ENGINEERING SEISMOLOGY HOMEWORK

ENGINEERING SEISMOLOGY

HOMEWORK

ISTANBUL TECHNICAL UNIVERSITY

STRUCTURAL EARTHQUAKE DEPARTMENT

SELÇUK BAŞ

501081221

SUPERVISOR: Prof.Dr. Zeki HASGÜR

CONTENTS

1. Determining the new Acceleration Time-Histories By multiplying the Original with

the new Coefficent given as Figure.

2. In Time-Domain, Strong Motion Acceleration, Velocity, Displacament.

3. In Frequency-Domain, Elastic Response Spectra For 5% Damping Ratio, Sa(0.05,T),

Sv(0.05,T), Sd(0.05,T).

4. Determining Tripartite Spectrum including Acceleration, Velocity, Displacement

Response Spectra on Logarithmic Scales.

5. By using Newmark Method, Obtaining f1, f2, f3 Frequencies.

6. Obtaining Desing Tripartite Spectrum By using Amplification Ratios With %5

Damping Ratio.

7. Gaining Fourier Amplitude And Velocity Spectrum (Sv(0,T), Comparing their Curve

By plotting the diagrams on to each other in a Single Graph.

8. Calculating Engineering intensities ;

i. SI0.2 : Housner Intensity

ii. IEAP : Earthquake Attack Power

iii. EPA : Effective Peak Acceleration

iv. EPV : Expected Peak Velocity

v. aeff : Effective acceleration

vi. teff : Effective Duration

vii. Av : EPV/30

1

⋕UNITS;

Acceleration : cm/sec2

Velocity : cm/sec

Displacement : cm

Phase : ° (degree)

Time : sec

⋕Information About Strong Motion Record : This record is from Sarayköy (E-W)

Geothermal Sites with date of 23.07.2003 in Denizli/Turkey. Multiplication coefficient

given to me is 2.4.

2

DETERMINING OLD AND NEW ACCELERATION;

⋕Old Acceleration Record And its Figure

MATLAB CODE FOR ACCELERATION TIME-HISTORY : This program is runned by using text file of ‘SaraykoEW which is not multiplyed with 2.4’ and ‘oldacctimehistory.m-file’ . All files are saved at CD.

*Matlab code;

clc; clear all; close all;

dt = 0.01;

acc = load('SaraykoyEW.txt');

time =acc(:,1);

ivme =acc(:,2);

numData = length(ivme);

figure

plot(time, ivme)

title('OLD ACCELERATION TIME-HISTORY')

xlabel('Time(sec)')

ylabel('Acceleration(cm/sn^2)')

grid on

*Figure of old acceleration record from matlab;

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3

⋕New Acceleration Record And its Figure

MATLAB CODE FOR ACCELERATION TIME-HISTORY : This program is runned by using text file of ‘yenikayıt

which is multiplyed with 2.4’ and ‘newacctimehistory.m-file’ .

*Matlab code;


dt = 0.01;

acc = load('yenikayıt.txt');

time =acc(:,1);

ivme =acc(:,2);


figure

plot(time,ivme)

title('NEW ACCELERATION TIME-HISTORY')

xlabel('Time(sec)')


grid on

*Figure of old acceleration record from matlab

4

TIME HISTORYO OF ACCELERATION, VELOCITY, DISPLACEMENT;

MATLAB CODE FOR TIME-HISTORY : This program is runned by using text file of ‘SaraykoEW which is not

multiplyed with 2.4’ and ‘TIMEHISTORY.m-file’ . Velocity and displacement is gained using numerical

integration by matlab.

*Matlab code;


dt = 0.01;

acc = load('SaraykoyEW.txt');

time = acc(:,1);

ivme = 2.4*acc(:,2);


figure

plot(time,ivme)

title('ACCELERATION-TIME HISTORY')

xlabel('Time(sec)')


grid on

[hiz, disp] = newmark(ivme, time, dt);

figure

plot(time,hiz)

title('VELOCITY-TIME HISTORY')

xlabel('Time(sec)')

ylabel('Velocity')

grid on

figure

plot(time,disp)

title('DISPLACEMENT-TIME HISTORY')

xlabel('Time(sec)')

ylabel('Displacement')

grid on

⋕Acceleration Time-History

2

5

⋕Velocity Time-History

⋕Displacement Time-History

6

FREQUENCY DOMAIN: RESPONSE SPECTRA SA(0.05,T), SV(0.05,T), SD(0.05,T)

