## 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')

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Out[1]:

image/svg+xml

Pin Support

Fixed Support

8000
4000
W310x97
W460x106
W310x97
Units: N, mm
A
B
C
D
frame-6-sidesway-delta

Roller Support

10

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``````

In [2]:

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

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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

===========

- - - none - - -

=============

- - - none - - -

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

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

==================

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

++++++++++++++++++++++++++

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.

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In [3]:

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

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Out[3]:

-72032.40300013451

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In [4]:

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

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Out[4]:

-7203.240300013451

``````