fuctio of the atural vibratio period T of the system, or a related parameter such as circular frequecy w or cyclic frequecy f, is called the respose spectrum for that quatity.

5 A variety of respose spectra ca be defied depedig o the respose quatity that is plotted. Cosider the followig peak resposes : u u o o u o T, x max u t,t, x T, x max u t,t, x T, x max u t,t, x The deformatio respose spectrum is a plot of u o agaist T for fixed x. A similar plot for ů o is the relative velocity respose spectrum, ad for ü o is the acceleratio respose spectrum

6 Deformatio Respose Spectrum

7 Pseudo-Velocity Respose Spectrum The pseudo-velocity respose spectrum is a plot of V as a fuctio of the atural vibratio period T, or atural vibratio frequecy f, of the system, where : V w D 2 D T (5) The prefix pseudo is used because V is ot equal to the peak velocity (ů o )

8 Pseudo-acceleratio Respose Spectrum The pseudo-acceleratio respose spectrum is a plot of A as a fuctio of the atural vibratio period, T, or atural vibratio frequecy, f of the system, where : A w D T D The quatity A has uits of acceleratio ad is related to the peak value of base shear V bo V bo f so ma A g w (6) (7) A/g may be iterpreted as the base shear coefficiet, usually used i buildig codes.

9 g = 386 i/sec 2 2 7, 47 23, 46 i/sec , 47 73, 73 i/sec 0, 191g

10 A combied plot showig all three of the spectral quatities (deformatio, pseudo-velocity ad pseudo acceleratio), developed for earthquake respose spectra, apparetly for the first time, by A.S.Veletsos ad N.M. Newmark (1960) This itegrated presetatio is possible because the three spectral quatities are iterrelated by the followig equatio A w V w D T 2 A V D (8) 2 T

12 Example 1 A 3,6 m-log vertical catilever, a 100 mm-omial diameter stadard steel pipe, supports a kgf weight attached at the tip as show if Figure. The properties of the pipe are : outside diameter, d o = 115 mm, iside diameter d i = 100 mm, thickess t = 7,5 mm, ad secod momet of cross-sectioal area, I = 3, mm 4. Elastic Modulus E = 200 GPa. Determie the peak deformatio ad bedig stress i the catilever due to the El Cetro groud motio. Assume x = 2%.

14 Example 2 (Homework) The stress computed i Example 1 exceeded the allowable stress ad the desiger decided to icrease the size of the pipe to a 200 mm omial stadard steel pipe. Its properties are d o = 220 mm, iside diameter d i = 200 mm, thickess t = 10 mm, ad secod momet of cross-sectioal area, I = 36, mm 4. Compute the bedig stress i the pipe, ad commet o the result compare with the 100 mm pipe.

15 Example 3 A small oe-story reiforced cocrete buildig is idealized for purposes of structural aalysis as a massless frame supportig a total dead load of kgf at the beam level. The frame is 7 m wide ad 3,6 m high. Each colum ad the beam has a 250 mm-square cross sectio. Assume that the Youg s modulus of cocrete is MPa ad the dampig ratio for the buildig is estimated as 5%. Determie the peak respose of this frame to the El Cetro groud motio. I particular, determie the peak lateral deformatio at the beam level.

17 Respose Spectrum Characteristic

18 For, T < T a = 0,035 sec, the pseudo-acceleratio A for all dampig values approaches ü go ad D is very small For T > T f = 15 sec, D for all dampig values approaches u go ad A is very small; thus the forces i the structure, which are related to ma, would be very small For short period system, T betwee T a = 0,035 sec ad T c = 0,5 sec, A exceeds ü go, with the amplificatio depedig o T ad x. For log period system, T betwee T d = 3 sec ad T f = 15 sec, D exceeds u go, with the amplificatio depedig o T ad x. For itermediate-period system, T betwee T c = 0,5 sec ad T d = 3 sec, V exceeds ů go

19 Elastic Desig Spectrum The desig spectrum should satisfy certai requiremets because it is iteded for the desig of ew structures, or the seismic safety evaluatio of existig structures, to resist future earthquakes It is ot possible to predict the jagged respose spectrum i all its detail for a groud motio that may occur i the future The desig spectrum should cosist of a set of smooth curves or a series of straight lies with oe curve for each level of dampig The factors that ifluece the costructio of desig spectrum iclude the magitude of earthquake, the distace of the site from earthquake fault, the fault mechaism, the geology of the travel path of seismic waves from the source to the site ad the local soil coditio

Dynamics of Structures 5th Edition Chopra SOLUTIONS MANUAL

Dynamics of Structures 5th Edition Chopra SOLUTIONS MANUAL Dyamics of Structures 5th Editio Chopra SOLUTIONS MANUAL Full dowload at : https://testbareal.com/dowload/dyamics-of-structures-5th-editio-choprasolutios-maual/ Problem.1 CHAPTER A heavy table is supported