2.4 Side conditions

The program selects the row index and finds column and element indexes (see excerpt 2.5). It inserts the side conditions of Eq. (2.51) into Eq. (2.1). The equations are inserted with the commands cmd = spA=spSisestaArv(spA,59,12,1); and cmd = spA=spSisestaArv(spA,60,54,1); (see excerpt 2.6).

Computing diary excerpt 2.5 ( spESTframe93LaheWFI.m )  

        
===============================================================
Element | Internal      | Joint  | Axial, shear, moment hinges
  No    |  reactions    | (node) |     0 - hinge 'false' 
        | N_    Q_   M_ |   No   |     1 - hinge 'true'
        |    indexes    |        |     
----------------------------------------------------------------
    1      10   11   12      1         0      0      1
    1       4    5    6      2         0      0      0
    2      22   23   24      2         0      0      0
    3      34   35   36      3         0      0      0
    2      16   17   18      4         0      0      0
    3      28   29   30      4         0      0      0
    4      46   47   48      4         0      0      0
    5      52   53   54      5         0      0      1
    4      40   41   42      6         0      0      0
    5      58   59   60      6         0      0      0

$$\mathbf{M^{\left( 1\right)}_{12}} = 0 \quad \mathrm{and} \quad \mathbf{M^{\left( 5\right)}_{54}} = 0 \qquad$$ (2.51)

The bending moment at the hinge location is zero exclusive of a plastic hinge^2.6.

Computing diary excerpt 2.6 ( spESTframe93LaheWFI.m )  

#====================================================================
  
-----Equilibrium equations are inserted into spA    
  
equilibrium_equations_rows =  16
non_zero_elements_in_equilibrium_equations =  43
  
#====================================================================  
 Side conditions  
From_rows = Side conditions begin from row: 59
#====================================================================  
cmd = spA=spSisestaArv(spA,59,12,1);
cmd = spA=spSisestaArv(spA,60,54,1);
----- 
 
spA_rows =  60
spA_cols =  67
spA_nnz = non_zero_elements_in_spA: 174
  
-----Side conditions are inserted into spA  
  
side_condition_rows =  2
non_zero_elements_in_side_condition =  2

#====================================================================