MATLAB CODE FOR RESPONSE SPECTRA :

This program use Duhammel integration method to determine elastic response spectra of a system under

any time-history ground acceleration then submit SDOFS system response spectrum for acceleration,

velocity and displacement as MATLAB output in three grapgs. General features of this program includes

one ‘m.file’ and an ‘Excel’ input file which to run this program both ‘spectrum.m’ and ‘Spectrum.xls’ must

be saved in MATLAB directory . Meanwhile notice that input file (Spectrum.xls) should be saved as ‘Excel

2003’. Using this program is useful for any acceleratıon record. So; This program is runned by using xls file

of ‘Spectrum.xls which is multiplyed with 2.4’ and ‘spectrum.m-file’ .

*Matlab code;

clc

clear all

%Input Data:

Ts=xlsread('Spectrum','input','E11');

td=xlsread('Spectrum','input','E12');

N=xlsread('Spectrum','input','E13');

T(1)=0;

for i=1:N-1

T(i+1)=i*(Ts);

end

F=xlsread('Spectrum','input','E22:E10018');

j=(td/Ts)+2;

F(j:N)=0;

F=F(1:N);

%Calculation of Natural Damped Frequency and Period:

n=1;

e=[0.05];

s=0;

for P=0.02:0.02:4

s=s+1;

W=2*pi/P;

WD=W*sqrt(1-e(n)^2);

%Calculation of Dynamic Response In Each Time Point:

A(1)=0; B(1)=0;

Y(1)=0;

for i=2:N;

dF(i)=F(i)-F(i-1);

dT(i)=T(i)-T(i-1);

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7

S12=exp(e(n)*W*T(i))*(e(n)*W*cos(WD*T(i))+WD*sin(WD*T(i)))/((e(n)*W)^

2+WD^2);

S11=exp(e(n)*W*T(i-1))*(e(n)*W*cos(WD*T(i-1))+WD*sin(WD*T(i-

1)))/((e(n)*W)^2+WD^2);

I1=S12-S11;

S22=exp(e(n)*W*T(i))*(e(n)*W*sin(WD*T(i))-

WD*cos(WD*T(i)))/((e(n)*W)^2+WD^2);

S21=exp(e(n)*W*T(i-1))*(e(n)*W*sin(WD*T(i-1))-WD*cos(WD*T(i-

1)))/((e(n)*W)^2+WD^2);

I2=S22-S21;

S32=(T(i)-

e(n)*W/((e(n)*W)^2+WD^2))*S22+WD/((e(n)*W)^2+WD^2)*S12;

S31=(T(i-1)-


I3=S32-S31;

S42=(T(i)-e(n)*W/((e(n)*W)^2+WD^2))*S12-

WD/((e(n)*W)^2+WD^2)*S22; S41=(T(i-1)-e(n)*W/((e(n)*W)^2+WD^2))*S11-WD/((e(n)*W)^2+WD^2)*S21; I4=S42-S41; A(i)=A(i-1)+(F(i-1)-T(i-1)*dF(i)/dT(i))*I1+dF(i)/dT(i)*I4;

B(i)=B(i-1)+(F(i-1)-T(i-1)*dF(i)/dT(i))*I2+dF(i)/dT(i)*I3;

%Solve for Displacement:

Y(i)=exp(-e(n)*W*T(i))/WD*(A(i)*sin(WD*T(i))-

B(i)*cos(WD*T(i)));

end

%Determination of Maximum Responses;

Sd=max(abs(Y));

Sv=W*Sd;

Sa=W*Sv;

spec(s,1,n)=P;

spec(s,2,n)=Sd;

spec(s,3,n)=Sv;

spec(s,4,n)=Sa;

end

%Analysis Results

%Displacement--------------------------------------------------------

------

figure(1);

hold on

plot(spec(:,1,1),spec(:,2,1),'b-','linewidth',2);

title('RESPONSE SPCTRUM FOR Sd');

xlabel('PERIOD(Sec)');

ylabel('DISPLACEMENT(Sd-cm)');

legend('\xi=0.05');

hold off;

grid on;

