Start of Abbreviated Output File

==========================================
Title : DESCRIPTION OF FINITE ELEMENT MESH                                 
==========================================

 Problem_Type:  Static Analysis

=======================
Profile of Problem Size
=======================

   Dimension of Problem        =      2

   Number Nodes                =     24
   Degrees of Freedom per node =      3
   Max No Nodes Per Element    =      2

   Number Elements             =     35
   Number Element Attributes   =      2
   Number Loaded Nodes         =     20
   Number Loaded Elements      =      0

------------------------------------------------------------
Node#      X_coord           Y_coord          Tx    Ty    Rz  
------------------------------------------------------------

    1    0.00000e+00 ft    0.00000E+00 ft    -1    -2    -3 
    2    2.00000e+01 ft    0.00000E+00 ft    -4    -5    -6 
    3    3.50000e+01 ft    0.00000E+00 ft    -7    -8    -9 
    4    5.50000e+01 ft    0.00000E+00 ft   -10   -11   -12 
    5    0.00000e+00 ft    1.00000E+01 ft     1     6     7 

   ...... details of nodal coordinates and modeling dof removed ....

   19    3.50000e+01 ft    4.00000E+01 ft     4    34    35 
   20    5.50000e+01 ft    4.00000E+01 ft     4    36    37 
   21    0.00000e+00 ft    5.00000E+01 ft     5    38    39 
   22    2.00000e+01 ft    5.00000E+01 ft     5    40    41 
   23    3.50000e+01 ft    5.00000E+01 ft     5    42    43 
   24    5.50000e+01 ft    5.00000E+01 ft     5    44    45 

--------------------------------------------------------------------
Element#       Type       node[1]       node[2]    Element_Attr_Name
--------------------------------------------------------------------

       1     FRAME_2D          1          5            mycolumn
       2     FRAME_2D          5          9            mycolumn
       3     FRAME_2D          9         13            mycolumn
       4     FRAME_2D         13         17            mycolumn

      ...... details of element connectivity removed ....

      33     FRAME_2D         21         22              mybeam
      34     FRAME_2D         22         23              mybeam
      35     FRAME_2D         23         24              mybeam

--------------------- 
Element Attribute Data :        
--------------------- 

ELEMENT_ATTR No.   1  : name = "mycolumn" 
                      : section = "mysection1" 
                      : material = "mymaterial" 
                      : type = FRAME_2D
                      : gdof [0] =    1 : gdof[1] =    2 : gdof[2] =    3
                      : Young's Modulus =  E =        2.900e+04 ksi
                      : Yielding Stress = fy =        3.600e+01 ksi
                      : Poisson's ratio = nu =        2.500e-01   
                      : Density         =        1.024e-06 lb/in^3
                      : Inertia Izz     =        1.542e+03 in^4
                      : Area            =        4.740e+01 in^2

ELEMENT_ATTR No.   2  : name = "mybeam" 
                      : section = "mysection2" 
                      : material = "mymaterial" 
                      : type = FRAME_2D
                      : gdof [0] =    1 : gdof[1] =    2 : gdof[2] =    3
                      : Young's Modulus =  E =        2.900e+04 ksi
                      : Yielding Stress = fy =        3.600e+01 ksi
                      : Poisson's ratio = nu =        2.500e-01   
                      : Density         =        1.024e-06 lb/in^3
                      : Inertia Izz     =        1.600e+03 in^4
                      : Area            =        2.146e+01 in^2
                        
EXTERNAL NODAL LOADINGS 
------------------------------------------------
Node#      Fx (lbf)      Fy (lbf)    Mz (lbf.in)
------------------------------------------------
    5       4253.33     -24000.00    -960000.00
    6          0.00     -42000.00     420000.00
    7          0.00     -42000.00    -420000.00
    8          0.00     -24000.00     960000.00
    9       8506.67     -24000.00    -960000.00
   10          0.00     -42000.00     420000.00
   11          0.00     -42000.00    -420000.00
   12          0.00     -24000.00     960000.00
   13      12760.00     -24000.00    -960000.00
   14          0.00     -42000.00     420000.00
   15          0.00     -42000.00    -420000.00
   16          0.00     -24000.00     960000.00
   17      17013.33     -24000.00    -960000.00
   18          0.00     -42000.00     420000.00
   19          0.00     -42000.00    -420000.00
   20          0.00     -24000.00     960000.00
   21      21266.67     -20000.00    -800000.00
   22          0.00     -35000.00     350000.00
   23          0.00     -35000.00    -350000.00
   24          0.00     -20000.00     800000.00

