Upload
jasmin-selimovic
View
26
Download
0
Embed Size (px)
DESCRIPTION
structur Interaction
Citation preview
ri.livici.www
S H A R I F O F U N I V E R S I T Y O F
T H E C N O L O G Y
D Y N A M I C O F S O I L - S T R U C T U R
I N T E R A C T I O N
P R O J E C T T E R M
K E S H A V A R Z . M O H A M M A D R E Z A - M O H A M M A D P O U R
P O U Y A
R O O M N U M B E R
Lecture's name:
Professor M.Ali.Ghannad
2014- winter- February
2 | P a g e
Problem define:
Two stories shear building with embedment square (10*10) m^2 foundation
Using CONAN software to plot the soil dynamic stiffness coefficients variations and
foundation input motion to dimensionless frequency (0
3 | P a g e
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
kh,c
h
a0
Sway dynamic stiffness coefficients kh ch
0.00
5.00
10.00
15.00
20.00
0 1 2 3 4 5
kh,c
h
a0
Sway DOF for surface foundationkh Embedment foundation:
For a0 more than 1.23 leads to ch
approximate equal to 1.22 and kh
values for a0 more than 0.95 are
less than 1 and converge to zero.
Surface foundation:
For a0 more than 0.45 leads to ch
approximate equal to less than1
and kh values are going converge
to zero but with lower speed than
the embedment foundation.
Static stiffness (horizontal) = 2.0831e+09
Static stiffness = 1.2130e+09 (surface foundation)
Using excel to plot the data as this way:
This graph express the variation of dynamic coefficients for sway DOF (horizontal) for different
values of dimensionless frequency (a0=.r
).as it's shown for lower values of a0, the dynamic
damping coefficient is very frequency dependent. And for excitation frequency till 25 rad/sec stiffness
coefficient kh=1. If compare this model of building with the surface foundation case we see that
there is some different and it's about that in this case we see, the ch is effected by soil-structure
interaction less than the embedment case.
4 | P a g e
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
16.00
18.00
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
kr,c
r
a0
Rocking dynamic stiffness coefficient kr cr
Static stiffness (rocking) = 9.4319e+10
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
ugh
/uc
a0
Sway FIM Re(ugh/uc) Im(ugh/uc)
This graph express the variation of dynamic coefficients for rocking DOF for different values of
dimensionless frequency (a0=.r
).
Conclusion:
The embedment foundations are more effected by increasing in damping ratio of soil-structure
system, in other hands by increasing embedment ratio (
), soil-structure systems affected in
damping ratio more than stiffness.
We run Conan again by input txt file and for foundation input motion plot graph like this:
5 | P a g e
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
ugr
/uc
a0
Rocking FIM Re(ugr/uc) Im(ugr/uc)
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
-10 0 10 20 30 40 50
acce
lera
tio
n (
g)
Time (sec)
Free Field Motion (FFM)
These graphs express how is the
For excitation data as *.txt file plot the dynamic stiffness coefficients variations and foundation
input motion to dimensionless frequency.
For determine the dynamic stiffness coefficients variations and FIM along the specific
earthquake, it should be in frequency domain, so we have to choose the suitable software to
change earthquake data from time domain to frequency domain.
We could us of Microsoft office excel or SIESMO SIGNAL or Matlab.
Now we have frequency domain data:
6 | P a g e
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0 10 20 30 40 50 60
FFT
mag
f (Hz)
Fourier amplitude of FFM
Free field motion in frequency domain:
Foundation input motion for excitation in control point motion as a specific time-history data:
7 | P a g e
8 | P a g e
Matlab code that is used for plot these graphs:
clc;
clear all;
load FFM.txt;
load h.txt;
load r.txt;
dt=input('please enter time step of inserted record> ');
a_surf=FFM';
H=h';
R=r';
n=length(a_surf);
F=zeros(2,n+1);
for index=1:n+1
F(1,index)=H(1,index)+1i*H(2,index);
F(2,index)=R(1,index)+1i*R(2,index);
end
b=a_surf(2,:);
acc=[0,b];
df=1/(n*dt);
t=0:dt:n*dt;
f=0:df:n*df;
a_fft=fft(acc)/n;
A_time=zeros(2,n+1);
for j=1:2
a_freq=a_fft.*F(j,:);
a_time=n*real(ifft(a_freq));
figure(j);
hold on;
if j==1
title('Horizontal FIM');
xlabel('Time (sec.)');
ylabel('ugh (m)');
else
title('Rocking FIM');
xlabel('Time (sec.)');
ylabel('ugr (Rad)');
end;
plot(t,a_time);
hold off;
figure(2+j);
hold on;
if j==1
title('Horizontal FIM');
xlabel('Frequency (Hz)');
ylabel('ugh (m)');
else
title('Rocking FIM');
xlabel('Frequency (Hz)');
ylabel('ugr (Rad)');
end;
plot(f,n*a_freq);
hold off;
end;
9 | P a g e
~
~ ~
~
~
Using Cone model concept for specific frequency to determine dynamic stiffness
coefficients, to simplify use the approximate formula in ATC3-06 for compute the period of
soil-structure system.