8

%Velocity------------------------------------------------------------

figure(2);

hold on


title('RESPONSE SPCTRUM FOR Sv');


ylabel('VELOCITY(Sv-cm/sec)');

legend('\xi=0.05');

hold off;

grid on;

%Acceleration--------------------------------------------------------

------

figure(3);

hold on


title('RESPONSE SPCTRUM FOR Sa');


ylabel('ACCELERATION(Sa-cm/sec^2)');

legend('\xi=0.05');

hold off;

grid on;

⋕Acceleration Response, Sa;

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⋕Velocity Response, Sv;

⋕Displacement Response, Sd;

10

DETERMINING TRIPARTITE SPECTRUM;

⋕Data from the record;

cm cmA 225.924 226 V = 9.55 9

max max2 secsec

225.924A = 0.23g d 10.9 11 cm

max,g max981

⋕Amplification Ratios for 0<T<4 as figure;

Displacement;Sd/dmax Velocity;Sv/Vmax Acceleration;Sa/amax

4

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IMPORTANT INFORMATIONS

1-) After these figures was shown, we will obtain smooth tripartite spectrum which is not real to

determine real tripartite spectrum wanted from me. Infact, smooth tripartite spectrum gives us

crossing points, which are f1’, f2’ and f3’, to plot real tripartite spectrum and to determine which

frequency steps it is. And then, we made stastically a approach . it is;

a)In tripartite spectrum, Displacement corresponds, as frequency, 0.1<f<f1’= 0.18. This frequency step corresponds big period in period-domain. So we applicated gauss normal distribution for 84% on this period step which determines as 5.56<T<10 sec corresponding as frequency 0.1<f<0.18( besides this period step corresponds generally Sd/dmax>1). But we applicated normal distribution at 5<T<10 to be general. And then we obtained a amplification factor, we multiplayed Sd(0.05,T) with this factor. And we will have obtained a new Sd to plot real tripartite spectrum.

b) In tripartite spectrum, Velocity corresponds, as frequency, f1’<f<f2’=4. This frequency step corresponds median period in period-domin. So we applicated gauss normal distribution for 84% on this period step which determines as 0.25<T<5.56 sec corresponding as frequency 0.18<f<4. But we applicated normal distribution at 0.02<T<6 to be general. And then we obtained a amplification factor, we multiplayed Sv(0.05,T) with this factor. And we will have obtained a new Sv to plot real tripartite spectrum.

c) In tripartite spectrum, acceleration corresponds, as frequency, f2’<f<f3’=40. This frequency step corresponds low period in period-domin. So we applicated gauss normal distribution for 84% on this period step which determines as 0.025<T<0.25 sec corresponding as frequency 4<f<40. But we applicated normal distribution at 0.02<T<0.7to be general. And then we obtained a amplification factor, we multiplayed Sa(0.05,T) with this factor. And we will have obtained a new Sa to plot real tripartite spectrum.

New magnificated response spectra was obtained in frequency domain using matlab codes. And tripartite spectrum is determined by marking specific point on logaritmic scale graph. All steps is shown below.

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⋕SMOOTH TRIPARTITE SPECTRUM

⋕Spectra Steps As Both Frequency And Period:

*Displacements; 5.56<T<10; 0,1<f<0.18 but we accept as 5<T<10 for calculating

*Velocity; 0.25<T<5.56; 0.18<f<4 but we accept as 0.02<T<6 for calculating

*Acceleration; 0.025<T<4; 4<f<40 but we accept 0.02<T<0.7 for calculating

STATICALLY APROACH

We accepted %84 exceedance probabilty which is related to El Centrino EQ for sample group of

amplification ratios. We used Excel Formula ‘Normters’ and calculated avarege(μ) and standart

seperation(σ) of sample group. Formula And Sample Groups;

Amax≈0.23g; Vmax≈9;

Dmax≈11

f1’=0.18 f2’=4 f3’=40

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*We couldn’t give all datas since it is very long unlike acceleration. Only specific part is given.But all

datas is Excel file in CD.