============= End of Finite Element Mesh Description ==============

------------------------------------------------------------
 Node                           Displacement
  No             displ-x           displ-y             rot-z
------------------------------------------------------------
 units               in                in               rad 
   1         0.00000e+00       0.00000e+00       0.00000e+00
   2         0.00000e+00       0.00000e+00       0.00000e+00
   3         0.00000e+00       0.00000e+00       0.00000e+00
   4         0.00000e+00       0.00000e+00       0.00000e+00
   5         1.02973e-01      -7.40873e-03      -1.23470e-03
   6         1.02973e-01      -1.64731e-02      -6.24404e-04
   7         1.02973e-01      -1.90281e-02      -8.22556e-04
   8         1.02973e-01      -1.27863e-02      -7.58887e-04
   9         2.55749e-01      -1.34750e-02      -1.19639e-03

   ....... details of displacements removed .....

  21         5.62354e-01      -2.29345e-02      -6.66741e-04
  22         5.62354e-01      -4.88997e-02      -8.48912e-05
  23         5.62354e-01      -5.50729e-02      -3.30685e-04
  24         5.62354e-01      -3.63403e-02       6.32278e-05

MEMBER FORCES 
------------------------------------------------------------------------------

Elmt No   1 : 
Coords (X,Y) = (     0.000 in,     60.000 in)
exx =  -6.17394e-05 , curva =   -0.00040508 , gamma =  -3.10985e-04

 Fx1 =   8.48669e+04 lbf  Fy1 =   8.97143e+03 lbf  Mz1 =   9.98366e+05 lbf.in
 Fx2 =  -8.48669e+04 lbf  Fy2 =  -8.97143e+03 lbf  Mz2 =   7.82053e+04 lbf.in

 Axial Force : x-direction =  -8.48669e+04 lbf
 Shear Force : y-direction =   8.97143e+03 lbf

Elmt No   6 : 
Coords (X,Y) = (   240.000 in,     60.000 in)
exx =  -1.37276e-04 , curva =   -0.00020486 , gamma =  -7.05134e-04

 Fx1 =   1.88700e+05 lbf  Fy1 =   2.03420e+04 lbf  Mz1 =   1.45319e+06 lbf.in
 Fx2 =  -1.88700e+05 lbf  Fy2 =  -2.03420e+04 lbf  Mz2 =   9.87850e+05 lbf.in

 Axial Force : x-direction =  -1.88700e+05 lbf
 Shear Force : y-direction =   2.03420e+04 lbf

Elmt No  11 : 
Coords (X,Y) = (   420.000 in,     60.000 in)
exx =  -1.58567e-04 , curva =   -0.00026987 , gamma =  -5.77161e-04

 Fx1 =   2.17967e+05 lbf  Fy1 =   1.66502e+04 lbf  Mz1 =   1.30552e+06 lbf.in
 Fx2 =  -2.17967e+05 lbf  Fy2 =  -1.66502e+04 lbf  Mz2 =   6.92505e+05 lbf.in

 Axial Force : x-direction =  -2.17967e+05 lbf
 Shear Force : y-direction =   1.66502e+04 lbf

Elmt No  16 : 
Coords (X,Y) = (   660.000 in,     60.000 in)
exx =  -1.06552e-04 , curva =   -0.00024898 , gamma =  -6.18281e-04

 Fx1 =   1.46467e+05 lbf  Fy1 =   1.78364e+04 lbf  Mz1 =   1.35297e+06 lbf.in
 Fx2 =  -1.46467e+05 lbf  Fy2 =  -1.78364e+04 lbf  Mz2 =   7.87403e+05 lbf.in

 Axial Force : x-direction =  -1.46467e+05 lbf
 Shear Force : y-direction =   1.78364e+04 lbf

Remark 1 :

We have printed the internal element forces for the columns between the foundation and the first floor level. The accuracy of the analysis can be checked by making sure the sum of column actions is balanced by the sum of external loads. In the horizontal direction we have:


====================================================================
External Forces                           Shear Forces in Columns
====================================================================
Roof           21,266.27 lbf                
Floor 4        17,013.33 lbf              Element  1    8,971.43 lbf
Floor 3        12,760.00 lbf              Element  6   20,342.00 lbf
Floor 2         8,506.67 lbf              Element 11   16,650.20 lbf
Floor 1         4,253.33 lbf              Element 16   17,836.40 lbf
====================================================================
Total          63,800.00 lbf              Total        63,800.03 lbf
====================================================================

And in the vertical direction we have:

