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The Value of Beam Elements in Structural Analysis

Figure 1: Cross Section Stress Plot of Composite Single Concrete and Steel Combined Beam Element
September 11, 2015 By: Peter Barrett

In the early days of FEA, nearly all analyses included beam elements because of their tremendous "bang-for-the-buck" results generated vs. computing resources. Model size was measured in terms of hundreds vs. today's millions of degrees of freedom. Each element was carefully meshed to provide the most value possible in the simulation and nearly all models were limited to linear calculations. These linear analyses utilized beams based on Euler–Bernoulli beam theory where the stiffness terms were computed from the elastic modulus, cross-sectional area and moments of inertia. The cubic shape function allows a single beam element to accurately model the small deflection bending response of each frame-type structure member. Models utilizing these elements were used to design many of the structural icons around the world. The earliest applications of "classic beam theory" were well before the computer age. The hand calculated relationship between force and deflection in a beam was even utilized in the design of the Eiffel Tower!

Finite element based beam elements have gone through many major enhancements over the years, and are now equipped to solve very complex problems. However, it is my experience that this current added value of beam elements is severely under-utilized by engineers. Even with the added complexity, these elements still provide a very powerful computationally economic solution that can expedite the design process across a large number of products and industries. Examples of today's beam element advanced features include:

  • The ability to simulate structural nonlinearities including large deflection, contact and plasticity.
  • Arbitrarily shaped numerically Integrated cross-sections that can include multiple nonlinear materials. (See Figure 1 above for an example of stress results in a composite steel-concrete cross-section).
  • Beams can be used in conjunction with contact elements to simulate beam-to-beam interaction where the beams can either cross each other or be co-axial where one can simulate, for example, the frictional loss of a tendon inside a conduit.
  • Postprocessing features range from local accumulated plastic strains to net forces and moments often needed for design.
  • It is also very easy to change properties (materials and/or cross-section) in a upfront design simulation without any issues with automatic re-meshing that can often limit robustness of continuum models in design sensitivity studies.
  • In areas where more detailed results are required, one can easily connect the beams to shells and/or solids using multi-point constraint (MPC) equations that automatically update with large deflections. Two examples of these types of connections are provided in the following figures.

Figure 2: Combined Beam and 3d Solid Model of a Monopole

Figure 2 illustrates the use of beams combined with solids to simulate a cell tower under the combined effects of wind and gravity loading.  By combining beam elements with the continuum elements, the monopole tower is modeled very efficiently. The detailed 3-d model of the support structure is combined with beam elements representing the superstructure where point and/or distributed loads can be applied. The model can be used for both static and dynamic nonlinear analyses since the beam elements combined with lumped mass elements can accurately model the inertial response of the pole and superstructure.

Modeling bolted connections with pretension loading is another effective way of combining beam elements with continuum elements.  In Figure 3, the model uses beam elements to simulate the bolts where a bolt-pretension element is used to simulate a sequential beam tightening sequence.  The preloaded beams are tied to continuum elements via MPC contact where explicit modeling of the bolt- nut-flange connection is simulated.

Figure 3 - Magnified Displacements from Bolt Sequential Tightening Simulation

What are ways you are using beam elements today?  I would love to hear from others on innovative ways to leverage the power of beam elements in today's structural finite element analyses.