Contents

TWO STORY STEEL FRAME, PUSH-OVER ANALYSIS WITH CONSTANT GRAVITY LOADS AND LATERAL FORCES UNDER LOAD CONTROL for NONLINEAR GEOMETRY

%  =========================================================================================
%  FEDEASLab - Release 2.6, July 2004
%  Matlab Finite Elements for Design, Evaluation and Analysis of Structures
%  Copyright(c) 1998-2004. The Regents of the University of California. All Rights Reserved.
%  Created by Professor Filip C. Filippou (filippou@ce.berkeley.edu)
%  Department of Civil and Environmental Engineering, UC Berkeley
%  =========================================================================================

Initialization: clear memory and define global variables

% all units in kip and inches
CleanStart

Create output file

IOW = Create_File (mfilename);

Create Model

Model_TwoStoryFrm
% echo input data of structural model to output file (optional)
Print_Model (Model,'Push-over analysis of two story steel frame');

Element properties

SimpleNLElemData
% print element properties (optional)
Structure ('data',Model,ElemData);

1. Loading (distributed loads and vertical forces on columns)

% define loading
for el=5:6 ElemData{el}.w = [0;-0.50]; end
for el=7:8 ElemData{el}.w = [0;-0.35]; end

Pe(2,2) =  -200;
Pe(3,2) =  -400;
Pe(5,2) =  -200;
Pe(6,2) =  -400;
GravLoading = Create_Loading (Model,Pe);

Nonlinear geometry option for columns

for el=1:4 ElemData{el}.Geom = 'PDelta'; end

Incremental analysis for distributed element loading (single load step)

% initialize state
State = Initialize_State(Model,ElemData);
% initialize solution strategy parameters
SolStrat = Initialize_SolStrat;
% specify initial load increment (even though it is the same as the default value and could be omitted)
SolStrat.IncrStrat.Dlam0 = 1;
% initialize analysis sequence
[State SolStrat] = Initialize(Model,ElemData,GravLoading,State,SolStrat);
% apply load in one increment
[State SolStrat] = Increment(Model,ElemData,GravLoading,State,SolStrat);
% perform equilibrium iterations (we assume that convergence will occur!)
[State SolStrat] = Iterate  (Model,ElemData,GravLoading,State,SolStrat);
% update State
State = Update_State(Model,ElemData,State);
% determine resisting force vector
State   = Structure ('forc',Model,ElemData,State);
% set plot counter and store results for post-processing
k = 1;
Post(k) = Structure ('post',Model,ElemData,State);

 Iteration: 1  Relative work increment = 5.832748e-009
 Iteration: 2  Relative work increment = 6.377350e-033
 Number of iterations = 2

2. Loading in sequence: horizontal forces

% specify nodal forces
% !!!! IMPORTANT!!!! CLEAR PREVIOUS PE
clear Pe;
Pe(2,1) =  20;
Pe(3,1) =  40;
Pe(5,1) =  20;
Pe(6,1) =  40;
LatLoading = Create_Loading (Model,Pe);

Incremental analysis for horizontal force pattern (load control is switched on)

%  (gravity forces are left on by not initializing State!)
% specify initial load increment and turn load control on (default value is 'no')
SolStrat.IncrStrat.Dlam0 = 0.40;
SolStrat.IncrStrat.LoadCtrl = 'yes';
SolStrat.IterStrat.LoadCtrl = 'yes';
% specify number of load steps
nostep = 20;
% initialize analysis sequence
[State SolStrat] = Initialize(Model,ElemData,LatLoading,State,SolStrat);

tic;
% for specified number of steps, Increment, Iterate and Update_State (we assume again convergence!)
for j=1:nostep
   [State SolStrat] = Increment(Model,ElemData,LatLoading,State,SolStrat);
   [State SolStrat] = Iterate  (Model,ElemData,LatLoading,State,SolStrat);
   State = Update_State(Model,ElemData,State);
   k = k+1;
   Post(k) = Structure ('post',Model,ElemData,State);
end
toc;

 Iteration: 1  Relative work increment = 1.196065e-008
 Iteration: 2  Relative work increment = 2.241850e-018
 Number of iterations = 2

 Iteration: 1  Relative work increment = 4.691924e-008
 Iteration: 2  Relative work increment = 8.838178e-018
 Number of iterations = 2

 Iteration: 1  Relative work increment = 1.051838e-007
 Iteration: 2  Relative work increment = 1.993086e-017
 Number of iterations = 2