1-) DISPLACEMENT SPECTRUM MAGNIFICATION FACTOR

Excel Formula: NORMTERS(olasılık; ortalama; standart_sapma)

Frequency Displacement dmax= 11.0000

Period Sd(0.05,T) Sd/dmax ortalama= 1.5175

0.2000 5.0000 10.2400 0.9309 stdsapma= 0.3205

0.1992 5.0200 10.2700 0.9336 84% Nor.Dağ.= 1.8362

0.1984 5.0400 10.3100 0.9373

0.1976 5.0600 10.3400 0.9400 0.1969 5.0800 10.3800 0.9436 0.1961 5.1000 10.4100 0.9464 0.1953 5.1200 10.4600 0.9509

0.1946 5.1400 10.5100 0.9555 0.1938 5.1600 10.5800 0.9618

0.1931 5.1800 10.6400 0.9673 0.1923 5.2000 10.7100 0.9736 0.1916 5.2200 10.7800 0.9800 0.1908 5.2400 10.8600 0.9873 0.1901 5.2600 10.9300 0.9936 0.1894 5.2800 11.0000 1.0000 0.1887 5.3000 11.0700 1.0064 0.1880 5.3200 11.1400 1.0127 0.1873 5.3400 11.2000 1.0182 0.1866 5.3600 11.2600 1.0236 0.1859 5.3800 11.3200 1.0291 0.1852 5.4000 11.3700 1.0336 0.1845 5.4200 11.4200 1.0382 0.1838 5.4400 11.4700 1.0427 0.1832 5.4600 11.5300 1.0482 0.1825 5.4800 11.6000 1.0545 0.1818 5.5000 11.6600 1.0600 0.1812 5.5200 11.7100 1.0645 0.1805 5.5400 11.7600 1.0691 0.1799 5.5600 11.8100 1.0736 0.1792 5.5800 11.8600 1.0782 0.1786 5.6000 11.9100 1.0827 0.1779 5.6200 11.9500 1.0864 0.1773 5.6400 11.9900 1.0900 0.1767 5.6600 12.0500 1.0955 0.1761 5.6800 12.1100 1.1009 0.1754 5.7000 12.1900 1.1082 0.1748 5.7200 12.2600 1.1145 0.1742 5.7400 12.3200 1.1200 0.1736 5.7600 12.3800 1.1255 0.1730 5.7800 12.4500 1.1318 0.1724 5.8000 12.5600 1.1418 0.1718 5.8200 12.6600 1.1509 0.1712 5.8400 12.7500 1.1591 0.1706 5.8600 12.8400 1.1673 0.1701 5.8800 12.9200 1.1745 0.1695 5.9000 13.0000 1.1818

0.1689 5.9200 13.0700 1.1882 *All datas is not given since very long long

Magnification

Factor For

Tripartite

Spectrum

14

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2-) VELOCITY SPECTRUM MAGNIFICATION FACTOR


Frequency Velocity dmax= 9.0000

Period Sv(0.05,T) Sv/Vmax ortalama= 1.2742

50.0000 0.0200 0.7180 0.0752 stdsapma= 0.4008

25.0000 0.0400 2.9430 0.3082 84% Nor.Dağ.= 1.6728

16.6667 0.0600 7.7960 0.8163

12.5000 0.0800 6.0740 0.6360 10.0000 0.1000 9.6170 1.0070 8.3333 0.1200 11.7900 1.2346 7.1429 0.1400 23.9200 2.5047 6.2500 0.1600 24.3900 2.5539 5.5556 0.1800 14.3100 1.4984 5.0000 0.2000 14.9300 1.5634 4.5455 0.2200 8.8230 0.9239 4.1667 0.2400 8.2140 0.8601 3.8462 0.2600 10.1800 1.0660 3.5714 0.2800 10.4600 1.0953 3.3333 0.3000 7.7990 0.8166 3.1250 0.3200 7.1780 0.7516 2.9412 0.3400 7.3010 0.7645 2.7778 0.3600 7.3800 0.7728 2.6316 0.3800 7.7010 0.8064 2.5000 0.4000 7.8360 0.8205 2.3810 0.4200 8.0100 0.8387 2.2727 0.4400 8.2040 0.8591 2.1739 0.4600 7.5830 0.7940 2.0833 0.4800 6.9760 0.7305 2.0000 0.5000 6.8760 0.7200 1.9231 0.5200 7.2940 0.7638 1.8519 0.5400 7.8880 0.8260 1.7857 0.5600 9.4700 0.9916 1.7241 0.5800 10.8600 1.1372 1.6667 0.6000 10.2100 1.0691 1.6129 0.6200 9.7760 1.0237 1.5625 0.6400 9.7100 1.0168 1.5152 0.6600 9.3430 0.9783 1.4706 0.6800 8.6730 0.9082 1.4286 0.7000 9.5420 0.9992 1.3889 0.7200 11.2200 1.1749 1.3514 0.7400 11.9900 1.2555 1.3158 0.7600 12.2200 1.2796 1.2821 0.7800 11.8800 1.2440 1.2500 0.8000 11.4000 1.1937 1.2195 0.8200 10.8400 1.1351 1.1905 0.8400 10.6700 1.1173 1.1628 0.8600 11.9100 1.2471 1.1364 0.8800 12.8100 1.3414 1.1111 0.9000 13.3500 1.3979 1.0870 0.9200 13.4500 1.4084

