Orienting frames in 3D

This example demonstrates how to orient beam elements in 3D.

The objective of this example is to demonstrate how to orient beam elements in 3D space. The model we’ll build is a simple 3-element portal frame with wide-flange sections.

Only certain relevant pieces of code will be shown in detail, but the full example script can be downloaded from the link above. In order to cover a wide range of cases, we’ll orient the first column, element 1, such that the strong axis of it’s section bends outside the plane of the portal, the strong axis of the second column, element 3, will resist bending inside the portal plane (See the image above). We’ll build two variations of the model; one where the 2nd coordinate $X_2$ is vertical, and another with the 3rd coordinate $X_3$ vertical. In both cases we begin by initializing a Model in ndm=3 dimensions with ndf=6 degrees of freedom per node:

import xara
model = xara.Model(ndm=3, ndf=6)

For the first case with $X_2$ vertical we have:

model.node(1, (    0,      0, 0))
model.node(2, (width,      0, 0))
model.node(3, (width, height, 0))
model.node(4, (    0, height, 0))

model.geomTransf("Linear", 1, (1, 0, 0))
model.geomTransf("Linear", 2, (0, 1, 0))
model.geomTransf("Linear", 3, (0, 0, 1))

and for $X_3$ vertical:

model.node(1, (    0, 0,      0))
model.node(2, (width, 0,      0))
model.node(3, (width, 0, height))
model.node(4, (    0, 0, height))

model.geomTransf("Linear", 1, (1, 0, 0))
model.geomTransf("Linear", 2, (0, 0, 1))
model.geomTransf("Linear", 3, (0,-1, 0))

Everything else is identical for both cases. The material is a simple ElasticIsotropic formulation and for the section we’ll use the shps package to build a fiber discretization of a wide-flange:

from xara.units.fps import inch
from shps.shapes import WideFlange
model.material("ElasticIsotropic", 1, 29e3, 0.3)

shape = WideFlange(d=8*inch, b=6.5*inch, tw=0.5*inch, tf=0.5*inch)
model.section("ShearFiber", 1)
for fiber in shape.create_fibers(origin="centroid"):
    model.fiber(**fiber, material=1, section=1)