Beams
Beam elements can resist bending, shear, and torsional loads. The typical
frame shown below is modeled with beams elements to transfer the load
to the supports. Modeling such frames with truss elements fails since there is no mechanism
to transfer the applied horizontal load to the supports.
Beam elements require defining the exact cross section so that the program
can calculate the moments of inertia, neutral axes and the distances from
the extreme fibers to the neutral axes. The stresses vary within the plane
of the cross-section and along the beam.
Consider a 3D beam with cross-sectional area (A) and the associated
mesh. Beam elements are displayed as hollow cylinders regardless of their
actual cross-section shape.
3D geometry
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Mesh (each hollow cylinder is an element)
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Now, the figure below shows a small segment along a beam element subjected
to simplified 2D forces ( axial force P, shearing force V, and bending
moment M):
In a
general case 3 forces and 3 moments act on the segment.
Uniform axial stress = P/A (similar to truss elements)
Uniform shearing stress = V/A
The bending moment M causes a bending stress that varies linearly with
the vertical distance y from the neutral axis.
Bending stress (bending in y direction) =
My/I
where I is the moment of inertia about the neutral axis.
The bending stress is the largest at the extreme fibers. In this example,
the largest compression occurs at the top fiber and the largest tension
occurs at the extreme bottom fibers.
Joints
A joint is identified at free ends of structural members and at the
intersection of two or more structural members. The Edit
Joint PropertyManager provides a tool to help you define joints properly.
The program creates a node at the center of the cross section of each
joint member. Due to trimming and the use of different cross sections
for different members, the nodes of members associated with a joint may
not coincide. The program creates special elements near the joint to simulate
a rigid connection based on geometric and material properties.
Material Properties
The modulus of elasticity and Poisson's Ratio are always required.
Density is required only if gravitational loads are considered.
Restraints
You can apply restraints to joints only. There are 6 degrees of freedom
at each joint. You can apply zero or non-zero prescribed translations
and rotations.
Bonding
In a study with beams, solids and shell surfaces, you can bond beams and beam joints to solid
and shell faces.
Bonding between touching structural members with a surface or sheet
metal face is automatically created.
Beam Stiffeners for Curved Surfaces
You can bond beams (straight or curved) that act as stiffeners to curved
surfaces of shells or sheet metal bodies.
The software automatically bonds beams to curved surfaces that have
touching geometries or are situated within reasonable clearance. The program
uses beam element sizes compatible with the surface mesh sizes. The feature
is available for static, frequency, and buckling studies.
Loads
You can apply:
Concentrated forces and moments at joints and
reference points.
Distributed loads along the whole length of a
beam.
Gravitational loads. The program calculates gravitational
forces based on the specified accelerations and densities.
Meshing
Beam and truss members are displayed as hollow cylinders regardless
of their actual cross-section shape. A structural member is automatically
identified as a beam and meshed by a number of uniform elements so you
can view the variation of deformation and stresses along the length of
the member.
Results for each element are presented in its local directions. There
is no averaging of stresses for truss and beam elements. You can view
uniform axial stresses, torsional, bending stresses in two orthogonal
directions (dir 1 and dir 2), and the worst stresses on extreme fibers
generated by combining axial and bending stresses.
A beam section is subjected to an axial force P and two moments M1 and
M2 as shown below. The moment M1 is about the dir 1 axis and the moment
M2 is about the dir 2 axis.
The software provides the following options for viewing stresses:
Axial:
Uniform axial stress = P/A
Bending in local
direction 1: Bending stresses due to M2. This is referred to as
Bending Ms/Ss in the plot name,
title, and legend.
Bending in local
direction 2: Bending stress due to M1. This is referred to as Bending Mt/St in the plot name, title,
and legend.
Click here to learn about beam directions.
In general, the software calculates
4 stress values at the extreme fibers of each end. When
viewing worst case stresses, the software shows one value for each beam
segment. This value is the largest in magnitude out of the 8 values calculated
for the beam segment. These values are accurate for beam with cross-sections
that are symmetric in two directions. These values are conservative for
other cases.