1.0638 0.9400 13.1500 1.3770 *All datas is not given

since very long long

Magnification

Factor For

Tripartite

Spectrum

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3-) ACCELERATION SPECTRUM MAGNIFICATION FACTOR


Frequency Acceleration dmax= 225.9240

Period Sa(0.05,T) Sa/Amax ortalama= 1.1948

50.0000 0.0200 225.9240 1.0000 stdsapma= 1.1713

25.0000 0.0400 462.3000 2.0463 84% Nor.Dağ.= 2.3596

16.6667 0.0600 816.4000 3.6136

12.5000 0.0800 477.0000 2.1113

10.0000 0.1000 604.2000 2.6744

8.3333 0.1200 617.1000 2.7314

7.1429 0.1400 1074.0000 4.7538

6.2500 0.1600 957.9000 4.2399

5.5556 0.1800 499.4000 2.2105

5.0000 0.2000 469.0000 2.0759

4.5455 0.2200 252.0000 1.1154

4.1667 0.2400 215.0000 0.9516

3.8462 0.2600 245.9000 1.0884

3.5714 0.2800 234.7000 1.0388

3.3333 0.3000 163.3000 0.7228

3.1250 0.3200 140.9000 0.6237

2.9412 0.3400 134.9000 0.5971

2.7778 0.3600 128.8000 0.5701

2.6316 0.3800 127.3000 0.5635

2.5000 0.4000 123.1000 0.5449

2.3810 0.4200 119.8000 0.5303

2.2727 0.4400 117.2000 0.5188

2.1739 0.4600 103.6000 0.4586

2.0833 0.4800 91.3200 0.4042

2.0000 0.5000 86.8400 0.3844

1.9231 0.5200 88.1400 0.3901

1.8519 0.5400 91.7800 0.4062

1.7857 0.5600 106.3000 0.4705

1.7241 0.5800 117.6000 0.5205

1.6667 0.6000 106.9000 0.4732

1.6129 0.6200 99.0800 0.4386

1.5625 0.6400 95.3300 0.4220

1.5152 0.6600 88.9400 0.3937

1.4706 0.6800 80.1400 0.3547

1.4286 0.7000 85.6500 0.3791 **All data is given

since short

Magnification

Factor For

Tripartite

Spectrum

16

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MAGNIFICATION SPECTRA IN FREQUENCY-DOMAIN

Displacement Spectrum

Velocity Spectrum

17

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Acceleration Spectrum

18

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PLOTTING THE TRIPARTITE SPECTRUM

Tripartite Spectrum


Dmax≈11

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Tripartite And Smooth Spectrum

OBTAINING f1, f2, f3 FREQUENCIES

*We will determine f1,f2,f3 by using Newmark method;

According to both Penzien and Newmark methods, f1 is found from

intersecting with Sv/Vmax and Sa/Amax corresponding to T1.So, first

of all we will determine curves of Sv/Vmax, Sa/Amax in a single

graph. And T1 will be found from corresponding its same numerical

data.

max max

2 2

max max

*Sv(0.05,T) = 25.5586 cm/sec *V = 9.55 cm/sec

*Sa(0.05,T) = 1087.2231 cm/sec *A = 225 .924 cm/sec

5


Dmax≈11

Tripartite

Spectrum

Smooth

Spectrum

20

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*Specific Part; *As a Figure;

*NOT: f1 is same both Newmark and Panzien. We saw easily that while

tirpartites are been drawing.But, According to Newmark method, f2 and

f3 are approximately same 8 hz and 33 hz, respectively.

