Example 9.4.1, Beaufait 1977

In [1]:

    

from Frame2D import Frame2D
from Frame2D.Members import Member


    

In [2]:

    

# because units are kips, inches

Member.E = 30000.    #ksi
Member.G = 11500.


    

In [3]:

    

from IPython import display
display.Image('data/Beaufait-9-4-1.d/fig1.jpg')


    

    
Out[3]:

In [4]:

    

frame = Frame2D('Beaufait-9-4-1')   # Example 9.4.1, p. 460
frame.input_all()
rs = frame.solve()
frame.print_input()
frame.print_results(rs,mult=[1.,1.,1./12.])


    

    




Frame Beaufait-9-4-1:
=====================


              # of nodal degrees of freedom: 12
  # of constrained nodal degrees of freedom: 6
# of unconstrained nodal degrees of freedom: 6  (= degree of kinematic indeterminacy)

                               # of members: 3
                             # of reactions: 6
                                 # of nodes: 4
                            # of conditions: 0
           degree of statical indeterminacy: 3



Nodes:
======

Node          X         Y  Constraints  DOF #s
----      -----     -----  -----------  ------
N1            0         0  FX,FY,MZ     6,7,8
N2            0       180               0,1,2
N3          288       300               3,4,5
N4          288         0  FX,FY,MZ     9,10,11



Members:
========

Member   Node-J  Node-K    Length       dcx       dcy  Size                Ix           A  Releases
------   ------  ------    ------   -------   -------  --------      --------       -----  --------
M1       N1      N2         180.0   0.00000   1.00000                     450          15  
M2       N2      N3         312.0   0.92308   0.38462                    1800          15  
M3       N3      N4         300.0   0.00000  -1.00000                     900          30  



Node Loads:
===========

Type      Node      FX          FY          MZ
----      ----  ----------  ----------  ----------
wind      N2             8           0           0

Member Loads:
=============

Type      Member  Load
----      ------  ----------------
snow      M2      PL(L=312.0,P=-24.0,a=156.0)
snow      M2      PLA(L=312.0,P=-10.0,a=156.0)

Support Displacements:
======================

 - - - none - - -

Load Combinations:
==================

Case   Type      Factor
-----  ----      ------
all    wind        1.00
 "     snow        1.00

Results for load case: all
++++++++++++++++++++++++++


Node Displacements:
===================

Node        DX         DY      Rotation
----      ------     ------   ---------
N1         0.000      0.000   0.0000000
N2         0.042     -0.001  -0.0003035
N3         0.042     -0.001   0.0001628
N4         0.000      0.000   0.0000000

Reactions:
==========

Node        FX         FY         MZ  
----     -------    -------    -------
N1        -2.724     11.787     33.075
N4        -5.276     14.213     57.813

Member End Forces:
==================

          /----- Axial -----/   /----- Shear -----/   /----- Moment ----/
Member       FX J       FX K       FY J       FY K       MZ J       MZ K
------     -------    -------    -------    -------    -------    -------
M1          11.787    -11.787      2.724     -2.724     33.075      7.780
M2           9.404      0.596      8.851     15.149     -7.780    -74.095
M3          14.213    -14.213      5.276     -5.276     74.095     57.813

In [5]:

    

import pandas as pd
efs = [('M1',11.77,2.72,33.06,-11.77,-2.72,7.75),  # end forces from soln, Beaufait, p 473
       ('M2',9.40,8.85,-7.83,0.60,15.15,-74.11),
       ('M3',14.18,5.27,74.10,-14.18,-5.27,57.81)]
BOOK_MEFS = pd.DataFrame(efs,columns='ID,FXJ,FYJ,MZJ,FXK,FYK,MZK'.split(',')).set_index('ID')
BOOK_MEFS[['MZJ','MZK']] *= 12.   # convert ft-kips to in-kips
BOOK_MEFS


    

    
Out[5]:







  

    

      

      
FXJ
      
FYJ
      
MZJ
      
FXK
      
FYK
      
MZK
    
    

      
ID
      

      

      

      

      

      

    
  
  

    

      
M1
      
11.77
      
2.72
      
396.72
      
-11.77
      
-2.72
      
93.00
    
    

      
M2
      
9.40
      
8.85
      
-93.96
      
0.60
      
15.15
      
-889.32
    
    

      
M3
      
14.18
      
5.27
      
889.20
      
-14.18
      
-5.27
      
693.72
    
  

In [6]:

    

HERE_MEFS = pd.DataFrame(frame.list_member_end_forces(rs),
                         columns='ID,FXJ,FYJ,MZJ,FXK,FYK,MZK'.split(',')).set_index('ID')
HERE_MEFS


    

    
Out[6]:







  

    

      

      
FXJ
      
FYJ
      
MZJ
      
FXK
      
FYK
      
MZK
    
    

      
ID
      

      

      

      

      

      

    
  
  

    

      
M1
      
11.787008
      
2.723643
      
396.897076
      
-11.787008
      
-2.723643
      
93.358711
    
    

      
M2
      
9.403948
      
8.850947
      
-93.358711
      
0.596052
      
15.149053
      
-889.145838
    
    

      
M3
      
14.212992
      
5.276357
      
889.145838
      
-14.212992
      
-5.276357
      
693.761182
    
  

In [7]:

    

pdiff = (100*(HERE_MEFS-BOOK_MEFS)/BOOK_MEFS)
pdiff.round(2)


    

    
Out[7]:







  

    

      

      
FXJ
      
FYJ
      
MZJ
      
FXK
      
FYK
      
MZK
    
    

      
ID
      

      

      

      

      

      

    
  
  

    

      
M1
      
0.14
      
0.13
      
0.04
      
0.14
      
0.13
      
0.39
    
    

      
M2
      
0.04
      
0.01
      
-0.64
      
-0.66
      
-0.01
      
-0.02
    
    

      
M3
      
0.23
      
0.12
      
-0.01
      
0.23
      
0.12
      
0.01
    
  

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