Matrix Methods Example - Frame 6

In [1]:

    

import nbformat


    

In [2]:

    

from __future__ import division, print_function
from IPython import display
import salib.nbloader    # so that we can directly import other notebooks


    

In [3]:

    

import Frame2D_v03 as f2d


    

In [4]:

    

frame = f2d.Frame2D()
frame.read_data('frame-6')
frame.doall()


    

    




ndof = 12, nfree = 7, nconstraints = 5



Nodes:
======

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



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  



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

Node  Dirn     Load
----  ----    -----
B     FX    -200000

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

Member  Load
------  ----------------
BC      UDL(L=8000.0,W1=-50)
BC      PL(L=8000.0,W1=-200000,A=5000.0)



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

Node        DX         DY      Rotation
----      ------     ------   ---------
A          0.000      0.000   0.0000000
B        -22.018     -0.522  -0.0028372
C        -22.109     -0.453   0.0091956
D          0.000      0.000   0.0036929



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

Node        FX         FY         MZ  
----     -------    -------    -------
A        230.540    321.302   -429.587
D        -30.540    278.698      --   



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

          /----- Axial -----/   /----- Shear -----/   /----- Moment ----/
Member       FX J       FX K       FY J       FY K       MZ J       MZ K
------     -------    -------    -------    -------    -------    -------
AB         321.302   -321.302   -230.540    230.540   -429.587   -492.573
BC          30.540    -30.540    321.302    278.698    492.573   -122.160
DC         278.698   -278.698     30.540    -30.540      0.000    122.160

In [5]:

    

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline
from IPython.display import display

def vm(self,loads,mefs=None):
    """Return shear and moment 'diagrams'.  Return (xv,v,xm,m) -
    xv and xm are positions along span, and v and m are shears and
    moments at those points.  Use normal sign convention (not beam sign 
    convention) - on left FBD, moments +ive CCW, shear +ive upwards.
    """
    def _getx(self,loads,attr):
        degree = 0
        pts = [0.,self.L]
        for load in loads:
            pt1,pt2,d = getattr(load,attr)
            for p in pt1,pt2:
                if p is not None:
                    pts.append(p)
            if d > degree:
                degree = d
        ptsv = np.array(pts)
        if degree > 1:
            ptsv = np.concatenate((ptsv,np.linspace(0,self.L)))
        ptsv.sort()
        return np.unique(ptsv)

    if mefs is None:
        mefs = self.mefs
    ##print(mefs)

    xv = _getx(self,loads,'vpts')
    xm = _getx(self,loads,'mpts')
    v = xv * 0. - mefs[1,0]
    m = xm * mefs[1,0] - mefs[2,0]
    for load in loads:
        v += load.shear(xv)
        m += load.moment(xm)
    return xv,v,xm,m


    

In [6]:

    

memb = 'BC'
m = frame.members[memb]
l = frame.membloads[memb]
xv,v,xm,m = vm(m,l)


    

In [7]:

    

display(xv,-v*1e-3)


    

    






array([    0.      ,  4999.999999,  5000.000001,  8000.      ])






    






array([ 321.301686,   71.301686, -128.698314, -278.698314])

In [8]:

    

plt.grid(True)
plt.plot(xv,-v*1e-3)


    

    
Out[8]:





[<matplotlib.lines.Line2D at 0x7ffa6e711ac8>]






    

In [9]:

    

plt.subplot(2,1,1)
plt.title('Member {}'.format(memb))
plt.grid(True)
plt.fill_between(x=xv,y1=-v*1e-3,color='lightgray',edgecolor='black')
plt.ylabel('Shear')
plt.subplot(2,1,2)
plt.grid(True)
plt.fill_between(xm,m*1e-6,color='lightblue',edgecolor='black')
plt.ylabel('Moment')
None


    

    




/usr/lib/python3/dist-packages/matplotlib/collections.py:549: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison
  if self._edgecolors == 'face':






    

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