====================================================================
Gravity Loads                             Axial Forces in Columns
====================================================================
Roof           -110,000 lbf                
Floor 4        -132,000 lbf               Element  1   -84,866.9 lbf
Floor 3        -132,000 lbf               Element  6  -188,700.0 lbf
Floor 2        -132,000 lbf               Element 11  -217,967.0 lbf
Floor 1        -132,000 lbf               Element 16  -146,467.0 lbf
====================================================================
Total          -638,000 lbf               Total       -638,000.9 lbf
====================================================================

Remark 2 :

The five story moment resistant frame may be modeled as a shear structure by fixing the nodal rotations and vertical displacements at floors 1 to 5, and lumping the horizontal displacements at each floor level. These tasks are accomplished by modifying Section [f] of the input file to

/* [f] : Apply full-fixity to columns at foundation level */

   for(nodeno = 1; nodeno <= 4; nodeno = nodeno + 1) {
       FixNode( nodeno, [ 1, 1, 1 ]);
   }

   for(nodeno = 5; nodeno <= 24; nodeno = nodeno + 1) {
       FixNode( nodeno, [ 0, 1, 1 ]);
   }

   LinkNode([  5,  6,  7,  8 ], [ 1, 0, 0] );
   LinkNode([  9, 10, 11, 12 ], [ 1, 0, 0] );
   LinkNode([ 13, 14, 15, 16 ], [ 1, 0, 0] );
   LinkNode([ 17, 18, 19, 20 ], [ 1, 0, 0] );
   LinkNode([ 21, 22, 23, 24 ], [ 1, 0, 0] );

Overall displacements in the frame will now be represented with five global degrees of freedom. Details of the stiffness and load vector are:

MATRIX : "eload"

row/col                  1   
        units                
   1      lbf   4.25333e+03
   2      lbf   8.50667e+03
   3      lbf   1.27600e+04
   4      lbf   1.70133e+04
   5      lbf   2.12667e+04

SKYLINE MATRIX : "stiff"

row/col                  1             2             3             4             5   
        units          N/m           N/m           N/m           N/m           N/m   
   1            4.35045e+08  -2.17523e+08   0.00000e+00   0.00000e+00   0.00000e+00 
   2           -2.17523e+08   4.35045e+08  -2.17523e+08   0.00000e+00   0.00000e+00 
   3            0.00000e+00  -2.17523e+08   4.35045e+08  -2.17523e+08   0.00000e+00 
   4            0.00000e+00   0.00000e+00  -2.17523e+08   4.35045e+08  -2.17523e+08 
   5            0.00000e+00   0.00000e+00   0.00000e+00  -2.17523e+08   2.17523e+08 

A summary of output is:


------------------------------------------------------------
 Node                           Displacement
  No             displ-x           displ-y             rot-z
------------------------------------------------------------
 units               in                in               rad 
   1         0.00000e+00       0.00000e+00       0.00000e+00
   2         0.00000e+00       0.00000e+00       0.00000e+00
   3         0.00000e+00       0.00000e+00       0.00000e+00
   4         0.00000e+00       0.00000e+00       0.00000e+00
   5         5.13652e-02       0.00000e+00       0.00000e+00
   6         5.13652e-02       0.00000e+00       0.00000e+00
   7         5.13652e-02       0.00000e+00       0.00000e+00
   8         5.13652e-02       0.00000e+00       0.00000e+00
   9         9.93061e-02       0.00000e+00       0.00000e+00
  10         9.93061e-02       0.00000e+00       0.00000e+00

  ...... details of displacements removed ......

  21         1.88339e-01       0.00000e+00       0.00000e+00
  22         1.88339e-01       0.00000e+00       0.00000e+00
  23         1.88339e-01       0.00000e+00       0.00000e+00
  24         1.88339e-01       0.00000e+00       0.00000e+00


MEMBER FORCES 
------------------------------------------------------------------------------

Elmt No   1 : 

 Axial Force : x-direction =   0.00000e+00 lbf
 Shear Force : y-direction =   1.59500e+04 lbf

Elmt No   6 : 

 Axial Force : x-direction =   0.00000e+00 lbf
 Shear Force : y-direction =   1.59500e+04 lbf

Elmt No  11 : 

 Axial Force : x-direction =   0.00000e+00 lbf
 Shear Force : y-direction =   1.59500e+04 lbf

Elmt No  16 : 

 Axial Force : x-direction =   0.00000e+00 lbf
 Shear Force : y-direction =   1.59500e+04 lbf

Fixing nodal rotations increases the overall stiffness of the structure -- the result is lateral displacements in the shear structure which are smaller than for the moment resistant frame (i.e. 1.8834e-01 inches versus 5.6235e-01 inches). Again, notice that shear forces across the base of the structure are balanced by the external loads (i.e 4 times 1.59500e+04 lbf = 6.3800e+04 lbf).

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