Example 6-b

In this example, all input data is given directly in the notebook cells below. The data is given in CSV form precisely as would be given in data files. For each table started by the cell magic %%Table, the table name follows immediately. If the data was instead provided in a data file the file name would be the table name + .csv.

This example is statically determinate for ease of checking -- the rightmost figure shows the reactions corresponding to factored values of the loads shown in the left figure. Units are $N$ and $mm$.

Test Frame

In [1]:
from IPython import display

image/svg+xml Pin Support Fixed Support 8000 4000 W310x97 W460x106 50 200000 200000 5000 W310x97 Units: N, mm A B C D frame-6b W310x97 W460x106 50x1.5 200000x1.75 200000x1.5 W310x97 A B C D Factored Loads, Reactions 487500 412500 350000 1400x106

In [2]:
from Frame2D import Frame2D

f6b = Frame2D('frame-6b')

Input Data


Table nodes (file nodes.csv) provides the $x$-$y$ coordinates of each node. Other columns, such as the $z$- coordinate are optional, and ignored if given.

In [3]:
%%Table nodes


Table supports (file supports.csv) specifies the support fixity, by indicating the constrained direction for each node. There can be 1, 2 or 3 constraints, selected from the set 'FX', 'FY' or 'MZ', in any order for each constrained node. Directions not mentioned are 'free' or unconstrained.

In [4]:
%%Table supports


Table members (file members.csv) specifies the member incidences. For each member, specify the id of the nodes at the 'j-' and 'k-' ends. These ends are used to interpret the signs of various values.

In [5]:
%%Table members


Table releases (file releases.csv) is optional and specifies internal force releases in some members. Currently only moment releases at the 'j-' end ('MZJ') and 'k-' end ('MZK') are supported. These specify that the internal bending moment at those locations are zero. You can only specify one release per line, but you can have more than one line for a member.

In [6]:
%%Table releases


Table properties (file properties.csv) specifies the member properties for each member. If the 'SST' library is available, you may specify the size of the member by using the designation of a shape in the CISC Structural Section Tables. If either IX or A is missing, it is retreived using the sst library. If the values on any line are missing, they are copied from the line above.

In [7]:
%%Table properties

Node Loads

Table node_loads (file node_loads.csv) specifies the forces applied directly to the nodes. DIRN (direction) may be one of 'FX,FY,MZ'. 'LOAD' is an identifier of the kind of load being applied and F is the value of the load, normally given as a service or specified load. A later input table will specify load combinations and factors.

In [8]:
%%Table node_loads

Support Displacements

Table support_displacements (file support_displacements.csv) is optional and specifies imposed displacements of the supports. DIRN (direction) is one of 'DX, DY, RZ'. LOAD is as for Node Loads, above.

Of course, in this example the frame is statically determinate and so the support displacement will have no effect on the reactions or member end forces.

In [9]:
%%Table support_displacements

Member Loads

Table member_loads (file member_loads.csv) specifies loads acting on members. Current types are PL (concentrated transverse, ie point load), CM (concentrated moment), UDL (uniformly distributed load over entire span), LVL (linearly varying load over a portion of the span) and PLA (point load applied parallel to member coincident with centroidal axis). Values W1 and W2 are loads or load intensities and A, B, and C are dimensions appropriate to the kind of load.

In [10]:
%%Table member_loads

Load Combinations

Table load_combinations (file load_combinations.csv) is optional and specifies factored combinations of loads. By default, there is always a load combination called all that includes all loads with a factor of 1.0. A frame solution (see below) indicates which CASE to use.

In [11]:
%%Table load_combinations


The following outputs all tables, prints a description of the input data, produces a solution for load case 'one' (all load and case names are case-insensitive) and finally prints the results.

In [12]:
RS = f6b.solve('one')

Frame frame-6b:

              # 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: 2
           degree of statical indeterminacy: 0


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


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  MZK
BC       B       C         8000.0   1.00000   0.00000  W460x106      4.88e+08       13500  
CD       C       D         4000.0   0.00000  -1.00000                2.22e+08       12300  MZJ

Node Loads:

Type      Node      FX          FY          MZ
----      ----  ----------  ----------  ----------
wind      B        -200000           0           0

Member Loads:

Type      Member  Load
----      ------  ----------------
live      BC      UDL(L=8000.0,w=-50)
live      BC      PL(L=8000.0,P=-200000,a=5000.0)

Support Displacements:

Type      Node      DX          DY          TZ
----      ----  ----------  ----------  ----------
other     A              0         -10           0

Load Combinations:

Case   Type      Factor
-----  ----      ------
one    live        1.50
 "     wind        1.75
 "     other       2.00
all    other       1.00
 "     live        1.00
 "     wind        1.00

Results for load case: one

Node Displacements:

Node        DX         DY      Rotation
----      ------     ------   ---------
A          0.000    -20.000   0.0000000
B       -168.168    -20.671  -0.0244748
C       -168.168     -0.793   0.0313654
D          0.000      0.000   0.0420420


Node        FX         FY         MZ  
----     -------    -------    -------
A        350.000    412.500  -1400.000
D         -0.000    487.500      --   

Member End Forces:

          /----- Axial -----/   /----- Shear -----/   /----- Moment ----/
Member       FX J       FX K       FY J       FY K       MZ J       MZ K
------     -------    -------    -------    -------    -------    -------
AB         412.500   -412.500   -350.000    350.000  -1400.000      0.000
BC           0.000      0.000    412.500    487.500     -0.000     -0.000
CD         487.500   -487.500      0.000     -0.000      0.000      0.000

In [ ]: