struct9.m

Benchmark Control Problems for Seismically Excited Nonlinear Building

%-----------------------------------------------------------------------
%|*********************************************************************|
%|*           Structural Data of the 9 Story 5 Bay Building           *|
%|*                                                                   *|
%|*                  University of Notre Dame                         *|
%|*                       November, 1999                              *|
%|*                                                                   *|
%|*               Coded by      Y.Ohtori                              *|
%|*                             R.E.Christenson                       *|
%|*               Supervised by B.F.Spencer, Jr.  	              *|
%|*********************************************************************|
%-----------------------------------------------------------------------

% UNITS: N - m

% ------------------------------------------------
% --- Define File Name of Structural Data File ---
% ---  for the SIMULINK S-function             ---
% ------------------------------------------------
     f1_name = 'structure.dat1';       % Name of Structural Data for SIMULINK

% --------------------------------------------
% --- Define Initial Data for Calculations ---
% --------------------------------------------
     T_str   = 0.0;                     % Start time of the Response Analysis
     T_end   = 100.0;                   % End time of the Response Analysis
     dt_cal  = 0.005;                   % Calculation Interval Delta_t
     dt_out  = 0.01;                   % Output Interval for file

    beta_val  = 1.0/4.0;               % beta  value for Newmark-beta Method
    gamma_val = 1.0/2.0;               % gamma value for Newmark-beta Method

% ----------------------
% --- Define Damping ---
% ----------------------
     zeta_cr   = 0.02;                % Critical Damping
     h_max     = 0.02;                % Maximum Damping for Type 2
     nCutOff   = 2;                   % Number of mode for cutting off

% -------------------------------------
% --- Set Data for Nodal Coordinate ---
% -------------------------------------
     Num_story = 9+1;                        % Number of stories + basement
     Num_bay   = 5;                          % Number of Bays
     Num_MRF   = 2;                          % Number of Moment Resisting Frame
     Num_node  = (Num_bay+1)*(Num_story+1);  % Number of Node
     Num_DOF   = 3*Num_node;                 % Number of Degree of Freedoms

     height = [ 3.6576 5.4864 3.9624 3.9624 3.9624 3.9624 ....
                3.9624 3.9624 3.9624 3.9624 ];  

     width  = [ 9.1440 9.1440 9.1440 9.1440 9.1440 ];

% ---------------------------------------------
% --- Define Material Table (left to right) ---
% ---------------------------------------------
     Num_beam  = Num_bay*Num_story;              % Number of Beams
     Num_col   = (Num_bay+1)*Num_story;          % Number of Coloms
     Num_elem  = Num_beam + Num_col;             % Number of Elements

     element_tbl = zeros(Num_elem,4);

%  - Column -

   for i=1:Num_col
     element_tbl(i,1) = i;
     element_tbl(i,2) = i + (Num_bay+1);
     element_tbl(i,4) = 1;
   end

  element_tbl(1:Num_col,3) = [
                         1     2     2     2     2     1  ...   %  basement
                         1     2     2     2     2     1  ...   %  1st floor
                         1    12    12    12    12     1  ...   %  2nd floor
                         1     3     3     3     3     1  ...   %  3rd floor
                        13    14    14    14    14    13  ...   %  4th floor
                         4     1     1     1     1     4  ...   %  5th floor
                        15    13    13    13    13    15 ...   %  6th floor
                         5     4     4     4     4     5 ...   %  7th floor
                        16    15    15    15    15    16 ...   %  8th floor
                         6     5     5     5     5     6 ...   %  9th floor
                                                        ]';

%  - Beam   -

   elem_no = Num_col;
   for i = 1:Num_story
     for j = 1:Num_bay
         elem_no = elem_no + 1;
         element_tbl(elem_no,1) = i*(Num_bay+1) + j;
         element_tbl(elem_no,2) = element_tbl(elem_no,1) + 1;
         element_tbl(elem_no,4) = 2;
     end
   end

  element_tbl(Num_col+1:Num_col+Num_beam,3) = [
                         7     7     7     7    7 ...   %  1st floor
                         7     7     7     7    7 ...   %  2nd floor
                         7     7     7     7    7 ...   %  3rd floor
                         8     8     8     8    8 ...   %  4th floor
                         8     8     8     8    8 ...   %  5th floor
                         8     8     8     8    8 ...   %  6th floor
                         8     8     8     8    8 ...   %  7th floor
                         9     9     9     9    9 ...   %  8th floor
                        10    10    10    10    10 ...   %  9th floor
                        11    11    11    11    11 ...   %  roof
                                                       ]'; 

  element_tbl(Num_col+[5 10 15 20 25 30 35 40 45 50],4) = 5;

