Frame 6: Lateral Displacement Applied

This is the frame of example frame-6 with a lateral displacement applied at node B (to do that, the input must specifiy a support constraint at that location). From this we will compute the lateral stiffness and compare it with the same frame having an applied force at the same node. (Note, they compare equal to 14 significant figures).



In [1]:

    
from Frame2D import Frame2D
from IPython import display
display.SVG('data/frame-6-sidesway-delta.d/frame-6-sidesway-delta.svg')









    Out[1]:



In [2]:

    
f = Frame2D('frame-6-sidesway-delta')
f.input_all()
f.print_input()
R = f.solve()
f.print_results(rs=R)









    



Frame frame-6-sidesway-delta:
=============================


              # 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
----      -----     -----  -----------  ------
A             0         0  FX,FY,MZ     6,7,8
B             0      4000  FX           9,0,1
C          8000      4000               2,3,4
D          8000         0  FX,FY        10,11,5



Members:
========

Member   Node-J  Node-K    Length       dcx       dcy  Size                Ix           A  Releases
------   ------  ------    ------   -------   -------  --------      --------       -----  --------
AB       A       B         4000.0   0.00000   1.00000  W310x97       2.22e+08       12300  
BC       B       C         8000.0   1.00000   0.00000  W460x106      4.88e+08       13500  
DC       D       C         4000.0   0.00000   1.00000                2.22e+08       12300  



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

 - - - none - - -

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

 - - - none - - -

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

Type      Node      DX          DY          TZ
----      ----  ----------  ----------  ----------
wind      B            -10           0           0

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

Case   Type      Factor
-----  ----      ------
one    wind        1.00
all    wind        1.00

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


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

Node        DX         DY      Rotation
----      ------     ------   ---------
A          0.000      0.000   0.0000000
B        -10.000     -0.032   0.0016556
C         -9.952      0.032   0.0005242
D          0.000      0.000   0.0034697

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

Node        FX         FY         MZ  
----     -------    -------    -------
A         55.685     19.798   -129.747
B        -72.032      --         --   
D         16.347    -19.798      --   

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

          /----- Axial -----/   /----- Shear -----/   /----- Moment ----/
Member       FX J       FX K       FY J       FY K       MZ J       MZ K
------     -------    -------    -------    -------    -------    -------
AB          19.798    -19.798    -55.685     55.685   -129.747    -92.993
BC         -16.347     16.347     19.798    -19.798     92.993     65.389
DC         -19.798     19.798    -16.347     16.347      0.000    -65.389

Lateral Stiffness

Now compute the lateral stiffness, in N/mm, of the frame at node B.



In [3]:

    
R.reaction_forces[3,0]   ## lateral force corresponding to 10mm of displacements









    Out[3]:





-72032.40300013451



In [4]:

    
R.reaction_forces[3,0]/10.   ## lateral stiffness









    Out[4]:





-7203.240300013451