Frame Sections

Introduction to the available section types for frame elements.

Introduction  

This page introduces three cross sectional models for the frame elements in xara. There are four primary beam formulations available in xara: there are four beam elements:

• PrismFrame  is a standard prismatic linear elastic beam.
• ForceFrame  is a force-interpolated distributed inelasticity element.
• ExactFrame  is a geometrically exact displacement-interpolated distributed inelasticity element.
• CubicFrame is a displacement-interpolated distributed inelasticity formulation.

Each of these follows the same construction syntax:

model.element(name, tag, nodes, section, transform, shear=None)

where:

• name is a string identifying the name of the element (eg, "PrismFrame", "ForceFrame", etc.).
• tag is a unique integer tag which is used to identify the element in post-processing.
• nodes is a tuple of integers identifying previously defined nodes which the element connects to. (PrismFrame, CubicFrame and ForceFrame accept 2 node tags; ExactFrame accepts 2 to 4 nodes).
• section is an integer tag of a previously defined frame cross section.
• transform is a tag of a previously defined geometric transformation.
• shear is an integer flag which can be used to enable shear deformations (Timoshenko beam theory) in the PrismFrame, CubicFrame, and ForceFrame elements. The ExactFrame always includes shear deformations, and supplying shear=0 will throw an error when this element is specified by name.

There are primarily three cross section types:

• ElasticFrame: an elastic cross section defined by specifying cross sectional integrals like $A$ , $I$ , $J$ , $E$ , G, etc,
• AxialFiber: a “fiber” section which is defined by a set of fibers discretizing the cross section, and specifying a uniaxial material law at each fiber
• ShearFiber: like ScalarFiber, but fibers are assigned multiaxial material laws (ie, a tensorial stress-strain relation)

There are two primary considerations that figure in selecting an appropriate cross section:

1. Material nonlinearity.
2. Shear deformability. Shear stiffness refers to the propensity of a cross section

Elastic  

The required constants are:

• E: Young’s modulus
• G: Shear modulus
• A: Cross sectional area
• Iy, Iz: Second moments of area
• J : Saint Venant’s torsion constant

# Shear given by GA
model.section("ElasticFrame", 1, E=E, G=G, A=A, Iy=Iy, Iz=Iz, J=J)
# Shear given by G A ky
model.section("ElasticFrame", 1, E=E, G=G, A=A, Iy=Iy, Iz=Iz, J=J, ky=0.83)

model.section("AxialFiber", G=G, J=J)

Fiber  

Uniaxial  

from xara.units import si
import xsection.library as xs
# 1) Create a shape
shape = xs.from_aisc("W18x40", units=si)
# 2) Create a material
model.uniaxialMaterial('Elastic', 1, E)

# 3) Create the section
model.section("AxialFiber", 1)
# 4) populate with fibers
for fiber in shape.create_fibers():
    model.fiber(**fiber, material=1, section=1)

Multiaxial  

from xara.units import si
import xsection.library as xs
# 1) Create a shape
shape = xs.from_aisc("W18x40", units=si)
# 2) Create a material
model.material('ElasticIsotropic', 1, E, nu)

# 3) Create the section
model.section("ShearFiber", 1)
# 4) populate with fibers
for fiber in shape.create_fibers():
    model.fiber(**fiber, material=1, section=1)

Warping