materials, or homogeneous beams with orthotropic material and material orientation not parallel to
the beam axis, the coupling between different generalized strains can be significant and generally leads
to full cross-section stiffness matrix.
The preintegrated composite beam section (SECTYPE,,COMB,MATRIX) is an abstract cross section type
that allows you to define a fully populated but symmetrical cross-section stiffness and mass matrix dir-
ectly. You can use preintegrated composite beam sections when using BEAM188 or BEAM189 elements,
provided that linear elastic material behavior is acceptable.
The full cross-section stiffness relates the generalized-stress to generalized-strain in the following form:
m1
21
211 12 13 14τ =15 16 17
22 23 24 25 26 27
333 34 35 36 37
44 45 46 47
55 56 57
66 67
771 ε
κ
κ 221
2χ
γ
γk where
N = Axial force
M 1 = Bending moment in plane XZ
M 2 = Bending moment in plane XY
τ = Torque
S 1 = Transverse shear force in plane XZ
S 2 = Transverse shear force in plane XY
Bm = Warping bi-moment
= Axial strain
κ1 = Curvature in plane XZ
κ2 = Curvature in plane XY
χ = Twist of the cross section
γ 1 = Transverse shear strain in plane XZ
γ 2 = Transverse shear strain in plane XY
Bk = Warping bi-curvature
Sij( T) (where i = 1,7 and j = i,7) = Stiffness constants in the upper triangle of the cross-section stiffness
matrix as a function of temperature
T = the current temperatureWith a unit beam length, the section mass matrix relates the resultant forces and torques to accelerations
and angular accelerations as follows (applicable to the local element coordinate system):
x y z x y z
=
x y z x y zRelease 15.0 - © SAS IP, Inc. All rights reserved. - Contains proprietary and confidential informationBeam Analysis and Cross Sections