Contents

TWO STORY STEEL FRAME, LINEAR ELASTIC ANALYSIS UNDER DIFFERENT LOAD COMBINATIONS

%  =========================================================================================
%  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,'Linear elastic analysis of two story steel frame');

Element properties

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

Sequence of linear analyses for three load cases and superposition

Load case 1 : distributed load in girders

% distributed load in elements 5 through 8
for el=5:6 ElemData{el}.w = [0;-0.50]; end
for el=7:8 ElemData{el}.w = [0;-0.35]; end
% there are no nodal forces for first load case
Loading = Create_Loading (Model);

% perform single linear analysis step
State = LinearStep (Model, ElemData, Loading);

% Post-processing
% print structural response (global forces and displacements)
Print_State (Model,State);
% print element response
Structure ('prin',Model,ElemData,State);

% plot deformed shape of structural model
MAGF = 100;       % magnification factor for deformed configuration
Create_Window(0.70,0.70);
Plot_Model(Model);
Structure ('defo',Model,ElemData,State);

% store element response for later post-processing
Post(1) = Structure ('post',Model,ElemData,State);

% plot moment distribution
Create_Window(0.70,0.70);
Plot_Model(Model);
Plot_ForcDistr (Model,ElemData,Post(1),'Mz');
title('Moment distribution of 2-story frame under gravity load in girders');

 Norm of equilibrium error = 1.438860e-012

Load case 2: horizontal forces

% set distributed load in elements 5 through 8 from previous load case to zero
for el=5:8;  ElemData{el}.w = [0;0]; end
% specify nodal forces
Pe(2,1) = 20;
Pe(3,1) = 40;
Pe(5,1) = 20;
Pe(6,1) = 40;
Loading = Create_Loading (Model,Pe);

% perform single linear step
State = LinearStep (Model, ElemData, Loading);

% post-processing
% print structural response (global forces and displacements)
Print_State (Model,State);
% print element response
Structure ('prin',Model,ElemData,State);

% plot deformed shape of structural model
MAGF = 50;       % magnification factor for deformed configuration
Create_Window(0.70,0.70);
Plot_Model(Model);
Structure ('defo',Model,ElemData,State);

% store element response for later post-processing
Post(2) = Structure ('post',Model,ElemData,State);

% plot moment distribution
Create_Window(0.70,0.70);
Plot_Model(Model);
Plot_ForcDistr (Model,ElemData,Post(2),'Mz');
title('Moment distribution of 2-story frame under horizontal forces');

 Norm of equilibrium error = 6.625476e-012

Load case 3: support displacement

% zero nodal forces from previous load case and impose horizontal support displacement
Pe = [];
Ue(1,1) = 0.2;   % horizontal support displacement
Loading = Create_Loading (Model,Pe,Ue);

% perform single linear step
State = LinearStep (Model, ElemData, Loading);

% post-processing
% print structural response (global forces and displacements)
Print_State (Model,State);
% print element response
Structure ('prin',Model,ElemData,State);

% plot deformed shape of structural model
MAGF = 100;       % magnification factor for deformed configuration
Create_Window(0.70,0.70);
Plot_Model(Model);
Structure ('defo',Model,ElemData,State);

% store element response for later post-processing
Post(3) = Structure ('post',Model,ElemData,State);

% plot moment distribution
Create_Window(0.70,0.70);
Plot_Model(Model);
Plot_ForcDistr (Model,ElemData,Post(3),'Mz');
title('Moment distribution of 2-story frame under support settlement');

 Norm of equilibrium error = 9.257498e-013

Load combination

% plot a new moment distribution for gravity and lateral force combination
% using LRFD load factors and assuming that horizontal forces are due to EQ
for el=1:Model.ne
   Post_Combi.Elem{el}.q =1.2.*Post(1).Elem{el}.q + 1.5.*Post(2).Elem{el}.q;
end

% include distributed load in elements 5 through 8 for moment diagram
for el=5:6 ElemData{el}.w = [0;-0.50]; end
for el=7:8 ElemData{el}.w = [0;-0.35]; end

% plot combined moment distribution
Create_Window(0.70,0.70);
Plot_Model(Model);
Plot_ForcDistr (Model,ElemData,Post_Combi,'Mz');
title('Moment distribution of 2-story frame under load combination of 1.2DL+1.5EQ');

% close output file
fclose(IOW);

Published with MATLAB® 7.0