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Example_Pushover_RCPlane_Frame_03.m
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Example_Pushover_RCPlane_Frame_03.m
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clc
clear all
% Example_Pushover_RCPlane_Frame_03
%----------------------------------------------------------------
% PURPOSE
% To compute the non-linear static Pushover analysis for a
% reinforced concrete plane frame
%
%
%----------------------------------------------------------------
% LAST MODIFIED: L.F.Veduzco 2023-02-23
% Faculty of Engineering
% Autonomous University of Queretaro
%----------------------------------------------------------------
nnodes=15;
nbars=20;
%% Materials
% f'c of each element
fpc=[300;
300;
300;
300;
280;
280;
280;
280;
300;
300;
300;
300;
280;
280;
280;
280;
300;
300;
300;
300];
% Elasticity modulus of each element in function of f'c
for i=1:nbars
E(i)=14000*(fpc(i))^0.5;
end
%% Geometry/Topology
dimensions=[35 70;
65 70;
55 70;
55 55;
55 110;
55 110;
35 70;
35 70;
65 105;
65 90;
65 90;
65 205;
35 70;
35 70;
35 70;
35 70;
65 70;
55 70;
45 60;
35 60];
for i=1:nbars
A(i)=dimensions(i,1)*dimensions(i,2);
I(i)=1/12*dimensions(i,1)*dimensions(i,2)^3;
end
% coordinates of each node for each bar
coordxy=[0 -150;
0 400;
0 800;
0 1200;
0 1600;
600 1600;
600 1200;
600 800;
600 400;
600 -150;
1200 -150;
1200 400;
1200 800;
1200 1200;
1200 1600];
%%%---- Initial-final node of each bar -----%%%
ni=[1;2;3;4;5;4;3;2;10;9;8;7;6; 7; 8; 9; 11;12;13;14];
nf=[2;3;4;5;6;7;8;9;9; 8;7;6;15;14;13;12;12;13;14;15];
L=sqrt((coordxy(nf,1)-coordxy(ni,1)).^2+...
(coordxy(nf,2)-coordxy(ni,2)).^2); % bar-length vector
% prescribed boudnary conditions [DOF, displacement]
bc=[1 0;
2 0;
3 0;
28 0;
29 0;
30 0;
31 0;
32 0;
33 0];
%% Loads
type_elem=[1 "Col";
2 "Col";
3 "Col";
4 "Col";
5 "Beam";
6 "Beam";
7 "Beam";
8 "Beam";
9 "Col";
10 "Col";
11 "Col";
12 "Col";
13 "Beam";
14 "Beam";
15 "Beam";
16 "Beam";
17 "Col";
18 "Col";
19 "Col";
20 "Col"];
beams_LL=[1 -80; % Uniformly distributed loads over the beams
2 -80;
3 -80;
4 -80;
5 -80;
6 -80;
7 -80;
8 -80];
elem_cols=[];
elem_beams=[];
beams=0;
cols=0;
for j=1:nbars
if type_elem(j,2)=="Beam"
beams=beams+1;
elem_beams=[elem_beams,j];
elseif type_elem(j,2)=="Col"
cols=cols+1;
elem_cols=[elem_cols,j];
end
end
supports=[1 "Empotrado" "Empotrado";
2 "Empotrado" "Empotrado";
3 "Empotrado" "Empotrado";
4 "Empotrado" "Empotrado";
5 "Empotrado" "Empotrado";
6 "Empotrado" "Empotrado";
7 "Empotrado" "Empotrado";
8 "Empotrado" "Empotrado";
9 "Empotrado" "Empotrado";
10 "Empotrado" "Empotrado";
11 "Empotrado" "Empotrado";
12 "Empotrado" "Empotrado";
13 "Empotrado" "Empotrado";
14 "Empotrado" "Empotrado";
15 "Empotrado" "Empotrado";
16 "Empotrado" "Empotrado";
17 "Empotrado" "Empotrado";
18 "Empotrado" "Empotrado";
19 "Empotrado" "Empotrado";
20 "Empotrado" "Empotrado"];
% Uniformly distributed loads considering self weight of the elements
qbary=zeros(nbars,2);
for i=1:beams
qbary(elem_beams(i),2)=1.1*(beams_LL(i,2));
end
% Plastic moments of each element's ends
Mp=[9680000 9680000;
8490000 8490000;
8363000 8976940;
7490000 7490000;
5680000 5680000;
7363000 7976940;
8363000 8976940;
9490000 9490000;
12680000 12680000;
11490000 11490000;
10363000 10976940;
9490000 9490000;
5680000 5680000;
7363000 7976940;
8363000 8976940;
9490000 9490000;
9680000 9680000;
8490000 8490000;
8363000 8976940;
7490000 7490000]; %Kg-cm
% Lateral equivalent seismic forces from a modal analysis. The number of
% forces must be equal to the number of floors
seismicForces=[1500; % lower floor
2000;
2500;
3000]; % upper floor
% Degrees of freedom over which each seismic force is applied (one for
% each seismic force)
dofSeismicForces=[4 7 10 13];
% Height of each floor
hfloor=[400; 400; 400; 400];
%%% PUSHOVER IN POSITIVE DIRECTION OF FORCES
[lambdaRight,pdriftDIRight,driftDIRight,defBasedDIRight,maxDispRight,...
barPlasNodeRight]=Pushover2DFrames2(qbary,A,Mp,E,I,coordxy,ni,nf,...
supports,bc,seismicForces,hfloor,dofSeismicForces,0.01,0.05);
%%% PUSHOVER IN NEGATIVE DIRECTION OF FORCES
seismicForces=-seismicForces;
[lambdaLeft,pdriftDILeft,driftDILeft,defBasedDILeft,maxDispLeft,...
barPlasNodeLeft]=Pushover2DFrames2(qbary,A,Mp,E,I,coordxy,ni,nf,...
supports,bc,seismicForces,hfloor,dofSeismicForces,0.01,0.05);
nfloors=length(hfloor);
%% Final results
SafetyFac=min([max(lambdaRight), max(lambdaLeft)])
pdriftDI=min([sum(pdriftDIRight)/nfloors,sum(pdriftDILeft)/nfloors])
driftDI=min([sum(driftDIRight)/nfloors,sum(driftDILeft)/nfloors])
dbDI=min([sum(defBasedDIRight)/nfloors,sum(defBasedDILeft)/nfloors])
Max_Displacement=max(max(maxDispLeft),max(maxDispRight))