PERIOD Sv/Vmax Sa/Amax

0 0 0.2077991

0.02 0.009484 0.2099008

0.04 0.103772 0.5159132

0.06 0.24615 0.7555073

0.08 0.212938 0.4486076

0.1 0.322202 0.5566159

0.12 0.430331 0.5768334

0.14 0.867877 1

≈0.165 0.934648 0.8969185

0.18 0.589372 0.4679478

0.2 0.591916 0.431914

0.22 0.439991 0.2337647

0.24 0.414182 0.2014923

0.26 0.393606 0.228247

0.28 0.441943 0.217264

0.3 0.376498 0.1501851

0.32 0.299997 0.1302503

0.34 0.283527 0.1244328

0.36 0.285006 0.1188596

0.38 0.341159 0.118432

0.4 0.373347 0.1138714

0.42 0.388328 0.1104913

0.44 0.36875 0.1081657

0.46 0.319845 0.0957033

0.48 0.293618 0.0843612

0.5 0.293507 0.0797777

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1 1

2 3

T 0.165 sec f 1/0.165 6 hz

f 8 hz , f 33 hz

DESING TRIPARTITE SPECTRUM

*Amplification Factor for One σ (84.1%) and 5% Damping Ratio

A=2.71 , V=2.3, D=2.01 and new maximum values of record;

⋕ Amax=0.23x2.71≈ 0.65g , ⋕ Vmax=2.3x9≈ 20 cm/sec , ⋕ Dmax=2.01x10≈20 cm

⋕Desing Tripartite Spectrum;

v

D

A

6

f1≈6

Amax=2.71*0.23g≈ 0.65g Vmax=2.3*9≈20 cm/sec Dmax=2.01*10.9≈21 cm

Dmax≈21

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Desing Spectrum

Smooth Spectrum

⋕Desing and Smooth Tripartite Spectrum;

GAINING FOURIER AMPLITUDE AND VELOCITY SPECTRUM (SV(0,T)

MATLAB CODE FOR TIME-HISTORY : This program is runned by using text file of ‘yenikayıt’, ‘Spectrum.xls’

and ‘fourierphasevelocity.m-file’ .

⋕Matlab code;

clc

clear all

%Input Data:

Ts=xlsread('Spectrum','input','E11');

td=xlsread('Spectrum','input','E12');

N=xlsread('Spectrum','input','E13');

T(1)=0;

for i=1:N-1

f2≈8 f1≈6 f3≈33

Amax=2.71*0.23g≈ 0.65g Vmax=2.3*9≈20 cm/sec Dmax=2.01*10.65≈21 cm

Dmax≈21

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T(i+1)=i*(Ts);

end

F=xlsread('Spectrum','input','E22:E10018');

j=(td/Ts)+2;

F(j:N)=0;

F=F(1:N);

%Calculation of Natural Damped Frequency and Period:

n=1;

e=[0];

s=0;

for P=0.1:0.01:10

s=s+1;

W=2*pi*P;

WD=W*sqrt(1-e(n)^2);

%Calculation of Dynamic Response In Each Time Point:

A(1)=0; B(1)=0;

Y(1)=0;

for i=2:N;

dF(i)=F(i)-F(i-1);

dT(i)=T(i)-T(i-1);

S12=exp(e(n)*W*T(i))*(e(n)*W*cos(WD*T(i))+WD*sin(WD*T(i)))/((e(n)*W)^

2+WD^2);

S11=exp(e(n)*W*T(i-1))*(e(n)*W*cos(WD*T(i-1))+WD*sin(WD*T(i-

1)))/((e(n)*W)^2+WD^2);

I1=S12-S11;

S22=exp(e(n)*W*T(i))*(e(n)*W*sin(WD*T(i))-

WD*cos(WD*T(i)))/((e(n)*W)^2+WD^2);

S21=exp(e(n)*W*T(i-1))*(e(n)*W*sin(WD*T(i-1))-WD*cos(WD*T(i-

1)))/((e(n)*W)^2+WD^2);

I2=S22-S21;

S32=(T(i)-


S31=(T(i-1)-


I3=S32-S31;

S42=(T(i)-e(n)*W/((e(n)*W)^2+WD^2))*S12-

WD/((e(n)*W)^2+WD^2)*S22;

S41=(T(i-1)-e(n)*W/((e(n)*W)^2+WD^2))*S11-

WD/((e(n)*W)^2+WD^2)*S21;

