Beam property module (pyfe3d.beamprop)

class pyfe3d.beamprop.BeamProp

General class to represent beam properties.

About shear correction factors, usually one should only apply the shear correction factor to the shear modulus G. It is, however, possible to have more complex scenarios where the different cross section parameters Ay, Az, J have different corrections applied due to geometric properties. It is the user’s responsability to apply these correction factors properly to achieve a general representation of the beam element behaviour by means of this property class. No shear correction factors or geometric correction factors are applied internally during the calculation of the structural matrices.

Attributes:

A,float

Area of the cross section

E,float

Young modulus

G,float

Shear modulus

Iyy,float

Second moment of area about the y axis \(\int_y \int_z z^2 dy dz\)

Izz,float

Second moment of area about the z axis \(\int_y \int_z y^2 dy dz\)

Iyz,float

Product moment of area \(\int_y \int_z y z dy dz\)

J,float

Torsion stiffness or torsion constant, see https://en.wikipedia.org/wiki/Torsion_constant.

Ay,float

Integral \(\int_y \int_z y dy dz\)

Az,float

Integral \(\int_y \int_z z dy dz\)

intrho,float

Integral \(\int_{y_e} \int_{z_e} \rho(y, z) dy dz\), where \(\rho\) Is the density

intrhoy,float

Integral \(\int_y \int_z y \rho(y, z) dy dz\)

intrhoz,float

Integral \(\int_y \int_z z \rho(y, z) dy dz\)

intrhoy2,float

Integral \(\int_y \int_z y^2 \rho(y, z) dy dz\)

intrhoz2,float

Integral \(\int_y \int_z z^2 \rho(y, z) dy dz\)

intrhoyz,float

Integral \(\int_y \int_z y z \rho(y, z) dy dz\)

Notes

For beams with homogeneous material along the cross section some of the quantities above can be calculated as follows, assuming that rho is the material density:

intrho = A*rho intrhoy2 = Izz*rho intrhoz2 = Iyy*rho intrhoyz = Iyz*rho

A

A: ‘double’

Ay

Ay: ‘double’

Az

Az: ‘double’

E

E: ‘double’

G

G: ‘double’

Iyy

Iyy: ‘double’

Iyz

Iyz: ‘double’

Izz

Izz: ‘double’

J

J: ‘double’

intrho

intrho: ‘double’

intrhoy

intrhoy: ‘double’

intrhoy2

intrhoy2: ‘double’

intrhoyz

intrhoyz: ‘double’

intrhoz

intrhoz: ‘double’

intrhoz2

intrhoz2: ‘double’