Nonlinear Static and Dynamic Analysis of Steel Structures with ...

Chapter 2 Finite element modeling with ABAQUS/Standard
2.2 Structural elements
There are six kinds of structural elements in Abaqus/Standard; membrane, truss, beam,
frame, elbow and shell elements. The most widely used are the beam-column and shell
finite elements, which are discussed below.
2.2.1 Beam elements
Timoshenko beams (B21, B22, B31, B31OS, B32, B32OS, PIPE21, PIPE22, PIPE31,
PIPE32, and their ―hybrid‖ equivalents) allow for transverse shear deformation. They can
be used for thick (―stout‖) as well as slender beams. For beams made from uniform
material, shear flexible beam theory can provide useful results for cross-sectional
dimensions up to 1/8 of typical axial distances or the wavelength of the highest natural
mode that contributes significantly to the response. Beyond this ratio the approximations
that allow the member's behavior to be described solely as a function of axial position no
longer provide adequate accuracy. It is assumed that the transverse shear behavior of
Timoshenko beams is linear elastic with a fixed modulus and, thus, independent of the
response of the beam section to axial stretch and bending. The Timoshenko beams can be
subjected to large axial strains. The axial strains due to torsion are assumed to be small. In
combined axial-torsion loading, torsional shear strains are calculated accurately only when
the axial strain is not large. The linear Timoshenko beam elements use a lumped mass
formulation. The quadratic Timoshenko beam elements use a consistent mass formulation,
except in dynamic procedures in which a lumped mass formulation with a 1/6, 2/3, 1/6
distribution is used. The shear factor k (Cowper, 1966) is defined as:
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Section type Shear factor, k
Arbitrary 1.0
Box 0.44
Circular 0.89
Elbow 0.85
Generalized 1.0
Hexagonal 0.53
I (and T) 0.44
L 1.0
Meshed 1.0
Nonlinear generalized 1.0
Pipe 0.53
Rectangular 0.85
Trapezoidal 0.822
Table 2.1: Shear factor k definition for Timoshenko beams