I4=S42-S41;

A(i)=A(i-1)+(F(i-1)-T(i-1)*dF(i)/dT(i))*I1+dF(i)/dT(i)*I4;

B(i)=B(i-1)+(F(i-1)-T(i-1)*dF(i)/dT(i))*I2+dF(i)/dT(i)*I3;

%Solve for Displacement:

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Y(i)=exp(-e(n)*W*T(i))/WD*(A(i)*sin(WD*T(i))-

B(i)*cos(WD*T(i)));

end

%Determination of Maximum Responses;

Sd=max(abs(Y));

Sv=W*Sd;

spec(s,1,n)=P;

spec(s,3,n)=Sv;

end

%Analysis Results

%Velocity------------------------------------------------------------

figure(1);

hold on

plot(spec(:,1,1),spec(:,3,1),'r-','linewidth',0.5);

title('RESPONSE SPCTRUM FOR Sv(f,0)');

xlabel('Frequency(Hertz)');

ylabel('VELOCITY(Sv-cm/sec)');

legend('\xi=0');

hold off;

grid on;

dt = 0.01;

acc = load('yenikayıt.txt');

time = acc(:,1);

ivme = 100*acc(:,2);


% Fourier Spectrum

[phas, freq, spect] = computefft(ivme, dt);

figure(2)

plot(freq(1:numData/10),spect(1:numData/10));

figure(3)

plot(freq(1:numData/50),phas(1:numData/50));

figure(4)

plot(spec(:,1,1),spec(:,3,1),'r-','linewidth',0.5);

hold on

plot(freq(1:numData/10),spect(1:numData/10), 'b-','linewidth',0.5);

grid on

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⋕FOURIER SPECTRUM

⋕Sv(0,T) SPECTRUM

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⋕FOURIER and Sv(0,T)SPECTRUM

⋕PHASE SPECTRUM

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2.5

I0.2

0.1

S = Sv(0.2,T )dT

AREA=HOUSNER INTENSITY

T=2.5

T=0.1

CALCULATING ENGINEERING INTENSITIES ;

⋕HOUSNER INTENSITY SI0.2;

**Haousner intensity is the area(integration)of the Velocity Spectrum of an EQ computed for

%20 damping ratio.

⋕Graph of Sv(0.2,T);

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PERIOD Sv0.1-2.5 AREAS PERIOD Sv0.1-2.6 ALANLAR PERIOD Sv0.1-2.7 AREAS