Page56 on ATC3-06:
Ta=CT.hn3/4 where for concrete frames: CT= 0.025
Ta=0.025*(22.965879)3/4=0.26sec
Page387 on ATC3-06:
For embedment foundation:
ky=8
2 1 +
2
3
=842.75(106)5.64
20.41 +
2
3
4
5.64= 1775.55E06 (N/m)
k=8^3
3(1) 1 + 2
=842.75(106)5.71^3
3(10.4)1 + 2
4
5.71= 84930.42E06 (N/m)
Page65 on ATC3-06:
W= 0.7*(280ton) = 196 ton, K=42
^2=42
196
0.26^2=114.46405E06 (N/m), h=0.7*7=4.9m
T=T1 +
ky(1 +
ky.2
k)=0.26*1 + 114.46405E06
1775.55E06(N/m)(1 +
1775.55E06(N/m).(4.9m)2
84930.42E06(N/m))=0.
27 sec
T
T=0.27
0.26=1.038,
H
=5.8
5.675=1.02
graph on page 71
0=0.025
= 0+0.05
(1.04)^3=0.07
So =2
T=23.27rad/sec ao=
.r
= (23.27*5.675)/150=0.88 dimensionless
frequency
a0 kh ch kr Cr
0.88 9.05E-01 1.28E+00 8.43E-01 3.77E-01
Static stiffness (horizontal) = 2.0831e+09, Static stiffness (rocking) = 9.4319e+10
10 | P a g e
S (a0=0.88) = (2.0831e+09)*( 9.05E-01+i*0.88*1.28E+00)= 1.8852e+09 +2.3464e+09i for sway DOF
S (a0=0.88) = (9.4319e+10)*( 8.43E-01+i*0.88*3.77E-01)= 7.9511e+10 +3.1291e+10i for rocking DOF
Modeling for standard software to analysis soil-structure interaction we should use above
coefficients for setting dashpot and spring for sway and rocking like this figure:
ky=1.8852e+09 (N/m)
cy=2.3464e+09(N.s/m)
kt= 7.9511e+10 (N/m)
ct= 10 +3.1291e+10(N.s/m)
Using reference [2] and compute the damping ratio and stiffness of soil-structure system for
first mod.
At the first we must write the mass and stiffness matrices:
m=[90 00 90
] , K=[2
],
11 | P a g e
~
~
A=k-2.m=103[430 215215 215
]=0, 1=x110^3
90=30.21rad/sec
fix=30.21rad/sec Tfix=0.207sec, ao=1.14
a0 kh ch kr cr
1.14 8.71E-01 1.24E+00 7.97E-01 3.74E-01
With assumption that the lateral force act to each story related by weight of itself, we have:
1=(12.5648.374
) mStr=173.1 ton, H=5.8 m,
=0.578,
=
=
(.)(+.)
(.+)(. +..+)(+.)=
0.0215 - 0.0399i=
=
.^2=(.+)(. +..)(+.)
(.)(.)(+.)=
13.7795 + 8.4522i=
=1+ + * + * * =15.7787 + 7.8703i
=fix2
+24(1+)= 29.1051 + 0.9915i
d=Real
() =29.1051 T= 0.22 sec and =
()
()=0.0340
T
T=0.22
0.207=1.063, 0=0.034
12 | P a g e
~
~
~
Using ATC3-06 to compute reduction of base shear for this building.
For no interaction effect:
A=0.3 for high relative hazard, B=2.75 from standard spectrum, I=1 for
building with intermediate importance factor, R=7 for intermediate concert moment frame
Cs(T, )=
=0.32.751
7=0.1179
V= Cs.W=0.1179*180ton=21.21ton For interaction effect:
= [Cs(T, ) Cs(T, ) (
) ^0.4]
Cs(T, )=0.1179
= [0.1179 0.1179 (0.05
0.07) ^0.4]
=2.6 Conclusion
For this specific building if use ATC guideline for SSI we reduce base shear
about 10% and if compare it with damping ratio that come from modal
simplified method, can see the increasing in damping ratio computed by
ATC approach it's not real and for this case SSI it's not so important and if
we want done with SSI, the more exact approaches is required.