## Frame 6: Lateral Force Applied

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

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In [1]:

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

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Out[1]:

image/svg+xml

Pin Support

Fixed Support

8000
4000
W310x97
W460x106
100000
W310x97
Units: N, mm
A
B
C
D
frame-6-sidesway-force

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In [2]:

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

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Frame frame-6-sidesway-force:
=============================

# of nodal degrees of freedom: 12
# of constrained nodal degrees of freedom: 5
# of unconstrained nodal degrees of freedom: 7  (= degree of kinematic indeterminacy)

# of members: 3
# of reactions: 5
# of nodes: 4
# of conditions: 0
degree of statical indeterminacy: 2

Nodes:
======

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

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

===========

Type      Node      FX          FY          MZ
----      ----  ----------  ----------  ----------
wind      B        -100000           0           0

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

- - - none - - -

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

- - - none - - -

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

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        -13.883     -0.045   0.0022983
C        -13.815      0.045   0.0007278
D          0.000      0.000   0.0048169

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

Node        FX         FY         MZ
----     -------    -------    -------
A         77.306     27.485   -180.123
D         22.694    -27.485      --

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

/----- Axial -----/   /----- Shear -----/   /----- Moment ----/
Member       FX J       FX K       FY J       FY K       MZ J       MZ K
------     -------    -------    -------    -------    -------    -------
AB          27.485    -27.485    -77.306     77.306   -180.123   -129.099
BC         -22.694     22.694     27.485    -27.485    129.099     90.778
DC         -27.485     27.485    -22.694     22.694      0.000    -90.778

``````

### Lateral Stiffness

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

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In [3]:

R.node_displacements[0,0]   # lateral displacement

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Out[3]:

-13.882641121915128

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In [4]:

100000./R.node_displacements[0,0]   # lateral stiffness

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Out[4]:

-7203.240300013234

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In [ ]:

``````