% -----------------------------------
% --- Define Master - Slave Nodes ---
% -----------------------------------
  slv_tbl = [
%   Master  Dir  Num_slv  Slv_1  Slv_2  Slv_3  Slv_4
     15      1     5       13     14      16     17     18   %  2nd floor
     21      1     5       19     20      22     23     24   %  3rd floor
     27      1     5       25     26      28     29     30   %  4th floor
     33      1     5       31     32      34     35     36   %  5th floor
     39      1     5       37     38      40     41     42   %  6th floor
     45      1     5       43     44      46     47     48   %  7th floor
     51      1     5       49     50      52     53     54   %  8th floor
     57      1     5       55     56      58     59     60   %  9th floor
     63      1     5       61     62      64     65     66   %  roof
      ];      
  Num_mst = length(slv_tbl(:,1));                    % Number of Master Nodes

% --------------------------
% --- Define Fixed Nodes ---
% --------------------------
%                       Fix: 1 , Free: 0 
%              Node_no  Hor.  Vert.  Rot.
  Fix_node = [    1       1     1     0 ;
                  2       1     1     0 ;
                  3       1     1     0 ;
                  4       1     1     0 ;
                  5       1     1     0 ;
                  6       1     1     0 ;
                  7       1     0     0 ;
                  8       1     0     0 ;
                  9       1     0     0 ;
                  10      1     0     0 ;
                  11      1     0     0 ;
                  12      1     0     0 ;
                  ];
  Num_BND   = length(Fix_node(:,1));         % Number of Fixed Nodes

% ---------------------------
% --- Define Element mass ---
% ---------------------------
  seismic_mass1 = 4.8159e+05;
  seismic_mass2 = 5.0349e+05;
  seismic_mass3 = 4.9473e+05;
  seismic_mass4 = 5.3414e+05;

  Element_mass = [
   zeros(1,Num_col)...
   seismic_mass1*(1/(Num_bay))*ones(1,Num_bay)...   %  1st floor
   seismic_mass2*(1/(Num_bay))*ones(1,Num_bay)...   %  2nd floor
   seismic_mass3*(1/(Num_bay))*ones(1,Num_bay)...   %  3rd floor
   seismic_mass3*(1/(Num_bay))*ones(1,Num_bay)...   %  4th floor
   seismic_mass3*(1/(Num_bay))*ones(1,Num_bay)...   %  5th floor
   seismic_mass3*(1/(Num_bay))*ones(1,Num_bay)...   %  6th floor
   seismic_mass3*(1/(Num_bay))*ones(1,Num_bay)...   %  7th floor
   seismic_mass3*(1/(Num_bay))*ones(1,Num_bay)...   %  8th floor
   seismic_mass3*(1/(Num_bay))*ones(1,Num_bay)...   %  9th floor
   seismic_mass4*(1/(Num_bay))*ones(1,Num_bay)...   %  roof
                 				  ]';
% -----------------------------
% --- Define Material Table --- 
% -----------------------------
% Type = 0: Spread Plasticity Model
%        1: Concentrated Plasticity Model

  mat_tbl = [
%Mat_no  EI1       EI2        EI3        EA         GA         d1        d2    type
1 4.5272e+08 4.0971e+08 1.3582e+07 1.4060e+10 8.8960e+15 1.0051e-02 1.0580e-02 1
2 6.8324e+08 6.1831e+08 2.0497e+07 1.8962e+10 8.8960e+15 9.5008e-03 1.0001e-02 1
3 5.9836e+08 5.4151e+08 1.7951e+07 1.7285e+10 8.8960e+15 9.6708e-03 1.0180e-02 1
4 3.1957e+08 2.8920e+08 9.5870e+06 1.0745e+10 8.8960e+15 1.0485e-02 1.1037e-02 1
5 2.8295e+08 2.5607e+08 8.4885e+06 9.7518e+09 8.8960e+15 1.0641e-02 1.1201e-02 1
6 2.5049e+08 2.2211e+08 7.5148e+06 8.8360e+09 8.8960e+15 1.0761e-02 1.1339e-02 1
7 8.1140e+08 6.8151e+08 2.4342e+07 6.0629e+09 8.8960e+15 4.0610e-03 4.2913e-03 1
8 6.4912e+08 5.5829e+08 1.9474e+07 5.1212e+09 8.8960e+15 4.1408e-03 4.3701e-03 1
9 3.3205e+08 2.8596e+08 9.9615e+06 3.7539e+09 8.8960e+15 4.9618e-03 5.2362e-03 1
10 2.3718e+08 2.2226e+08 7.1154e+06 3.1992e+09 8.8960e+15 5.4325e-03 5.7087e-03 1
11 1.5229e+08 1.3940e+08 4.5688e+06 2.5929e+09 8.8960e+15 6.1373e-03 6.4567e-03 1
                ];
% Add splice elements
  mat_tbl = [mat_tbl
12         (6/13)*mat_tbl(2,2:8)+(7/13)*mat_tbl(3,2:8)                         1
13         (6/13)*mat_tbl(1,2:8)+(7/13)*mat_tbl(4,2:8)                         1
14         (6/13)*mat_tbl(3,2:8)+(7/13)*mat_tbl(1,2:8)                         1
15         (6/13)*mat_tbl(4,2:8)+(7/13)*mat_tbl(5,2:8)                         1
16         (6/13)*mat_tbl(5,2:8)+(7/13)*mat_tbl(6,2:8)                         1
                ];