0.1 5.7066 0.1346095 0.94 8.0573 0.162283 1.78 9.7236 0.196525

0.12 7.7544 0.1718314 0.96 8.1711 0.164327 1.8 9.9289 0.200603

0.14 9.4288 0.19809 0.98 8.2616 0.165922 1.82 10.1314 0.204436

0.16 10.3803 0.2148137 1 8.3306 0.167108 1.84 10.3123 0.207836

0.18 9.6594 0.2008334 1.02 8.3802 0.167931 1.86 10.4713 0.210852

0.2 8.8948 0.186093 1.04 8.4129 0.16844 1.88 10.6139 0.213464

0.22 8.0751 0.1659759 1.06 8.4311 0.16868 1.9 10.7326 0.215694

0.24 7.6277 0.1527816 1.08 8.4370 0.168784 1.92 10.8368 0.217617

0.26 7.6505 0.1534156 1.1 8.4325 0.168781 1.94 10.9249 0.21933

0.28 7.6911 0.1548357 1.12 8.4192 0.168591 1.96 11.0082 0.22096

0.3 7.5898 0.1539535 1.14 8.3986 0.168242 1.98 11.0879 0.222415

0.32 7.3739 0.1487187 1.16 8.3717 0.167759 2 11.1536 0.223678

0.34 7.2499 0.145313 1.18 8.3391 0.167158 2.02 11.2141 0.224764

0.36 7.2814 0.1470223 1.2 8.3016 0.166453 2.04 11.2623 0.225616

0.38 7.4209 0.149677 1.22 8.2594 0.165653 2.06 11.2993 0.226284

0.4 7.5469 0.1514323 1.24 8.2128 0.164763 2.08 11.3290 0.226846

0.42 7.5964 0.1523093 1.26 8.1621 0.163789 2.1 11.3556 0.227284

0.44 7.5582 0.152123 1.28 8.1074 0.162734 2.12 11.3728 0.227534

0.46 7.4623 0.1503529 1.3 8.0488 0.161599 2.14 11.3806 0.22763

0.48 7.3517 0.1482206 1.32 7.9864 0.160388 2.16 11.3788 0.227695

0.5 7.2330 0.1453035 1.34 7.9204 0.159019 2.18 11.3668 0.227562

0.52 7.1688 0.1440339 1.36 7.8594 0.158437 2.2 11.3442 0.227147

0.54 7.1029 0.1429122 1.38 7.9843 0.160861 2.22 11.3180 0.226733

0.56 7.0175 0.1415282 1.4 8.1018 0.163136 2.24 11.2806 0.22611

0.58 6.8998 0.1395411 1.42 8.2118 0.165261 2.26 11.2309 0.225242

0.6 6.7453 0.1353013 1.44 8.3143 0.167234 2.28 11.1685 0.224122

0.62 6.7848 0.1375893 1.46 8.4091 0.169055 2.3 11.0932 0.222745

0.64 6.9741 0.1413042 1.48 8.4964 0.170726 2.32 11.0052 0.22111

0.66 7.1563 0.1448056 1.5 8.5762 0.172248 2.34 10.9046 0.219219

0.68 7.3242 0.1479572 1.52 8.6486 0.173625 2.36 10.7919 0.217062

0.7 7.4715 0.1506452 1.54 8.7138 0.174859 2.38 10.6696 0.214674

0.72 7.5930 0.1527793 1.56 8.7721 0.175956 2.4 10.5413 0.211705

0.74 7.6849 0.1542893 1.58 8.8235 0.176919 2.42 10.4535 0.209075

0.76 7.7440 0.1551188 1.6 8.8684 0.178259 2.44 10.4540 0.209108

0.78 7.7679 0.1554927 1.62 8.9575 0.18031 2.46 10.4513 0.209084

0.8 7.7543 0.1556076 1.64 9.0735 0.182563 2.48 10.4455 0.208997

0.82 7.7021 0.1549496 1.66 9.1828 0.184682 2.5 10.4368

0.84 7.6113 0.1535028 1.68 9.2854 0.186671 Housner Int.= 21.55582

0.86 7.4836 0.1505507 1.7 9.3816 0.188532

0.88 7.5715 0.1532826 1.72 9.4715 0.190267

0.9 7.7568 0.1567586 1.74 9.5552 0.191979

0.92 7.9191 0.2375733 1.76 9.6428 0.193663

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2.5

I0.2

0.1

S = Sv(0.2,T )dT

ΔT=0.02

Sv(0.2,T)

T

S1 S2

Ai

A

A

⋕AREAS=0.02*(H22+MUTLAK(H23-H22)*0,5) Excel Formula

⋕How this equation runs and table which is above prepares is that ;

Ai=0.02x(S1+mutlak(S1-S2)x0.5) A=ΣAi

SI0.2 = 21.55 cm

**This equation/formula is saved at CD as Excel file.

⋕EFFECTİVE TIME (teff) and ACCELERATION(aeff);

**These datas are obtained from seismosignal software;

⋕Effectiıve Acceleration; aeff = Effective Desing Acceleration=198.278 cm/sec2

aeff =Effective acceleration is the max. acceleration

value obtained by cutting off yhe acceleration time-

history of an Earthquake from top and bottom

which gives the 90% value of the velocity response

spectrum for 5% damping ratio.

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teff=12.97

Velocity related with

acceleration.

⋕Effective Time; teff ; teff=37.37-24.4=12.97 sec

⋕EPA (Effective Peak Acceleration ) = Amax 0.65g

EPA= = =0.26g2.5 2.5

⋕EPV(Expected Peak Velocity) =Vmax 20

EPV= = =8 cm/sec2.5 2.5

⋕Av =EPV 8

Av= = =0.267 cm/sec30 30

⋕ IEAP (Earthquake Attack Power): eff

EAP

0.2

a ×teff 198.278 12.97I = = =286.4

SI 21.55/2.4

2.4

***All program code and figure are saved at cd.

All Formulas are

given from

Prof.Dr. Zeki Hasgür

in Seismology

lecture.

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ENGINEERING SEISMOLOGY HOMEWORK

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