 Iteration: 1  Relative work increment = 1.867544e-007
 Iteration: 2  Relative work increment = 3.567576e-017
 Number of iterations = 2

 Iteration: 1  Relative work increment = 6.892077e-002
 Iteration: 2  Relative work increment = 2.452292e-008
 Iteration: 3  Relative work increment = 4.456754e-018
 Number of iterations = 3

 Iteration: 1  Relative work increment = 3.250944e-002
 Iteration: 2  Relative work increment = 1.372842e-008
 Iteration: 3  Relative work increment = 2.034212e-017
 Number of iterations = 3

 Iteration: 1  Relative work increment = 1.394003e-007
 Iteration: 2  Relative work increment = 5.944331e-017
 Number of iterations = 2

 Iteration: 1  Relative work increment = 1.810720e-007
 Iteration: 2  Relative work increment = 9.915722e-017
 Number of iterations = 2

 Iteration: 1  Relative work increment = 6.315634e-002
 Iteration: 2  Relative work increment = 5.545414e-009
 Iteration: 3  Relative work increment = 8.214241e-018
 Number of iterations = 3

 Iteration: 1  Relative work increment = 3.398183e-001
 Iteration: 2  Relative work increment = 1.983728e-007
 Iteration: 3  Relative work increment = 2.563714e-016
 Iteration: 4  Relative work increment = 6.851871e-025
 Number of iterations = 4

 Iteration: 1  Relative work increment = 3.538129e-006
 Iteration: 2  Relative work increment = 9.864370e-015
 Iteration: 3  Relative work increment = 2.756329e-023
 Number of iterations = 3

 Iteration: 1  Relative work increment = 3.977749e-006
 Iteration: 2  Relative work increment = 1.151785e-014
 Iteration: 3  Relative work increment = 3.327520e-023
 Number of iterations = 3

 Iteration: 1  Relative work increment = 2.474425e+000
 Iteration: 2  Relative work increment = 2.541561e-006
 Iteration: 3  Relative work increment = 6.809939e-027
 Number of iterations = 3

 Iteration: 1  Relative work increment = 3.477990e-014
 Iteration: 2  Relative work increment = 1.800988e-029
 Number of iterations = 2

 Iteration: 1  Relative work increment = 4.041558e-014
 Iteration: 2  Relative work increment = 5.948243e-030
 Number of iterations = 2

 Iteration: 1  Relative work increment = 4.648730e-014
 Iteration: 2  Relative work increment = 2.027529e-029
 Number of iterations = 2

 Iteration: 1  Relative work increment = 5.299504e-014
 Iteration: 2  Relative work increment = 6.524311e-030
 Number of iterations = 2

 Iteration: 1  Relative work increment = 5.993882e-014
 Iteration: 2  Relative work increment = 3.478578e-030
 Number of iterations = 2

 Iteration: 1  Relative work increment = 6.731864e-014
 Iteration: 2  Relative work increment = 4.620881e-029
 Number of iterations = 2

 Iteration: 1  Relative work increment = 7.513448e-014
 Iteration: 2  Relative work increment = 2.341973e-029
 Number of iterations = 2
Elapsed time is 1.360000 seconds.

Post-processing

% extract displacements from Post
np = length(Post);
x = zeros(np,1);
y = zeros(np,1);
pltDOF = Model.DOF(1,6);
supDOF = [Model.DOF(1,1) Model.DOF(1,4)];
for k=1:np
   x(k) = Post(k).U(pltDOF);
   y(k) = -sum(Post(k).Pr(supDOF))/120;
end

% plot force displacement relation in new window
fig = Create_Window(0.70,0.70);
ph1 = plot(x,y,'s-');
set (ph1,'MarkerSize',4,'MarkerFaceColor','b');
grid('on');
xlabel ('Horizontal roof displacement');
ylabel ('Load factor {\lambda}');
axis ([0 10 0 3]);
title ('Load factor-displacement');

% plot moment distribution at end of push-over
Create_Window(0.70,0.70);
Plot_Model(Model);
Plot_ForcDistr (Model,ElemData,Post(end),'Mz');
title('Moment distribution and plastic hinge locations near incipient collapse');
% show plastic hinge locations
Plot_PlasticHingeswPost(Model,Post(end));

% plot deformed shape of structure and plastic hinge locations
Create_Window(0.70,0.70);
Plot_Model(Model);
Structure('defo',Model,ElemData,State);
Plot_PlasticHingeswPost(Model,Post(end),State.U);
Resize_Plot;

% close output file
fclose(IOW);

Published with MATLAB® 7.0